%% This model incorporates the Hai-Murphy crossbridge ODEs to the BG-AW-heterogeneity 
%% model being developed.

function [t,NN,air,U,UVDOT,VVDOT,force,phosphorylation,summ,pa_bar,R,Ptm]=coup(order,kappa)%,rinitial)
tic

numBr = 2^order - 1;     % number of airways
numOrd1 = (numBr+1)/2;
% initial values for airways (mm)
rimax = [0.296 0.318 0.337 0.358 0.384 0.414 0.445 0.484 0.539 0.608 ...
    0.692 0.793 0.913 1.052 1.203 1.374];
rinitial=[];
for k=1:order
    rinitial=[rinitial;rimax(k)*ones(2.^(order-k),1)];
end
rinitial=rinitial+0.01*rand(1,length(rinitial))'; % peturbation of rinitial

M = 1; Mp = 0; AMp = 0; AM = 0;

RR0= [M; Mp; AMp; AM];
r(:,1)=rinitial; %airways, order 1 : order n
uv(:,1) = zeros(numBr,1); % pressure in airway
vv(:,1) = zeros(numBr,1); % airflow within the airway
vds(:,1) = zeros((numBr+1)/2,1); % airflow entering alveoli
RR(:,1) = RR0;
y0 = [r(:,1); uv(:,1); vv(:,1); vds(:,1); RR(:,1)]; %ICs vector

%Stepwise kappa value
    tspan = linspace(0,100,1000);


    parm = kappa;


    % Set numerical accuracy options for ODE solver
    options = odeset('RelTol', 1e-08, 'AbsTol', 1e-08, 'MaxStep', 0.1);
    
    [t,NN]=ode15s(@(t,y) seven_airway(t,y,order,parm), tspan, y0, options);
    U = zeros(length(NN),length(r)); % pressure including viscous damping
    UVDOT = zeros(length(NN),length(r));
    VVDOT = zeros(length(NN),length(r)); %airflow
    force = zeros(length(NN),length(r));
    phosphorylation = zeros(length(NN),length(r));
    pmid = zeros(length(NN),length(r));
    for j = 1:length(NN)
        [U(j,:),UVDOT(j,:),VVDOT(j,:),force(j,:),phosphorylation(j,:),pa_bar(j,:),R(j,:),Ptm(j,:)] = seven_airway2(t(j),NN(j,:),order,parm);
    end
toc
% CM=jet(length(rinitial));
r_new = NN(:,1:numBr);
air = zeros(length(NN),length(r));
for i=1:length(rinitial)
    for j = 1:length(t)
     if r_new(j,i) <= 0.01
       air(j,i)=0;
      else
       air(j,i)=1;
     end
    end

end
for i = 1:(numOrd1)
%     figure(1);
%     subplot(order,order,i);
%     plot(t,r_new(:,i))
%     title(sprintf('Radius of airway {%d}',i))
% %     
% %     figure(2);
% %     subplot(order,10,i);
% % %     M{i} = findpeaks(r_new(:,i));
% %     DataInv(:,i) = 1.01*max(r_new(:,i)) - r_new(:,i);
% %     [Minima_P{i},MinIIdx{i}] = findpeaks(DataInv(:,i));
% %     abc = r_new(:,i); 
% %     Minima_P{i} = abc(MinIIdx{i}); 
% %     plot(t(MinIIdx{i}),Minima_P{i},'-o');
%     
    figure(2);
    subplot(order,order,i);
    plot(t,VVDOT(:,i))
    title(sprintf('Flow in airway {%d}',i))
% % %     
    figure(3);
    subplot(order,order,i);
    plot(t,U(:,i))
    title(sprintf('Pressure in airway {%d}',i))
%     
%     figure(5)
%     subplot(order,order,i);
%     plot(t,pmid(:,i))
end
% %     
% %     
% legendStr = cell(1,length(rinitial));
% for i = 1:length(legendStr)
%     legendStr{i} = sprintf('r_{%d}',i);
% 
% end
% legend(legendStr,'Location','BestOutside');
% %% Measure for state of heterogeniety
x = cell(1,numOrd1);
for i = 1:length(x)
    x{i} = air(:,i);
end
summ = zeros(1,length(x{1}));
for i = 1:length(x)
    switch i
        case 1
            neighbour_diff = sqrt((x{:,i} - x{:,end}).^2 + (x{:,i} - x{:,i+1}).^2);
        case length(x)
            neighbour_diff = sqrt((x{:,i} - x{:,i-1}).^2 + (x{:,i} - x{:,1}).^2);
        otherwise
            neighbour_diff = sqrt((x{:,i} - x{:,i-1}).^2 + (x{:,i} - x{:,i+1}).^2);
    end
    summ = summ + neighbour_diff';
    
    
end
summ=summ./(2^(order-3)*4*sqrt(2));

y=cell(1,numOrd1);
 for k=1:length(y)
     y{k}=VVDOT(:,k);
 end
    flow_sum = zeros(1,length(y{1}));
 
    for ii = 1:length(y)
      switch ii
          case 1
              neighbour_diff1 = sqrt((y{:,ii} - y{:,end}).^2 + (y{:,ii} - y{:,ii+1}).^2);
          case length(y)
              neighbour_diff1 = sqrt((y{:,ii} - y{:,ii-1}).^2 + (y{:,ii} - y{:,1}).^2);
          otherwise
              neighbour_diff1 = sqrt((y{:,ii} - y{:,ii-1}).^2 + (y{:,ii} - y{:,ii+1}).^2);
      end
     flow_sum = flow_sum + neighbour_diff1';
     
    end
flow_sum=flow_sum./(2^(order-3)*4*sqrt(2));%numOrd1;


% %% graphing airways
node1 = zeros(1,numBr);
    node2 = zeros(1,numBr);
    
    % e.g. for an order 4: node1 = [1 2 2 3 3 4 4 5 5 6 6 7 7 8 8];
    node1(1) = 1;
    for i = 1:(numBr-1)/2
        node1(2*i:2*i+1) = [i+1 i+1];
    end
   
    % e.g. for an order 4: node2 = [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16];
    for i = 1:numBr
        node2(i) = i+1;
    end
    
    ind = zeros(1,numBr);
    for i = 1:numBr
        ind(i) = i;
    end
%     figure,
    A=fliplr(air(end,:));
    
    figure(4);
    G = graph(node1,node2,A);
    h=plot(G,'LineWidth',2);
    h.EdgeCData=A;
    labelnode(h,[node1 node2],'')
    labeledge(h,ind,G.Edges.Weight(ind));
    colormap jet

    

% for i = 1:8
% subplot(4,2,i);
% plot(time,VVDOT(:,i))
% title(sprintf('Flow of airway {%d}',i))
% end