onsider a $3-$compartment model of pharmacokinetics $($drug delivery$)$ where the patient is receiving a drug

by IV infusion. The drug is input into the Central compartment and then is transported to and from two

peripheral compartments $-$ one of highly perfused tissues and one of scarcely perfused tissues and organs.

Assume constant volume in each compartment. The concentration in each compartment is written as

$C_1(t),C_2(t),C_3(t)$ and assume $C_1(0)=C_2(0)=C_3(0)=0.$

a$.$ For the diagram above, write three model equations $($using an unsteady state mass balance approach$)$

for the concentration of the drug in all three compartments. The input rate can be given as $m_{0}m\frac{g}{m}in$

and the infusion will last for $20$ minutes.

b$.$ Use 'ode$15$s$\text{'}$ to solve your model from part a$)$ over a time interval of $20$ minutes. Use the model

parameters from the table below. The infusion is input at a rate of $0\mathrm{.}004m\frac{g}{m}in$ per kilogram of

body mass. Assume the patient is $70kg.$

c$.$ After $20$ minutes, the infusion is stopped. Modify your equations in part a to indicate this. Use 'ode $15s\text{'}$

to solve for the concentration of the drug in each compartment during this time after the infusion has

stopped over a period of $5$ hours $($use appropriate "initial" conditions here$).$ What are the drug

concentrations in each compartment at the end of this time?

d$.$ Concatenate your two plots from b and $c$ to show a full time course of the drug concentrations from

the start of the infusion and the five following hours. All plots should be clearly labeled.

e$.$ What is the maximum concentration of the drug in the blood? At what time $($minutes after the infusion

is started$)$ does this occur?