Trying to graph two ode45 functions on a single plot

Hello I am working with this windkessel model with different parameters

%% Defining Physiological Parameters

clc,clear;

% Defining parameters for 2 element model 
R = 1.08; %systemic peripheral resistance (mmHg/cm^3/sec)
C = 1.1; %systemic arterial compliance in (cm^3/mmHg)


% Heart rate and cycle times
HR = 60; %beats per minute
Tc = 60/HR; %Length of one cardiac cycle (in seconds)
Ts = (2/5)*Tc; %Length of systole is 40% of the cardiac cycle
InCond = 80; %pressure during diastole (80mmHg)


Timespan=[0 Tc];
twoelemmodel = @(t,P) (1/C).*(QF(t,HR)-(P./R));
[t,P] = ode45(twoelemmodel,Timespan,InCond);
plot(t,P,'r')
title('2 Element Windkessel Model (Physiological Parameters)');
xlabel('time (in seconds)'); 
ylabel('Pressure (in mmHg)');


%% %% Defining Theoretical Parameters



% Defining parameters for 2 element model 
R = 1.3; %systemic peripheral resistance (mmHg/cm^3/sec)
C = 1.1; %systemic arterial compliance in (cm^3/mmHg)

% Heart rate and cycle times
HR = 120; %beats per minute
Tc = 60/HR; %Length of one cardiac cycle (in seconds)
Ts = (2/5)*Tc; %Length of systole is 40% of the cardiac cycle
InCond = 80; %pressure during diastole (80mmHg)

Timespan=[0 Tc];
twoelemmodel = @(t,P) (1/C).*(QF(t,HR)-(P./R));
[t,P] = ode45(twoelemmodel,Timespan,InCond);
plot(t,P,'b')
title('2 Element Windkessel Model (Theoretical Parameters)');
xlabel('time (in seconds)'); 
ylabel('Pressure (in mmHg)');

Functions I am using:

% Functions
function Qout = QF(t,HR)

HR = 60;%Heart Rate in beats per minute
Tc = 60/HR; %Length of one cardiac cycle (in seconds)
Ts =(2/5)*Tc; %Length of systole is 40% of the cardiac cycle
if HR == 60
    Qo = 260;
else
    Qo = 520;
end
if t > Ts
    Qo = 0;
end
Qout = Qo.*sin((2.*pi.*t/Tc));

function dqdt = dQf(t,HR)

Tc = 60/HR; %Length of one cardiac cycle (in seconds)
Ts = (2/5)*Tc; %Length of systole is 40% of the cardiac cycle
if HR == 60
    Qo = 260;
else 
    Qo = 520;
end
if t > Ts
    Qo = 0;
end
dqdt = (2.*pi/Tc).*Qo.*cos((2.*pi.*t)/Tc);

I can't seem to get the two grpahs to plot together.

Hold on functions seem to work, but the plots seem identical.

Any idea?

[darova]

You don't use dQf?

Answer 1

[Star Strider]

For the first integration, save the outputs as:

[t{1},P{1}] = ode45(twoelemmodel,Timespan,InCond);

and the second as:

[t{2},P{2}] = ode45(twoelemmodel,Timespan,InCond);

and delete the existing plot calls, then plot the integration results as:

figure
plot(t{1}, P{1})
hold on
plot(t{2}, P{2})
hold off
grid
legend('Physiological Parameters', 'Theoretical Parameters')
title('2 Element Windkessel Model')
xlabel('time (in seconds)'); 
ylabel('Pressure (in mmHg)');

See the documentation on the hold (link) function for details.

[Walter Roberson]

Or just

plot(t{1}, P{1}, 'r', t{2}, P{2}, 'b')