/Users/max_neal/Dropbox/Semantic Project/Annotated CellML models/siebert_rode_herzog_till_blickhan_2008/siebert_CC_2008.cellml
<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> Nonlinearities make a difference: comparison of two common Hill-type models with real muscle <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil> </affiliation> </author> </articleinfo> Model Status This CellML model represents the [CC] model from the original published paper. Parameter values have been taken from table 2, SOL1 for the [CC] model. The CellML model runs in OpenCell to recreate the published results. The units have been checked and are consistent. The model will not run in COR due to the presence of differential algebraic equations - or "circular arguments". <sect1 id="sec_structure"> Model Structure ABSTRACT: Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component (model [CC+SEC]), or is connected in parallel only with the contractile component (model [CC]). As soon as at least one of the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off, the two models are mechanically different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus better. Ramp experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using supramaximal nerve stimulation. Hill-type models containing force-length and force-velocity relationship, excitation-contraction coupling and series and parallel elastic force-elongation relations were fitted to the data. To test which model might represent the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations with negligible passive force, the force-velocity relation and the series elastic component relation are independent of the chosen model. In contrast to model [CC+SEC], these relations predicted by model [CC] were in accordance with experimental relations. In conclusion model [CC] seemed to better represent the cat soleus contraction dynamics and should be preferred in the nonlinear regression of muscle parameters and in musculoskeletal modeling. The original paper is cited below: Nonlinearities make a difference: comparison of two common Hill-type models with real muscle, Tobias Siebert, Christian Rode, Walter Herzog, Olaf Till and Reinhard Blickhan, 2008, Biological Cybernetics , 98, 133-143. PubMed ID: 18049823 <informalfigure float="0" id="figure"> <mediaobject> <imageobject> <imagedata fileref="siebert_2008.png" /> </imageobject> </mediaobject> Two different variants of the Hill muscle model. Isometric force is defined by a piecewise equation. </informalfigure> </sect1> </documentation>
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Tensile velocity
A physical entity that is defined by linking multiple physical entity terms with structural relations.
A mathematical and/or logical expression that determines the value of a data structure.
An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities.
A physical dependency defined in a specific SemSim model.
A physical entity defined in a specific SemSim model.
A physical process defined in a specific SemSim model.
A physical property defined in a specific SemSim model.
A computational element that stores numerical and/or logical information related to the model.
A data structure whose value is limited to decimals.
A data structure whose value is limited to the whole numbers.
A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process.
A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants.
A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element.
A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process.
A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values.
A data structure whose value is limited to the real numbers.
A physical dependency that is defined using a term in an external knowledge resource.
A physical entity that is defined using a term from an external knowledge resource.
A physical process that is defined using a term in an external knowledge resource.
A physical property that is defined using a term in an external knowledge resource.
A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0.
A computational or physical element of a SemSim model.
A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel.
A physical quantity chosen as a standard in terms of which other physical quantities may be expressed.
Contraction of contractile element
Contraction of the modeled contractile element
Activation state
Force at which the series elastic component force-elongation relation changes from exponential to linear
The maximum active isometric force of the muscle
Curve-shaping parameter determining width of muscle force-length relationship
Muscle length at which the ascending limb changes slope
Curve-shaping parameter that sets the length of the force-length plateau
The contractile component length minus the optimal contractile component length
The constant sum of the slack length of the series elastic component and the optimal length of the contractile component (used in the [CC] model, but not the [CC+SEC] model)
Length of the muscle-tendon complex
Curve-shaping parameter determining relationship between f_v and v_cc
The length at which the force–elongation relation changes from exponential to linear
Elongation of series elastic component
Length at which the series elastic component force-elongation relation changes from exponential to linear
Length-based force factor in overall contractile component force
The force at which the ascending limb changes slope
Force generated in series elastic component
Velocity-based force factor in overall contractile component force
Scaling parameter for the series elastic component's force-elongation relationship
Curve-shaping parameter for setting the parallel elastic component's force-velocity relationship
Shaping parameter for the series elastic component's force-elongation relationship
Time constant for muscle activation
Time
Time solution domain
Velocity of contractile component
Maximal contractile component shortening velocity
<apply> <eq /> <ci>delta_L_sec</ci> <apply> <minus /> <apply> <minus /> <ci>L_mtc</ci> <ci>L_cc</ci> </apply> <ci>L_m</ci> </apply> </apply> <apply> <eq /> <ci>f_sec</ci> <piecewise> <piece> <apply> <times /> <apply> <divide /> <ci>F_1</ci> <apply> <minus /> <apply> <exp /> <ci>k_sh</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> <apply> <minus /> <apply> <exp /> <apply> <divide /> <apply> <times /> <ci>k_sh</ci> <ci>delta_L_sec</ci> </apply> <ci>delta_L_sec1</ci> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> <apply> <and /> <apply> <gt /> <ci>delta_L_sec</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm">0</cn> </apply> <apply> <lt /> <ci>delta_L_sec</ci> <ci>delta_L_sec1</ci> </apply> </apply> </piece> <piece> <apply> <plus /> <ci>F_1</ci> <apply> <times /> <ci>k</ci> <apply> <minus /> <ci>delta_L_sec</ci> <ci>delta_L_sec1</ci> </apply> </apply> </apply> <apply> <leq /> <ci>delta_L_sec</ci> <ci>delta_L_sec1</ci> </apply> </piece> </piecewise> </apply> <apply> <eq /> <ci>v_cc</ci> <apply> <times /> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm_newton_per_second">1</cn> <ci>f_v</ci> </apply> <apply> <divide /> <ci>f_sec</ci> <apply> <times /> <ci>A</ci> <ci>f_L</ci> <ci>F_im</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>L_cc</ci> </apply> <ci>v_cc</ci> </apply> <apply> <eq /> <ci>f_v</ci> <apply> <divide /> <apply> <minus /> <ci>v_max</ci> <ci>v_cc</ci> </apply> <apply> <plus /> <ci>v_max</ci> <apply> <times /> <ci>v_cc</ci> <ci>curv</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>f_L</ci> <piecewise> <piece> <apply> <times /> <apply> <divide /> <ci>f_c</ci> <apply> <minus /> <ci>L_2</ci> <ci>L_1</ci> </apply> </apply> <apply> <minus /> <ci>L_cc</ci> <ci>L_1</ci> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>L_cc</ci> <ci>L_1</ci> </apply> <apply> <leq /> <ci>L_cc</ci> <ci>L_2</ci> </apply> </apply> </piece> <piece> <apply> <times /> <apply> <divide /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="newton">1</cn> <ci>f_c</ci> </apply> <apply> <minus /> <ci>L_2</ci> </apply> </apply> <apply> <minus /> <ci>L_cc</ci> <ci>L_2</ci> </apply> </apply> <apply> <and /> <apply> <gt /> <ci>L_cc</ci> <ci>L_2</ci> </apply> <apply> <leq /> <ci>L_cc</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm">0</cn> </apply> </apply> </piece> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="newton">1</cn> <apply> <and /> <apply> <gt /> <ci>L_cc</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm">0</cn> </apply> <apply> <leq /> <ci>L_cc</ci> <ci>L_3</ci> </apply> </apply> </piece> <piece> <apply> <times /> <apply> <divide /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="newton">1</cn> </apply> <apply> <minus /> <ci>L_4</ci> <ci>L_3</ci> </apply> </apply> <apply> <minus /> <ci>L_cc</ci> <ci>L_3</ci> </apply> </apply> <apply> <and /> <apply> <gt /> <ci>L_cc</ci> <ci>L_3</ci> </apply> <apply> <leq /> <ci>L_cc</ci> <ci>L_4</ci> </apply> </apply> </piece> </piecewise> </apply> <apply> <eq /> <ci>L_mtc</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm">0.29</cn> <apply> <leq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">1</cn> </apply> </piece> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm">0.22</cn> <apply> <and /> <apply> <gt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">1</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">5</cn> </apply> </apply> </piece> <otherwise> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm">0.19</cn> </otherwise> </piecewise> </apply>