Question

given values :

c_0 = 200

k_a= 0.065

k_c= 2.159

Backround info:

The first order compartment model for pharmacokinetics describes the passage of an ingested compound, such as theophylline, from the stomach into the bloodstream. Over the course of a few hours, the amount in the stomach, y1(t) and bloodstream, y2(t)

vary from their initial values.

The compound is absorbed from the stomach into the bloodstream, such that the rate of change of the amount in the stomach is given by the following model:

dy1/dt= -k_ay₁

with initial amount y1(0) =c₀ having units mg

Q1

:Given the information about the units of y₁ and t, state the value of k_q with appropriate units. Show your working/explain your reasoning.

Q2

BAckround info:

The rate of change of the amount in the bloodstream is driven by the absorption from the stomach as well as the clearance of the compound from the bloodstream through the kidneys, with rate parameter k_c. The model is

dy₂/dt= k_ay₁ - k_cy₂

What is an appropriate initial condition for the amount of the compound in the bloodstream? State it with appropriate units.

Q3

Given the information about the units of y₁,y₂k_a and t, state the value of k_c with appropriate units. Show your working/explain your reasoning.

Q4

show that y₁(t)= C₀e^-k_at is the solution to the above differential equation for y₁(t)

Answer 1