The document presents two differential equations modeling carbon dioxide transfer between the lungs, tissues, and blood. The equations include variables for lung volume, tissue volume, blood flow rate, and initial carbon dioxide levels in the lungs and tissues. The document also provides sample code to numerically solve the differential equations over time and plot the results.

1. KL * dFACO2/dt = FICO2 * VA + 8.63* Q *(CTCO2-CaCO2)/(B-47)-FACO2*VA
10*KT*dCTCO2/dt= MRCO2 + 10*Q*(CaCO2-CTCO2)
Where KL =9 (liters)
KT=60 (liters)
Q =5(l/min)
VA=4.71*CTCO2-246
CaCO2=48+6*(PaCO2-40)/7
PaCO2=(B-47)*FACO2
Initial Conditions: FACO2(0)=.07 CTCO2(0)=56.7 ml/100 ml
function yp=vcalc(t,y)
Fico2=.04;
Faco2=y(1);
Ctco2=y(2);%ml
KL=5;%lung volume in L
KT=30; %tissue volume in L
Q=6;%cardiac output L/min
B=760;
Cvco2=Fico2*B;
if t>40
Fico2=0;
end
VA=4.71*Ctco2-246; %Ctco2=y(2)
Paco2=(B-47)*Faco2; % Faco2= y(1)
Caco2=48+6*(Paco2-40)/7;
Mrco2=300
yp(1)=(Fico2*VA+8.63*Q*(Ctco2-Caco2)/(B-47)-Faco2*VA)/(KL);
yp(2)=(Mrco2+10*Q*(Caco2-Ctco2))/(KT*10);
yp=yp';
end
VA=4.71*Ctco2-246; %Ctco2=y(2)

2. Paco2=(B-47)*Faco2; % Faco2= y(1)
Caco2=48+6*(Paco2-40)/7;
Mrco2=250
yp(1)=(Fico2*VA+8.63*Q*(Ctco2-Caco2)/(B-47)-Faco2*VA)/(KL);
yp(2)=(Mrco2+10*Q*(Caco2-Ctco2))/(KT*10);
yp=yp';
end
[t,y]=ode45(@vqcalc,[0 45],[.058 53.3]);
VA=4.71*y(:,2)-246;
VA=((VA-min(VA))/(max(VA)-min(VA)));
hold on
plot(t,VA)
[t2,y2]=ode45(@vqcalc2,[0 45],[.058 53.3]);
VA2=4.71*y2(:,2)-246;
VA2=((VA2-min(VA2))/(max(VA2)-min(VA2)));
plot(t2,VA2,'r')
hold off
xlabel('Time(min)')
ylabel('VA(lit/min)')
legend('KT=30','KT=40')
x=1:1:45;
y1=[35,85,143,202,247,284,312,336,359,373,392,405,418,424,434,441,446,450,455,460,465,470,473,47
4,475,477,478,478,478,459,315,217,138,89,63,41,29,19,12,9,0,0,0,0,0];
y2=[58,147,225,282,320,357,384,400,418,431,442,450,457,465,468,471,475,477,478,478,478,478,478,4
78,478,478,478,478,478,459,315,163,84,42,25,9,0,0,0,0,0,0,0,0,0];
y1=y1./478;
y2=y2./478;
hold on

3. plot(x,y1,'r')
plot(x,y2,'b')
xlabel('Time(min)')
ylabel('VA(lit/min)')
legend('1','2')
[t,y]=ode45(@vqcalc,[0 45],[.058 53.3]);
VA=4.71*y(:,2)-246;
VA=((VA-min(VA))/(max(VA)-min(VA)));
hold on
plot(t,VA)
[t2,y2]=ode45(@vqcalc2,[0 45],[.058 53.3]);
VA2=4.71*y2(:,2)-246;
VA2=((VA2-min(VA2))/(max(VA2)-min(VA2)));
plot(t2,VA2,'r')
ww=1:1:45;
c1=[35,85,143,202,247,284,312,336,359,373,392,405,418,424,434,441,446,450,455,460,465,470,473,47
4,475,477,478,478,478,459,315,217,138,89,63,41,29,19,12,9,0,0,0,0,0];
c2=[58,147,225,282,320,357,384,400,418,431,442,450,457,465,468,471,475,477,478,478,478,478,478,4
78,478,478,478,478,478,459,315,163,84,42,25,9,0,0,0,0,0,0,0,0,0];
c1=c1./478;
c2=c2./478;
plot(ww,c1,'b','*')
plot(ww,c1,'*')
plot(ww,c2,'--')
legend('KT=30','KT=40','grodin1','grodin2')