- Author:
- aram148 <42922407+aram148@users.noreply.github.com>
- Date:
- 2022-07-26 11:49:42+12:00
- Desc:
- updated documentation and renamed model
- Permanent Source URI:
- https://models.fieldml.org/workspace/7e5/rawfile/30e6db7fb82a9bb715b0121cdfc131c19e5cb2ff/Peripheral_matlab_dell_updated/generalised_model/seven_airway2.m
% A function that solves the 7 coupled airway BG model
function [U,UVDOT,VVDOT] = seven_airway2(t,y,order,parm)
numBr = 2^order - 1;
r = y(1:numBr);
uv = y(numBr+1: 2*numBr)';
vv = y(2*numBr+1:3*numBr)';
vds = y(3*numBr+1:(end))';
% r1 = [y(1) y(2) y(3) y(4) y(5) y(6) y(7)];
% uv1 = [y(8) y(9) y(10) y(11) y(12) y(13) y(14)];
% vv1 = [y(15) y(16) y(17) y(18) y(19) y(20) y(21)];
% vds1 =[y(22) y(23) y(24) y(25)];
%% Construct the constant array as a persistent variable
% So that repeated calls to this function doesn't result in repeated
% calculations of C
persistent C
if isempty(C)
fprintf('Constructing the structure array of constants...\n');
C = createConstSymm(order);
fprintf('Finished.\n');
end
%% Parameters for MoC model
rho=2;
%% Define the constants
f = 0.33;
A = 5e5; % Used to be 5e5;
Pref = 10+ 10*sin(2*pi*f*t);
% Rref = 0.2792;
Rref=0.4140;
ptop = Pref;
kappa = parm(1,:);
% epsilon = 10^(parm(2,:)); % A parameter that controls sliding between Type II and Type I + II
epsilon = 0;
qhat = -50;
N = 2^order - 1; % number of branches for symmetric trees
numOrd1 = (N+1)/2;
E1 = 0.25;
%% Setting up BG parameters
E = 25;
h1 = 0.9732;
rho1 = 1.225;
R = zeros(N,1);
Rv = zeros(N,1);
CC = zeros(N,1);
I = zeros(N,1);
pa_bar = zeros(N,1);
alph = zeros(N,1);
pbot = zeros(N,1);
u=zeros(N,1);
for i=1:N
air_ord = C.order(i);
CC(i) = (2*pi*C.L(air_ord).*r(i).^3)/(E*h1);
I(i) = rho1*C.L(air_ord)/(pi.*r(i).^2);
R(i) = C.alpha(air_ord).*r(i).^(-4);
Rv(i) = 0.01/CC(i);
pa_bar(i) = (10*E1)./sqrt(E1.^2 + (2*pi*f*R(i)).^2);
alph(i) = atan((2*pi*f*R(i))./E1);
pbot(i) = 10+pa_bar(i)*sin(2*pi*f*t-alph(i));
end
%%
for a = numOrd1+1:N
uv(a) = (vv(a)-vv(2*(a-numOrd1))-vv(2*(a-numOrd1)-1))/CC(a);
u(a) = uv(a) +Rv(a)*((2*(a-numOrd1))-vv(2*(a-numOrd1)-1));
end
for b = 1:numOrd1
uv(b) = (vv(b)-vds(b))/CC(b);
u(b) = uv(b) + Rv(b)*(vv(b)-vds(b));
vds(b) = (uv(b)-pbot(b)-(R(b)/2)*vds(b))/(I(b)/2);
end
for d = 1:N-1
a(d) =((2*d) - 1);
aa = a(a<N-1);
b(d) = 2*d;
bb = b(b<=N-1);
end
% for i = 1: length(aa)
% % if (aa(i)) <=numBr && bb(i) <=numBr
% vv(aa(i)) = (uv(numOrd1+i) - u(aa(i)) - (R(aa(i))*vv(aa(i)))/2)./(I(aa(i))/2);
% vv(bb(i)) = (uv(numOrd1+i) - u(bb(i)) - (R(bb(i))*vv(bb(i)))/2)./(I(bb(i))/2);
% % elseif (aa(i)) > numBr && bb(i) > numBr
% % vv(aa(i)) = (uv(numOrd1+i) - u(aa(i)) - (R(aa(i))*vv(aa(i))))./(I(aa(i)));
% % vv(bb(i)) = (uv(numOrd1+i) - u(bb(i)) - (R(bb(i))*vv(bb(i))))./(I(bb(i)));
% % end
% end
% vv(N) = (Pref - u(N) - R(N)*vv(N))/I(N);
%% Set up uv1 - uv7
% uv(1) = (vv(1)-vds(1))/CC(1);
% u(1) = uv(1)+Rv(1)*(vv(1)-vds(1));
% uv(2) = (vv(2)-vds(2))/CC(2);
% u(2) = uv(2)+Rv(2)*(vv(2)-vds(2));
% uv(3) = (vv(3)-vds(3))/CC(3);
% u(3) = uv(3)+Rv(3)*(vv(3)-vds(3));
% uv(4) = (vv(4)-vds(4))/CC(4);
% u(4) = uv(4)+Rv(4)*(vv(4)-vds(4));
% uv(5) = (vv(5)-vv(2)-vv(1))/CC(5);
% u(5) = uv(5)+Rv(5)*(vv(5)-vv(2)-vv(1));
% uv(6) = (vv(6)-vv(4)-vv(3))/CC(6);
% u(6) = uv(6)+Rv(6)*(vv(6)-vv(4)-vv(3));
% uv(7) = (vv(7)-vv(6)-vv(5))/CC(5);
% u(7) = uv(7)+Rv(7)*(vv(7)-vv(6)-vv(5));
%% Set up v1 - v7
% vv(1) = (u(5) - u(1) - (vv(1)*R(1))/2)/(I(1)/2);
% vv(2) = (u(5) - u(2) - (vv(2)*R(2))/2)/(I(2)/2);
% vv(3) = (u(6) - u(3) - (vv(3)*R(3))/2)/(I(3)/2);
% vv(4) = (u(6) - u(4) - (vv(4)*R(4))/2)/(I(4)/2);
for i = 1: (numOrd1/2)
vv(aa(i)) = (u(numOrd1+i) - u(aa(i)) - (R(aa(i))*vv(aa(i)))/2)./(I(aa(i))/2);
vv(bb(i)) = (u(numOrd1+i) - u(bb(i)) - (R(bb(i))*vv(bb(i)))/2)./(I(bb(i))/2);
end
for i = (numOrd1/2)+1 : length(aa)
vv(aa(i)) = (u(numOrd1+i) - u(aa(i)) - (vv(aa(i))*R(aa(i))))/(I(aa(i)));
vv(bb(i)) = (u(numOrd1+i) - u(bb(i)) - (vv(bb(i))*R(bb(i))))/(I(bb(i)));
end
% vv(7) = (ptop - u(7) - (vv(7)*R(7)))/(I(7));
vv(N) = (Pref - u(N) - R(N)*vv(N))/I(N);
%% Set up vds1 - vds4
% vds(1) = (u(1)-pbot(1)-(R(1)/2)*vds(1))/(I(1)/2);
% vds(2) = (u(2)-pbot(2)-(R(2)/2)*vds(2))/(I(2)/2);
% vds(3) = (u(3)-pbot(3)-(R(3)/2)*vds(3))/(I(3)/2);
% vds(4) = (u(4)-pbot(4)-(R(4)/2)*vds(4))/(I(4)/2);
%% Determine what R is (airway radius)
RDOT=zeros(N,1);
%% Find expressions for the pressure and flows
Ci = C.Ciplus - C.Ciminus1 - C.Ciminus2;
% size(C.alpha.^(-1))
% size(r')
Dalphar = diag(C.alpha.^(-1).*r'.^4);
% size(Dalphar)
% return
W = Ci*Dalphar*(C.Cjplus - C.Cjminus);
lambda = dot(C.alpha.^(-1).*r'.^4, C.vbot);
temp = (W\(Ci*Dalphar*(C.vbot*C.vbot')*Dalphar*C.Cjplus))/lambda; %optimising code
Lambda = eye(size(temp)) - temp;
p = Lambda\(W\(Ci*Dalphar*(-ptop*C.vtop - 1/lambda*qhat*C.vbot))); %optimising code
gammajplus = C.Cjplus*p + ptop.*C.vtop;
gammajminus = C.Cjminus*p + pbot.*C.vbot;
deltap = gammajplus - gammajminus;
%
T = C.T; % The transformation matrix that will map mu_hat to mu
%
% %% Determine what mu is (parenchymal shear modulus)
%
mu = zeros(N,1);
%
for i = 1:numOrd1 % Wanting to loop through only the order 1 airways
% Add the Type 1 coupling by putting in the dependence on the
% neighbours.
if i == 1
mu(i) = abs(A/3*(deltap(i)*r(i)^4 + epsilon*(deltap(numOrd1)*r(numOrd1)^4 + deltap(i+1)*r(i+1)^4)))/2;
elseif i == numOrd1
mu(i) = abs(A/3*(deltap(i)*r(i)^4 + epsilon*(deltap(i-1)*r(i-1)^4 + deltap(1)*r(1)^4)))/2;
else
mu(i) = abs(A/3*(deltap(i)*r(i)^4 + epsilon*(deltap(i-1)*r(i-1)^4 + deltap(i+1)*r(i+1)^4)))/2;
end
end
%
% % Use the transformation matrix, T, to create the full mu vector
mu = T*mu;
%
% %% Determine what tau is (parenchymal tethering pressure)
tau = 2*mu.*(((Rref - r')/Rref) + 1.5*((Rref - r')/Rref).^2);
%
% %% Determine what Ptm is (transmural pressure)
%
%
pmid = 0.5*(gammajplus + gammajminus);
Ptm = zeros(N,1);
for i=1:N
air_ord = C.order(i); % Determine the order of the current airway
Ptm(i) = pmid(i) - (kappa*Rref/r(i))+ tau(i);
if Ptm(i) <= 0
R(i) = sqrt((C.Ri(air_ord).^2)*(1 - Ptm(i)./C.P1(air_ord)).^(-C.n1(air_ord)));
elseif Ptm(i) >= 0
R(i) = sqrt(C.rimax(air_ord).^2 - (C.rimax(air_ord).^2 - C.Ri(air_ord).^2)*(1 - Ptm(i)/C.P2(air_ord)).^(-C.n2(air_ord)));
end
RDOT=rho*((R)-r');
end
RRDOT=RDOT';
% size(RRDOT)
UVDOT = uv';
% size(UVDOT)
VVDOT = vv';
% size(VVDOT)
VDSDOT = vds';
% size(VDSDOT)
% NN = [RRDOT;UVDOT;VVDOT;VDSDOT];
U=u';
