- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-11-04 16:02:42+13:00
- Desc:
- Updated USMC-Bursztyn model
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/6b0/rawfile/4c1ab73f48d7150c2094cf8017425482a1594ccf/USMC/DM+Mijaailovich_huxley_copy/ZahM.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,force,stiffness,phosphorylation,m10,m20,nmp,nm]=ZahM(trange,N,M,xrange)
%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
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];
% g=@(r) mis1(r);
% options = optimoptions('fsolve');
% [R,~,exitflag]=fsolve(g,R,options);
for i=1:N %loop over number of timesteps to update then run euler
t=trange(1)+i*dt;
X=X0;
%V=velvar(t,f);
% [~,V]=lengthvar(t,f);
[F1,~,~,~,~]=DM_funcs_1(t,R);
[F2,~,~,~,~]=DM_funcs_1(t+(dt/2),R+(dt/2)*F1);
[F3,~,~,~,~]=DM_funcs_1(t+(dt/2),R+(dt/2)*F2);
[F4,q1,q2,p1,p2]=DM_funcs_1(t+dt,R+(dt*F3));
Rnew = R + (dt/6)*(F1+(2*F2)+(2*F3)+F4);
R=Rnew;
% A rebuild of the distribution approximation for
n1=(R(1)/((sqrt(2*pi))*q1)).*exp(-((X-p1).^(2))/(2*(q1.^(2))));
n2=(R(4)/((sqrt(2*pi))*q2)).*exp(-((X-p2).^(2))/(2*(q2.^(2))));
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);
force(i)=R(2)+R(5);
stiffness(i)=R(1)+R(4);
nMpave(i)=nmp(i);
nAmpave(i)=R(1);
phosphorylation(i)=(nMpave(i)+nAmpave(i));
end
