- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-11-04 16:02:42+13:00
- Desc:
- Updated USMC-Bursztyn model
- Permanent Source URI:
- http://models.cellml.org/workspace/6b0/rawfile/4c1ab73f48d7150c2094cf8017425482a1594ccf/USMC/Maggio2012/RK4ZahM_ASM.m
%% Date: 01/03/2021
%
% Author: Anand Rampadarath
% Version 1
% This model represents the Uterine smooth muscle cell as
% developed by Maggio et al 2012. It is a variant of the
% Hai-Murphy model including spatian dependence of the
% cross-bridges, similar to Mijailovich et al.
% We us the DM approximation to reduce the computational complexity.
%
function [X0,T,R,rLum,force,stiffness,phosphorylation,m10,m20,nmp,nm,P_0,V,Raw,radius,Pab,vv,tau]=RK4ZahM_ASM(trange,N,M,xrange,lambda,rho,s,f,P01,gamma,Pawb)
%N number of time points
%trange specifies the interval of time steps
%T time grid
%X0 space grid
%gamma=25 rho=1 s=airway generation lambda=force activation
T=linspace(trange(1),trange(2),N);
X0=linspace(xrange(1),xrange(2),M);
dt=(trange(2)-trange(1))/(N); % dt must be <=0.1
%% Initial conditions f
M10=0.309120293063990;
M11=0.118325676501984;
M12=0.066855519431672;
M20=0.134379171029593;
M21=-0.045132660622671;
M22=0.101673063419951;
C=0.6;
R=[M10;M11;M12;M20;M21;M22;C];
%% This run of fsolve finds the equilibria as Initial condition
% g=@(r) mis2(r,lambda,rho,N1(s),N2(s),P1(s),P2(s),rmax_sq(s),Ri_sq(s),P01);
% options = optimset('fsolve');
% [R,~,exitflag]=fsolve(g,R,options);
% R=[0.620322306169257; 0.310009711094628; 0.206570517906060; 0.174751423933002; 0.086923224037493; 0.057784269634018; 0.5];
stiffness = zeros(1,N);
force = zeros(1,N);
phosphorylation = zeros(1,N);
m10 = zeros(1,N);
m20 = zeros(1,N);
nmp = zeros(1,N);
nm = zeros(1,N);
nMpave = zeros(1,N);
nAmpave = zeros(1,N);
%[k1,k2] = rates(N,trange);
for i=1:N %loop over number of timesteps to update then run euler
t=trange(1)+(i)*dt;
[F1,~,~,~,~]=DM_funcs(t,R,lambda,f,rho,gamma);
[F2,~,~,~,~]=DM_funcs(t+(dt/2),R+((dt/2)*F1),lambda,f,rho,N1(s),N2(s),Ri_sq(s),rmax_sq(s),rmax(s),P1(s),P2(s),gamma,Pawb,P01);%,t1,t2);%,k1,k2(i));
[F3,~,~,~,~]=DM_funcs(t+(dt/2),R+((dt/2)*F2),lambda,f,rho,N1(s),N2(s),Ri_sq(s),rmax_sq(s),rmax(s),P1(s),P2(s),gamma,Pawb,P01);%,t1,t2);%,k1,k2(i));
[F4,~,~,~,~,P_0(i),V(i),Raw(i),radius(i),Pab(i),vv(i),tau(i)]=DM_funcs(t+(dt),R+((dt)*F3),lambda,f,rho,N1(s),N2(s),Ri_sq(s),rmax_sq(s),rmax(s),P1(s),P2(s),gamma,Pawb,P01);%,t1,t2);%,k1,k2(i));
Rnew = R + (dt/6)*(F1+(2*F2)+(2*F3)+F4);
R=Rnew;
%% A rebuild of the distribution approximation for Namp(M10:M12) and Nam(M20:M22)
% n1=(R(1)/((sqrt(2*pi))*q1)).*exp(-((X0-p1).^(2))/(2*(q1.^(2))));
% n2=(R(4)/((sqrt(2*pi))*q2)).*exp(-((X0-p2).^(2))/(2*(q2.^(2))));
%% ASM stiffness and radii of airway lumen
stiffness(i)=R(1)+R(4);
rLum(i)=R(8) ;
%% Crossbridge populations
nmp(i)=1-R(7)-R(1);
nm(i)=1-R(4)-R(1)-nmp(i);
m10(i)=R(1);
% m11(i)=R(2);
% m21(i)=R(5);
m20(i)=R(4);
nMpave(i)=nmp(i);
nAmpave(i)=R(1);
%%ASM phosphorylation and Force
phosphorylation(i)=(nMpave(i)+nAmpave(i));
%% Emperical L-T relationship taken from Donovan 2016
force_l(i)=(sin((pi*R(8))/(2*rmax(s)))).^3.*(R(8)<=2*rmax(s))+0.*(R(8)>2*rmax(s));
% force_l(i)=1;
force_a(i)=lambda*(R(2)+R(5));
force(i)=force_l(i)*force_a(i);
%% plotting cross-bridge distributions
% if (mod(i,100)==0);% && i==8000 )
% % figure,
% plot(X0,n1+n2)
% xlim([-5 5])
% % title('Namp+Nam distribution plot for DM')
% % ylabel('n_{AMp}+n_{AM} state populations')
% drawnow
% % break
% hold on
% % pause
% %
% % figure(2)
% % plot(X0,n2)
% % xlim([-5 5])
% % title('N_{AM} distribution plot for DM')
% % drawnow
% % hold on
% % pause
% %
% % figure(3)
% % plot(X0,n1)
% % title('Namp distribution for DM')
% % drawnow
% % hold on
%
% % pause
% end
end
