%CREATED: JUNE 2009 by ARC
%This code is designed to implement Fung's sheet flow model for perfusion in the capillary bed.

%%-----------------------INPUT-------------------------
%The input to this function is inlet and outlet pressure for the system and the number of sheets in the acinus.

%%----------------------OUTPUT----------------------------
% This code outputs resistance and RBC transit times through the capillary sheet.

function [R_cap,TT]=CAP_FUNCTION(Pin_cap,Pout_cap,sheet_number,Parameters)
% Area of this particular sheet (=area of all sheets in acinus/no of sheets
% in acinus)
area_sheet=Parameters.area/sheet_number;

%---------------CAPILLARY --------
%  Parameters.Sheet flow model constant C
C=Parameters.S*area_sheet/(4*Parameters.mu_min*Parameters.K*Parameters.F*Parameters.L_cap^2*Parameters.alpha_S); 

%Blood pressure in and out of the capillary sheet
P_a=Pin_cap;        
P_v=Pout_cap;         
%Zone 2 (waterfall) scaling 
waterfall_scale=1-Parameters.F_sheet+Parameters.F_sheet*exp(-(P_v-Parameters.Palv)^2/(2*Parameters.sigma^2));

if ((P_a-Parameters.Palv)<Parameters.Plb) 
% Arteriole and venule pressure both less than alveolar pressure - the
% sheet is collapsed
    Hart=0;
    Hven=0;             
    Q_cap=1.e-12;%very small to prevent divide by zero errors
    RBC_tt=0; 
elseif  ((P_a-Parameters.Palv)<=Parameters.Pub)&&((P_v-Parameters.Palv)<=Parameters.Plb) 
    Hart=Parameters.H0+Parameters.alpha_S*(P_a-Parameters.Palv);
    Hven=Parameters.H0;
    Q_cap=C*(Hart^4-Parameters.H0^4);
    Q_cap=Q_cap*waterfall_scale;
    RBC_tt= (3*Parameters.mu_min*Parameters.F*Parameters.K*Parameters.L_cap^2*Parameters.alpha_S)/(Hart^3-Parameters.H0^3);
    RBC_tt=RBC_tt/waterfall_scale;
elseif ((P_a-Parameters.Palv)>Parameters.Pub)&&((P_v-Parameters.Palv)<=Parameters.Plb)
    Hart=Parameters.Hmax_art;
    Hven=Parameters.H0;
    Q_cap=4*C*Parameters.alpha_S*(Parameters.Hmax_art^3*(P_a-Parameters.Palv-Parameters.Pub)+(Parameters.Hmax_art^4-Parameters.H0^4)/(4*Parameters.alpha_S));
    Q_cap=Q_cap*waterfall_scale;
    RBC_tt=(3*Parameters.mu_min*Parameters.F*Parameters.K*Parameters.L_cap^2*Parameters.alpha_S)/(waterfall_scale*(3*Parameters.alpha_S*Parameters.Hmax_art^2*(P_a-Parameters.Palv-Parameters.Pub)+(Parameters.Hmax_art^3-Parameters.H0^3))); 
elseif ((P_a-Parameters.Palv)<=Parameters.Pub)&&((P_v-Parameters.Palv)<=Parameters.Pub)
	Hart=Parameters.H0+Parameters.alpha_S*(P_a-Parameters.Palv);
	Hven=Parameters.H0+Parameters.alpha_S*(P_v-Parameters.Palv);
	Q_cap=C*(Hart^4-Hven^4);
	RBC_tt=(3*Parameters.mu_min*Parameters.F*Parameters.K*Parameters.L_cap^2*Parameters.alpha_S)/(Hart^3-Hven^3);
elseif ((P_a-Parameters.Palv)>Parameters.Pub)&&((P_v-Parameters.Palv)<=Parameters.Pub)
    Hart=Parameters.Hmax_art;
    Hven=Parameters.H0+Parameters.alpha_S*(P_v-Parameters.Palv);
    Hub=Parameters.H0+Parameters.alpha_S*Parameters.Pub;
    Q_cap=Parameters.S*area_sheet*(Parameters.Hmax_art^3*(P_a-Parameters.Palv-Parameters.Pub)+(Hub^4-Hven^4)/(4*Parameters.alpha_S))/(Parameters.mu_min*Parameters.F*Parameters.K*Parameters.L_cap^2);
	RBC_tt=(3*Parameters.mu_min*Parameters.F*Parameters.K*Parameters.L_cap^2*Parameters.alpha_S)/(3*Parameters.alpha_S*Parameters.Hmax_art^2*(P_a-Parameters.Palv-Parameters.Pub)+(Parameters.Hmax_art^3-Hven^3));
elseif ((P_a-Parameters.Palv)>Parameters.Pub)&&((P_v-Parameters.Palv)>Parameters.Pub)
    Hart=Parameters.Hmax_art;
    Hven=Parameters.Hmax_vein;
    Q_cap=4*C*Parameters.alpha_S*Hart^3*(P_a-P_v);
    RBC_tt=(Parameters.mu_min*Parameters.F*Parameters.K*Parameters.L_cap^2)/(Hart^2*(P_a-P_v));
else
    %code should not enter here!
    Q_cap=1e-12;
    RBC_tt=0;
end
%C...   RBC transit time (1.4 times faster than blood)
       RBC_tt=RBC_tt/1.4;

%C...  Resistance through a single capillary sheet, Pa.s/m^3
R_cap=(Pin_cap-Pout_cap)/Q_cap;
%RBC TT
TT=RBC_tt;