Compartmental Modeling - Introduction to Biomedical Engineering - page 432

22. Given the cell described in Figure 7.7 with a ¼ 500 mM, P K ¼ 1 : 0, and P Na ¼ 0 : 04, at steady

state, plot the relationship between J p and V :

23. Suppose 500 mg of dyewas introduced into the plasma compartment. After reaching steady state,
the concentration in the blood is 0.0893 mg

cm 3 . Find the volume of the plasma compartment.
24. Suppose 1 g bolus of solute is injected into a plasma compartment of 3 L. The transfer rate out
of the compartment equals 0

7hr 1 . Solve for the solute concentration. What is the half-life of
the solute in the plasma compartment?
25. An unknown quantity of radioactive iodine (

:

131 ) is instantaneously passed into the plasma.

I

131 in the plasma exhibits an exponential decay from
100 mg with a time constant of 1 day, while the urine shows an exponential rise from zero to
75 mg with a time constant of 1 day. Assuming the compartment model in Example Problem
7.5, determine the transfer rates and the half-life.
26. Suppose a patient ingested a small quantity of radioactive Iodine (

The time dependence of the quantity of

I

131 ). A simple model

I

131 from the bloodstream into the urine and thyroid is given in
Example Problem 7.5. (a) Sketch the response of the system. (b) Suppose the thyroid is not
functioning and does not take up any

describing the removal of I

131 . Sketch the response of the abnormal system and

I

compare to the result from (a).
27. A radioactive bolus of

131 is injected into a plasma compartment. The time dependence of the

I

mg
100 mL . The amount of

131 is 10 K mg.
Assuming the compartmental model in Example Problem 7.5, find (a) the volume of the
plasma compartment, (b)

131

e 1:6 t concentration of I in the plasma is c 1 ¼ 143 I

K ¼ K 1 þ K 2 , and (c) the half-life.
28. Find the half-life for the model given in Eq. (7.33) and Figure 7.8.
29. Use SIMULINK to simulate the model given in Eq. (7.33) and Figure 7.8. Use the parameters
given in Figure 7.11.
30. Demonstrate for the one-compartment pharmacokinetic model given in Section 7.5.3 with
Eq. (7.33) and Figure 7.8 that as g increases, both t max and q 1 ð t max Þ decrease.

e 2 t u ð t Þ: 31. An antibiotic is exponentially administered into the body, with f ð t Þ¼ 75 Assume

(a) Analytically solve for the quantity of the
antibiotic in the plasma. (b) Simulate the quantity of the antibiotic in the plasma using
SIMULINK. (c) What is the time to maximum concentration, and what is the quantity in the
plasma at that time?
32. For the one-compartment repeat dosage in Section 7.5.4, derive Eq. (7.42) from (7.41) and
Eq. (7.44) from (7.33).
33. A 2 g bolus of antibiotic is administered to a person with a plasma volume of 3 L. The average
impulse response for this drug is shown in Figure 7.35. Assuming a one-compartment model,
determine the transfer rate. If the concentration of the drug is not to fall below 10 percent of
the initial dosage at steady state, how often does the drug need to be given to maintain this
minimum level?
34. A 4 g bolus of antibiotic is administered to a person with a plasma volume of 3 L. The average
washout response for this drug in a plasma volume of 3 L is shown in Figure 7.36. Assuming
a one-compartment model, determine the transfer rate. If the concentration of the drug is not
to fall below 25 percent of the initial dosage at steady state, how often does the drug need to
be given to maintain this minimum level?

the model given in Figure 7.8 with K 10 ¼ 0 : 3 :