% The function hlu_init_cond.m computes the initial values of the % heart-lung unit. 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] = hlu_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(2)*th(23) + th(1)*th(23); b = [temp+th(6)*th(23)-th(5)*th(23); temp+(Ts/th(15))*th(29); temp-(Td/th(17))*th(30); temp; temp; temp]; A = [th(1), -th(2), -th(5), th(6), 0, 0; th(1)+(Ts/th(15)), -th(2), 0, 0, 0, 0; th(1), -th(2), 0, -Td/th(17), 0, 0; th(1), -th(2), Ts/th(18), 0, -Ts/th(18), 0; th(1), -th(2), 0, 0, 1/(th(22)*th(19)), -1/(th(22)*th(19)); th(1), -(th(2)+Td/th(20)), 0, 0, 0, Td/th(20)]; x = A\b; P = [x(2), th(29), th(30), x(4:6)']'; % 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) > P(2)) q(2) = (P(1)-P(2))/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) > P(5)) q(5) = (P(4)-P(5))/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)]; Q(2) = 0; Q(3) = 0; 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