AM Exercise 2. The Standard First-Order Absorption Model with Metabolite Concentration
In this exercise we will consider drug absorption under the following extended assumptions:
(a) A single oral dose has been administered,
(b) At time t = 0, we begin with 100% dissolution at the absorption site, namely the GI tract,
(c) The absorbing region of the body is represented as a single well-stirred compartment,
(d) The absorption process is first-order,
(e) The drug elimination pathway is first-order via the urinary tract,
(f) The (drug changed to) metabolite process is first-order,
(g) The metabolite elimination pathway is first-order via the urinary tract.
Also, the %-concentration functions for the Model are:
P0(t) = percent of dose that is drug in the gut as a function of time,
P1(t) = percent of dose that is drug in the blood (absorbed within the body) as a function of time,
P2(t) = percent of dose that is drug in the urine as a function of time,
P3(t) = percent of dose that is (drug changed to) metabolite as a function of time,
P4(t) = percent of dose that is metabolite in the urine as a function of time.

1. View a plot of the %-concentration functions and the Structural Diagram for the Model:

2. Using the Structural Diagram for the Model that is located on the plot, write out the first-order rate equations.
 
 
 
 
 
 

3. Given that k1 = .5, k2 = .1, k3 = .15, and k4 = .75 for the example on the plot, then the %-concentration functions are:

4. Verify that these %-concentration functions satisfy some of the rate equations in 2. above.
Check the rate equation for P1'(t) here:
 
 
 
 
 
 

Check the rate equation for P3'(t) here:
 
 
 
 
 
 

5. Find the time at which the % of metabolite concentration within the body reaches a maximum, and the value of this maximum percentage.
 
 
 
 
 
 
 
 

6. Compute the average % of metabolite concentration from t = 2 hours to t = 5 hours, and compare with the maximum % of metabolite concentration that you found above in 5.