<?xml version='1.0' encoding='UTF-8'?>
<model name="modules" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <component name="constant_flow_BC_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="P" public_interface="in" units="J_per_m3"/>
        <variable name="v" private_interface="in" public_interface="out" units="m3_per_s"/>
    </component>
    <component name="constant_flow_2_BC_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="v_1" private_interface="in" public_interface="out" units="m3_per_s"/>
        <variable name="v_2" private_interface="in" public_interface="out" units="m3_per_s"/>
    </component>
    <component name="constant_pressure_BC_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="v" public_interface="in" units="m3_per_s"/>
        <variable name="P" private_interface="in" public_interface="out" units="J_per_m3"/>
    </component>
    <component name="fourier_flow_8_BC_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="P" public_interface="in" units="J_per_m3"/>
        <variable name="v" public_interface="out" units="m3_per_s"/>
        <variable name="v_0" public_interface="out" units="m3_per_s"/>
        <variable name="v_1" public_interface="out" units="m3_per_s"/>
        <variable name="v_2" public_interface="out" units="m3_per_s"/>
        <variable name="v_3" public_interface="out" units="m3_per_s"/>
        <variable name="v_4" public_interface="out" units="m3_per_s"/>
        <variable name="v_5" public_interface="out" units="m3_per_s"/>
        <variable name="v_6" public_interface="out" units="m3_per_s"/>
        <variable name="v_7" public_interface="out" units="m3_per_s"/>
        <variable name="v_8" public_interface="out" units="m3_per_s"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="omega_0" public_interface="out" units="per_s"/>
        <variable name="omega_1" public_interface="out" units="per_s"/>
        <variable name="omega_2" public_interface="out" units="per_s"/>
        <variable name="omega_3" public_interface="out" units="per_s"/>
        <variable name="omega_4" public_interface="out" units="per_s"/>
        <variable name="omega_5" public_interface="out" units="per_s"/>
        <variable name="omega_6" public_interface="out" units="per_s"/>
        <variable name="omega_7" public_interface="out" units="per_s"/>
        <variable name="omega_8" public_interface="out" units="per_s"/>
        <variable name="A_0" public_interface="in" units="m3_per_s"/>
        <variable name="A_1" public_interface="in" units="m3_per_s"/>
        <variable name="A_2" public_interface="in" units="m3_per_s"/>
        <variable name="A_3" public_interface="in" units="m3_per_s"/>
        <variable name="A_4" public_interface="in" units="m3_per_s"/>
        <variable name="A_5" public_interface="in" units="m3_per_s"/>
        <variable name="A_6" public_interface="in" units="m3_per_s"/>
        <variable name="A_7" public_interface="in" units="m3_per_s"/>
        <variable name="A_8" public_interface="in" units="m3_per_s"/>
        <variable name="phi_0" public_interface="in" units="dimensionless"/>
        <variable name="phi_1" public_interface="in" units="dimensionless"/>
        <variable name="phi_2" public_interface="in" units="dimensionless"/>
        <variable name="phi_3" public_interface="in" units="dimensionless"/>
        <variable name="phi_4" public_interface="in" units="dimensionless"/>
        <variable name="phi_5" public_interface="in" units="dimensionless"/>
        <variable name="phi_6" public_interface="in" units="dimensionless"/>
        <variable name="phi_7" public_interface="in" units="dimensionless"/>
        <variable name="phi_8" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>omega_0</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">0</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">1</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_3</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">3</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_4</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">4</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_5</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">5</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_6</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">6</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_7</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">7</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>omega_8</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <cn cellml:units="dimensionless">8</cn>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_0</ci>
                <apply>
                    <times/>
                    <ci>A_0</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_0</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_0</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_1</ci>
                <apply>
                    <times/>
                    <ci>A_1</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_1</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_2</ci>
                <apply>
                    <times/>
                    <ci>A_2</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_2</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_3</ci>
                <apply>
                    <times/>
                    <ci>A_3</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_3</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_3</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_4</ci>
                <apply>
                    <times/>
                    <ci>A_4</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_4</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_4</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_5</ci>
                <apply>
                    <times/>
                    <ci>A_5</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_5</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_5</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_6</ci>
                <apply>
                    <times/>
                    <ci>A_6</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_6</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_6</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_7</ci>
                <apply>
                    <times/>
                    <ci>A_7</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_7</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_7</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_8</ci>
                <apply>
                    <times/>
                    <ci>A_8</ci>
                    <apply>
                        <cos/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>omega_8</ci>
                                <ci>t</ci>
                            </apply>
                            <ci>phi_8</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v</ci>
                <apply>
                    <plus/>
                    <ci>v_0</ci>
                    <ci>v_1</ci>
                    <ci>v_2</ci>
                    <ci>v_3</ci>
                    <ci>v_4</ci>
                    <ci>v_5</ci>
                    <ci>v_6</ci>
                    <ci>v_7</ci>
                    <ci>v_8</ci>
                </apply>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////// module baroreceptor firing rate from carotid and aortic arch pressures ///
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="baroreceptor_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="P_sys" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="P_baro" public_interface="out" units="J_per_m3"/>
        <variable name="f_ab" public_interface="out" units="per_s"/>
        <variable name="dP_sys_dt" public_interface="in" units="J_per_m3s"/>
        <!-- Constants-->
        <variable name="P_nom" public_interface="in" units="J_per_m3"/>
        <variable name="f_ab_min" public_interface="in" units="per_s"/>
        <variable name="f_ab_max" public_interface="in" units="per_s"/>
        <variable name="k_ab" public_interface="in" units="J_per_m3"/>
        <variable name="tau_zb" public_interface="in" units="second"/>
        <variable name="tau_pb" public_interface="in" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P_baro</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <ci>P_sys</ci>
                            <apply>
                                <times/>
                                <ci>tau_zb</ci>
                                <ci>dP_sys_dt</ci>
                            </apply>
                        </apply>
                        <ci>P_baro</ci>
                    </apply>
                    <ci>tau_pb</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>f_ab</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <ci>f_ab_min</ci>
                        <apply>
                            <times/>
                            <ci>f_ab_max</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <minus/>
                                        <ci>P_baro</ci>
                                        <ci>P_nom</ci>
                                    </apply>
                                    <ci>k_ab</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci>P_baro</ci>
                                    <ci>P_nom</ci>
                                </apply>
                                <ci>k_ab</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="chemoreceptor_type">
        <variable name="t" public_interface="in" units="second"/>
        <!--inp variables-->
        <variable name="C_CO2_a" public_interface="in" units="dimensionless"/>
        <variable name="C_O2_a" public_interface="in" units="dimensionless"/>
        <variable name="dot_C_CO2_a" public_interface="in" units="per_s"/>
        <!--output variables-->
        <variable name="X_O2" public_interface="out" units="dimensionless"/>
        <variable name="phi_stat" public_interface="out" units="per_s"/>
        <variable initial_value="0.0" name="phi_CO2_dyn" public_interface="out" units="per_s"/>
        <variable name="f_c_stat" public_interface="out" units="per_s"/>
        <variable name="f_c_dyn" public_interface="out" units="per_s"/>
        <variable name="f_apc" public_interface="out" units="per_s"/>
        <variable initial_value="0.0" name="phi_apc" public_interface="out" units="per_s"/>
        <variable name="P_O2_a" public_interface="out" units="J_per_m3"/>
        <!-- Constants-->
        <variable name="AA" public_interface="in" units="dimensionless"/>
        <variable name="BB" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_a_nom" public_interface="in" units="dimensionless"/>
        <variable name="K_O2" public_interface="in" units="dimensionless"/>
        <variable name="K_CO2" public_interface="in" units="per_s"/>
        <variable name="K_stat" public_interface="in" units="per_s"/>
        <variable name="K_dyn" public_interface="in" units="per_s"/>
        <variable name="tau_cap" public_interface="in" units="second"/>
        <variable name="tau_CO2_cc_dyn" public_interface="in" units="second"/>
        <!-- equations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>X_O2</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <ci>AA</ci>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>S_O2_a</ci>
                        </apply>
                    </apply>
                    <ci>BB</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>phi_stat</ci>
                <apply>
                    <times/>
                    <ci>K_CO2</ci>
                    <apply>
                        <minus/>
                        <ci>C_CO2_a</ci>
                        <ci>C_CO2_a_nom</ci>
                    </apply>
                    <ci>K_O2</ci>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci>X_O2</ci>
                                </apply>
                                <ci>K_O2</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>f_c_stat</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>K_stat</ci>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <minus/>
                                            <ci>phi_stat</ci>
                                        </apply>
                                        <ci>K_stat</ci>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>C_CO2_a</ci>
                            <ci>C_CO2_a_nom</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="per_s">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>phi_CO2_dyn</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <ci>dot_C_CO2_a</ci>
                            <ci>tau_CO2_cc_dyn</ci>
                        </apply>
                        <ci>phi_CO2_dyn</ci>
                    </apply>
                    <ci>tau_cap</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>f_c_dyn</ci>
                <apply>
                    <times/>
                    <ci>K_dyn</ci>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci>phi_CO2_dyn</ci>
                                </apply>
                                <ci>K_dyn</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>phi_apc</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <ci>f_c_stat</ci>
                            <ci>f_c_dyn</ci>
                        </apply>
                        <ci>phi_apc</ci>
                    </apply>
                    <ci>tau_cap</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>f_apc</ci>
                <apply>
                    <max/>
                    <ci>phi_apc</ci>
                    <cn cellml:units="per_s">0</cn>
                </apply>
            </apply>
        </math>
        <!--Calculate saturation-->
        <variable name="C_O2_a_diss" public_interface="out" units="dimensionless"/>
        <variable name="S_O2_a" public_interface="out" units="dimensionless"/>
        <variable name="Hgb" public_interface="in" units="kg_per_m3"/>
        <!-- from inverted dissociation-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>P_O2_a</ci>
                <apply>
                    <plus/>
                    <ci>r_1</ci>
                    <apply>
                        <root/>
                        <apply>
                            <minus/>
                            <apply>
                                <power/>
                                <ci>r_1</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>s_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- P_CO2_a = d_2*(1{dimensionless}+alpha_2*P_O2_p)/(1{dimensionless}+beta_2*P_O2_p);-->
            <apply>
                <eq/>
                <ci>C_O2_a_diss</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_O2_a</ci>
                                <cn cellml:units="dimensionless">0.003</cn>
                            </apply>
                            <cn cellml:units="dimensionless">100</cn>
                        </apply>
                        <apply>
                            <geq/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <ci>C_O2_sat</ci>
                                    <apply>
                                        <times/>
                                        <ci>Hgb</ci>
                                        <cn cellml:units="m3_per_kg" type="e-notation">1.34<sep/>-3</cn>
                                    </apply>
                                </apply>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>P_O2_a</ci>
                                        <cn cellml:units="dimensionless">0.003</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">100</cn>
                                </apply>
                            </apply>
                            <cn cellml:units="dimensionless">0</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <minus/>
                            <ci>C_O2_sat</ci>
                            <apply>
                                <times/>
                                <ci>Hgb</ci>
                                <cn cellml:units="m3_per_kg" type="e-notation">1.34<sep/>-3</cn>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>S_O2_a</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>C_O2_a</ci>
                        <ci>C_O2_a_diss</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>Hgb</ci>
                        <cn cellml:units="m3_per_kg" type="e-notation">1.34<sep/>-3</cn>
                    </apply>
                </apply>
            </apply>
        </math>
        <!--____________ inverted dissociation curve below here___________-->
        <variable name="k_1" public_interface="in" units="J_per_m3"/>
        <variable name="k_2" public_interface="in" units="J_per_m3"/>
        <variable name="h_1" public_interface="in" units="dimensionless"/>
        <variable name="h_2" public_interface="in" units="dimensionless"/>
        <variable name="d_1" public_interface="out" units="J_per_m3"/>
        <variable name="d_2" public_interface="out" units="J_per_m3"/>
        <variable name="r_1" public_interface="out" units="J_per_m3"/>
        <variable name="r_2" public_interface="out" units="J_per_m3"/>
        <variable name="s_1" public_interface="out" units="J2_per_m6"/>
        <variable name="s_2" public_interface="out" units="J2_per_m6"/>
        <variable name="alpha_1" public_interface="in" units="m3_per_J"/>
        <variable name="alpha_2" public_interface="in" units="m3_per_J"/>
        <variable name="beta_1" public_interface="in" units="m3_per_J"/>
        <variable name="beta_2" public_interface="in" units="m3_per_J"/>
        <variable name="C_O2_sat" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_sat" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>d_1</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_1</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_O2_a</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_O2_sat</ci>
                                    <ci>C_O2_a</ci>
                                </apply>
                            </apply>
                            <ci>h_1</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>d_2</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_2</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_CO2_a</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_CO2_sat</ci>
                                    <ci>C_CO2_a</ci>
                                </apply>
                            </apply>
                            <ci>h_2</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_1</ci>
                                        <ci>d_2</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_2</ci>
                                    <ci>d_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>alpha_2</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_2</ci>
                                        <ci>d_1</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_1</ci>
                                    <ci>d_2</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>alpha_1</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_1</ci>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_2</ci>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="afferent_to_vagal_efferent_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constants-->
        <variable name="f_ev_0" public_interface="in" units="per_s"/>
        <variable name="f_ev_inf" public_interface="in" units="per_s"/>
        <variable name="f_ab_0" public_interface="in" units="per_s"/>
        <variable name="theta_v" public_interface="in" units="per_s"/>
        <variable name="W_cv" public_interface="in" units="dimensionless"/>
        <!-- var W_pv: dimensionless {pub: in}; not yet including lung stretch receptor effects-->
        <variable name="k_ev" public_interface="in" units="per_s"/>
        <!-- Variables-->
        <variable name="f_apc" public_interface="in" units="per_s"/>
        <variable name="f_ab" public_interface="in" units="per_s"/>
        <!-- var f_ap: per_s {pub: in};-->
        <variable name="f_v" public_interface="out" units="per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>f_v</ci>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <apply>
                                <plus/>
                                <ci>f_ev_0</ci>
                                <apply>
                                    <times/>
                                    <ci>f_ev_inf</ci>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>f_ab</ci>
                                                <ci>f_ab_0</ci>
                                            </apply>
                                            <ci>k_ev</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <minus/>
                                            <ci>f_ab</ci>
                                            <ci>f_ab_0</ci>
                                        </apply>
                                        <ci>k_ev</ci>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>W_cv</ci>
                            <ci>f_apc</ci>
                        </apply>
                    </apply>
                    <ci>theta_v</ci>
                </apply>
            </apply>
        </math>
        <!-- + W_pv*f_ap-->
    </component>
    <component name="afferent_to_sympathetic_efferent_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constants-->
        <variable name="f_es_0" public_interface="in" units="per_s"/>
        <variable name="f_es_inf" public_interface="in" units="per_s"/>
        <variable name="f_es_max" public_interface="in" units="per_s"/>
        <variable name="k_es" public_interface="in" units="per_s"/>
        <!-- var theta_s: per_s {pub: in}; //currently ignoring CNS-->
        <variable name="W_bs" public_interface="in" units="dimensionless"/>
        <variable name="W_cs" public_interface="in" units="dimensionless"/>
        <!-- var W_ps: dimensionless {pub: in}; not yet including lung stretch receptor effects-->
        <!-- Variables-->
        <variable name="f_apc" public_interface="in" units="per_s"/>
        <variable name="f_ab" public_interface="in" units="per_s"/>
        <!-- var f_ap: per_s {pub: in};-->
        <variable name="f_s_premax" public_interface="out" units="per_s"/>
        <variable name="f_s" public_interface="out" units="per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>f_s_premax</ci>
                <apply>
                    <plus/>
                    <ci>f_es_inf</ci>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>f_es_0</ci>
                            <ci>f_es_inf</ci>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>k_es</ci>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <times/>
                                        <ci>W_bs</ci>
                                        <ci>f_ab</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>W_cs</ci>
                                        <ci>f_apc</ci>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!--IGNORING CNS and LUNG STRETCH-->
            <apply>
                <eq/>
                <ci>f_s</ci>
                <piecewise>
                    <piece>
                        <ci>f_s_premax</ci>
                        <apply>
                            <leq/>
                            <ci>f_s_premax</ci>
                            <ci>f_es_max</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <ci>f_es_max</ci>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
    </component>
    <component name="efferent_resistance_effector_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- IMPORTANT: THIS MODULE ASSUMES NO DELAY CONSTANTS, WHICH IS DIFFERENT TO THE ORIGINAL PAPER, ALBANESE2016-->
        <!-- Constants-->
        <variable name="G_theta" public_interface="in" units="Js_per_m6"/>
        <variable name="f_es_min" public_interface="in" units="per_s"/>
        <variable name="tau_theta" public_interface="in" units="second"/>
        <!-- Variables-->
        <variable name="f_s" public_interface="in" units="per_s"/>
        <variable initial_value="0.0" name="Delta_theta" public_interface="out" units="Js_per_m6"/>
        <variable name="sigma_theta" public_interface="out" units="Js_per_m6"/>
        <!-- Equations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>sigma_theta</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>G_theta</ci>
                            <apply>
                                <ln/>
                                <apply>
                                    <times/>
                                    <cn cellml:units="second">1</cn>
                                    <apply>
                                        <plus/>
                                        <apply>
                                            <minus/>
                                            <ci>f_s</ci>
                                            <ci>f_es_min</ci>
                                        </apply>
                                        <cn cellml:units="per_s">1</cn>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>f_s</ci>
                            <ci>f_es_min</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="Js_per_m6">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Delta_theta</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>Delta_theta</ci>
                        </apply>
                        <ci>sigma_theta</ci>
                    </apply>
                    <ci>tau_theta</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="efferent_heart_elastance_effector_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- IMPORTANT: THIS MODULE ASSUMES NO DELAY CONSTANTS, WHICH IS DIFFERENT TO THE ORIGINAL PAPER, ALBANESE2016-->
        <!-- Constants-->
        <variable name="G_theta" public_interface="in" units="J_per_m6"/>
        <variable name="f_es_min" public_interface="in" units="per_s"/>
        <variable name="tau_theta" public_interface="in" units="second"/>
        <!-- Variables-->
        <variable name="f_s" public_interface="in" units="per_s"/>
        <variable initial_value="0.0" name="Delta_theta" public_interface="out" units="J_per_m6"/>
        <variable name="sigma_theta" public_interface="out" units="J_per_m6"/>
        <!-- Equations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>sigma_theta</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>G_theta</ci>
                            <apply>
                                <ln/>
                                <apply>
                                    <times/>
                                    <cn cellml:units="second">1</cn>
                                    <apply>
                                        <plus/>
                                        <apply>
                                            <minus/>
                                            <ci>f_s</ci>
                                            <ci>f_es_min</ci>
                                        </apply>
                                        <cn cellml:units="per_s">1</cn>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>f_s</ci>
                            <ci>f_es_min</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="J_per_m6">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Delta_theta</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>Delta_theta</ci>
                        </apply>
                        <ci>sigma_theta</ci>
                    </apply>
                    <ci>tau_theta</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="efferent_venous_compliance_effector_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- IMPORTANT: THIS MODULE ASSUMES NO DELAY CONSTANTS, WHICH IS DIFFERENT TO THE ORIGINAL PAPER, ALBANESE2016-->
        <!-- IMPORTANT: THIS MODULE HAS BEEN MODIFIED TO CONTROL COMPLIANCE INSTEAD OF UNSTRESSED VOLUME. PARAMS ARE UNVALIDATED-->
        <!-- Constants-->
        <variable name="G_theta" public_interface="in" units="m3"/>
        <variable name="f_es_min" public_interface="in" units="per_s"/>
        <variable name="tau_theta" public_interface="in" units="second"/>
        <!-- Variables-->
        <variable name="f_s" public_interface="in" units="per_s"/>
        <variable initial_value="0.0" name="Delta_theta" public_interface="out" units="m3"/>
        <variable name="sigma_theta" public_interface="out" units="m3"/>
        <!-- Equations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>sigma_theta</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>G_theta</ci>
                            <apply>
                                <ln/>
                                <apply>
                                    <times/>
                                    <cn cellml:units="second">1</cn>
                                    <apply>
                                        <plus/>
                                        <apply>
                                            <minus/>
                                            <ci>f_s</ci>
                                            <ci>f_es_min</ci>
                                        </apply>
                                        <cn cellml:units="per_s">1</cn>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>f_s</ci>
                            <ci>f_es_min</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="m3">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Delta_theta</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>Delta_theta</ci>
                        </apply>
                        <ci>sigma_theta</ci>
                    </apply>
                    <ci>tau_theta</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="efferent_heart_period_effector_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- IMPORTANT: THIS MODULE ASSUMES NO DELAY CONSTANTS, WHICH IS DIFFERENT TO THE ORIGINAL PAPER, ALBANESE2016-->
        <!-- Constants-->
        <variable name="G_Ts" public_interface="in" units="second"/>
        <variable name="G_Tv" public_interface="in" units="second"/>
        <variable name="f_es_min" public_interface="in" units="per_s"/>
        <variable name="tau_Ts" public_interface="in" units="second"/>
        <variable name="tau_Tv" public_interface="in" units="second"/>
        <!-- Variables-->
        <variable name="f_s" public_interface="in" units="per_s"/>
        <variable name="f_v" public_interface="in" units="per_s"/>
        <variable initial_value="0.0" name="Delta_Ts" public_interface="out" units="second"/>
        <variable initial_value="0.0" name="Delta_Tv" public_interface="out" units="second"/>
        <variable name="Delta_T" public_interface="out" units="second"/>
        <variable name="sigma_Ts" public_interface="out" units="second"/>
        <variable name="sigma_Tv" public_interface="out" units="second"/>
        <!-- Equations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>sigma_Ts</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>G_Ts</ci>
                            <apply>
                                <ln/>
                                <apply>
                                    <times/>
                                    <cn cellml:units="second">1</cn>
                                    <apply>
                                        <plus/>
                                        <apply>
                                            <minus/>
                                            <ci>f_s</ci>
                                            <ci>f_es_min</ci>
                                        </apply>
                                        <cn cellml:units="per_s">1</cn>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>f_s</ci>
                            <ci>f_es_min</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="second">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Delta_Ts</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>Delta_Ts</ci>
                        </apply>
                        <ci>sigma_Ts</ci>
                    </apply>
                    <ci>tau_Ts</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>sigma_Tv</ci>
                <apply>
                    <times/>
                    <ci>G_Tv</ci>
                    <ci>f_v</ci>
                </apply>
            </apply>
            <!--DELAY IGNORED-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Delta_Tv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>Delta_Tv</ci>
                        </apply>
                        <ci>sigma_Tv</ci>
                    </apply>
                    <ci>tau_Tv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Delta_T</ci>
                <apply>
                    <plus/>
                    <ci>Delta_Tv</ci>
                    <ci>Delta_Ts</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="local_flow_control_muscle_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="x_O2" public_interface="out" units="dimensionless"/>
        <variable name="phi_P_CO2_a" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.0" name="x_CO2" public_interface="out" units="dimensionless"/>
        <variable name="C_O2_a" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_a" public_interface="in" units="dimensionless"/>
        <variable name="C_O2_p" public_interface="in" units="dimensionless"/>
        <variable name="P_CO2_a" public_interface="out" units="dimensionless"/>
        <variable name="R_local_multiplier" public_interface="out" units="dimensionless"/>
        <variable name="P_O2_a" public_interface="out" units="J_per_m3"/>
        <!-- Constants-->
        <variable name="P_CO2_a_nom" public_interface="in" units="J_per_m3"/>
        <variable name="k_CO2_m" public_interface="in" units="J_per_m3"/>
        <variable name="C_O2_vm_nom" public_interface="in" units="dimensionless"/>
        <variable name="tau_O2" public_interface="in" units="second"/>
        <variable name="tau_CO2" public_interface="in" units="second"/>
        <variable name="g_O2_m" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>x_O2</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <minus/>
                                <ci>x_O2</ci>
                            </apply>
                            <ci>C_O2_p</ci>
                        </apply>
                        <ci>C_O2_vm_nom</ci>
                    </apply>
                    <ci>tau_O2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>phi_P_CO2_a</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci>P_CO2_a</ci>
                                    <ci>P_CO2_a_nom</ci>
                                </apply>
                                <ci>k_CO2_m</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci>P_CO2_a</ci>
                                    <ci>P_CO2_a_nom</ci>
                                </apply>
                                <ci>k_CO2_m</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>x_CO2</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>x_CO2</ci>
                        </apply>
                        <ci>phi_P_CO2_a</ci>
                    </apply>
                    <ci>tau_CO2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_local_multiplier</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>x_CO2</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <times/>
                            <ci>g_O2_m</ci>
                            <ci>x_O2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- from inverted dissociation-->
            <apply>
                <eq/>
                <ci>P_O2_a</ci>
                <apply>
                    <plus/>
                    <ci>r_1</ci>
                    <apply>
                        <root/>
                        <apply>
                            <minus/>
                            <apply>
                                <power/>
                                <ci>r_1</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>s_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_CO2_a</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>d_2</ci>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>P_O2_a</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <times/>
                            <ci>beta_2</ci>
                            <ci>P_O2_a</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <variable name="k_1" public_interface="in" units="J_per_m3"/>
        <variable name="k_2" public_interface="in" units="J_per_m3"/>
        <variable name="h_1" public_interface="in" units="dimensionless"/>
        <variable name="h_2" public_interface="in" units="dimensionless"/>
        <variable name="d_1" public_interface="out" units="J_per_m3"/>
        <variable name="d_2" public_interface="out" units="J_per_m3"/>
        <variable name="r_1" public_interface="out" units="J_per_m3"/>
        <variable name="r_2" public_interface="out" units="J_per_m3"/>
        <variable name="s_1" public_interface="out" units="J2_per_m6"/>
        <variable name="s_2" public_interface="out" units="J2_per_m6"/>
        <variable name="alpha_1" public_interface="in" units="m3_per_J"/>
        <variable name="alpha_2" public_interface="in" units="m3_per_J"/>
        <variable name="beta_1" public_interface="in" units="m3_per_J"/>
        <variable name="beta_2" public_interface="in" units="m3_per_J"/>
        <variable name="C_O2_sat" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_sat" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>d_1</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_1</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_O2_a</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_O2_sat</ci>
                                    <ci>C_O2_a</ci>
                                </apply>
                            </apply>
                            <ci>h_1</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>d_2</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_2</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_CO2_a</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_CO2_sat</ci>
                                    <ci>C_CO2_a</ci>
                                </apply>
                            </apply>
                            <ci>h_2</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_1</ci>
                                        <ci>d_2</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_2</ci>
                                    <ci>d_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>alpha_2</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_2</ci>
                                        <ci>d_1</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_1</ci>
                                    <ci>d_2</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>alpha_1</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_1</ci>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_2</ci>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="local_flow_control_brain_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="x_O2" public_interface="out" units="dimensionless"/>
        <variable name="phi_P_CO2_a" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.0" name="x_CO2" public_interface="out" units="dimensionless"/>
        <variable name="C_O2_a" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_a" public_interface="in" units="dimensionless"/>
        <variable name="C_O2_p" public_interface="in" units="dimensionless"/>
        <variable name="P_CO2_a" public_interface="out" units="dimensionless"/>
        <variable name="R_local_multiplier" public_interface="out" units="dimensionless"/>
        <variable name="P_O2_a" public_interface="out" units="J_per_m3"/>
        <variable name="G_p" public_interface="out" units="dimensionless"/>
        <!-- Constants-->
        <variable name="P_CO2_a_nom" public_interface="in" units="J_per_m3"/>
        <variable name="C_O2_vb_nom" public_interface="in" units="dimensionless"/>
        <variable name="tau_O2" public_interface="in" units="second"/>
        <variable name="tau_CO2" public_interface="in" units="second"/>
        <variable name="g_O2_b" public_interface="in" units="dimensionless"/>
        <variable name="A_b_lc" public_interface="in" units="dimensionless"/>
        <variable name="B_b_lc" public_interface="in" units="dimensionless"/>
        <variable name="C_b_lc" public_interface="in" units="dimensionless"/>
        <variable name="D_b_lc" public_interface="in" units="dimensionless"/>
        <variable name="G_pn" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>x_O2</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <minus/>
                                <ci>x_O2</ci>
                            </apply>
                            <ci>C_O2_p</ci>
                        </apply>
                        <ci>C_O2_vb_nom</ci>
                    </apply>
                    <ci>tau_O2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>phi_P_CO2_a</ci>
                <apply>
                    <minus/>
                    <apply>
                        <divide/>
                        <apply>
                            <plus/>
                            <ci>A_b_lc</ci>
                            <apply>
                                <divide/>
                                <ci>B_b_lc</ci>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>C_b_lc</ci>
                                        <apply>
                                            <exp/>
                                            <apply>
                                                <times/>
                                                <ci>D_b_lc</ci>
                                                <apply>
                                                    <ln/>
                                                    <ci>P_CO2_a</ci>
                                                </apply>
                                            </apply>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>A_b_lc</ci>
                            <apply>
                                <divide/>
                                <ci>B_b_lc</ci>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>C_b_lc</ci>
                                        <apply>
                                            <exp/>
                                            <apply>
                                                <times/>
                                                <ci>D_b_lc</ci>
                                                <apply>
                                                    <ln/>
                                                    <ci>P_CO2_a_nom</ci>
                                                </apply>
                                            </apply>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <cn cellml:units="dimensionless">1</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>x_CO2</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>x_CO2</ci>
                        </apply>
                        <ci>phi_P_CO2_a</ci>
                    </apply>
                    <ci>tau_CO2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>G_p</ci>
                <apply>
                    <times/>
                    <ci>G_pn</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <times/>
                                <ci>g_O2_b</ci>
                                <ci>x_O2</ci>
                            </apply>
                        </apply>
                        <ci>x_CO2</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_local_multiplier</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">1</cn>
                    <ci>G_p</ci>
                </apply>
            </apply>
            <!-- from inverted dissociation-->
            <apply>
                <eq/>
                <ci>P_O2_a</ci>
                <apply>
                    <plus/>
                    <ci>r_1</ci>
                    <apply>
                        <root/>
                        <apply>
                            <minus/>
                            <apply>
                                <power/>
                                <ci>r_1</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>s_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_CO2_a</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>d_2</ci>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>P_O2_a</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <times/>
                            <ci>beta_2</ci>
                            <ci>P_O2_a</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <variable name="k_1" public_interface="in" units="J_per_m3"/>
        <variable name="k_2" public_interface="in" units="J_per_m3"/>
        <variable name="h_1" public_interface="in" units="dimensionless"/>
        <variable name="h_2" public_interface="in" units="dimensionless"/>
        <variable name="d_1" public_interface="out" units="J_per_m3"/>
        <variable name="d_2" public_interface="out" units="J_per_m3"/>
        <variable name="r_1" public_interface="out" units="J_per_m3"/>
        <variable name="r_2" public_interface="out" units="J_per_m3"/>
        <variable name="s_1" public_interface="out" units="J2_per_m6"/>
        <variable name="s_2" public_interface="out" units="J2_per_m6"/>
        <variable name="alpha_1" public_interface="in" units="m3_per_J"/>
        <variable name="alpha_2" public_interface="in" units="m3_per_J"/>
        <variable name="beta_1" public_interface="in" units="m3_per_J"/>
        <variable name="beta_2" public_interface="in" units="m3_per_J"/>
        <variable name="C_O2_sat" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_sat" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>d_1</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_1</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_O2_a</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_O2_sat</ci>
                                    <ci>C_O2_a</ci>
                                </apply>
                            </apply>
                            <ci>h_1</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>d_2</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_2</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_CO2_a</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_CO2_sat</ci>
                                    <ci>C_CO2_a</ci>
                                </apply>
                            </apply>
                            <ci>h_2</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_1</ci>
                                        <ci>d_2</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_2</ci>
                                    <ci>d_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>alpha_2</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_2</ci>
                                        <ci>d_1</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_1</ci>
                                    <ci>d_2</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>alpha_1</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_1</ci>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_2</ci>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pv_0D_1D_coupler_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constants-->
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <!-- Inputs-->
        <variable name="P_t_star" public_interface="in" units="J_per_m3"/>
        <variable name="A_star" public_interface="in" units="m3"/>
        <variable name="P_s_0D" public_interface="in" units="J_per_m3"/>
        <!-- Latent variables-->
        <variable name="P_s_star" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_star" public_interface="out" units="m3_per_s"/>
        <!-- Outputs-->
        <variable initial_value="0.0" name="flux" public_interface="out" units="m3_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>P_s_star</ci>
                <apply>
                    <minus/>
                    <ci>P_t_star</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">0.5</cn>
                        <ci>rho</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>q_star</ci>
                                <ci>A_star</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_star</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_s_star</ci>
                        <ci>P_s_0D</ci>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>flux</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>rho</ci>
                    <ci>Q_star</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="imposter_1D">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Inputs-->
        <variable name="P_t_star" private_interface="in" public_interface="out" units="J_per_m3"/>
        <variable name="A_star" private_interface="in" public_interface="out" units="m3"/>
        <variable name="flux" public_interface="in" units="m3_per_s"/>
    </component>
    <component name="p_observer_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="u" private_interface="in" public_interface="out" units="J_per_m3"/>
        <!--var v_out: m3_per_s {pub: out};
var u_out: J_per_m3 {pub: out};-->
        <!--v_out = v_in;
u_out = u_in;-->
    </component>
    <component name="f_observer_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="v" private_interface="in" public_interface="out" units="m3_per_s"/>
        <!--var v_out: m3_per_s {pub: out};
var u_out: J_per_m3 {pub: out};-->
        <!--v_out = v_in;
u_out = u_in;-->
    </component>
    <component name="controller_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I_T" public_interface="out" units="Js2_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_T" public_interface="out" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <!-- State Variables-->
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <!-- v_T is the output flow to the venous side-->
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
        <variable name="R_T_wCont" public_interface="out" units="Js_per_m6"/>
        <variable name="error_flow_percent" public_interface="out" units="dimensionless"/>
        <variable name="u_a" public_interface="in" units="J_per_m3"/>
        <variable name="v_a" public_interface="in" units="m3_per_s"/>
        <variable name="meanflow_4dflow" public_interface="in" units="m3_per_s"/>
        <variable name="BFF_ASL" public_interface="in" units="dimensionless"/>
        <variable name="pressure_d" public_interface="in" units="J_per_m3"/>
        <variable name="error" public_interface="out" units="J_per_m3"/>
        <variable name="check" public_interface="out" units="dimensionless"/>
        <variable name="x1" units="dimensionless"/>
        <variable name="x2" units="dimensionless"/>
        <variable name="x3" units="dimensionless"/>
        <variable name="u2" units="dimensionless"/>
        <variable name="u5" units="dimensionless"/>
        <variable name="u8" units="dimensionless"/>
        <variable initial_value="100" name="aa2" units="dimensionless"/>
        <variable initial_value="100" name="cc2" units="dimensionless"/>
        <variable initial_value="100" name="aa5" units="dimensionless"/>
        <variable initial_value="100" name="cc5" units="dimensionless"/>
        <variable initial_value="100" name="aa8" public_interface="out" units="dimensionless"/>
        <variable initial_value="100" name="cc8" units="dimensionless"/>
        <variable initial_value="1e6" name="learning_rate" units="dimensionless"/>
        <variable initial_value="0.001" name="K_a" units="dimensionless"/>
        <variable name="critic" public_interface="out" units="dimensionless"/>
        <variable name="r_a" public_interface="out" units="dimensionless"/>
        <!-- Conservation Laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>r_a</ci>
                <apply>
                    <minus/>
                    <ci>BFF_ASL</ci>
                    <apply>
                        <divide/>
                        <ci>v_a</ci>
                        <ci>meanflow_4dflow</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>error</ci>
                <apply>
                    <minus/>
                    <ci>pressure_d</ci>
                    <ci>u_a</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>critic</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless" type="e-notation">1<sep/>-6</cn>
                    </apply>
                    <ci>error</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>v</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>-4</cn>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>x1</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">1</cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <minus/>
                                        <ci>error</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless" type="e-notation">1<sep/>0</cn>
                                </apply>
                                <cn cellml:units="dimensionless">0.01</cn>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>x2</ci>
                <apply>
                    <exp/>
                    <apply>
                        <minus/>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>error</ci>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>0</cn>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>x3</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">1</cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <ci>error</ci>
                                    <cn cellml:units="dimensionless" type="e-notation">1<sep/>0</cn>
                                </apply>
                                <cn cellml:units="dimensionless">0.01</cn>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u2</ci>
                <apply>
                    <divide/>
                    <ci>x1</ci>
                    <apply>
                        <plus/>
                        <ci>x1</ci>
                        <ci>x2</ci>
                        <ci>x3</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u5</ci>
                <apply>
                    <divide/>
                    <ci>x2</ci>
                    <apply>
                        <plus/>
                        <ci>x1</ci>
                        <ci>x2</ci>
                        <ci>x3</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u8</ci>
                <apply>
                    <divide/>
                    <ci>x3</ci>
                    <apply>
                        <plus/>
                        <ci>x1</ci>
                        <ci>x2</ci>
                        <ci>x3</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>aa2</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u2</ci>
                    <ci>error</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>cc2</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>aa5</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u5</ci>
                    <ci>error</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>cc5</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u5</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>aa8</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u8</ci>
                    <ci>error</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>cc8</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u8</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>check</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <ci>u2</ci>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>aa2</ci>
                                <ci>error</ci>
                            </apply>
                            <ci>cc2</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>u5</ci>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>aa5</ci>
                                <ci>error</ci>
                            </apply>
                            <ci>cc5</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>u8</ci>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>aa8</ci>
                                <ci>error</ci>
                            </apply>
                            <ci>cc8</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_T</ci>
                <piecewise>
                    <piece>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <leq/>
                            <ci>check</ci>
                            <cn cellml:units="dimensionless">0</cn>
                        </apply>
                    </piece>
                    <piece>
                        <ci>check</ci>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>check</ci>
                                <cn cellml:units="dimensionless">0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>check</ci>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>13</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <cn cellml:units="dimensionless" type="e-notation">1<sep/>13</cn>
                        <apply>
                            <gt/>
                            <ci>check</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>13</cn>
                        </apply>
                    </piece>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>error_flow_percent</ci>
                <apply>
                    <times/>
                    <ci>r_a</ci>
                    <cn cellml:units="dimensionless">100</cn>
                </apply>
            </apply>
            <!-- Improve this R_v estimate?-->
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_T</ci>
                <cn cellml:units="Js_per_m6" type="e-notation">1<sep/>-6</cn>
            </apply>
            <!-- Conservation Laws-->
            <!-- For now terminals don't have a gravity effect, change this for leg terminals
u_out = 0{J_per_m3};-->
            <apply>
                <eq/>
                <ci>u_out</ci>
                <cn cellml:units="dimensionless">0</cn>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <divide/>
                    <ci>q_T</ci>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v_T</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_T_wCont</ci>
                <ci>R_T</ci>
            </apply>
        </math>
    </component>
    <component name="controller2_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I_T" public_interface="out" units="Js2_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_T" public_interface="out" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <!-- State Variables-->
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <!-- v_T is the output flow to the venous side-->
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
        <variable name="R_T_wCont" public_interface="out" units="Js_per_m6"/>
        <variable name="error_flow_percent" public_interface="out" units="Js_per_m6"/>
        <variable name="u_a" public_interface="in" units="J_per_m3"/>
        <variable name="v_a" public_interface="in" units="m3_per_s"/>
        <variable name="meanflow_4dflow" public_interface="in" units="m3_per_s"/>
        <variable name="BFF_ASL" public_interface="in" units="dimensionless"/>
        <variable name="pressure_d" public_interface="in" units="J_per_m3"/>
        <variable name="error" public_interface="out" units="J_per_m3"/>
        <variable name="check" public_interface="out" units="dimensionless"/>
        <variable name="x1" units="dimensionless"/>
        <variable name="x2" units="dimensionless"/>
        <variable name="x3" units="dimensionless"/>
        <variable name="u2" units="dimensionless"/>
        <variable name="u5" units="dimensionless"/>
        <variable name="u8" units="dimensionless"/>
        <variable initial_value="100" name="aa2" units="dimensionless"/>
        <variable initial_value="100" name="cc2" units="dimensionless"/>
        <variable initial_value="100" name="aa5" units="dimensionless"/>
        <variable initial_value="100" name="cc5" units="dimensionless"/>
        <variable initial_value="100" name="aa8" public_interface="out" units="dimensionless"/>
        <variable initial_value="100" name="cc8" units="dimensionless"/>
        <variable initial_value="1e8" name="learning_rate" units="dimensionless"/>
        <variable initial_value="0.01" name="K_a" units="dimensionless"/>
        <variable name="critic" public_interface="out" units="dimensionless"/>
        <variable name="r_a" public_interface="out" units="dimensionless"/>
        <!-- Conservation Laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>r_a</ci>
                <apply>
                    <minus/>
                    <ci>BFF_ASL</ci>
                    <apply>
                        <divide/>
                        <ci>v_a</ci>
                        <ci>meanflow_4dflow</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>error</ci>
                <apply>
                    <minus/>
                    <ci>pressure_d</ci>
                    <ci>u_a</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>critic</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless" type="e-notation">1<sep/>-6</cn>
                    </apply>
                    <ci>error</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>v</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>-6</cn>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>x1</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">1</cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <minus/>
                                        <ci>error</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless" type="e-notation">1<sep/>0</cn>
                                </apply>
                                <cn cellml:units="dimensionless">0.01</cn>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>x2</ci>
                <apply>
                    <exp/>
                    <apply>
                        <minus/>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>error</ci>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>0</cn>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>x3</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">1</cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <ci>error</ci>
                                    <cn cellml:units="dimensionless" type="e-notation">1<sep/>0</cn>
                                </apply>
                                <cn cellml:units="dimensionless">0.01</cn>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u2</ci>
                <apply>
                    <divide/>
                    <ci>x1</ci>
                    <apply>
                        <plus/>
                        <ci>x1</ci>
                        <ci>x2</ci>
                        <ci>x3</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u5</ci>
                <apply>
                    <divide/>
                    <ci>x2</ci>
                    <apply>
                        <plus/>
                        <ci>x1</ci>
                        <ci>x2</ci>
                        <ci>x3</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u8</ci>
                <apply>
                    <divide/>
                    <ci>x3</ci>
                    <apply>
                        <plus/>
                        <ci>x1</ci>
                        <ci>x2</ci>
                        <ci>x3</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>aa2</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u2</ci>
                    <ci>error</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>cc2</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>aa5</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u5</ci>
                    <ci>error</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>cc5</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u5</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>aa8</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u8</ci>
                    <ci>error</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>cc8</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>learning_rate</ci>
                    <apply>
                        <minus/>
                        <ci>critic</ci>
                        <apply>
                            <times/>
                            <ci>K_a</ci>
                            <ci>r_a</ci>
                        </apply>
                    </apply>
                    <ci>u8</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>check</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <ci>u2</ci>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>aa2</ci>
                                <ci>error</ci>
                            </apply>
                            <ci>cc2</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>u5</ci>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>aa5</ci>
                                <ci>error</ci>
                            </apply>
                            <ci>cc5</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>u8</ci>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>aa8</ci>
                                <ci>error</ci>
                            </apply>
                            <ci>cc8</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_T</ci>
                <piecewise>
                    <piece>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <leq/>
                            <ci>check</ci>
                            <cn cellml:units="dimensionless">0</cn>
                        </apply>
                    </piece>
                    <piece>
                        <ci>check</ci>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>check</ci>
                                <cn cellml:units="dimensionless">0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>check</ci>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>13</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <cn cellml:units="dimensionless" type="e-notation">1<sep/>13</cn>
                        <apply>
                            <gt/>
                            <ci>check</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>13</cn>
                        </apply>
                    </piece>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>error_flow_percent</ci>
                <apply>
                    <times/>
                    <ci>r_a</ci>
                    <cn cellml:units="dimensionless">100</cn>
                </apply>
            </apply>
            <!-- Improve this R_v estimate?-->
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_T</ci>
                <cn cellml:units="Js_per_m6" type="e-notation">1<sep/>-6</cn>
            </apply>
            <!-- Conservation Laws-->
            <!-- For now terminals don't have a gravity effect, change this for leg terminals
u_out = 0{J_per_m3};-->
            <apply>
                <eq/>
                <ci>u_out</ci>
                <cn cellml:units="dimensionless">0</cn>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <divide/>
                    <ci>q_T</ci>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v_T</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_T_wCont</ci>
                <ci>R_T</ci>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
/////////////module for simple O2 and CO2 calculation in a terminal ///
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="tissue_GE_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="q_0" public_interface="in" units="m3"/>
        <variable name="v" public_interface="in" units="m3_per_s"/>
        <variable name="M_O2" public_interface="in" units="m3_per_s"/>
        <variable name="M_CO2" public_interface="in" units="m3_per_s"/>
        <variable name="C_O2_a" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_a" public_interface="in" units="dimensionless"/>
        <variable initial_value="0.15" name="C_O2_p" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.38" name="C_CO2_p" public_interface="out" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_O2_p</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>v</ci>
                            <apply>
                                <minus/>
                                <ci>C_O2_a</ci>
                                <ci>C_O2_p</ci>
                            </apply>
                        </apply>
                        <ci>M_O2</ci>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_CO2_p</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>v</ci>
                            <apply>
                                <minus/>
                                <ci>C_CO2_a</ci>
                                <ci>C_CO2_p</ci>
                            </apply>
                        </apply>
                        <ci>M_CO2</ci>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
/////////////module for O2 and CO2 calculation in a pulmonary system///
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="pulmonary_GE_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="q_0" public_interface="in" units="m3"/>
        <variable name="v" public_interface="in" units="m3_per_s"/>
        <variable name="M_O2" public_interface="out" units="m3_per_s"/>
        <variable name="M_CO2" public_interface="out" units="m3_per_s"/>
        <variable name="C_O2_v" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_v" public_interface="in" units="dimensionless"/>
        <variable initial_value="0.2" name="C_O2_p" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.34" name="C_CO2_p" public_interface="out" units="dimensionless"/>
        <!-- New params-->
        <variable name="k_O2" public_interface="in" units="m6_per_Js"/>
        <variable name="k_CO2" public_interface="in" units="m6_per_Js"/>
        <variable name="P_O2_A" public_interface="in" units="J_per_m3"/>
        <variable name="P_CO2_A" public_interface="in" units="J_per_m3"/>
        <variable name="shunt_fraction" public_interface="in" units="dimensionless"/>
        <!--New vars-->
        <variable name="P_O2_p" public_interface="out" units="J_per_m3"/>
        <variable name="P_CO2_p" public_interface="out" units="J_per_m3"/>
        <variable name="C_O2_a" public_interface="out" units="dimensionless"/>
        <variable name="C_CO2_a" public_interface="out" units="dimensionless"/>
        <variable name="v_p" public_interface="out" units="m3_per_s"/>
        <variable name="v_sh" public_interface="out" units="m3_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>M_O2</ci>
                <apply>
                    <times/>
                    <ci>k_O2</ci>
                    <apply>
                        <minus/>
                        <ci>P_O2_A</ci>
                        <ci>P_O2_p</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>M_CO2</ci>
                <apply>
                    <times/>
                    <ci>k_CO2</ci>
                    <apply>
                        <minus/>
                        <ci>P_CO2_A</ci>
                        <ci>P_CO2_p</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_O2_p</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>v_p</ci>
                            <apply>
                                <minus/>
                                <ci>C_O2_v</ci>
                                <ci>C_O2_p</ci>
                            </apply>
                        </apply>
                        <ci>M_O2</ci>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_CO2_p</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>v_p</ci>
                            <apply>
                                <minus/>
                                <ci>C_CO2_v</ci>
                                <ci>C_CO2_p</ci>
                            </apply>
                        </apply>
                        <ci>M_CO2</ci>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
            <!-- from inverted dissociation-->
            <apply>
                <eq/>
                <ci>P_O2_p</ci>
                <apply>
                    <plus/>
                    <ci>r_1</ci>
                    <apply>
                        <root/>
                        <apply>
                            <minus/>
                            <apply>
                                <power/>
                                <ci>r_1</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>s_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_CO2_p</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>d_2</ci>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>P_O2_p</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <times/>
                            <ci>beta_2</ci>
                            <ci>P_O2_p</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- flows from shunt todo model this??-->
            <apply>
                <eq/>
                <ci>v_p</ci>
                <apply>
                    <times/>
                    <ci>v</ci>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>shunt_fraction</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_sh</ci>
                <apply>
                    <times/>
                    <ci>v</ci>
                    <ci>shunt_fraction</ci>
                </apply>
            </apply>
            <!-- calculate arterial gas concentration due to pulmonary shunt-->
            <apply>
                <eq/>
                <ci>C_O2_a</ci>
                <apply>
                    <max/>
                    <apply>
                        <divide/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>v_p</ci>
                                <ci>C_O2_p</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>v_sh</ci>
                                <ci>C_O2_v</ci>
                            </apply>
                        </apply>
                        <ci>v</ci>
                    </apply>
                    <cn cellml:units="m3_per_s">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C_CO2_a</ci>
                <apply>
                    <max/>
                    <apply>
                        <divide/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>v_p</ci>
                                <ci>C_CO2_p</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>v_sh</ci>
                                <ci>C_CO2_v</ci>
                            </apply>
                        </apply>
                        <ci>v</ci>
                    </apply>
                    <cn cellml:units="m3_per_s">0</cn>
                </apply>
            </apply>
        </math>
        <!--____________ inverted dissociation curve below here___________-->
        <variable name="k_1" public_interface="in" units="J_per_m3"/>
        <variable name="k_2" public_interface="in" units="J_per_m3"/>
        <variable name="h_1" public_interface="in" units="dimensionless"/>
        <variable name="h_2" public_interface="in" units="dimensionless"/>
        <variable name="d_1" public_interface="out" units="J_per_m3"/>
        <variable name="d_2" public_interface="out" units="J_per_m3"/>
        <variable name="r_1" public_interface="out" units="J_per_m3"/>
        <variable name="r_2" public_interface="out" units="J_per_m3"/>
        <variable name="s_1" public_interface="out" units="J2_per_m6"/>
        <variable name="s_2" public_interface="out" units="J2_per_m6"/>
        <variable name="alpha_1" public_interface="in" units="m3_per_J"/>
        <variable name="alpha_2" public_interface="in" units="m3_per_J"/>
        <variable name="beta_1" public_interface="in" units="m3_per_J"/>
        <variable name="beta_2" public_interface="in" units="m3_per_J"/>
        <variable name="C_O2_sat" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_sat" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>d_1</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_1</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_O2_p</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_O2_sat</ci>
                                    <ci>C_O2_p</ci>
                                </apply>
                            </apply>
                            <ci>h_1</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>d_2</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_2</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_CO2_p</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_CO2_sat</ci>
                                    <ci>C_CO2_p</ci>
                                </apply>
                            </apply>
                            <ci>h_2</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_1</ci>
                                        <ci>d_2</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_2</ci>
                                    <ci>d_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>alpha_2</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_2</ci>
                                        <ci>d_1</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_1</ci>
                                    <ci>d_2</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>alpha_1</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_1</ci>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_2</ci>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pulmonary_GE_5_lobe_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="q_0" public_interface="in" units="m3"/>
        <variable name="v_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_2" public_interface="in" units="m3_per_s"/>
        <variable name="v_3" public_interface="in" units="m3_per_s"/>
        <variable name="v_4" public_interface="in" units="m3_per_s"/>
        <variable name="v_5" public_interface="in" units="m3_per_s"/>
        <variable name="v" public_interface="out" units="m3_per_s"/>
        <variable name="M_O2" public_interface="out" units="m3_per_s"/>
        <variable name="M_CO2" public_interface="out" units="m3_per_s"/>
        <variable name="C_O2_v" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_v" public_interface="in" units="dimensionless"/>
        <variable initial_value="0.2" name="C_O2_p" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.34" name="C_CO2_p" public_interface="out" units="dimensionless"/>
        <!-- New params-->
        <variable name="k_O2" public_interface="in" units="m6_per_Js"/>
        <variable name="k_CO2" public_interface="in" units="m6_per_Js"/>
        <variable name="P_O2_A" public_interface="in" units="J_per_m3"/>
        <variable name="P_CO2_A" public_interface="in" units="J_per_m3"/>
        <variable name="shunt_fraction" public_interface="in" units="dimensionless"/>
        <!--New vars-->
        <variable name="P_O2_p" public_interface="out" units="J_per_m3"/>
        <variable name="P_CO2_p" public_interface="out" units="J_per_m3"/>
        <variable name="C_O2_a" public_interface="out" units="dimensionless"/>
        <variable name="C_CO2_a" public_interface="out" units="dimensionless"/>
        <variable name="v_p" public_interface="out" units="m3_per_s"/>
        <variable name="v_sh" public_interface="out" units="m3_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>M_O2</ci>
                <apply>
                    <times/>
                    <ci>k_O2</ci>
                    <apply>
                        <minus/>
                        <ci>P_O2_A</ci>
                        <ci>P_O2_p</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>M_CO2</ci>
                <apply>
                    <times/>
                    <ci>k_CO2</ci>
                    <apply>
                        <minus/>
                        <ci>P_CO2_A</ci>
                        <ci>P_CO2_p</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_O2_p</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>v_p</ci>
                            <apply>
                                <minus/>
                                <ci>C_O2_v</ci>
                                <ci>C_O2_p</ci>
                            </apply>
                        </apply>
                        <ci>M_O2</ci>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_CO2_p</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>v_p</ci>
                            <apply>
                                <minus/>
                                <ci>C_CO2_v</ci>
                                <ci>C_CO2_p</ci>
                            </apply>
                        </apply>
                        <ci>M_CO2</ci>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
            <!-- from inverted dissociation-->
            <apply>
                <eq/>
                <ci>P_O2_p</ci>
                <apply>
                    <plus/>
                    <ci>r_1</ci>
                    <apply>
                        <root/>
                        <apply>
                            <minus/>
                            <apply>
                                <power/>
                                <ci>r_1</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>s_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_CO2_p</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>d_2</ci>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>P_O2_p</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <times/>
                            <ci>beta_2</ci>
                            <ci>P_O2_p</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- sum love flows for now-->
            <apply>
                <eq/>
                <ci>v</ci>
                <apply>
                    <plus/>
                    <ci>v_1</ci>
                    <ci>v_2</ci>
                    <ci>v_3</ci>
                    <ci>v_4</ci>
                    <ci>v_5</ci>
                </apply>
            </apply>
            <!-- flows from shunt todo model this??-->
            <apply>
                <eq/>
                <ci>v_p</ci>
                <apply>
                    <times/>
                    <ci>v</ci>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>shunt_fraction</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_sh</ci>
                <apply>
                    <times/>
                    <ci>v</ci>
                    <ci>shunt_fraction</ci>
                </apply>
            </apply>
            <!-- calculate arterial gas concentration due to pulmonary shunt-->
            <apply>
                <eq/>
                <ci>C_O2_a</ci>
                <apply>
                    <max/>
                    <apply>
                        <divide/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>v_p</ci>
                                <ci>C_O2_p</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>v_sh</ci>
                                <ci>C_O2_v</ci>
                            </apply>
                        </apply>
                        <ci>v</ci>
                    </apply>
                    <cn cellml:units="m3_per_s">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C_CO2_a</ci>
                <apply>
                    <max/>
                    <apply>
                        <divide/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>v_p</ci>
                                <ci>C_CO2_p</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>v_sh</ci>
                                <ci>C_CO2_v</ci>
                            </apply>
                        </apply>
                        <ci>v</ci>
                    </apply>
                    <cn cellml:units="m3_per_s">0</cn>
                </apply>
            </apply>
        </math>
        <!--____________ inverted dissociation curve below here___________-->
        <variable name="k_1" public_interface="in" units="J_per_m3"/>
        <variable name="k_2" public_interface="in" units="J_per_m3"/>
        <variable name="h_1" public_interface="in" units="dimensionless"/>
        <variable name="h_2" public_interface="in" units="dimensionless"/>
        <variable name="d_1" public_interface="out" units="J_per_m3"/>
        <variable name="d_2" public_interface="out" units="J_per_m3"/>
        <variable name="r_1" public_interface="out" units="J_per_m3"/>
        <variable name="r_2" public_interface="out" units="J_per_m3"/>
        <variable name="s_1" public_interface="out" units="J2_per_m6"/>
        <variable name="s_2" public_interface="out" units="J2_per_m6"/>
        <variable name="alpha_1" public_interface="in" units="m3_per_J"/>
        <variable name="alpha_2" public_interface="in" units="m3_per_J"/>
        <variable name="beta_1" public_interface="in" units="m3_per_J"/>
        <variable name="beta_2" public_interface="in" units="m3_per_J"/>
        <variable name="C_O2_sat" public_interface="in" units="dimensionless"/>
        <variable name="C_CO2_sat" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>d_1</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_1</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_O2_p</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_O2_sat</ci>
                                    <ci>C_O2_p</ci>
                                </apply>
                            </apply>
                            <ci>h_1</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>d_2</ci>
                <apply>
                    <max/>
                    <apply>
                        <times/>
                        <ci>k_2</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>C_CO2_p</ci>
                                <apply>
                                    <minus/>
                                    <ci>C_CO2_sat</ci>
                                    <ci>C_CO2_p</ci>
                                </apply>
                            </apply>
                            <ci>h_2</ci>
                        </apply>
                    </apply>
                    <cn cellml:units="J_per_m3">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_1</ci>
                                        <ci>d_2</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_2</ci>
                                    <ci>d_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>alpha_2</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>r_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>beta_2</ci>
                                        <ci>d_1</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta_1</ci>
                                    <ci>d_2</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>alpha_1</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_1</ci>
                            <apply>
                                <times/>
                                <ci>alpha_1</ci>
                                <ci>d_1</ci>
                                <ci>d_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_2</ci>
                        <apply>
                            <times/>
                            <ci>alpha_2</ci>
                            <ci>beta_1</ci>
                            <ci>d_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>s_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>d_2</ci>
                            <apply>
                                <times/>
                                <ci>alpha_2</ci>
                                <ci>d_2</ci>
                                <ci>d_1</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>beta_1</ci>
                        <apply>
                            <times/>
                            <ci>alpha_1</ci>
                            <ci>beta_2</ci>
                            <ci>d_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="gas_transport_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.18" name="C_O2_in" public_interface="in" units="dimensionless"/>
        <variable initial_value="0.36" name="C_CO2_in" public_interface="in" units="dimensionless"/>
        <variable initial_value="0.18" name="C_O2_out" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.36" name="C_CO2_out" public_interface="out" units="dimensionless"/>
        <variable name="dot_C_CO2_out" public_interface="out" units="per_s"/>
        <variable name="q_0" public_interface="in" units="m3"/>
        <variable name="v" public_interface="in" units="m3_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_O2_out</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>v</ci>
                        <apply>
                            <minus/>
                            <ci>C_O2_in</ci>
                            <ci>C_O2_out</ci>
                        </apply>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dot_C_CO2_out</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>v</ci>
                        <apply>
                            <minus/>
                            <ci>C_CO2_in</ci>
                            <ci>C_CO2_out</ci>
                        </apply>
                    </apply>
                    <ci>q_0</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>C_CO2_out</ci>
                </apply>
                <ci>dot_C_CO2_out</ci>
            </apply>
        </math>
    </component>
    <component name="respiratory_gas_transport_type">
        <variable name="t" public_interface="in" units="second"/>
        <!--constants-->
        <variable name="F_O2_i" public_interface="in" units="dimensionless"/>
        <variable name="F_CO2_i" public_interface="in" units="dimensionless"/>
        <variable name="P_atm" public_interface="in" units="J_per_m3"/>
        <variable name="P_ws" public_interface="in" units="J_per_m3"/>
        <!-- This K causes a loss in mass? fix when turning into bond-graph-->
        <variable name="K_LOSSES" public_interface="in" units="dimensionless"/>
        <!-- volume fractions-->
        <variable initial_value="0.21" name="F_O2_D" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.000421" name="F_CO2_D" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.21" name="F_O2_A" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.000421" name="F_CO2_A" public_interface="out" units="dimensionless"/>
        <!-- partial pressures, outputs to the pulmonary gas exchange model-->
        <variable name="P_O2_A" public_interface="out" units="J_per_m3"/>
        <variable name="P_CO2_A" public_interface="out" units="J_per_m3"/>
        <!-- inputs from lung model-->
        <variable name="v_ml" public_interface="in" units="m3_per_s"/>
        <variable name="v_bA" public_interface="in" units="m3_per_s"/>
        <variable name="q_D" public_interface="in" units="m3"/>
        <variable name="q_A" public_interface="in" units="m3"/>
        <!--inputs from pulmonary gas exchange model-->
        <variable name="M_O2" public_interface="in" units="m3_per_s"/>
        <variable name="M_CO2" public_interface="in" units="m3_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>F_O2_D</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <max/>
                                <ci>v_ml</ci>
                                <cn cellml:units="m3_per_s">0</cn>
                            </apply>
                            <apply>
                                <minus/>
                                <ci>F_O2_i</ci>
                                <ci>F_O2_D</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <max/>
                                <apply>
                                    <minus/>
                                    <ci>v_bA</ci>
                                </apply>
                                <cn cellml:units="m3_per_s">0</cn>
                            </apply>
                            <apply>
                                <minus/>
                                <ci>F_O2_D</ci>
                                <ci>F_O2_A</ci>
                            </apply>
                        </apply>
                    </apply>
                    <ci>q_D</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>F_CO2_D</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <max/>
                                <ci>v_ml</ci>
                                <cn cellml:units="m3_per_s">0</cn>
                            </apply>
                            <apply>
                                <minus/>
                                <ci>F_CO2_i</ci>
                                <ci>F_CO2_D</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <max/>
                                <apply>
                                    <minus/>
                                    <ci>v_bA</ci>
                                </apply>
                                <cn cellml:units="m3_per_s">0</cn>
                            </apply>
                            <apply>
                                <minus/>
                                <ci>F_CO2_D</ci>
                                <ci>F_CO2_A</ci>
                            </apply>
                        </apply>
                    </apply>
                    <ci>q_D</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>F_O2_A</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <max/>
                                <ci>v_bA</ci>
                                <cn cellml:units="m3_per_s">0</cn>
                            </apply>
                            <apply>
                                <minus/>
                                <ci>F_O2_D</ci>
                                <ci>F_O2_A</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>K_LOSSES</ci>
                            <ci>M_O2</ci>
                        </apply>
                    </apply>
                    <ci>q_A</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>F_CO2_A</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <max/>
                                <ci>v_bA</ci>
                                <cn cellml:units="m3_per_s">0</cn>
                            </apply>
                            <apply>
                                <minus/>
                                <ci>F_CO2_D</ci>
                                <ci>F_CO2_A</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>K_LOSSES</ci>
                            <ci>M_CO2</ci>
                        </apply>
                    </apply>
                    <ci>q_A</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_O2_A</ci>
                <apply>
                    <times/>
                    <ci>F_O2_A</ci>
                    <apply>
                        <minus/>
                        <ci>P_atm</ci>
                        <ci>P_ws</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_CO2_A</ci>
                <apply>
                    <times/>
                    <ci>F_CO2_A</ci>
                    <apply>
                        <minus/>
                        <ci>P_atm</ci>
                        <ci>P_ws</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="temp">
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>C_O2_out</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>v</ci>
                            <ci>C_O2_in</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>v</ci>
                            <ci>C_O2_out</ci>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>v</ci>
                        <ci>v</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////// Bond graph lung model //////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="simple_lung_bond_graph_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- ______  Pressures _________
 atmospheric/mouth pressure-->
        <variable name="P_m" public_interface="in" units="J_per_m3"/>
        <!-- larynx pressure-->
        <variable name="P_l" public_interface="out" units="J_per_m3"/>
        <!-- trachea pressure-->
        <variable name="P_t" public_interface="out" units="J_per_m3"/>
        <!-- bronchea pressure-->
        <variable name="P_b" public_interface="out" units="J_per_m3"/>
        <!-- Alveolar pressure-->
        <variable name="P_A" public_interface="out" units="J_per_m3"/>
        <!-- Pleural pressure-->
        <variable name="P_pl" public_interface="out" units="J_per_m3"/>
        <!-- resp muscle pressure-->
        <variable name="P_mus" public_interface="out" units="J_per_m3"/>
        <variable name="P_mus_min" public_interface="in" units="J_per_m3"/>
        <variable name="P_plEE" public_interface="in" units="J_per_m3"/>
        <!-- ______  volumes_________
 larynx volume-->
        <variable initial_value="1.0e-2" name="q_l" public_interface="out" units="m3"/>
        <variable initial_value="1.0e-3" name="q_t" public_interface="out" units="m3"/>
        <variable initial_value="1.0e-3" name="q_b" public_interface="out" units="m3"/>
        <variable initial_value="0.0" name="q_A_stressed" public_interface="out" units="m3"/>
        <variable name="q_A" public_interface="out" units="m3"/>
        <variable initial_value="0.0" name="q_pl" public_interface="out" units="m3"/>
        <variable name="q_D" public_interface="out" units="m3"/>
        <!-- ______  flows _________-->
        <variable name="v_ml" public_interface="out" units="m3_per_s"/>
        <variable name="v_lt" public_interface="out" units="m3_per_s"/>
        <variable name="v_tb" public_interface="out" units="m3_per_s"/>
        <variable name="v_bA" public_interface="out" units="m3_per_s"/>
        <variable name="v_twall" public_interface="out" units="m3_per_s"/>
        <variable name="v_bwall" public_interface="out" units="m3_per_s"/>
        <variable name="v_plwall" public_interface="out" units="m3_per_s"/>
        <!-- ______  Resistances_________-->
        <variable name="R_ml" public_interface="in" units="Js_per_m6"/>
        <variable name="R_lt" public_interface="in" units="Js_per_m6"/>
        <variable name="R_tb" public_interface="in" units="Js_per_m6"/>
        <variable name="R_bA" public_interface="in" units="Js_per_m6"/>
        <variable name="R_plwall" public_interface="in" units="Js_per_m6"/>
        <!-- ______  Compliances_________-->
        <variable name="C_l" public_interface="in" units="J_per_m6"/>
        <variable name="C_t" public_interface="in" units="J_per_m6"/>
        <variable name="C_b" public_interface="in" units="J_per_m6"/>
        <variable name="C_A" public_interface="in" units="J_per_m6"/>
        <variable name="C_pl" public_interface="in" units="J_per_m6"/>
        <!-- periods/times-->
        <variable name="t_floor" public_interface="out" units="second"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="T_I" public_interface="out" units="second"/>
        <variable name="T_E" public_interface="out" units="second"/>
        <variable name="tau" public_interface="out" units="second"/>
        <variable name="IE_ratio" public_interface="in" units="dimensionless"/>
        <!-- unstressed volumes-->
        <variable name="q_l_us" public_interface="in" units="m3"/>
        <variable name="q_t_us" public_interface="in" units="m3"/>
        <variable name="q_b_us" public_interface="in" units="m3"/>
        <variable name="q_A_us" public_interface="in" units="m3"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>T_E</ci>
                <apply>
                    <divide/>
                    <ci>T</ci>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>IE_ratio</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_I</ci>
                <apply>
                    <times/>
                    <ci>T_E</ci>
                    <ci>IE_ratio</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>tau</ci>
                <apply>
                    <divide/>
                    <ci>T_E</ci>
                    <cn cellml:units="dimensionless">5</cn>
                </apply>
            </apply>
            <!-- TODO split this into submodules-->
            <apply>
                <eq/>
                <ci>v_ml</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_m</ci>
                        <ci>P_l</ci>
                    </apply>
                    <ci>R_ml</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_l</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_ml</ci>
                    <ci>v_lt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_l</ci>
                <apply>
                    <divide/>
                    <ci>q_l</ci>
                    <ci>C_l</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_lt</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_l</ci>
                        <ci>P_t</ci>
                    </apply>
                    <ci>R_lt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_twall</ci>
                <apply>
                    <minus/>
                    <ci>v_lt</ci>
                    <ci>v_tb</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_t</ci>
                </apply>
                <ci>v_twall</ci>
            </apply>
            <apply>
                <eq/>
                <ci>P_t</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_t</ci>
                        <ci>C_t</ci>
                    </apply>
                    <ci>P_pl</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_tb</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_t</ci>
                        <ci>P_b</ci>
                    </apply>
                    <ci>R_tb</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_bwall</ci>
                <apply>
                    <minus/>
                    <ci>v_tb</ci>
                    <ci>v_bA</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_b</ci>
                </apply>
                <ci>v_bwall</ci>
            </apply>
            <apply>
                <eq/>
                <ci>P_b</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_b</ci>
                        <ci>C_b</ci>
                    </apply>
                    <ci>P_pl</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_bA</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_b</ci>
                        <ci>P_A</ci>
                    </apply>
                    <ci>R_bA</ci>
                </apply>
            </apply>
            <!-- v_Awall = v_bA-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_A_stressed</ci>
                </apply>
                <ci>v_bA</ci>
            </apply>
            <apply>
                <eq/>
                <ci>P_A</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_A_stressed</ci>
                        <ci>C_A</ci>
                    </apply>
                    <ci>P_pl</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_pl</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>v_plwall</ci>
                            <ci>v_twall</ci>
                        </apply>
                        <ci>v_bwall</ci>
                    </apply>
                    <ci>v_bA</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_pl</ci>
                <apply>
                    <minus/>
                    <apply>
                        <divide/>
                        <ci>q_pl</ci>
                        <ci>C_pl</ci>
                    </apply>
                    <ci>P_plEE</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_plwall</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_mus</ci>
                        <ci>P_pl</ci>
                    </apply>
                    <ci>R_plwall</ci>
                </apply>
            </apply>
            <!-- Dead space volume-->
            <apply>
                <eq/>
                <ci>q_D</ci>
                <apply>
                    <plus/>
                    <ci>q_l</ci>
                    <ci>q_t</ci>
                    <ci>q_b</ci>
                    <ci>q_l_us</ci>
                    <ci>q_t_us</ci>
                    <ci>q_b_us</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q_A</ci>
                <apply>
                    <plus/>
                    <ci>q_A_stressed</ci>
                    <ci>q_A_us</ci>
                </apply>
            </apply>
            <!-- TODO + unstressed volume-->
            <!-- calculate time through this period-->
            <apply>
                <eq/>
                <ci>t_floor</ci>
                <apply>
                    <minus/>
                    <ci>t</ci>
                    <apply>
                        <times/>
                        <apply>
                            <floor/>
                            <apply>
                                <divide/>
                                <ci>t</ci>
                                <ci>T</ci>
                            </apply>
                        </apply>
                        <ci>T</ci>
                    </apply>
                </apply>
            </apply>
            <!-- TODO swap this muscle model for the one used in ben tal and smith 2008-->
            <apply>
                <eq/>
                <ci>P_mus</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <minus/>
                                        <ci>P_mus_min</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>T_I</ci>
                                        <ci>T_E</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <power/>
                                    <ci>t_floor</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>P_mus_min</ci>
                                        <ci>T</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>T_I</ci>
                                        <ci>T_E</ci>
                                    </apply>
                                </apply>
                                <ci>t_floor</ci>
                            </apply>
                        </apply>
                        <apply>
                            <lt/>
                            <ci>t_floor</ci>
                            <ci>T_I</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <ci>P_mus_min</ci>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>T_E</ci>
                                            </apply>
                                            <ci>tau</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                            <apply>
                                <minus/>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <minus/>
                                            <apply>
                                                <minus/>
                                                <ci>t_floor</ci>
                                                <ci>T_I</ci>
                                            </apply>
                                        </apply>
                                        <ci>tau</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <minus/>
                                            <ci>T_E</ci>
                                        </apply>
                                        <ci>tau</ci>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// non-BC Vessel ////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////   -->
    <component name="pv_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u_in</ci>
                                <ci>u</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_out</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//
&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//-->
    <component name="vp_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!--C = 2{dimensionless}*pi*pow(r, 3{dimensionless})*l/(E*h);-->
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <ci>u_out</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_in</ci>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//
&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//-->
    <component name="pp_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v_d" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u_in</ci>
                                <ci>u</ci>
                            </apply>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <ci>R</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                </apply>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>I</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_d</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_d</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_d</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <ci>R</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>v_d</ci>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>I</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vv_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <variable initial_value="0.0" name="q_C_d" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <ci>u_d</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_in</ci>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C_d</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_out</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C_d</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pv_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- emperical relation-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_out</ci>
                </apply>
            </apply>
            <!-- constitutive laws-->
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pp_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v_d" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <ci>R</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>I</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_d</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_d</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_d</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <ci>R</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>v_d</ci>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>I</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vv_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C_d" public_interface="out" units="J_per_m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_d</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_in</ci>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C_d</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_out</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C_d</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vv_rigid_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <!-- State Variables-->
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <!-- Conservation Laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v_in</ci>
                        <ci>v_out</ci>
                    </apply>
                    <ci>R</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vp_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_in</ci>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vp_ven_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T_change" public_interface="out" units="m3"/>
        <variable name="q_T" public_interface="out" units="m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable name="q_us_0" public_interface="in" units="m3"/>
        <variable name="q_us_wCont" public_interface="out" units="m3"/>
        <variable name="Delta_q_us" public_interface="in" units="m3"/>
        <!-- TODO double check that this applies to veins-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T_change</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_in</ci>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q_T</ci>
                <apply>
                    <plus/>
                    <ci>q_T_change</ci>
                    <ci>q_us_0</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>q_T</ci>
                            <ci>q_us_wCont</ci>
                        </apply>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q_us_wCont</ci>
                <apply>
                    <plus/>
                    <ci>q_us_0</ci>
                    <ci>Delta_q_us</ci>
                </apply>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// output-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="pp_T_fixed_I_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I_T" public_interface="out" units="Js2_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_T" public_interface="in" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <!-- v_T is the output flow to the venous side-->
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
        <!-- Improve this R_v estimate?-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_T</ci>
                <cn cellml:units="Js_per_m6" type="e-notation">1<sep/>-6</cn>
            </apply>
            <!-- Conservation Laws-->
            <!-- For now terminals don't have a gravity effect, change this for leg terminals-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_T</ci>
                        <ci>C_T</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <!-- + u_ext;-->
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v</ci>
                                <ci>R_T</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v_T</ci>
                                <ci>R_T</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pp_T_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I_T" public_interface="in" units="Js2_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_1_T" public_interface="in" units="Js_per_m6"/>
        <variable name="R_2_T" public_interface="in" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <!-- v_T is the output flow to the venous side-->
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
        <!-- Improve this R_v estimate?-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <!-- For now terminals don't have a gravity effect, change this for leg terminals-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_T</ci>
                        <ci>C_T</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <!-- + u_ext;-->
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v</ci>
                                <ci>R_1_T</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v_T</ci>
                                <ci>R_2_T</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pp_T_type_prop">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I_T" public_interface="in" units="Js2_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_1_T" public_interface="in" units="Js_per_m6"/>
        <variable name="R_2_T" units="Js_per_m6"/>
        <!-- remove in for R_2_T-->
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <variable name="R1_R2_ratio" public_interface="in" units="dimensionless"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <!-- v_T is the output flow to the venous side-->
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
        <!-- Improve this R_v estimate?-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <!-- Identify R_1_T and scale R_2_T in relation-->
            <apply>
                <eq/>
                <ci>R_2_T</ci>
                <apply>
                    <times/>
                    <ci>R_1_T</ci>
                    <ci>R1_R2_ratio</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <!-- For now terminals don't have a gravity effect, change this for leg terminals-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_T</ci>
                        <ci>C_T</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <!-- + u_ext;-->
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v</ci>
                                <ci>R_1_T</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v_T</ci>
                                <ci>R_2_T</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pp_T_wCont_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I_T" public_interface="in" units="Js2_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_T" public_interface="in" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <!-- v_T is the output flow to the venous side-->
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
        <variable name="R_T_wCont" public_interface="out" units="Js_per_m6"/>
        <variable name="Delta_R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_local_multiplier" public_interface="in" units="dimensionless"/>
        <!-- Improve this R_v estimate?-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <!-- For now terminals don't have a gravity effect, change this for leg terminals-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_T</ci>
                        <ci>C_T</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v_T</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_T_wCont</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <ci>R_T</ci>
                        <ci>Delta_R</ci>
                    </apply>
                    <ci>R_local_multiplier</ci>
                </apply>
            </apply>
        </math>
    </component>
    <!--/////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////// Junctions //////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <!-- Bifurcation-->
    <component name="pv_split_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable name="du_C_dt" public_interface="out" units="J_per_m3s"/>
        <variable name="v_out_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_out_2" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u_in</ci>
                                <ci>u</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <!-- The below assumes constant compliance and is only used as an approximate output for the baroreceptor-->
            <apply>
                <eq/>
                <ci>du_C_dt</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out_1</ci>
                        </apply>
                        <ci>v_out_2</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- the below allows non constant compliance-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_out_1</ci>
                    </apply>
                    <ci>v_out_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>v</ci>
                                <ci>v_out_1</ci>
                            </apply>
                            <ci>v_out_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="pv_split_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
        </math>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <variable name="du_C_dt" public_interface="out" units="J_per_m3s"/>
        <variable name="v_out_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_out_2" public_interface="in" units="m3_per_s"/>
        <!-- Conservation Laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <!-- The below assumes constant compliance and is only used as an approximate output for the baroreceptor-->
            <apply>
                <eq/>
                <ci>du_C_dt</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out_1</ci>
                        </apply>
                        <ci>v_out_2</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- the below allows non constant compliance-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_out_1</ci>
                    </apply>
                    <ci>v_out_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>v</ci>
                                <ci>v_out_1</ci>
                            </apply>
                            <ci>v_out_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vv_split_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <variable name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C_d" public_interface="out" units="m3"/>
        <variable name="v_out_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_out_2" public_interface="in" units="m3_per_s"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <ci>u_d</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_in</ci>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C_d</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_out_1</ci>
                    </apply>
                    <ci>v_out_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C_d</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>v</ci>
                                <ci>v_out_1</ci>
                            </apply>
                            <ci>v_out_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vv_split_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
        </math>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <variable name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C_d" public_interface="out" units="m3"/>
        <variable name="v_out_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_out_2" public_interface="in" units="m3_per_s"/>
        <!-- Conservation Laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_d</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_in</ci>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C_d</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_out_1</ci>
                    </apply>
                    <ci>v_out_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C_d</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>v</ci>
                                <ci>v_out_1</ci>
                            </apply>
                            <ci>v_out_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//
&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//-->
    <!-- 2 in 2 out junction-->
    <component name="vv_2in2out_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_in_2" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_out_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_out_2" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <variable initial_value="0.0" name="q_C_d" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <ci>u_d</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_in_1</ci>
                        <ci>v_in_2</ci>
                    </apply>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C_d</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_out_1</ci>
                    </apply>
                    <ci>v_out_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C_d</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>v_in_1</ci>
                                <ci>v_in_2</ci>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>v</ci>
                                <ci>v_out_1</ci>
                            </apply>
                            <ci>v_out_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!-- 2in1out merge vv-->
    <component name="vv_merge_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_in_2" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <variable initial_value="0.0" name="q_C_d" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <ci>u_d</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_in_1</ci>
                        <ci>v_in_2</ci>
                    </apply>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C_d</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_out</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C_d</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>v_in_1</ci>
                                <ci>v_in_2</ci>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!-- 2in1out merge vp-->
    <component name="vp_merge_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mu" public_interface="in" units="Js_per_m3"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="g" public_interface="in" units="m_per_s2"/>
        <variable name="beta_g" public_interface="in" units="dimensionless"/>
        <variable name="theta" public_interface="in" units="dimensionless"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="a_vessel" public_interface="in" units="dimensionless"/>
        <variable name="b_vessel" public_interface="in" units="per_m"/>
        <variable name="c_vessel" public_interface="in" units="dimensionless"/>
        <variable name="d_vessel" public_interface="in" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_in_2" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c_vessel</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d_vessel</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <ci>u_out</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>v</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta_g</ci>
                            <ci>rho</ci>
                            <ci>g</ci>
                            <ci>l</ci>
                            <apply>
                                <cos/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>theta</ci>
                                        <pi/>
                                    </apply>
                                    <cn cellml:units="dimensionless">180</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_in_1</ci>
                        <ci>v_in_2</ci>
                    </apply>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>v_in_1</ci>
                                <ci>v_in_2</ci>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="vp_merge_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_in_2" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <!-- ode(u_C, t) = (v_in_1+v_in_2-v)/C;-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_in_1</ci>
                        <ci>v_in_2</ci>
                    </apply>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <ci>C</ci>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>v_in_1</ci>
                                <ci>v_in_2</ci>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!-- 2in1out merge vv simple-->
    <component name="vv_merge_simple_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I" public_interface="in" units="Js2_per_m6"/>
        <variable name="C" public_interface="in" units="m6_per_J"/>
        <variable name="R" public_interface="in" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
        </math>
        <!-- State Variables-->
        <variable name="u_ext" public_interface="in" units="J_per_m3"/>
        <variable name="v_in_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_in_2" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <variable initial_value="0.0" name="q_C" public_interface="out" units="m3"/>
        <variable initial_value="0.0" name="q_C_d" public_interface="out" units="m3"/>
        <!-- Conservation Laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_d</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_in_1</ci>
                        <ci>v_in_2</ci>
                    </apply>
                    <ci>v</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_C_d</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_out</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <ci>q_C_d</ci>
                        <apply>
                            <divide/>
                            <ci>C</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>u_ext</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>v_in_1</ci>
                                <ci>v_in_2</ci>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="zero_flow">
        <variable name="v_zero" public_interface="out" units="m3_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>v_zero</ci>
                <cn cellml:units="m3_per_s">0</cn>
            </apply>
        </math>
    </component>
    <component name="flow_sum_2_type">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="v_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_2" public_interface="in" units="m3_per_s"/>
        <variable name="v_total" public_interface="out" units="m3_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>v_total</ci>
                <apply>
                    <plus/>
                    <ci>v_1</ci>
                    <ci>v_2</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="W_controller2_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="I_T" public_interface="out" units="Js2_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_T" public_interface="in" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <!-- State Variables-->
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable name="u_C" public_interface="out" units="J_per_m3"/>
        <!-- v_T is the output flow to the venous side-->
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
        <variable name="R_T_wCont" public_interface="out" units="Js_per_m6"/>
        <!-- Conservation Laws-->
        <!-- Improve this R_v estimate?-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_T</ci>
                <cn cellml:units="Js_per_m6" type="e-notation">1<sep/>-6</cn>
            </apply>
            <!-- Conservation Laws-->
            <!-- For now terminals don't have a gravity effect, change this for leg terminals
u_out = 0{J_per_m3};-->
            <apply>
                <eq/>
                <ci>u_out</ci>
                <cn cellml:units="dimensionless">0</cn>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_T</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <ci>v_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_C</ci>
                <apply>
                    <divide/>
                    <ci>q_T</ci>
                    <ci>C_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>v_T</ci>
                                <ci>R_T_wCont</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <ci>I_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_T_wCont</ci>
                <ci>R_T</ci>
            </apply>
        </math>
    </component>
    <component name="heart_simple_wCont">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="s" public_interface="out" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mt" units="second"/>
        <variable name="e_a" units="dimensionless"/>
        <variable name="e_v" units="dimensionless"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="T_ac" public_interface="in" units="second"/>
        <variable name="T_ar" public_interface="in" units="second"/>
        <!-- var T_ac_norm: dimensionless;
 var T_ar_norm: dimensionless;-->
        <variable name="t_astart" public_interface="in" units="second"/>
        <variable name="t_astart_norm" units="dimensionless"/>
        <variable name="T_vc" public_interface="in" units="second"/>
        <variable name="T_vr" public_interface="in" units="second"/>
        <!-- var T_vc_norm: dimensionless;
 var T_vr_norm: dimensionless;-->
        <variable name="t_vstart" public_interface="in" units="second"/>
        <variable name="t_vstart_norm" units="dimensionless"/>
        <variable name="T_wCont" public_interface="out" units="second"/>
        <variable name="T_ac_wCont" public_interface="out" units="second"/>
        <variable name="T_ar_wCont" public_interface="out" units="second"/>
        <variable name="T_vc_wCont" public_interface="out" units="second"/>
        <variable name="T_vr_wCont" public_interface="out" units="second"/>
        <variable name="E_lv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_lv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_B" public_interface="in" units="J_per_m6"/>
        <variable name="q_ra_0" public_interface="in" units="m3"/>
        <variable name="q_rv_0" public_interface="in" units="m3"/>
        <variable name="q_la_0" public_interface="in" units="m3"/>
        <variable name="q_lv_0" public_interface="in" units="m3"/>
        <!-- State Variables-->
        <variable name="u_ra" public_interface="out" units="J_per_m3"/>
        <variable name="u_rv" units="J_per_m3"/>
        <variable name="u_la" public_interface="out" units="J_per_m3"/>
        <variable name="u_lv" units="J_per_m3"/>
        <variable name="u_root" public_interface="in" units="J_per_m3"/>
        <variable name="u_par" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0" name="v_trv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_puv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_miv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_aov" public_interface="out" units="m3_per_s"/>
        <variable name="v_svc" public_interface="in" units="m3_per_s"/>
        <variable name="v_ivc" public_interface="in" units="m3_per_s"/>
        <variable name="v_pvn" public_interface="in" units="m3_per_s"/>
        <variable name="L_trv" units="dimensionless"/>
        <variable name="L_puv" units="dimensionless"/>
        <variable name="L_miv" units="dimensionless"/>
        <variable name="L_aov" units="dimensionless"/>
        <variable name="A_eff_trv" units="m2"/>
        <variable name="A_eff_puv" units="m2"/>
        <variable name="A_eff_miv" units="m2"/>
        <variable name="A_eff_aov" units="m2"/>
        <variable name="A_nn_trv" public_interface="in" units="m2"/>
        <variable name="A_nn_puv" public_interface="in" units="m2"/>
        <variable name="A_nn_miv" public_interface="in" units="m2"/>
        <variable name="A_nn_aov" public_interface="in" units="m2"/>
        <variable name="l_eff" public_interface="in" units="metre"/>
        <variable name="K_vo_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="M_rg_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_aov" public_interface="in" units="dimensionless"/>
        <variable name="M_st_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_aov" public_interface="in" units="dimensionless"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="B_trv" units="dimensionless"/>
        <variable name="B_puv" units="dimensionless"/>
        <variable name="B_miv" units="dimensionless"/>
        <variable name="B_aov" units="dimensionless"/>
        <variable name="zeta_trv" units="dimensionless"/>
        <variable name="zeta_puv" units="dimensionless"/>
        <variable name="zeta_miv" units="dimensionless"/>
        <variable name="zeta_aov" units="dimensionless"/>
        <variable initial_value="0" name="zeta_trv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_puv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_miv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_aov_pre" units="dimensionless"/>
        <variable initial_value="1e-14" name="eps" units="dimensionless"/>
        <variable initial_value="0.07" name="eps_1" units="dimensionless"/>
        <variable initial_value="0.02" name="eps_2" units="dimensionless"/>
        <!-- TODO the below parameters should be set in an init_states parameter file
 q_lv gets identified, the others are set arbitrarily, identifying q_lv sets the stressed volume of the system.-->
        <variable initial_value="0.00069934" name="q_lv" units="m3"/>
        <variable initial_value="1e-05" name="q_rv" units="m3"/>
        <variable initial_value="4e-06" name="q_la" units="m3"/>
        <variable initial_value="4e-06" name="q_ra" units="m3"/>
        <!-- calculate modified time due to changes in heart period. This can now be modified throughout a simulation.-->
        <variable initial_value="0.0" name="chi_a" units="dimensionless"/>
        <variable name="chi_afloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_afloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_a</ci>
                    <apply>
                        <floor/>
                        <ci>chi_a</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_a</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac_wCont</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_astart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac_wCont</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_astart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac_wCont</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_afloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ar_wCont</ci>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>chi_afloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <variable initial_value="0.0" name="chi_v" units="dimensionless"/>
        <variable name="chi_vfloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_vfloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_v</ci>
                    <apply>
                        <floor/>
                        <ci>chi_v</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_v</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc_wCont</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_vstart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc_wCont</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_vstart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc_wCont</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_vfloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vr_wCont</ci>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>chi_vfloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>s</ci>
                </apply>
                <apply>
                    <divide/>
                    <cn cellml:units="second">1</cn>
                    <ci>T_wCont</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mt</ci>
                <apply>
                    <minus/>
                    <ci>s</ci>
                    <apply>
                        <floor/>
                        <ci>s</ci>
                    </apply>
                </apply>
            </apply>
        </math>
        <!-- control effects Assume all subperiods scale linearly for now. TODO IMPROVE THIS-->
        <variable name="Delta_T" public_interface="in" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>T_wCont</ci>
                <apply>
                    <plus/>
                    <ci>T</ci>
                    <ci>Delta_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ac_wCont</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>T_ac</ci>
                        <ci>T_wCont</ci>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ar_wCont</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>T_ar</ci>
                        <ci>T_wCont</ci>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vc_wCont</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>T_vc</ci>
                        <ci>T_wCont</ci>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vr_wCont</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>T_vr</ci>
                        <ci>T_wCont</ci>
                    </apply>
                    <ci>T</ci>
                </apply>
            </apply>
            <!-- Elastance Functions-->
            <apply>
                <eq/>
                <ci>t_astart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_astart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <!-- T_ac_norm = T_ac/T;
 T_ar_norm = T_vc/T;-->
            <apply>
                <eq/>
                <ci>t_vstart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_vstart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <!-- T_vc_norm = T_vc/T;
 T_vr_norm = T_vr/T;-->
            <apply>
                <eq/>
                <ci>e_a</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_afloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_v</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_vfloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- Valve model-->
            <apply>
                <eq/>
                <ci>B_trv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_trv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_puv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_puv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_miv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_miv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_aov</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_aov</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_trv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_trv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_puv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_puv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_miv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_miv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_aov</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_aov</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_trv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_trv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_trv</ci>
                        <ci>A_nn_trv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_puv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_puv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_puv</ci>
                        <ci>A_nn_puv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_miv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_miv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_miv</ci>
                        <ci>A_nn_miv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_aov</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                        </apply>
                        <ci>zeta_aov</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_aov</ci>
                        <ci>A_nn_aov</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_trv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_trv_pre</ci>
                            </apply>
                            <ci>K_vo_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_ra</ci>
                            <ci>u_rv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_trv_pre</ci>
                            <ci>K_vc_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_puv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_puv_pre</ci>
                            </apply>
                            <ci>K_vo_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_rv</ci>
                            <ci>u_par</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_puv_pre</ci>
                            <ci>K_vc_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_miv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_miv_pre</ci>
                            </apply>
                            <ci>K_vo_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_la</ci>
                            <ci>u_lv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_miv_pre</ci>
                            <ci>K_vc_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_aov_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_aov_pre</ci>
                            </apply>
                            <ci>K_vo_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_lv</ci>
                            <ci>u_root</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_aov_pre</ci>
                            <ci>K_vc_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <!-- The below ensures zeta can't be negative-->
            <apply>
                <eq/>
                <ci>zeta_trv</ci>
                <apply>
                    <max/>
                    <ci>zeta_trv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_puv</ci>
                <apply>
                    <max/>
                    <ci>zeta_puv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_miv</ci>
                <apply>
                    <max/>
                    <ci>zeta_miv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_aov</ci>
                <apply>
                    <max/>
                    <ci>zeta_aov_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <!-- calculate the flow through the valves-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_trv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_trv</ci>
                                </apply>
                                <ci>v_trv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_trv</ci>
                                </apply>
                            </apply>
                            <ci>u_ra</ci>
                        </apply>
                        <ci>u_rv</ci>
                    </apply>
                    <ci>L_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_puv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_puv</ci>
                                </apply>
                                <ci>v_puv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_puv</ci>
                                </apply>
                            </apply>
                            <ci>u_rv</ci>
                        </apply>
                        <ci>u_par</ci>
                    </apply>
                    <ci>L_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_miv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_miv</ci>
                                </apply>
                                <ci>v_miv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_miv</ci>
                                </apply>
                            </apply>
                            <ci>u_la</ci>
                        </apply>
                        <ci>u_lv</ci>
                    </apply>
                    <ci>L_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_aov</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_aov</ci>
                                </apply>
                                <ci>v_aov</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_aov</ci>
                                </apply>
                            </apply>
                            <ci>u_lv</ci>
                        </apply>
                        <ci>u_root</ci>
                    </apply>
                    <ci>L_aov</ci>
                </apply>
            </apply>
        </math>
        <!-- Control from sympathetic-->
        <variable name="E_rv_A_wCont" public_interface="out" units="J_per_m6"/>
        <variable name="E_lv_A_wCont" public_interface="out" units="J_per_m6"/>
        <!-- TODO The current control modifies the E_max-E_min instead of E_max.-->
        <variable name="Delta_E_rv" public_interface="in" units="J_per_m6"/>
        <variable name="Delta_E_lv" public_interface="in" units="J_per_m6"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>E_rv_A_wCont</ci>
                <apply>
                    <plus/>
                    <ci>E_rv_A</ci>
                    <ci>Delta_E_rv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_lv_A_wCont</ci>
                <apply>
                    <plus/>
                    <ci>E_lv_A</ci>
                    <ci>Delta_E_lv</ci>
                </apply>
            </apply>
            <!-- Constitutive Relations-->
            <apply>
                <eq/>
                <ci>u_ra</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_ra_A</ci>
                        </apply>
                        <ci>E_ra_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_ra</ci>
                        <ci>q_ra_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_rv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_rv_A_wCont</ci>
                        </apply>
                        <ci>E_rv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_rv</ci>
                        <ci>q_rv_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_la</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_la_A</ci>
                        </apply>
                        <ci>E_la_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_la</ci>
                        <ci>q_la_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_lv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_lv_A_wCont</ci>
                        </apply>
                        <ci>E_lv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_lv</ci>
                        <ci>q_lv_0</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_ra</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_svc</ci>
                        <ci>v_ivc</ci>
                    </apply>
                    <ci>v_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_rv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_trv</ci>
                    <ci>v_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_la</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_pvn</ci>
                    <ci>v_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_lv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_miv</ci>
                    <ci>v_aov</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="heart_simple">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="s" public_interface="out" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mt" units="second"/>
        <variable name="e_a" units="dimensionless"/>
        <variable name="e_v" units="dimensionless"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="T_ac" public_interface="in" units="second"/>
        <variable name="T_ar" public_interface="in" units="second"/>
        <variable name="T_ac_norm" units="dimensionless"/>
        <variable name="T_ar_norm" units="dimensionless"/>
        <variable name="t_astart" public_interface="in" units="second"/>
        <variable name="t_astart_norm" units="dimensionless"/>
        <variable name="T_vc" public_interface="in" units="second"/>
        <variable name="T_vr" public_interface="in" units="second"/>
        <variable name="T_vc_norm" units="dimensionless"/>
        <variable name="T_vr_norm" units="dimensionless"/>
        <variable name="t_vstart" public_interface="in" units="second"/>
        <variable name="t_vstart_norm" units="dimensionless"/>
        <variable name="E_lv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_lv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_B" public_interface="in" units="J_per_m6"/>
        <variable name="q_ra_0" public_interface="in" units="m3"/>
        <variable name="q_rv_0" public_interface="in" units="m3"/>
        <variable name="q_la_0" public_interface="in" units="m3"/>
        <variable name="q_lv_0" public_interface="in" units="m3"/>
        <!-- State Variables-->
        <variable name="u_ra" public_interface="out" units="J_per_m3"/>
        <variable name="u_rv" units="J_per_m3"/>
        <variable name="u_la" public_interface="out" units="J_per_m3"/>
        <variable name="u_lv" units="J_per_m3"/>
        <variable name="u_root" public_interface="in" units="J_per_m3"/>
        <variable name="u_par" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0" name="v_trv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_puv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_miv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_aov" public_interface="out" units="m3_per_s"/>
        <variable name="v_svc" public_interface="in" units="m3_per_s"/>
        <variable name="v_ivc" public_interface="in" units="m3_per_s"/>
        <variable name="v_pvn" public_interface="in" units="m3_per_s"/>
        <variable name="L_trv" units="dimensionless"/>
        <variable name="L_puv" units="dimensionless"/>
        <variable name="L_miv" units="dimensionless"/>
        <variable name="L_aov" units="dimensionless"/>
        <variable name="A_eff_trv" units="m2"/>
        <variable name="A_eff_puv" units="m2"/>
        <variable name="A_eff_miv" units="m2"/>
        <variable name="A_eff_aov" units="m2"/>
        <variable name="A_nn_trv" public_interface="in" units="m2"/>
        <variable name="A_nn_puv" public_interface="in" units="m2"/>
        <variable name="A_nn_miv" public_interface="in" units="m2"/>
        <variable name="A_nn_aov" public_interface="in" units="m2"/>
        <variable name="l_eff" public_interface="in" units="metre"/>
        <variable name="K_vo_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="M_rg_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_aov" public_interface="in" units="dimensionless"/>
        <variable name="M_st_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_aov" public_interface="in" units="dimensionless"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="B_trv" units="dimensionless"/>
        <variable name="B_puv" units="dimensionless"/>
        <variable name="B_miv" units="dimensionless"/>
        <variable name="B_aov" units="dimensionless"/>
        <variable name="zeta_trv" units="dimensionless"/>
        <variable name="zeta_puv" units="dimensionless"/>
        <variable name="zeta_miv" units="dimensionless"/>
        <variable name="zeta_aov" units="dimensionless"/>
        <variable initial_value="0" name="zeta_trv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_puv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_miv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_aov_pre" units="dimensionless"/>
        <variable initial_value="1e-14" name="eps" units="dimensionless"/>
        <variable initial_value="0.07" name="eps_1" units="dimensionless"/>
        <variable initial_value="0.02" name="eps_2" units="dimensionless"/>
        <!-- TODO the below parameters should be set in an init_states parameter file
 q_lv gets identified, the others are set arbitrarily, identifying q_lv sets the stressed volume of the system.-->
        <variable initial_value="0.00069934" name="q_lv" units="m3"/>
        <variable initial_value="1e-05" name="q_rv" units="m3"/>
        <variable initial_value="4e-06" name="q_la" units="m3"/>
        <variable initial_value="4e-06" name="q_ra" units="m3"/>
        <!-- calculate modified time due to changes in heart period. This can now be modified throughout a simulation.-->
        <variable initial_value="0.0" name="chi_a" units="dimensionless"/>
        <variable name="chi_afloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_afloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_a</ci>
                    <apply>
                        <floor/>
                        <ci>chi_a</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_a</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_astart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_astart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_afloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ar</ci>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>chi_afloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <variable initial_value="0.0" name="chi_v" units="dimensionless"/>
        <variable name="chi_vfloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_vfloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_v</ci>
                    <apply>
                        <floor/>
                        <ci>chi_v</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_v</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_vstart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_vstart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_vfloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vr</ci>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>chi_vfloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>s</ci>
                </apply>
                <apply>
                    <divide/>
                    <cn cellml:units="second">1</cn>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mt</ci>
                <apply>
                    <minus/>
                    <ci>s</ci>
                    <apply>
                        <floor/>
                        <ci>s</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Elastance Functions-->
            <apply>
                <eq/>
                <ci>t_astart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_astart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ac_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ac</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ar_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ar</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>t_vstart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_vstart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vc_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vc</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vr_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vr</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_a</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_afloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_v</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_vfloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- Valve model-->
            <apply>
                <eq/>
                <ci>B_trv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_trv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_puv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_puv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_miv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_miv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_aov</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_aov</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_trv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_trv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_puv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_puv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_miv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_miv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_aov</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_aov</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_trv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_trv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_trv</ci>
                        <ci>A_nn_trv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_puv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_puv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_puv</ci>
                        <ci>A_nn_puv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_miv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_miv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_miv</ci>
                        <ci>A_nn_miv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_aov</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                        </apply>
                        <ci>zeta_aov</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_aov</ci>
                        <ci>A_nn_aov</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_trv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_trv_pre</ci>
                            </apply>
                            <ci>K_vo_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_ra</ci>
                            <ci>u_rv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_trv_pre</ci>
                            <ci>K_vc_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_puv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_puv_pre</ci>
                            </apply>
                            <ci>K_vo_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_rv</ci>
                            <ci>u_par</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_puv_pre</ci>
                            <ci>K_vc_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_miv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_miv_pre</ci>
                            </apply>
                            <ci>K_vo_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_la</ci>
                            <ci>u_lv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_miv_pre</ci>
                            <ci>K_vc_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_aov_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_aov_pre</ci>
                            </apply>
                            <ci>K_vo_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_lv</ci>
                            <ci>u_root</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_aov_pre</ci>
                            <ci>K_vc_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <!-- The below ensures zeta can't be negative-->
            <apply>
                <eq/>
                <ci>zeta_trv</ci>
                <apply>
                    <max/>
                    <ci>zeta_trv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_puv</ci>
                <apply>
                    <max/>
                    <ci>zeta_puv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_miv</ci>
                <apply>
                    <max/>
                    <ci>zeta_miv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_aov</ci>
                <apply>
                    <max/>
                    <ci>zeta_aov_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <!-- calculate the flow through the valves-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_trv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_trv</ci>
                                </apply>
                                <ci>v_trv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_trv</ci>
                                </apply>
                            </apply>
                            <ci>u_ra</ci>
                        </apply>
                        <ci>u_rv</ci>
                    </apply>
                    <ci>L_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_puv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_puv</ci>
                                </apply>
                                <ci>v_puv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_puv</ci>
                                </apply>
                            </apply>
                            <ci>u_rv</ci>
                        </apply>
                        <ci>u_par</ci>
                    </apply>
                    <ci>L_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_miv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_miv</ci>
                                </apply>
                                <ci>v_miv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_miv</ci>
                                </apply>
                            </apply>
                            <ci>u_la</ci>
                        </apply>
                        <ci>u_lv</ci>
                    </apply>
                    <ci>L_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_aov</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_aov</ci>
                                </apply>
                                <ci>v_aov</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_aov</ci>
                                </apply>
                            </apply>
                            <ci>u_lv</ci>
                        </apply>
                        <ci>u_root</ci>
                    </apply>
                    <ci>L_aov</ci>
                </apply>
            </apply>
            <!-- Constitutive Relations-->
            <apply>
                <eq/>
                <ci>u_ra</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_ra_A</ci>
                        </apply>
                        <ci>E_ra_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_ra</ci>
                        <ci>q_ra_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_rv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_rv_A</ci>
                        </apply>
                        <ci>E_rv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_rv</ci>
                        <ci>q_rv_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_la</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_la_A</ci>
                        </apply>
                        <ci>E_la_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_la</ci>
                        <ci>q_la_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_lv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_lv_A</ci>
                        </apply>
                        <ci>E_lv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_lv</ci>
                        <ci>q_lv_0</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_ra</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_svc</ci>
                        <ci>v_ivc</ci>
                    </apply>
                    <ci>v_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_rv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_trv</ci>
                    <ci>v_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_la</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_pvn</ci>
                    <ci>v_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_lv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_miv</ci>
                    <ci>v_aov</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="heart_new_valve">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="s" public_interface="out" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mt" units="second"/>
        <variable name="e_a" units="dimensionless"/>
        <variable name="e_v" units="dimensionless"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="T_ac" public_interface="in" units="second"/>
        <variable name="T_ar" public_interface="in" units="second"/>
        <variable name="T_ac_norm" units="dimensionless"/>
        <variable name="T_ar_norm" units="dimensionless"/>
        <variable name="t_astart" public_interface="in" units="second"/>
        <variable name="t_astart_norm" units="dimensionless"/>
        <variable name="T_vc" public_interface="in" units="second"/>
        <variable name="T_vr" public_interface="in" units="second"/>
        <variable name="T_vc_norm" units="dimensionless"/>
        <variable name="T_vr_norm" units="dimensionless"/>
        <variable name="t_vstart" public_interface="in" units="second"/>
        <variable name="t_vstart_norm" units="dimensionless"/>
        <variable name="E_lv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_lv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_B" public_interface="in" units="J_per_m6"/>
        <variable name="q_ra_0" public_interface="in" units="m3"/>
        <variable name="q_rv_0" public_interface="in" units="m3"/>
        <variable name="q_la_0" public_interface="in" units="m3"/>
        <variable name="q_lv_0" public_interface="in" units="m3"/>
        <!-- State Variables-->
        <variable name="u_ra" public_interface="out" units="J_per_m3"/>
        <variable name="u_rv" units="J_per_m3"/>
        <variable name="u_la" public_interface="out" units="J_per_m3"/>
        <variable name="u_lv" units="J_per_m3"/>
        <variable name="u_root" public_interface="in" units="J_per_m3"/>
        <variable name="u_par" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0" name="v_trv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_puv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_miv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_aov" public_interface="out" units="m3_per_s"/>
        <variable name="v_svc" public_interface="in" units="m3_per_s"/>
        <variable name="v_ivc" public_interface="in" units="m3_per_s"/>
        <variable name="v_pvn" public_interface="in" units="m3_per_s"/>
        <variable name="L_trv" units="dimensionless"/>
        <variable name="L_puv" units="dimensionless"/>
        <variable name="L_miv" units="dimensionless"/>
        <variable name="L_aov" units="dimensionless"/>
        <variable name="A_eff_trv" units="m2"/>
        <variable name="A_eff_puv" units="m2"/>
        <variable name="A_eff_miv" units="m2"/>
        <variable name="A_eff_aov" units="m2"/>
        <variable name="A_nn_trv" public_interface="in" units="m2"/>
        <variable name="A_nn_puv" public_interface="in" units="m2"/>
        <variable name="A_nn_miv" public_interface="in" units="m2"/>
        <variable name="A_nn_aov" public_interface="in" units="m2"/>
        <variable name="l_eff" public_interface="in" units="metre"/>
        <variable name="K_vo_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="M_rg_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_aov" public_interface="in" units="dimensionless"/>
        <variable name="M_st_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_aov" public_interface="in" units="dimensionless"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="B_trv" units="dimensionless"/>
        <variable name="B_puv" units="dimensionless"/>
        <variable name="B_miv" units="dimensionless"/>
        <variable name="B_aov" units="dimensionless"/>
        <variable name="zeta_trv" units="dimensionless"/>
        <variable name="zeta_puv" units="dimensionless"/>
        <variable name="zeta_miv" units="dimensionless"/>
        <variable name="zeta_aov" units="dimensionless"/>
        <variable initial_value="0" name="zeta_trv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_puv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_miv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_aov_pre" units="dimensionless"/>
        <variable initial_value="1e-14" name="eps" units="dimensionless"/>
        <variable initial_value="0.07" name="eps_1" units="dimensionless"/>
        <variable initial_value="0.02" name="eps_2" units="dimensionless"/>
        <!-- TODO the below parameters should be set in an init_states parameter file
 q_lv gets identified, the others are set arbitrarily, identifying q_lv sets the stressed volume of the system.-->
        <variable initial_value="0.00069934" name="q_lv" units="m3"/>
        <variable initial_value="1e-05" name="q_rv" units="m3"/>
        <variable initial_value="4e-06" name="q_la" units="m3"/>
        <variable initial_value="4e-06" name="q_ra" units="m3"/>
        <!-- calculate modified time due to changes in heart period. This can now be modified throughout a simulation.-->
        <variable initial_value="0.0" name="chi_a" units="dimensionless"/>
        <variable name="chi_afloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_afloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_a</ci>
                    <apply>
                        <floor/>
                        <ci>chi_a</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_a</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_astart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_astart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_afloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ar</ci>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>chi_afloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <variable initial_value="0.0" name="chi_v" units="dimensionless"/>
        <variable name="chi_vfloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_vfloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_v</ci>
                    <apply>
                        <floor/>
                        <ci>chi_v</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_v</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_vstart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_vstart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_vfloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vr</ci>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>chi_vfloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>s</ci>
                </apply>
                <apply>
                    <divide/>
                    <cn cellml:units="second">1</cn>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mt</ci>
                <apply>
                    <minus/>
                    <ci>s</ci>
                    <apply>
                        <floor/>
                        <ci>s</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Elastance Functions-->
            <apply>
                <eq/>
                <ci>t_astart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_astart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ac_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ac</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ar_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ar</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>t_vstart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_vstart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vc_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vc</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vr_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vr</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_a</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_afloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_v</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_vfloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <!-- Valve model-->
        <variable name="Rmod_valve_trv" public_interface="in" units="dimensionless"/>
        <variable name="Rmod_valve_puv" public_interface="in" units="dimensionless"/>
        <variable name="Rmod_valve_aov" public_interface="in" units="dimensionless"/>
        <variable name="Rmod_valve_miv" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>B_trv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>Rmod_valve_trv</ci>
                        <ci>rho</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_trv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_puv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>Rmod_valve_puv</ci>
                        <ci>rho</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_puv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_miv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>Rmod_valve_miv</ci>
                        <ci>rho</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_miv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_aov</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>Rmod_valve_aov</ci>
                        <ci>rho</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_aov</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_trv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_trv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_puv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_puv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_miv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_miv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_aov</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_aov</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_trv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_trv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_trv</ci>
                        <ci>A_nn_trv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_puv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_puv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_puv</ci>
                        <ci>A_nn_puv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_miv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_miv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_miv</ci>
                        <ci>A_nn_miv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_aov</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                        </apply>
                        <ci>zeta_aov</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_aov</ci>
                        <ci>A_nn_aov</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_trv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_trv_pre</ci>
                            </apply>
                            <ci>K_vo_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_ra</ci>
                            <ci>u_rv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_trv_pre</ci>
                            <ci>K_vc_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_puv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_puv_pre</ci>
                            </apply>
                            <ci>K_vo_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_rv</ci>
                            <ci>u_par</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_puv_pre</ci>
                            <ci>K_vc_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_miv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_miv_pre</ci>
                            </apply>
                            <ci>K_vo_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_la</ci>
                            <ci>u_lv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_miv_pre</ci>
                            <ci>K_vc_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_aov_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_aov_pre</ci>
                            </apply>
                            <ci>K_vo_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_lv</ci>
                            <ci>u_root</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_aov_pre</ci>
                            <ci>K_vc_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <!-- The below ensures zeta can't be negative-->
            <apply>
                <eq/>
                <ci>zeta_trv</ci>
                <apply>
                    <max/>
                    <ci>zeta_trv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_puv</ci>
                <apply>
                    <max/>
                    <ci>zeta_puv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_miv</ci>
                <apply>
                    <max/>
                    <ci>zeta_miv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_aov</ci>
                <apply>
                    <max/>
                    <ci>zeta_aov_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <!-- calculate the flow through the valves-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_trv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_trv</ci>
                                </apply>
                                <ci>v_trv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_trv</ci>
                                </apply>
                            </apply>
                            <ci>u_ra</ci>
                        </apply>
                        <ci>u_rv</ci>
                    </apply>
                    <ci>L_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_puv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_puv</ci>
                                </apply>
                                <ci>v_puv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_puv</ci>
                                </apply>
                            </apply>
                            <ci>u_rv</ci>
                        </apply>
                        <ci>u_par</ci>
                    </apply>
                    <ci>L_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_miv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_miv</ci>
                                </apply>
                                <ci>v_miv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_miv</ci>
                                </apply>
                            </apply>
                            <ci>u_la</ci>
                        </apply>
                        <ci>u_lv</ci>
                    </apply>
                    <ci>L_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_aov</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_aov</ci>
                                </apply>
                                <ci>v_aov</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_aov</ci>
                                </apply>
                            </apply>
                            <ci>u_lv</ci>
                        </apply>
                        <ci>u_root</ci>
                    </apply>
                    <ci>L_aov</ci>
                </apply>
            </apply>
        </math>
        <!-- calculate velocities from flow and nominal (constant) area-->
        <variable name="vel_trv" units="m_per_s"/>
        <variable name="vel_puv" units="m_per_s"/>
        <variable name="vel_miv" units="m_per_s"/>
        <variable name="vel_aov" units="m_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>vel_trv</ci>
                <apply>
                    <divide/>
                    <ci>v_trv</ci>
                    <ci>A_nn_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_puv</ci>
                <apply>
                    <divide/>
                    <ci>v_puv</ci>
                    <ci>A_nn_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_miv</ci>
                <apply>
                    <divide/>
                    <ci>v_miv</ci>
                    <ci>A_nn_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_aov</ci>
                <apply>
                    <divide/>
                    <ci>v_aov</ci>
                    <ci>A_nn_aov</ci>
                </apply>
            </apply>
            <!-- Constitutive Relations-->
            <apply>
                <eq/>
                <ci>u_ra</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_ra_A</ci>
                        </apply>
                        <ci>E_ra_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_ra</ci>
                        <ci>q_ra_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_rv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_rv_A</ci>
                        </apply>
                        <ci>E_rv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_rv</ci>
                        <ci>q_rv_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_la</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_la_A</ci>
                        </apply>
                        <ci>E_la_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_la</ci>
                        <ci>q_la_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_lv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_lv_A</ci>
                        </apply>
                        <ci>E_lv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_lv</ci>
                        <ci>q_lv_0</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_ra</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_svc</ci>
                        <ci>v_ivc</ci>
                    </apply>
                    <ci>v_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_rv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_trv</ci>
                    <ci>v_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_la</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_pvn</ci>
                    <ci>v_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_lv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_miv</ci>
                    <ci>v_aov</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="heart_simple_LVprop">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="s" public_interface="out" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mt" units="second"/>
        <variable name="e_a" units="dimensionless"/>
        <variable name="e_v" units="dimensionless"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="T_ac" public_interface="in" units="second"/>
        <variable name="T_ar" public_interface="in" units="second"/>
        <variable name="T_ac_norm" units="dimensionless"/>
        <variable name="T_ar_norm" units="dimensionless"/>
        <variable name="t_astart" public_interface="in" units="second"/>
        <variable name="t_astart_norm" units="dimensionless"/>
        <variable name="T_vc" public_interface="in" units="second"/>
        <variable name="T_vr" public_interface="in" units="second"/>
        <variable name="T_vc_norm" units="dimensionless"/>
        <variable name="T_vr_norm" units="dimensionless"/>
        <variable name="t_vstart" public_interface="in" units="second"/>
        <variable name="t_vstart_norm" units="dimensionless"/>
        <variable name="E_lv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_lv_B" public_interface="in" units="J_per_m6"/>
        <!--removed in for all E -->
        <variable name="E_la_A" units="J_per_m6"/>
        <variable name="E_la_B" units="J_per_m6"/>
        <variable name="E_rv_A" units="J_per_m6"/>
        <variable name="E_rv_B" units="J_per_m6"/>
        <variable name="E_ra_A" units="J_per_m6"/>
        <variable name="E_ra_B" units="J_per_m6"/>
        <variable name="q_ra_0" public_interface="in" units="m3"/>
        <variable name="q_rv_0" public_interface="in" units="m3"/>
        <variable name="q_la_0" public_interface="in" units="m3"/>
        <variable name="q_lv_0" public_interface="in" units="m3"/>
        <!-- State Variables-->
        <variable name="u_ra" public_interface="out" units="J_per_m3"/>
        <variable name="u_rv" units="J_per_m3"/>
        <variable name="u_la" public_interface="out" units="J_per_m3"/>
        <variable name="u_lv" units="J_per_m3"/>
        <variable name="u_root" public_interface="in" units="J_per_m3"/>
        <variable name="u_par" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0" name="v_trv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_puv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_miv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_aov" public_interface="out" units="m3_per_s"/>
        <variable name="v_svc" public_interface="in" units="m3_per_s"/>
        <variable name="v_ivc" public_interface="in" units="m3_per_s"/>
        <variable name="v_pvn" public_interface="in" units="m3_per_s"/>
        <variable name="L_trv" units="dimensionless"/>
        <variable name="L_puv" units="dimensionless"/>
        <variable name="L_miv" units="dimensionless"/>
        <variable name="L_aov" units="dimensionless"/>
        <variable name="A_eff_trv" units="m2"/>
        <variable name="A_eff_puv" units="m2"/>
        <variable name="A_eff_miv" units="m2"/>
        <variable name="A_eff_aov" units="m2"/>
        <variable name="A_nn_trv" public_interface="in" units="m2"/>
        <variable name="A_nn_puv" public_interface="in" units="m2"/>
        <variable name="A_nn_miv" public_interface="in" units="m2"/>
        <variable name="A_nn_aov" public_interface="in" units="m2"/>
        <variable name="l_eff" public_interface="in" units="metre"/>
        <variable name="K_vo_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="M_rg_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_aov" public_interface="in" units="dimensionless"/>
        <variable name="M_st_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_aov" public_interface="in" units="dimensionless"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="B_trv" units="dimensionless"/>
        <variable name="B_puv" units="dimensionless"/>
        <variable name="B_miv" units="dimensionless"/>
        <variable name="B_aov" units="dimensionless"/>
        <variable name="zeta_trv" units="dimensionless"/>
        <variable name="zeta_puv" units="dimensionless"/>
        <variable name="zeta_miv" units="dimensionless"/>
        <variable name="zeta_aov" units="dimensionless"/>
        <variable initial_value="0" name="zeta_trv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_puv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_miv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_aov_pre" units="dimensionless"/>
        <variable initial_value="1e-14" name="eps" units="dimensionless"/>
        <variable initial_value="0.07" name="eps_1" units="dimensionless"/>
        <variable initial_value="0.02" name="eps_2" units="dimensionless"/>
        <!-- TODO the below parameters should be set in an init_states parameter file
 q_lv gets identified, the others are set arbitrarily, identifying q_lv sets the stressed volume of the system.-->
        <variable initial_value="1.5e-04" name="q_lv" units="m3"/>
        <variable initial_value="1e-05" name="q_rv" units="m3"/>
        <variable initial_value="4e-06" name="q_la" units="m3"/>
        <variable initial_value="4e-06" name="q_ra" units="m3"/>
        <!-- calculate modified time due to changes in heart period. This can now be modified throughout a simulation.-->
        <variable initial_value="0.0" name="chi_a" units="dimensionless"/>
        <variable name="chi_afloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_afloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_a</ci>
                    <apply>
                        <floor/>
                        <ci>chi_a</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_a</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_astart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_astart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_afloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ar</ci>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>chi_afloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <variable initial_value="0.0" name="chi_v" units="dimensionless"/>
        <variable name="chi_vfloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_vfloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_v</ci>
                    <apply>
                        <floor/>
                        <ci>chi_v</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_v</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_vstart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_vstart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_vfloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vr</ci>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>chi_vfloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>s</ci>
                </apply>
                <apply>
                    <divide/>
                    <cn cellml:units="second">1</cn>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mt</ci>
                <apply>
                    <minus/>
                    <ci>s</ci>
                    <apply>
                        <floor/>
                        <ci>s</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Elastance Functions-->
            <apply>
                <eq/>
                <ci>t_astart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_astart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ac_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ac</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ar_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ar</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>t_vstart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_vstart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vc_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vc</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vr_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vr</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_a</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_afloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_v</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_vfloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- Valve model-->
            <apply>
                <eq/>
                <ci>B_trv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_trv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_puv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_puv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_miv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_miv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_aov</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_aov</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_trv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_trv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_puv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_puv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_miv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_miv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_aov</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_aov</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_trv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_trv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_trv</ci>
                        <ci>A_nn_trv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_puv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_puv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_puv</ci>
                        <ci>A_nn_puv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_miv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_miv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_miv</ci>
                        <ci>A_nn_miv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_aov</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                        </apply>
                        <ci>zeta_aov</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_aov</ci>
                        <ci>A_nn_aov</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_trv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_trv_pre</ci>
                            </apply>
                            <ci>K_vo_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_ra</ci>
                            <ci>u_rv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_trv_pre</ci>
                            <ci>K_vc_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_puv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_puv_pre</ci>
                            </apply>
                            <ci>K_vo_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_rv</ci>
                            <ci>u_par</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_puv_pre</ci>
                            <ci>K_vc_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_miv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_miv_pre</ci>
                            </apply>
                            <ci>K_vo_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_la</ci>
                            <ci>u_lv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_miv_pre</ci>
                            <ci>K_vc_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_aov_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_aov_pre</ci>
                            </apply>
                            <ci>K_vo_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_lv</ci>
                            <ci>u_root</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_aov_pre</ci>
                            <ci>K_vc_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <!-- The below ensures zeta can't be negative-->
            <apply>
                <eq/>
                <ci>zeta_trv</ci>
                <apply>
                    <max/>
                    <ci>zeta_trv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_puv</ci>
                <apply>
                    <max/>
                    <ci>zeta_puv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_miv</ci>
                <apply>
                    <max/>
                    <ci>zeta_miv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_aov</ci>
                <apply>
                    <max/>
                    <ci>zeta_aov_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <!-- calculate the flow through the valves-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_trv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_trv</ci>
                                </apply>
                                <ci>v_trv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_trv</ci>
                                </apply>
                            </apply>
                            <ci>u_ra</ci>
                        </apply>
                        <ci>u_rv</ci>
                    </apply>
                    <ci>L_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_puv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_puv</ci>
                                </apply>
                                <ci>v_puv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_puv</ci>
                                </apply>
                            </apply>
                            <ci>u_rv</ci>
                        </apply>
                        <ci>u_par</ci>
                    </apply>
                    <ci>L_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_miv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_miv</ci>
                                </apply>
                                <ci>v_miv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_miv</ci>
                                </apply>
                            </apply>
                            <ci>u_la</ci>
                        </apply>
                        <ci>u_lv</ci>
                    </apply>
                    <ci>L_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_aov</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_aov</ci>
                                </apply>
                                <ci>v_aov</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_aov</ci>
                                </apply>
                            </apply>
                            <ci>u_lv</ci>
                        </apply>
                        <ci>u_root</ci>
                    </apply>
                    <ci>L_aov</ci>
                </apply>
            </apply>
        </math>
        <!-- calculate velocities from flow and nominal (constant) area-->
        <variable name="vel_trv" units="m_per_s"/>
        <variable name="vel_puv" units="m_per_s"/>
        <variable name="vel_miv" units="m_per_s"/>
        <variable name="vel_aov" units="m_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>vel_trv</ci>
                <apply>
                    <divide/>
                    <ci>v_trv</ci>
                    <ci>A_nn_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_puv</ci>
                <apply>
                    <divide/>
                    <ci>v_puv</ci>
                    <ci>A_nn_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_miv</ci>
                <apply>
                    <divide/>
                    <ci>v_miv</ci>
                    <ci>A_nn_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_aov</ci>
                <apply>
                    <divide/>
                    <ci>v_aov</ci>
                    <ci>A_nn_aov</ci>
                </apply>
            </apply>
            <!-- Constitutive Relations-->
            <apply>
                <eq/>
                <ci>u_ra</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_ra_A</ci>
                        </apply>
                        <ci>E_ra_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_ra</ci>
                        <ci>q_ra_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_rv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_rv_A</ci>
                        </apply>
                        <ci>E_rv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_rv</ci>
                        <ci>q_rv_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_la</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_la_A</ci>
                        </apply>
                        <ci>E_la_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_la</ci>
                        <ci>q_la_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_lv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_lv_A</ci>
                        </apply>
                        <ci>E_lv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_lv</ci>
                        <ci>q_lv_0</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Identify LV elastances and scale all others in relation-->
            <apply>
                <eq/>
                <ci>E_rv_A</ci>
                <apply>
                    <times/>
                    <ci>E_lv_A</ci>
                    <cn cellml:units="dimensionless">0.8</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_ra_A</ci>
                <apply>
                    <times/>
                    <ci>E_lv_A</ci>
                    <cn cellml:units="dimensionless">0.02</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_la_A</ci>
                <apply>
                    <times/>
                    <ci>E_lv_A</ci>
                    <cn cellml:units="dimensionless">0.02</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_la_B</ci>
                <apply>
                    <times/>
                    <ci>E_lv_B</ci>
                    <cn cellml:units="dimensionless">0.9</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_ra_B</ci>
                <apply>
                    <times/>
                    <ci>E_lv_B</ci>
                    <cn cellml:units="dimensionless">0.9</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_rv_B</ci>
                <apply>
                    <times/>
                    <ci>E_lv_B</ci>
                    <cn cellml:units="dimensionless">0.6</cn>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_ra</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_svc</ci>
                        <ci>v_ivc</ci>
                    </apply>
                    <ci>v_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_rv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_trv</ci>
                    <ci>v_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_la</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_pvn</ci>
                    <ci>v_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_lv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_miv</ci>
                    <ci>v_aov</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="heart_devel">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="s" public_interface="out" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mt" units="second"/>
        <variable name="e_a" units="dimensionless"/>
        <variable name="e_v" units="dimensionless"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="T_ac" public_interface="in" units="second"/>
        <variable name="T_ar" public_interface="in" units="second"/>
        <variable name="T_ac_norm" units="dimensionless"/>
        <variable name="T_ar_norm" units="dimensionless"/>
        <variable name="t_astart" public_interface="in" units="second"/>
        <variable name="t_astart_norm" units="dimensionless"/>
        <variable name="T_vc" public_interface="in" units="second"/>
        <variable name="T_vr" public_interface="in" units="second"/>
        <variable name="T_vc_norm" units="dimensionless"/>
        <variable name="T_vr_norm" units="dimensionless"/>
        <variable name="t_vstart" public_interface="in" units="second"/>
        <variable name="t_vstart_norm" units="dimensionless"/>
        <variable name="E_lv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_lv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_la_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_rv_B" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_ra_B" public_interface="in" units="J_per_m6"/>
        <variable name="q_ra_0" public_interface="in" units="m3"/>
        <variable name="q_rv_0" public_interface="in" units="m3"/>
        <variable name="q_la_0" public_interface="in" units="m3"/>
        <variable name="q_lv_0" public_interface="in" units="m3"/>
        <!-- State Variables-->
        <variable name="u_ra" public_interface="out" units="J_per_m3"/>
        <variable name="u_rv" units="J_per_m3"/>
        <variable name="u_la" public_interface="out" units="J_per_m3"/>
        <variable name="u_lv" units="J_per_m3"/>
        <variable name="u_root" public_interface="in" units="J_per_m3"/>
        <variable name="u_par" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0" name="v_trv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_puv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_miv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_aov" public_interface="out" units="m3_per_s"/>
        <variable name="v_svc" public_interface="in" units="m3_per_s"/>
        <variable name="v_ivc" public_interface="in" units="m3_per_s"/>
        <variable name="v_pvn" public_interface="in" units="m3_per_s"/>
        <variable name="L_trv" units="dimensionless"/>
        <variable name="L_puv" units="dimensionless"/>
        <variable name="L_miv" units="dimensionless"/>
        <variable name="L_aov" units="dimensionless"/>
        <variable name="A_eff_trv" units="m2"/>
        <variable name="A_eff_puv" units="m2"/>
        <variable name="A_eff_miv" units="m2"/>
        <variable name="A_eff_aov" units="m2"/>
        <variable name="A_nn_trv" public_interface="in" units="m2"/>
        <variable name="A_nn_puv" public_interface="in" units="m2"/>
        <variable name="A_nn_miv" public_interface="in" units="m2"/>
        <variable name="A_nn_aov" public_interface="in" units="m2"/>
        <variable name="l_eff" public_interface="in" units="metre"/>
        <variable name="K_vo_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="M_rg_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_aov" public_interface="in" units="dimensionless"/>
        <variable name="M_st_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_aov" public_interface="in" units="dimensionless"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="B_trv" units="dimensionless"/>
        <variable name="B_puv" units="dimensionless"/>
        <variable name="B_miv" units="dimensionless"/>
        <variable name="B_aov" units="dimensionless"/>
        <variable name="zeta_trv" units="dimensionless"/>
        <variable name="zeta_puv" units="dimensionless"/>
        <variable name="zeta_miv" units="dimensionless"/>
        <variable name="zeta_aov" units="dimensionless"/>
        <variable initial_value="0" name="zeta_trv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_puv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_miv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_aov_pre" units="dimensionless"/>
        <variable initial_value="1e-22" name="eps" units="dimensionless"/>
        <variable initial_value="0.07" name="eps_1" units="dimensionless"/>
        <variable initial_value="0.02" name="eps_2" units="dimensionless"/>
        <!-- TODO the below parameters should be set in an init_states parameter file
 q_lv gets identified, the others are set arbitrarily, identifying q_lv sets the stressed volume of the system.-->
        <variable initial_value="0.00069934" name="q_lv" units="m3"/>
        <variable initial_value="1e-05" name="q_rv" units="m3"/>
        <variable initial_value="4e-06" name="q_la" units="m3"/>
        <variable initial_value="4e-06" name="q_ra" units="m3"/>
        <!-- calculate modified time due to changes in heart period. This can now be modified throughout a simulation.-->
        <variable initial_value="0.0" name="chi_a" units="dimensionless"/>
        <variable name="chi_afloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_afloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_a</ci>
                    <apply>
                        <floor/>
                        <ci>chi_a</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_a</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_astart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_astart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_afloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ar</ci>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>chi_afloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <variable initial_value="0.0" name="chi_v" units="dimensionless"/>
        <variable name="chi_vfloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_vfloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_v</ci>
                    <apply>
                        <floor/>
                        <ci>chi_v</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_v</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_vstart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_vstart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_vfloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vr</ci>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>chi_vfloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>s</ci>
                </apply>
                <apply>
                    <divide/>
                    <cn cellml:units="second">1</cn>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mt</ci>
                <apply>
                    <minus/>
                    <ci>s</ci>
                    <apply>
                        <floor/>
                        <ci>s</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Elastance Functions-->
            <apply>
                <eq/>
                <ci>t_astart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_astart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ac_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ac</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ar_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ar</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>t_vstart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_vstart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vc_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vc</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vr_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vr</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_a</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_afloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_v</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_vfloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <!-- Valve model-->
        <variable name="B_trv_pre" units="dimensionless"/>
        <variable name="B_puv_pre" units="dimensionless"/>
        <variable name="B_miv_pre" units="dimensionless"/>
        <variable name="B_aov_pre" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>B_trv_pre</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_trv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_puv_pre</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_puv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_miv_pre</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_miv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
        </math>
        <!-- B_aov = rho/(2{dimensionless}*sqr(A_eff_aov)+eps);-->
        <variable name="gamma" public_interface="in" units="dimensionless"/>
        <variable name="beta" public_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>B_aov_pre</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>gamma</ci>
                        <ci>rho</ci>
                        <apply>
                            <power/>
                            <apply>
                                <times/>
                                <pi/>
                                <apply>
                                    <power/>
                                    <ci>r_ao</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                </apply>
                            </apply>
                            <ci>beta</ci>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <power/>
                                <ci>r_lvot</ci>
                                <cn cellml:units="dimensionless">4</cn>
                            </apply>
                            <apply>
                                <power/>
                                <ci>A_eff_aov</ci>
                                <ci>beta</ci>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_trv</ci>
                <piecewise>
                    <piece>
                        <ci>B_trv_pre</ci>
                        <apply>
                            <lt/>
                            <ci>B_trv_pre</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>B_trv_pre</ci>
                                            </apply>
                                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>B_puv</ci>
                <piecewise>
                    <piece>
                        <ci>B_puv_pre</ci>
                        <apply>
                            <lt/>
                            <ci>B_puv_pre</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>B_puv_pre</ci>
                                            </apply>
                                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>B_miv</ci>
                <piecewise>
                    <piece>
                        <ci>B_miv_pre</ci>
                        <apply>
                            <lt/>
                            <ci>B_miv_pre</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>B_miv_pre</ci>
                                            </apply>
                                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>B_aov</ci>
                <piecewise>
                    <piece>
                        <ci>B_aov_pre</ci>
                        <apply>
                            <lt/>
                            <ci>B_aov_pre</ci>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>10</cn>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>B_aov_pre</ci>
                                            </apply>
                                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>16</cn>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>L_trv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_trv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_puv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_puv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_miv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_miv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <!-- L_aov = rho*l_eff/(A_eff_aov + eps);-->
            <apply>
                <eq/>
                <ci>L_aov</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r_lvot</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_trv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_trv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_trv</ci>
                        <ci>A_nn_trv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_puv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_puv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_puv</ci>
                        <ci>A_nn_puv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_miv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_miv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_miv</ci>
                        <ci>A_nn_miv</ci>
                    </apply>
                </apply>
            </apply>
            <!-- A_eff_aov = (M_st_aov*A_nn_aov-M_rg_aov*A_nn_aov)*zeta_aov+M_rg_aov*A_nn_aov;-->
            <apply>
                <eq/>
                <ci>A_eff_aov</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_aov</ci>
                                <ci>A_aov</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_aov</ci>
                                <ci>A_aov</ci>
                            </apply>
                        </apply>
                        <ci>zeta_aov</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_aov</ci>
                        <ci>A_aov</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_trv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_trv_pre</ci>
                            </apply>
                            <ci>K_vo_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_ra</ci>
                            <ci>u_rv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_trv_pre</ci>
                            <ci>K_vc_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_puv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_puv_pre</ci>
                            </apply>
                            <ci>K_vo_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_rv</ci>
                            <ci>u_par</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_puv_pre</ci>
                            <ci>K_vc_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_miv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_miv_pre</ci>
                            </apply>
                            <ci>K_vo_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_la</ci>
                            <ci>u_lv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_miv_pre</ci>
                            <ci>K_vc_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_aov_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_aov_pre</ci>
                            </apply>
                            <ci>K_vo_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_lv</ci>
                            <ci>u_root</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_aov_pre</ci>
                            <ci>K_vc_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <!-- The below ensures zeta can't be negative-->
            <apply>
                <eq/>
                <ci>zeta_trv</ci>
                <apply>
                    <max/>
                    <ci>zeta_trv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_puv</ci>
                <apply>
                    <max/>
                    <ci>zeta_puv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_miv</ci>
                <apply>
                    <max/>
                    <ci>zeta_miv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_aov</ci>
                <apply>
                    <max/>
                    <ci>zeta_aov_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <!-- calculate the flow through the valves-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_trv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_trv</ci>
                                </apply>
                                <ci>v_trv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_trv</ci>
                                </apply>
                            </apply>
                            <ci>u_ra</ci>
                        </apply>
                        <ci>u_rv</ci>
                    </apply>
                    <ci>L_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_puv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_puv</ci>
                                </apply>
                                <ci>v_puv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_puv</ci>
                                </apply>
                            </apply>
                            <ci>u_rv</ci>
                        </apply>
                        <ci>u_par</ci>
                    </apply>
                    <ci>L_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_miv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_miv</ci>
                                </apply>
                                <ci>v_miv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_miv</ci>
                                </apply>
                            </apply>
                            <ci>u_la</ci>
                        </apply>
                        <ci>u_lv</ci>
                    </apply>
                    <ci>L_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_aov</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_aov</ci>
                                </apply>
                                <ci>v_aov</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_aov</ci>
                                </apply>
                            </apply>
                            <ci>u_lv</ci>
                        </apply>
                        <ci>u_root</ci>
                    </apply>
                    <ci>L_aov</ci>
                </apply>
            </apply>
        </math>
        <!-- calculate velocities from flow and nominal (constant) area-->
        <variable name="vel_aov" public_interface="out" units="m_per_s"/>
        <variable name="r_lvot" public_interface="in" units="metre"/>
        <variable name="r_ao" public_interface="in" units="metre"/>
        <variable name="A_aov" public_interface="in" units="m2"/>
        <!-- A_nn_aov = A_aov;-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>vel_aov</ci>
                <apply>
                    <divide/>
                    <ci>v_aov</ci>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <cn cellml:units="dimensionless">3</cn>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r_lvot</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- Constitutive Relations-->
            <apply>
                <eq/>
                <ci>u_ra</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_ra_A</ci>
                        </apply>
                        <ci>E_ra_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_ra</ci>
                        <ci>q_ra_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_rv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_rv_A</ci>
                        </apply>
                        <ci>E_rv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_rv</ci>
                        <ci>q_rv_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_la</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_la_A</ci>
                        </apply>
                        <ci>E_la_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_la</ci>
                        <ci>q_la_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_lv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_lv_A</ci>
                        </apply>
                        <ci>E_lv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_lv</ci>
                        <ci>q_lv_0</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_ra</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_svc</ci>
                        <ci>v_ivc</ci>
                    </apply>
                    <ci>v_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_rv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_trv</ci>
                    <ci>v_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_la</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_pvn</ci>
                    <ci>v_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_lv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_miv</ci>
                    <ci>v_aov</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="heart_simple_LVprop_preterm">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="s" public_interface="out" units="second"/>
        <!-- Constitutive parameters-->
        <variable name="mt" units="second"/>
        <variable name="e_a" units="dimensionless"/>
        <variable name="e_v" units="dimensionless"/>
        <variable name="T" public_interface="in" units="second"/>
        <variable name="T_ac" public_interface="in" units="second"/>
        <variable name="T_ar" public_interface="in" units="second"/>
        <variable name="T_ac_norm" units="dimensionless"/>
        <variable name="T_ar_norm" units="dimensionless"/>
        <variable name="t_astart" public_interface="in" units="second"/>
        <variable name="t_astart_norm" units="dimensionless"/>
        <variable name="T_vc" public_interface="in" units="second"/>
        <variable name="T_vr" public_interface="in" units="second"/>
        <variable name="T_vc_norm" units="dimensionless"/>
        <variable name="T_vr_norm" units="dimensionless"/>
        <variable name="t_vstart" public_interface="in" units="second"/>
        <variable name="t_vstart_norm" units="dimensionless"/>
        <variable name="E_lv_A" public_interface="in" units="J_per_m6"/>
        <variable name="E_lv_B" public_interface="in" units="J_per_m6"/>
        <!--removed in for all E -->
        <variable name="E_la_A" units="J_per_m6"/>
        <variable name="E_la_B" units="J_per_m6"/>
        <variable name="E_rv_A" units="J_per_m6"/>
        <variable name="E_rv_B" units="J_per_m6"/>
        <variable name="E_ra_A" units="J_per_m6"/>
        <variable name="E_ra_B" units="J_per_m6"/>
        <variable name="q_ra_0" public_interface="in" units="m3"/>
        <variable name="q_rv_0" public_interface="in" units="m3"/>
        <variable name="q_la_0" public_interface="in" units="m3"/>
        <variable name="q_lv_0" public_interface="in" units="m3"/>
        <!-- State Variables-->
        <variable name="u_ra" public_interface="out" units="J_per_m3"/>
        <variable name="u_rv" units="J_per_m3"/>
        <variable name="u_la" public_interface="out" units="J_per_m3"/>
        <variable name="u_lv" units="J_per_m3"/>
        <variable name="u_root" public_interface="in" units="J_per_m3"/>
        <variable name="u_par" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0" name="v_trv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_puv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_miv" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_aov" public_interface="out" units="m3_per_s"/>
        <variable initial_value="0" name="v_fo" public_interface="out" units="m3_per_s"/>
        <!-- flow through foramen ovale-->
        <variable name="v_svc" public_interface="in" units="m3_per_s"/>
        <variable name="v_ivc" public_interface="in" units="m3_per_s"/>
        <variable name="v_pvn" public_interface="in" units="m3_per_s"/>
        <variable name="L_trv" units="dimensionless"/>
        <variable name="L_puv" units="dimensionless"/>
        <variable name="L_miv" units="dimensionless"/>
        <variable name="L_aov" units="dimensionless"/>
        <variable initial_value="1.5e3" name="L_fo" units="dimensionless"/>
        <variable name="A_eff_trv" units="m2"/>
        <variable name="A_eff_puv" units="m2"/>
        <variable name="A_eff_miv" units="m2"/>
        <variable name="A_eff_aov" units="m2"/>
        <variable name="A_nn_trv" public_interface="in" units="m2"/>
        <variable name="A_nn_puv" public_interface="in" units="m2"/>
        <variable name="A_nn_miv" public_interface="in" units="m2"/>
        <variable name="A_nn_aov" public_interface="in" units="m2"/>
        <variable name="A_nn_fo" public_interface="in" units="m2"/>
        <variable name="l_eff" public_interface="in" units="metre"/>
        <variable name="K_vo_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vo_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_trv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_puv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_miv" public_interface="in" units="m3_per_Js"/>
        <variable name="K_vc_aov" public_interface="in" units="m3_per_Js"/>
        <variable name="M_rg_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_rg_aov" public_interface="in" units="dimensionless"/>
        <variable name="M_st_trv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_puv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_miv" public_interface="in" units="dimensionless"/>
        <variable name="M_st_aov" public_interface="in" units="dimensionless"/>
        <variable name="rho" public_interface="in" units="Js2_per_m5"/>
        <variable name="B_trv" units="dimensionless"/>
        <variable name="B_puv" units="dimensionless"/>
        <variable name="B_miv" units="dimensionless"/>
        <variable name="B_aov" units="dimensionless"/>
        <variable name="B_fo" units="dimensionless"/>
        <variable name="zeta_trv" units="dimensionless"/>
        <variable name="zeta_puv" units="dimensionless"/>
        <variable name="zeta_miv" units="dimensionless"/>
        <variable name="zeta_aov" units="dimensionless"/>
        <variable initial_value="0" name="zeta_trv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_puv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_miv_pre" units="dimensionless"/>
        <variable initial_value="0" name="zeta_aov_pre" units="dimensionless"/>
        <variable initial_value="1e-14" name="eps" units="dimensionless"/>
        <variable initial_value="0.07" name="eps_1" units="dimensionless"/>
        <variable initial_value="0.02" name="eps_2" units="dimensionless"/>
        <!-- TODO the below parameters should be set in an init_states parameter file
 q_lv gets identified, the others are set arbitrarily, identifying q_lv sets the stressed volume of the system.-->
        <variable initial_value="1.5445e-04" name="q_lv" units="m3"/>
        <variable initial_value="1e-05" name="q_rv" units="m3"/>
        <variable initial_value="4e-06" name="q_la" units="m3"/>
        <variable initial_value="4e-06" name="q_ra" units="m3"/>
        <!-- calculate modified time due to changes in heart period. This can now be modified throughout a simulation.-->
        <variable initial_value="0.0" name="chi_a" units="dimensionless"/>
        <variable name="chi_afloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_afloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_a</ci>
                    <apply>
                        <floor/>
                        <ci>chi_a</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_a</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_astart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_astart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_astart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ac</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_afloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_afloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_ar</ci>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>chi_afloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <variable initial_value="0.0" name="chi_v" units="dimensionless"/>
        <variable name="chi_vfloor" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>chi_vfloor</ci>
                <apply>
                    <minus/>
                    <ci>chi_v</ci>
                    <apply>
                        <floor/>
                        <ci>chi_v</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>chi_v</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>mt</ci>
                                <ci>t_vstart_norm</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <apply>
                                    <plus/>
                                    <ci>t_vstart_norm</ci>
                                    <ci>eps_1</ci>
                                </apply>
                                <cn cellml:units="dimensionless">1.0</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>mt</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>t_vstart_norm</ci>
                                        <ci>eps_1</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vc</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>chi_vfloor</ci>
                                <ci>eps_2</ci>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>chi_vfloor</ci>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="second">0.5</cn>
                            <ci>T_vr</ci>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>chi_vfloor</ci>
                            <cn cellml:units="dimensionless">0.5</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="dimensionless">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>s</ci>
                </apply>
                <apply>
                    <divide/>
                    <cn cellml:units="second">1</cn>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mt</ci>
                <apply>
                    <minus/>
                    <ci>s</ci>
                    <apply>
                        <floor/>
                        <ci>s</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Elastance Functions-->
            <apply>
                <eq/>
                <ci>t_astart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_astart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ac_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ac</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_ar_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_ar</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>t_vstart_norm</ci>
                <apply>
                    <divide/>
                    <ci>t_vstart</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vc_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vc</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>T_vr_norm</ci>
                <apply>
                    <divide/>
                    <ci>T_vr</ci>
                    <ci>T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_a</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_afloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_v</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.5</cn>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <cos/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <ci>chi_vfloor</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- Valve model-->
            <apply>
                <eq/>
                <ci>B_trv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_trv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_puv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_puv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_miv</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_miv</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_aov</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <power/>
                                <ci>A_eff_aov</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_fo</ci>
                <apply>
                    <divide/>
                    <ci>rho</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <apply>
                            <power/>
                            <ci>A_nn_fo</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_trv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_trv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_puv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_puv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_miv</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_miv</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L_aov</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l_eff</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>A_eff_aov</ci>
                        <ci>eps</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_trv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_trv</ci>
                                <ci>A_nn_trv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_trv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_trv</ci>
                        <ci>A_nn_trv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_puv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_puv</ci>
                                <ci>A_nn_puv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_puv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_puv</ci>
                        <ci>A_nn_puv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_miv</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_miv</ci>
                                <ci>A_nn_miv</ci>
                            </apply>
                        </apply>
                        <ci>zeta_miv</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_miv</ci>
                        <ci>A_nn_miv</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_eff_aov</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>M_st_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>M_rg_aov</ci>
                                <ci>A_nn_aov</ci>
                            </apply>
                        </apply>
                        <ci>zeta_aov</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>M_rg_aov</ci>
                        <ci>A_nn_aov</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_trv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_trv_pre</ci>
                            </apply>
                            <ci>K_vo_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_ra</ci>
                            <ci>u_rv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_trv_pre</ci>
                            <ci>K_vc_trv</ci>
                            <apply>
                                <minus/>
                                <ci>u_ra</ci>
                                <ci>u_rv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_puv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_puv_pre</ci>
                            </apply>
                            <ci>K_vo_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_rv</ci>
                            <ci>u_par</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_puv_pre</ci>
                            <ci>K_vc_puv</ci>
                            <apply>
                                <minus/>
                                <ci>u_rv</ci>
                                <ci>u_par</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_miv_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_miv_pre</ci>
                            </apply>
                            <ci>K_vo_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_la</ci>
                            <ci>u_lv</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_miv_pre</ci>
                            <ci>K_vc_miv</ci>
                            <apply>
                                <minus/>
                                <ci>u_la</ci>
                                <ci>u_lv</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>zeta_aov_pre</ci>
                </apply>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>zeta_aov_pre</ci>
                            </apply>
                            <ci>K_vo_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                        <apply>
                            <geq/>
                            <ci>u_lv</ci>
                            <ci>u_root</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <ci>zeta_aov_pre</ci>
                            <ci>K_vc_aov</ci>
                            <apply>
                                <minus/>
                                <ci>u_lv</ci>
                                <ci>u_root</ci>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <!-- The below ensures zeta can't be negative-->
            <apply>
                <eq/>
                <ci>zeta_trv</ci>
                <apply>
                    <max/>
                    <ci>zeta_trv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_puv</ci>
                <apply>
                    <max/>
                    <ci>zeta_puv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_miv</ci>
                <apply>
                    <max/>
                    <ci>zeta_miv_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>zeta_aov</ci>
                <apply>
                    <max/>
                    <ci>zeta_aov_pre</ci>
                    <cn cellml:units="dimensionless">0</cn>
                </apply>
            </apply>
            <!-- calculate the flow through the valves-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_trv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_trv</ci>
                                </apply>
                                <ci>v_trv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_trv</ci>
                                </apply>
                            </apply>
                            <ci>u_ra</ci>
                        </apply>
                        <ci>u_rv</ci>
                    </apply>
                    <ci>L_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_puv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_puv</ci>
                                </apply>
                                <ci>v_puv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_puv</ci>
                                </apply>
                            </apply>
                            <ci>u_rv</ci>
                        </apply>
                        <ci>u_par</ci>
                    </apply>
                    <ci>L_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_miv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_miv</ci>
                                </apply>
                                <ci>v_miv</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_miv</ci>
                                </apply>
                            </apply>
                            <ci>u_la</ci>
                        </apply>
                        <ci>u_lv</ci>
                    </apply>
                    <ci>L_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_aov</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_aov</ci>
                                </apply>
                                <ci>v_aov</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_aov</ci>
                                </apply>
                            </apply>
                            <ci>u_lv</ci>
                        </apply>
                        <ci>u_root</ci>
                    </apply>
                    <ci>L_aov</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_fo</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>B_fo</ci>
                                </apply>
                                <ci>v_fo</ci>
                                <apply>
                                    <abs/>
                                    <ci>v_fo</ci>
                                </apply>
                            </apply>
                            <ci>u_la</ci>
                        </apply>
                        <ci>u_ra</ci>
                    </apply>
                    <ci>L_fo</ci>
                </apply>
            </apply>
        </math>
        <!-- calculate velocities from flow and nominal (constant) area-->
        <variable name="vel_trv" units="m_per_s"/>
        <variable name="vel_puv" units="m_per_s"/>
        <variable name="vel_miv" units="m_per_s"/>
        <variable name="vel_aov" units="m_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>vel_trv</ci>
                <apply>
                    <divide/>
                    <ci>v_trv</ci>
                    <ci>A_nn_trv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_puv</ci>
                <apply>
                    <divide/>
                    <ci>v_puv</ci>
                    <ci>A_nn_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_miv</ci>
                <apply>
                    <divide/>
                    <ci>v_miv</ci>
                    <ci>A_nn_miv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vel_aov</ci>
                <apply>
                    <divide/>
                    <ci>v_aov</ci>
                    <ci>A_nn_aov</ci>
                </apply>
            </apply>
            <!-- Constitutive Relations-->
            <apply>
                <eq/>
                <ci>u_ra</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_ra_A</ci>
                        </apply>
                        <ci>E_ra_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_ra</ci>
                        <ci>q_ra_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_rv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_rv_A</ci>
                        </apply>
                        <ci>E_rv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_rv</ci>
                        <ci>q_rv_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_la</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_a</ci>
                            <ci>E_la_A</ci>
                        </apply>
                        <ci>E_la_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_la</ci>
                        <ci>q_la_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_lv</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>e_v</ci>
                            <ci>E_lv_A</ci>
                        </apply>
                        <ci>E_lv_B</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>q_lv</ci>
                        <ci>q_lv_0</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Identify LV elastances and scale all others in relation-->
            <apply>
                <eq/>
                <ci>E_rv_A</ci>
                <apply>
                    <times/>
                    <ci>E_lv_A</ci>
                    <cn cellml:units="dimensionless">0.7</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_ra_A</ci>
                <apply>
                    <times/>
                    <ci>E_lv_A</ci>
                    <cn cellml:units="dimensionless">0.02</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_la_A</ci>
                <apply>
                    <times/>
                    <ci>E_lv_A</ci>
                    <cn cellml:units="dimensionless">0.02</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_la_B</ci>
                <apply>
                    <times/>
                    <ci>E_lv_B</ci>
                    <cn cellml:units="dimensionless">0.5</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_ra_B</ci>
                <apply>
                    <times/>
                    <ci>E_lv_B</ci>
                    <cn cellml:units="dimensionless">0.3</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>E_rv_B</ci>
                <apply>
                    <times/>
                    <ci>E_lv_B</ci>
                    <cn cellml:units="dimensionless">0.6</cn>
                </apply>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_ra</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>v_svc</ci>
                        <ci>v_ivc</ci>
                        <ci>v_fo</ci>
                    </apply>
                    <ci>v_trv</ci>
                </apply>
            </apply>
            <!--ode(q_ra, t) = v_svc+v_ivc-v_trv;-->
            <!-- add in flow through FO-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_rv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_trv</ci>
                    <ci>v_puv</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_la</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v_pvn</ci>
                        <ci>v_fo</ci>
                    </apply>
                    <ci>v_miv</ci>
                </apply>
            </apply>
            <!--ode(q_la, t) = v_pvn-v_miv;-->
            <!-- subtract flow through FO-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_lv</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_miv</ci>
                    <ci>v_aov</ci>
                </apply>
            </apply>
        </math>
    </component>
</model>
