# ODE 45 Solver Help

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Skye Cameron on 12 Apr 2021
Answered: Arthi Sathyamurthi on 26 May 2021
I had this code working previously and made a few adjustments and I can not work out how I should resolve this and get it working again, the code is in 2 separate files. The equation at the bottom of the first file (CsBEV) is what I added in and I need to plot it
First file is as follows
function diff=ode_sys_2equations(t,var)
y1=var(1);
y2=var(2);
y3=var(3);
y4=var(4);
% Parameters for DOX
Dose_DOX = (170/1000); % g/m^2/s check this
Tiv_DOX = 7200; % s
t_half_DOX = 1194.8; % s
kclr_DOX = log(2)/t_half_DOX; % 1/s
ke_DOX = 5.8E-4; % 1/s
Vdist_DOX = 0.00225; % m^3/kg
Mass = 85; % kg
P_DOX = 3.0E-6; % m/s
% Parameters for Bevacizumab
Dose_BV = (850/1000); % g/s for 7200s at 5mg/kg every 2 weeks
Tiv_BV = 7200; % s
t_half_BV = 1728000; % s (half life = 20 days for a male)
kclr_BV = log(2)/t_half_BV
ka_BV = 0; % 1/s *** NOT REQUIRED
Vdist_BV = 0.00329; % m3 or 4.7E-5 m3/kg for a 70kg male
Mass = 85; % kg
% Paramaters
alpha=-4.1E-6;
beta=1.22E-5;
gamma=-8.1E-6;
kak=5E-7;
r_tumour=0.03; % m
Vt=(4/3)*pi*r_tumour^3; % m^3
a=0.35; % Dimensionless (taken from table 1 - paramaters for brain tumour/normal tissue)
Ve=Vt*a; % m^3
s_v=20000; % m^-1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if 0<=t & t<=Tiv_DOX
Rin_DOX=1; % mg/kg *** CHECK THIS ***
elseif 86400<=t & t<=93600
Rin_DOX=1;
elseif 172800<=t & t<=180000
Rin_DOX=1
elseif 259200<=t & t<=266400
Rin_DOX=1
elseif 345600<=t & t<=352800
Rin_DOX=1
else
Rin_DOX=0
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if 0<=t && t<=Tiv_BV
Rin_BV=1
elseif 1123200<=t && t<1130400
Rin_BV=1
else
Rin_BV=0
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Concn TMZ BLOOD TEST
diff(1,1)=(-kclr_DOX*y1)+(Rin_DOX*Dose_DOX); % y1 - Zhan *********
% Concn BV BLOOD TEST - ZHAN - y2
diff(2,1)=(-kclr_BV*y2)+(Rin_BV*Dose_BV); % y2 - Zhan ************
% Normalised Bevacizumab Concentration - Check the units for this equation
% or the equation itself and then everything should work ok.
% Anti-Angiogenic Effect
diff(3,1)=y3*(alpha+beta*y3+gamma*y3^2)-y3*kak*CsBEV; % Skye ********
% Concn of TMZ in Tumour
diff(4,1)=((P_DOX*y4*s_v*Vt)*(y1-y4)-(ke_DOX*y4*Ve))/Ve % Skye ***
end
CsBEV = y2/(Dose_BV/Vdist_BV);
Second FILE
clc
% Working with ODE 1, 2, & 3 (Concn Blood, Cancer Cell Effect &
% Endothelial Cell Effect)
range=[0:86400*30]; % 864000(s)=10days
% Initial conditions of system [Ctmz]
ICs=[0,0,1,0];
% Solve ODEs using ODE45
[tsol,varsol]=ode45(@WORKING_ODE_SYS, range, ICs);
% plot of Concentration of TMZ in Blood against time (g/m2/s)
figure(1)
plot(tsol/86400,varsol(:,1))
title('Concentration of DOX in Blood vs. Time')
xlabel('Time (hr)')
ylabel('Concentration of DOX in Blood (g/m^2)')
% plot of Concentration of BV in Blood against time (g)
figure(2)
plot(tsol/86400,varsol(:,2))
title('Concentration of Bevacizumab vs. Time')
xlabel('Concentration of Bevacizumab in Blood (g)')
ylabel('Time (hr)')
% plot of Anti-Angiogenic Effect
figure(3)
plot(tsol/86400,varsol(:,3))
title('Plot of Anti-Angiogenic Effect vs. Time')
xlabel('Time (hr)')
ylabel('Anti-Angiogenic Effect (%)')
% plot of Concnetration of TMZ in Tumour against time
figure(4)
plot(tsol/86400,varsol(:,4))
title('Concentration of DOX in Tumour vs. Time')
xlabel('Time (hr)')
ylabel('Concentration of DOX (g/m^2)')
figure(5)
plot(tsol,varsol(:,1))
hold on
plot(tsol,varsol(:,4))
title('Concentration of DOX in Blood & Tumour')
xlabel('Time (hr)')
ylabel('Concentration of DOX (g/m^2)')
hold off

Arthi Sathyamurthi on 26 May 2021
Hi Skye,
In your first file you have missed to change the function handle name to the name of second file ‘ode_sys_2equations’ and in your second file the position of the equation CsBEV is outside the function and also it should be placed before the diff(3,1) equation as it requires the CsBEV value.
First file
% Solve ODEs using ODE45
[tsol,varsol]=ode45(@ode_sys_2equations, range, ICs);
Second File last part
% Concn TMZ BLOOD TEST
diff(1,1)=(-kclr_DOX*y1)+(Rin_DOX*Dose_DOX); % y1 - Zhan *********
% Concn BV BLOOD TEST - ZHAN - y2
diff(2,1)=(-kclr_BV*y2)+(Rin_BV*Dose_BV); % y2 - Zhan ************
CsBEV = y2/(Dose_BV/Vdist_BV);
% Normalised Bevacizumab Concentration - Check the units for this equation
% or the equation itself and then everything should work ok.
% Anti-Angiogenic Effect
diff(3,1)=y3*(alpha+beta*y3+gamma*y3^2)-y3*kak*CsBEV; % Skye ********
% Concn of TMZ in Tumour
diff(4,1)=((P_DOX*y4*s_v*Vt)*(y1-y4)-(ke_DOX*y4*Ve))/Ve % Skye ***