% Understanding the behaviour of systems pharmacology
% models: mathematical analysis of differential equations
% Suruchi Bakshi, Elizabeth C. de Lange, Piet H. van der Graaf, Meindert
% Danhof, and Lambertus A. Peletier


% Run the pool model with PF with a PK model of SC dosing from Kozielska et
% al 2012. Generates figure 8 in the manuscript

% This file needs pool_pf_odes.m OR pool_pf_odes_wo_if_condition.m to run

clear all
clc
close all

global ks kel kr ec50_de emax_de ec50_prl emax_prl bsl k_a Cl V1 V2 Cl12

% PD parameters
ks = 35.7;
kr = 0.57;
kel = 5.72;
ec50_prl = 12.4;
emax_prl = 3.47;
ec50_de = 0.08;
emax_de = 25;
bsl = ks/kel;

% PK parameters
k_a = 2.84;
Cl = 1.62;
V1 = 1.29;
Cl12 = 0.0882;
V2 = 0.169;

dose = [0.05; 0.1; 1; 2]; % Select various doses

% Initial conditions
cpl_ss = bsl; % the second steady state is = bsl + bsl*emax_prl - ec50_prl;
cla_ss = ks/kr; % ks/kr + ks*emax_prl/kr - ec50_prl*kel/kr;

% Mesh points for drawing nullclines
v_mesh = 0:0.01:5;
u_mesh = 0:1:10;

% Nullclines
% R_null = (kr/kel).*(P_mesh);
% P_null = (ks/kr).*(1+ emax_prl.*(R_mesh-bsl)./(ec50_prl + R_mesh-bsl));
beta = emax_prl;
gamma = ec50_prl/cpl_ss;
v_null = u_mesh;
u_null = 1 + beta*(v_mesh-1)./(gamma + v_mesh-1);

a0 = dose;
b0 = 0;
c0 = 0;

tspan = 40;

figure(1);
figure(1);subplot(1,2,1); set(gca,'Fontsize',16);hold all;
figure(1);subplot(1,2,2); set(gca,'Fontsize',16);hold all;
figure(2);set(gca,'Fontsize',16);hold all;
figure(3);set(gca,'Fontsize',16);hold all;
figure(4);set(gca,'Fontsize',16);hold all;
%plot(u_null,v_mesh,':k','Linewidth',2); % P nullcline no if
plot(u_null(find(u_null==1):end),v_mesh(find(v_mesh==1):end),':k','Linewidth',2); % P nullcline with if
plot(u_mesh,v_null,'--k','Linewidth',2); % R nullcline

for i = 1:length(dose)
    % Solve the PK/PD model
    y0 = [a0(i); b0; c0; cla_ss+0.01;cpl_ss+0.01]; % starting a simulation at a value slightly greater than baseline steady state
    options = odeset('RelTol',1e-4,'AbsTol',1e-6);
    [t,y] = ode15s(@pool_pf_odes,[0 tspan],y0',options); % Use @pool_pf_odes to get the results for the model with the if condition
    % Plotting results
    figure(1);subplot(1,2,1); plot(t,y(:,4)./cla_ss,'Linewidth',2); % Plots lactotroph PRL vs time
    figure(1);subplot(1,2,2); plot(t,y(:,5)./cpl_ss,'Linewidth',2); % Plots plasma PRL vs time
    figure(2); plot(t,y(:,5)./cpl_ss,'Linewidth',2); % Plots plasma PRL vs time
    figure(3); plot(t,y(:,2)./V1,'Linewidth',2); % Plots drug PK vs time
    figure(4); plot(y(:,4)./cla_ss,y(:,5)./cpl_ss,'Linewidth',2);
end
figure(1);subplot(1,2,1); ylabel('Lactotroph PRL \rm{[ng/ml]}'); xlabel('Time [hr]');legend('0.05','0.1','1','2');
figure(1);subplot(1,2,2); ylabel('Plasma PRL \rm{[ng/ml]}'); xlabel('Time [hr]');legend('0.05','0.1','1','2');

figure(2);ylabel('\it{v}'); xlabel('t');legend('0.05 mg/kg','0.1 mg/kg','1 mg/kg','2 mg/kg');
figure(3);ylabel('Drug plasma PK \rm{[ng/ml]}'); xlabel('Time [hr]');legend('0.05 mg/kg','0.1 mg/kg','1 mg/kg','2 mg/kg');
figure(3); xlim([0 10]);
figure(4); xlim([0 3]); ylim([0 7]); xlabel('\it{u}'); ylabel('\it{v}'); legend('u nullcline','v nullcline','0.05 mg/kg','0.1 mg/kg','1 mg/kg','2 mg/kg');
figure(4); line([0 3],[1 1]);
figure(4); line([1 1],[0 1]);