% The function sc_init_cond.m computes the initial values of the % systemic circulation. The initial values are computed based % on conservation laws of a linearized model. % % Function arguments: % th - vector containing the initial parameter values % % Function outputs: % P - a 6x1 vector containing the six initial pressures % = [Pl(0); Pa(0); Pv(0); Pr(0); Ppa(0); Ppv(0)] % Q - a 6x1 vector containing the six initial volumes % = [Ql(0); Qa(0); Qv(0); Qr(0); Qpa(0); Qpv(0)] % q - a 6x1 vector containing the six initial flow rates % = [qpv(0); ql(0); qa(0); qv(0); qr(0); qpa(0)] % ve - a 2x1 vector containing the initial variable elastance values % = [El(0); Er(0)]; % function [P,Q,q,ve] = sc_init_cond(th) % Storing nonlinear ventricular compliance values for % subsequent initial ventricular volume calculation. Cld = th(2); Crd = th(6); % Converting ventricular compliances to linear values which % is necessary for estimating initial pressures. th(1) = th(1)*((th(26)-th(9))/th(31)); th(2) = th(2)*((th(26)-th(9))/th(31)); th(5) = th(5)*((th(27)-th(12))/th(32)); th(6) = th(6)*((th(27)-th(12))/th(32)); % Estimating initial pressures. Ts = .3*sqrt(1/th(22)); Td = 1/th(22) - Ts; temp = -th(6)*th(23) + th(5)*th(23); b = [temp+(Ts*th(28)/th(18)); temp; temp; th(33)*(th(3)+th(4))]; A = [0, 0, (Ts/th(18))+th(5), -th(6); 0, Td/th(17), th(5), (-(Td/th(17))-th(6)); 1/(th(22)*th(16)), -1/(th(22)*th(16)), th(5), -th(6); th(3), th(4), 0, 0]; x = A\b; P = [th(33) x(1) x(2) x(4) th(33) th(33)]'; % Establishing initial flow rates. q = zeros(6,1); if (P(6) > P(1)) q(1) = (P(6)-P(1))/th(20); else q(1) = 0; end if (P(1) > th(33)) q(2) = (P(1)-th(33))/th(15); else q(2) = 0; end q(3) = (P(2)-P(3))/th(16); if (P(3) > P(4)) q(4) = (P(3)-P(4))/th(17); else q(4) = 0; end if (P(4) > th(28)) q(5) = (P(4)-th(28))/th(18); else q(5) = 0; end q(6) = (P(5)-P(6))/th(19); % Establishing initial variable ventricular elastance values. ve = [1/th(2) 1/th(6)]'; % Establishing initial volumes. Q = [th(2) th(3) th(4) th(6) th(7) th(8)]'.*(P-th(23)*[1 0 0 1 1 1]') + [th(9:14)]; if (P(1) <= th(23)) Q(1) = th(9)*(2/pi)*atan(((P(1)-th(23))/((2/pi)*th(9)*ve(1)))) + th(9); else yl = (P(1)-th(23))/th(31); xl = vent_vol(0.5,yl,1/Cld); Q(1) = (th(26)-th(9))*xl+th(9); end if (P(4) < th(23)) Q(4) = th(12)*(2/pi)*atan(((P(4)-th(23))/((2/pi)*th(12)*ve(2)))) + th(12); else yr = (P(4)-th(23))/th(32); xr = vent_vol(0.5,yr,1/Crd); Q(4) = (th(27)-th(12))*xr+th(12); end