%% CREATED: JUNE 2009 by ARC
%This code represents the ladder model for perfusion over an acinus
%starting at the level below the arteries/veins accompanying the  transitional bronchiole.
%% NB - THE ACINUS IS DEFINED TO BE ALL GENERATIONS THAT HAVE
%% ALVEOLARISATION _ THIS INCLUDES THE TRANSITIONAL BRONCHIOLE THIS CODE DOES NOT INCLUDE THE TRASITIONAL
%% BRONCHIOLE WHICH IS ASSUMED TO HAVE INSIGNIFICANT ALVEOLARISATION
%
%% --------------INPUT-----------------------------
%% Pin -
%Pressure out of the artery accompanying the transitional bronchiole
%% Pout - 
%Pressure into the vein accompanying the transitional bronchiole 
%% -----------OUTPUT------------------------------
%% GUESS_NEW - 
%Pressure and flow solutions throughout the acinus
%% R_CAP_NEW - 
%Resistance across an individual capillary sheet in each
% acinar generation
%% TT_CAP_NEW -
%RBC Transit times across capillary sheets in each acinar generation
%% ---------------------------------------------------------------------
function [GUESS_NEW,R_CAP_NEW,TT_CAP_NEW]=FCM_NEW_ART_CAP_VEN(Pin_acin,Pout_acin,Parameters,Parameters2)
%% --------------INITIAL GUESS FOR SOLUTIONS ---------------------------
%PRESSURES and flows.Solution is independent of (reasonably physiological) initial conditions
GUESS=[1000; 1000; 100; 100];
for gen=2:Parameters.num_symm_gen-1
  GUESS=[GUESS; 1000; 1000; 100; 100]; %GUESS PRESSURES
end
GUESS=[GUESS;0.1;0.1;0.1];
for gen=2:Parameters.num_symm_gen-1
  GUESS=[GUESS; 0.1]; %GUESS FLOWS
end   
%% ---------------INITIALISE ITERATIONS----------------------------
%INITIALISE ITERATIONS
it=0;
%INITIALISE SOLUTION MATRIX SOLMAT=A, SOL_VEC=B, SOLVE A\B for pressures,
%capillary flows and total flow through system
matrixsize=5*Parameters.num_symm_gen-3;
submatrixsize=4*Parameters.num_symm_gen-4;
SOL_MAT=zeros(matrixsize,matrixsize); %DELTA P=QR + continuity of flow = 5N-3 equations
SOL_VEC=zeros(matrixsize,1);
%BOUNDARY CONDITIONS (PRESSURE BCs)
    SOL_VEC(1)=-Pin_acin;
    SOL_VEC(3)=Pout_acin;
%ELEMENTS OF THE SOLUTION MATRIX THAT ARE INDEPENDENT OF THE ITERATION
for gen=1:Parameters.num_symm_gen-1
    if gen==1
        %FIRST GENERATION NON CAPILLARY VESSELS delta p=QR
        SOL_MAT(1,1)=-1;SOL_MAT(2,2)=-1;SOL_MAT(3,3)=1;SOL_MAT(4,4)=1;SOL_MAT(2,1)=1;SOL_MAT(4,3)=-1;
        % FLOW CONSERVATION  %Q=2Qcap1+2Qcap2+...2^NQ_capN
        SOL_MAT(matrixsize,matrixsize)=1; %Q
        %Qcap1 and Qcap2 (do for gen above)
        SOL_MAT(matrixsize,submatrixsize+1)=-2; SOL_MAT(matrixsize,submatrixsize+2)=-2^2;
        %CONNECTIONS VIA CAPILLARIES delta p=QR
        SOL_MAT(submatrixsize+gen,1)=1;SOL_MAT(submatrixsize+gen,3)=-1; 
        if Parameters.num_symm_gen==2
            %ADDING TERMINAL SHEETS FOR N=2
            SOL_MAT(matrixsize-1,submatrixsize)=-1; SOL_MAT(matrixsize-1,submatrixsize-2)=1;
        end
    elseif gen==Parameters.num_symm_gen-1
        %FINAL GENERATION BEFORE THE TERMINAL SHEETS 
        %NON_CAPILLARY VESSELS delta p=QR
        SOL_MAT(submatrixsize-3,submatrixsize-3)=-1;SOL_MAT(submatrixsize-2,submatrixsize-2)=-1;SOL_MAT(submatrixsize-1,submatrixsize-1)=1;SOL_MAT(submatrixsize,submatrixsize)=1;
        SOL_MAT(submatrixsize-2,submatrixsize-3)=1;SOL_MAT(submatrixsize,submatrixsize-1)=-1;
        %join to previous generation delta p=QR
        SOL_MAT(submatrixsize-3,submatrixsize-6)=1;SOL_MAT(submatrixsize-1,submatrixsize-4)=-1;
        %FLOW CONSERVATION%Q=Qcap1+2Qcap2+...2^NQ_capN (this is for final
        %gen)
        SOL_MAT(matrixsize,submatrixsize+gen+1)=-2^(gen+1);
        %CONNECTIONS VIA CAPILLARIES delta p=QR
        SOL_MAT(submatrixsize+gen,submatrixsize-3)=1;SOL_MAT(submatrixsize+gen,submatrixsize-1)=-1; SOL_MAT(matrixsize-1,submatrixsize)=-1; SOL_MAT(matrixsize-1,submatrixsize-2)=1;
    else
        %INTERMEDIATE GENERATIONS
        %NON_CAPILLARY VESSELS delta p=QR
        SOL_MAT(4*gen-3,4*gen-3)=-1;SOL_MAT(4*gen-2,4*gen-2)=-1;SOL_MAT(4*gen-1,4*gen-1)=1;SOL_MAT(4*gen,4*gen)=1;
        SOL_MAT(4*gen-2,4*gen-3)=1;SOL_MAT(4*gen,4*gen-1)=-1;
        %JOIN TO PREVIOUS GENERATIONS delta p=QR
        SOL_MAT(4*gen-3,4*gen-6)=1;SOL_MAT(4*gen-1,4*gen-4)=-1;
        %FLOW CONSERVATION Q=Qcap1+2Qcap2+...2^(N-1)Q_capN (this is for gen
        %above)
        SOL_MAT(matrixsize,submatrixsize+gen+1)=-2^(gen+1);
        %CONNECTIONS VIA CAPILLARIES delta p=QR
        SOL_MAT(submatrixsize+gen,4*gen-3)=1;SOL_MAT(submatrixsize+gen,4*gen-1)=-1;
    end
end
%% START OF ITERATIVE LOOP
err=100;
it=0;
while (abs(err)>1e-15)&it<=100
        clear R_art R_ven rad_update 
        it=it+1;%COUNT ITERATIONS   
        Q=GUESS(matrixsize); %UPDATE TOTAL FLOW
    for gen=1:Parameters.num_symm_gen-1
        %FIRST HALF OF ARTERIOLE
        %Update radius of arteriole based on inlet pressure
        if (GUESS(4*gen-3)-Parameters.Palv)<=Parameters.Pub_a_v
            radupdate(gen,1)=Parameters2.rad_a(gen)*(1+(GUESS(4*gen-3)-Parameters.Palv)*Parameters.alpha_a);
        else
            radupdate(gen,1)=Parameters2.rad_a(gen)*(1+Parameters.Pub_a_v*Parameters.alpha_a);
        end
        %Calculate Poiseuille resistance in first half of arteriole - (only
        %half total generation length)
        R_art(gen,1)=(8*Parameters2.mu_app(gen)*Parameters2.L_a(gen)/2)/(pi*radupdate(gen,1)^4);
        %update solution matrix - delta p =FLOW R - As there is one vessel
        %generation 1 FLOW=Q, generation 2 FLOW =(Q-Qcap1)/2 this updates
        %the Q term in each (dividing by 2^(gen-1) - capillary terms are
        %updated below...
        SOL_MAT(4*gen-3,matrixsize)=-R_art(gen,1)/2^gen; 
        %FIRST HALF OF VENULE        
        %Update radius of venule based on inlet pressure NB: May need to
        %update this later to give an average of inlet and outlet radii
        if (GUESS(4*gen-1)-Parameters.Palv)<=Parameters.Pub_a_v
            radupdate(gen,1)=Parameters2.rad_v(gen)*(1+(GUESS(4*gen-1)-Parameters.Palv)*Parameters.alpha_v);
        else
            radupdate(gen,1)=Parameters2.rad_v(gen)*(1+Parameters.Pub_a_v*Parameters.alpha_v);
        end
        %Calculate Poiseuille resistance in first half of venule
        R_ven(gen,1)=(8*Parameters2.mu_app(gen)*Parameters2.L_v(gen)/2)/(pi*radupdate(gen,1)^4);
        %update soln matrix - capillary terms updated below
        SOL_MAT(4*gen-1,matrixsize)=-R_ven(gen,1)/2^gen;
        %CAPILLARY ELEMENT (arteriole + venule + capillary)
        %the input sheet number is the total number of sheets in an acinus -
        sheet_number=num;
        %pressure into the capillaries
        Pin_cap=GUESS(4*gen-3);
        %pressure out
        Pout_cap=GUESS(4*gen-1);
        %calulate resistance and transit time through a single capillary
        [R_cap,TT]=CAP_FUNCTION(Pin_cap,Pout_cap,sheet_number,Parameters);
        %update resistance flow and TT in a single capillary
        TT_cap(gen)=TT;
        Q_cap(gen)=(Pin_cap-Pout_cap)/R_cap;
        Rcap(gen)=R_cap;
        % Update soln matrix (delta p=QR across a cap)
        SOL_MAT(submatrixsize+gen,submatrixsize+gen)=-R_cap;
        Qsheets(gen)=2^(gen-1)*Q_cap(gen);
        %SECOND HALF OF ARTERIOLE
        %Update radius of arteriole based on inlet pressure 
        if (GUESS(4*gen-2)-Parameters.Palv)<=Parameters.Pub_a_v
            radupdate(gen,2)=Parameters2.rad_a(gen)*(1+(GUESS(4*gen-2)-Parameters.Palv)*Parameters.alpha_a);
        else
            radupdate(gen,2)=Parameters2.rad_a(gen)*(1+Parameters.Pub_a_v*Parameters.alpha_a);
        end
        %Calculate Poiseuille resistance in second half of arteriole - (only
        %half total generation length)
        R_art(gen,2)=(8*Parameters2.mu_app(gen)*Parameters2.L_a(gen)/2)/(pi*radupdate(gen,2)^4);
        %update soln matrix - capillary terms updated below
        SOL_MAT(4*gen-2,matrixsize)=-R_art(gen,2)/2^gen;
        SOL_MAT(4*gen-2,submatrixsize+gen)=R_art(gen,2);
        %% SECOND HALF OF VENULE
        % Update radius - linear with pressure or constant at high pressure
        if (GUESS(4*gen)-Parameters.Palv)<=Parameters.Pub_a_v
            radupdate(gen,2)=Parameters2.rad_v(gen)*(1+(GUESS(4*gen)-Parameters.Palv)*Parameters.alpha_v);
        else
            radupdate(gen,2)=Parameters2.rad_v(gen)*(1+Parameters.Pub_a_v*Parameters.alpha_v);
        end
        %Poiseuille resistance in second half of venule
        R_ven(gen,2)=(8*Parameters2.mu_app(gen)*Parameters2.L_v(gen)/2)/(pi*radupdate(gen,2)^4);
        %update soln matrix - capillary terms updated below
        SOL_MAT(4*gen,matrixsize)=-R_ven(gen,2)/2^gen;
        SOL_MAT(4*gen,submatrixsize+gen)=R_ven(gen,2);
        for i=2:12 %Fill in gaps in solution matrix
            if gen>=i
                SOL_MAT(4*gen-3,submatrixsize+(i-1))=R_art(gen,1)/2^(gen-(i-1));
                SOL_MAT(4*gen-2,submatrixsize+(i-1))=R_art(gen,2)/2^(gen-(i-1));
                SOL_MAT(4*gen-1,submatrixsize+(i-1))=R_ven(gen,1)/2^(gen-(i-1));     
                SOL_MAT(4*gen,submatrixsize+(i-1))=R_ven(gen,2)/2^(gen-(i-1));
             end
        end
    end
%% ------------FINAL GENERATION----------------------------
%% --------The capillaries covering the alveolar sacs---------
%These are just capillary beds without an associated arteriole/venule - the
%9th generation airways in the acinus are completely alveolarised.
    %the input sheet number is the total number of sheets in an acinus -
    sheet_number=num;%
    Pin_cap=GUESS(4*Parameters.num_symm_gen-6); %pressure into final capillary sheets
    Pout_cap=GUESS(4*Parameters.num_symm_gen-4); %pressure out of final capillary sheets
    [R_cap,TT]=CAP_FUNCTION(Pin_cap,Pout_cap,sheet_number,Parameters); %caculate resistance and transit time in a single sheet using CAP_FUNCTION
    TT_cap(Parameters.num_symm_gen)=TT; %TT in the final sheets
    Q_cap(Parameters.num_symm_gen)=(Pin_cap-Pout_cap)/(R_cap);%flow through an indiviual cappillary sheet
    Rcap(Parameters.num_symm_gen)=R_cap;%resistance in each sheet of final generation
    SOL_MAT(matrixsize-1,matrixsize-1)=-R_cap; %update resistace in solution matrix
    Qsheets(Parameters.num_symm_gen)=2^Parameters.num_symm_gen*Q_cap(Parameters.num_symm_gen);%flow through all the sheets in the final generation
    %%  -----SOLVE SYSTEM-----------------------------------
    GUESS2=SOL_MAT\SOL_VEC;
    err=max(abs((GUESS-GUESS2)./(GUESS2)));%calculate maximum difference between successive iteraions
    GUESS=GUESS2;%update solution
%% END OF ITERATIVE LOOP
end
%% ---FUNCTION OUTPUT
GUESS_NEW=GUESS; 
R_CAP_NEW=Rcap;
TT_CAP_NEW=TT_cap;