- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-10-11 21:47:30+13:00
- Desc:
- Peripheral airway pseudo-BG
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/6b0/rawfile/55efde1e181fb28eb5ec12c06d40e63dfe2ca938/USMC/Maggio2012/ftu_fns.m
function [odes,Ptm,Plumen,Paw] = ftu_fns(t,R)
M=R(1); AM=R(2); Mp=R(3); AMp=R(4);
r=R(5); PA=R(6); VA=R(7); fo=R(8);
fc=R(9);po=R(10); pc=R(11); z=R(12);
dPtau=R(13);
k2 = 0.5; %s^-1
k7 = 0.01; %s^-1
k3 = 0.4; %s^-1
k4 = 0.1; %s^-1
k5 = 0.5; %s^-1
% Ri_sq = 0.0174; %mm^2
Ri_sq = 0.000174; %cm^2
% rmax_sq = 0.1980; %mm^2 %
rmax_sq = 0.00198; %cm^2;
N1 = 1; %dimensionless
N2 = 8; %dimensionless
% P1 = 0.295768328; %mmHg
P1 = 0.40209999959928; %cmH2O
% P2 = -24.52310023; %mmHg
P2 = -33.339399993687; %cmH2O
rho = 1; %dimensionless
% rmax = 0.4450; %mm
rmax = 0.04450; %cm^2
P0 = 10; %cmH20
f = 0.25; %s^-1
% Pmin = 10;
% PL = 2;
kappa = 1; %dimensionless
aa = 10.19716213; % Conversion factor for kg*(mm)^(-1)*(s)^(-2) to cmH20
moo = 1.9008e-8; % dynamic viscosity kg(mm)^(-1)s^(-1)
% E = 186; %mmHg/ml
E = 252.8688649029042; %cmH2O/ml
% L = 2.6;
% Do = 0.0000156; %mols^(-1)mmHg^(-1)
Do = 1.1475e-05; %mols^(-1)cmH2O(-1)
% Dc = 0.0000316; %mols^(-1)mmHg^(-1)
Dc = 2.3244e-05; %mols^(-1)cmH2O(-1)
fom = 0.21; %dimensionless
fcm = 0; %dimensionless
% VD = 0.151; %litres
VD = 151; %ml
% VT = 0.41; %litres
VT = 410; %ml
% L = 2.6; %mm
L = 0.26; %cm
KT = 10000; %dimensionless
Kc = 3600000; %dimensionless
% sigma = 0.0000014; %mol L^-1 mmHg
sigma = 1.9033e-06; %mol L^-1 cmH2O
% Vc = 0.071; %litre
Vc = 71; %ml
Th = 2e-6; %mol l^-1
l2 = 164000; %dimensionless
r2 = 0.12; %s^-1
% sigmac = 0.000033; %mol l^-1 mmHg
sigmac = 4.4864e-05; %mol L^-1 cmH2O
% z = 0.00000044219; %dimensionless
delta = 10^1.9; %dimensionless
hin = 1.00000.*1^-9; %dimensionless
% A=5e5;
%
% mu = abs(A/(3*r.^4))/2;
%
Paw = P0.* sin( 2.00000.* pi.*f.*t);
k1=0.35.*(t<5)+0.06.*(t>=5);
k6=k1;
df_satdp = ( ( L.*power(1.00000+ KT.*sigma.*po, 4.00000)+power(1.00000+ Kc.*sigma.*po, 4.00000)).*( 3.00000.*L.*power(KT, 2.00000).*power(sigma, 2.00000).*po.*1.00000.*power(1.00000+ KT.*sigma.*po, 2.00000)+ L.*KT.*sigma.*1.00000.*power(1.00000+ KT.*sigma.*po, 3.00000)+ 3.00000.*power(Kc, 2.00000).*power(sigma, 2.00000).*po.*1.00000.*power(1.00000+ Kc.*sigma.*po, 2.00000)+ Kc.*sigma.*1.00000.*power(1.00000+ Kc.*sigma.*po, 3.00000)) - ( L.*KT.*sigma.*po.*power(1.00000+ KT.*sigma.*po, 3.00000)+ Kc.*sigma.*po.*power(1.00000+ Kc.*sigma.*po, 3.00000)).*( 4.00000.*L.*KT.*sigma.*1.00000.*power(1.00000+ KT.*sigma.*po, 3.00000)+ 4.00000.*Kc.*sigma.*1.00000.*power(1.00000+ Kc.*sigma.*po, 3.00000)))./power( L.*power(1.00000+ KT.*sigma.*po, 4.00000)+power(1.00000+ Kc.*sigma.*po, 4.00000), 2.00000);
% v = 0.200000+ 0.00400000.*PA;
% x = 1.00000 - r./power(v, 0.330000);
% Ptau = 2*mu*(PA+ PA.*( 1.40000.*x+ 2.10000.*power(x, 2.00000)));
% Ptau = 2*mu.*((rmax - r)/rmax + 1.5*((rmax - r)/rmax).^2);
Raw = ( 8.00000.*aa.*L.*moo)./( pi.*power(r, 4.00000));
Ptau = P0 -(0.5.*Raw.*f.*VT).*sin(f.*t)-E.*(2.5-0.5.*VT.*cos(f.*t));
Pab = ( P0.*E)./power((power(E, 2.00000)+power( 2.00000.* pi.*f.*Raw, 2.00000)), 1.0 ./ 2);
stress = AMp+AM;
fL = power( sin( (( pi.*r)./2.00000).*rmax), 3.00000);
Plumen = (Paw+PA)./2.00000;
Ptm = (Plumen - ( fL*kappa.*stress)./r)+Ptau;
pac = fc.*(PA - Paw);
q = (Pab - PA)./Raw;
pao = fo.*(PA - Paw);
QA = q+ 1.00000.*Dc.*(pc - pac)+ 1.00000.*Do.*(po - pao);
% phos = AMp+Mp;
% alpha = atan(( 2.00000.* pi.*f.*t.*Raw)./E);
% P0 = Plumen - PA;
if Ptm<=0
% a=a0(s).*(1-(Ptm./P1)).^(-N1(s));
rad=sqrt(Ri_sq*(1-(Ptm/P1)).^-N1);
elseif Ptm>=0
% a=(1-((1-a0(s)).*(1-(Ptm./P2)).^(-N2(s))));
rad=sqrt(rmax_sq-(rmax_sq-Ri_sq)*(1-(Ptm/P2)).^-N2);
end
% radius=rad;
if VT>=VD
foi=(fo.*VD+ fom.*(VT - VD))./VT;
elseif VT<VD
foi=fo;
end
if VT>=VD
fci=(fc.*VD+ fcm.*(VT - VD))./VT;
elseif VT<VD
fci=fc;
end
% dPtau = PA.*( 4.20000.*x.*dxdt+ 1.40000.*dxdt)+( Pab.*E.*QA)./( PA.*1.00000)+ dPtau.*( 1.40000.*x+ 2.10000.*(x).^2);
% = 2*mu*(-(3*(rmax-r)*rho*(rad-r))/rmax.^2-(rho*(rad-r)/rmax))
% dPtau = -0.5*Raw*f^2*VT*cos(f*t)-E*(2.5-0.5*VT*sin(f*t));
% dxdt = ((( 0.00132000.*r.*Pab.*E.*QA)./( PA.*1.00000)+dPtau)./( 0.00400000.*PA+0.200000).^1.33000 - rdot./( 0.00400000.*PA+0.200000).^0.330000);
% dPtau = 2*mu(-(3*(rmax-r)*rho*(rad-r))/rmax.^2-(rho*(rad-r)/rmax));
odes =[ - k1.*M+ k2.*Mp+ k7.*AM; k5.*AMp - (k6+k7).*AM; ( k4.*AMp+ k1.*M) - (k2+k3).*Mp; ( k3.*Mp+ k6.*AM) - (k5+k4).*AMp;
rho.*(rad - r); ( Pab.*E.*QA)./PA+ dPtau; ((Pab - Ptau) - VA.*E)./Raw; (1.00000./VA).*(( 1.00000.*Do.*(po - pao)+ (foi - fo).*q) - fo.*( 1.00000.*Dc.*(pc - pac)+ 1.00000.*Do.*(po - pao)));
(1.00000./VA).*(( 1.00000.*Dc.*(pc - pac)+ (fci - fc).*q) - fc.*( 1.00000.*Do.*(po - pao)+ 1.00000.*Dc.*(pc - pac)));
(Do./( sigma.*Vc)).*power(1.00000+ (( 4.00000.*Th)./sigma).*df_satdp, - 1.00000).*( fo.*(PA - Paw) - po);
( (Dc./( sigmac.*Vc)).*(pac - pc)+ (( 1.00000.*delta.*l2)./sigmac).*hin.*z) - delta.*r2.*pc;( delta.*r2.*sigmac.*pc)./1.00000 - delta.*l2.*hin.*z;
-0.5.*Raw.*f^2.*VT.*cos(f.*t)-E.*(2.5-0.5.*VT.*sin(f.*t))];
