Compartmental Modeling - Introduction to Biomedical Engineering - page 434

38. Given the two-compartment model shown in Figure 7.17 with a zd ð Þ u ð t Þ u ð t t 0 ð Þ

ingestion of solute in the digestive system and removal of solute via metabolism and excretion
in urine, solve for the plasma concentration.
39. Consider the two-compartment model shown in Figure 7.15 with

ð t Þþ 1 z

K 12 ¼ 0, K 10 ¼ 0 : 5, K 21 ¼ 0 : 3,

Assume that the initial conditions are zero. (a) Solve for
the quantity in each compartment. (b) Find the maximum amount of solute in compartment 1.
40. Consider the two-compartment model shown in Figure 7.15 with

K 20 ¼ 0 : 9, f 1 ð t Þ¼ 0, and f 2 ð t Þ¼ 5dð t Þ:

K 12 ¼ 0 : 2, K 10 ¼ 0 : 7,

K 21 ¼ 0, K 20 ¼ 1, f 1 ð t Þ¼ 2 u ð t Þ , and f 2 ð t Þ¼ 0 : Assume that the initial conditions are zero. Solve

for the quantity in each compartment.
41. Consider the two-compartment model shown in Figure 7.15 with K 12 ¼ 0, K 10 ¼ 0 : 6,

K 21 ¼ 0 : 1, K 20 ¼ 0 : 8, f 1 ð t Þ¼ 0, and f 2 ð t Þ¼dð t Þþ 5 u ð t Þ: Assume that the initial conditions are

zero. Solve for the quantity in each compartment.
42. Consider the two-compartment model shown in Figure 7.15 with K 12 ¼ 0 : 3, K 10 ¼ 0 : 2,

K 21 ¼ 0, K 20 ¼ 0 : 4, f 1 ð t Þ¼ 4 u ð t Þ , and f 2 ð t Þ¼ 5dð t Þ: Assume that the initial conditions are zero.

Solve for the quantity in each compartment.
43. Consider the two-compartment model shown in Figure 7.15 with

K 12 ¼ 0 : 3, K 10 ¼ 0 : 5,

K 21 ¼ 0, K 20 ¼ 1, f 1 ð t Þ¼ 2 u ð t Þ , and f 2 ð t Þ¼ 3dð t Þ: Assume that the initial conditions are zero.

Solve for the quantity in each compartment.
44. Consider the two-compartment model shown in Figure 7.15 with

K 12 ¼

0,

K 10 ¼

0 : 6,

K 21 ¼ 0 : 1, K 20 ¼ 0 : 5, f 1 ð t Þ¼ 0, and f 2 ð t Þ¼ d ð t Þþ 5 u ð t Þ: Assume that the initial conditions are

zero. Solve for the quantity in each compartment.
45. Consider the two-compartment model shown in Figure 7.15 with

K 12 ¼ 0 : 3, K 10 ¼ 0 : 7,

K 21 ¼ 0, K 20 ¼ 0 : 1, f 1 ð t Þ¼ 3d ð t Þ , and f 2 ð t Þ¼ 0 : Assume that the initial conditions are zero.

Solve for the quantity in each compartment.
46. Consider the two-compartment model shown in Figure 7.15 with K 12 ¼ 0 : 4, K 10 ¼ 1 : 0,

K 21 ¼ 0, K 20 ¼ 0 : 3, f 1 ð t Þ¼ 2 u ð t Þ , and f 2 ð t Þ¼ 0 : Assume that the initial conditions are zero.

Solve for the quantity in each compartment.
47. Consider the two-compartment model shown in Figure 7.15 with K 12 ¼ 0 : 2, K 10 ¼ 0 : 8,

K 21 ¼ 0, K 20 ¼ 0 : 3, f 1 ð t Þ¼dð t Þþ 2 u ð t Þ , and f 2 ð t Þ¼ 0 : Assume that the initial conditions are

zero. Solve for the quantity in each compartment.
48. Consider the two-compartment model shown in Figure 7.15 with K 12 ¼ 0 : 3, K 10 ¼ 0 : 5,

K 21 ¼ 0 : 1, K 20 ¼ 0 : 4, f 1 ð t Þ¼ 2 u ð t Þ , and f 2 ð t Þ¼ 5dð t Þ: Assume that the initial conditions are

zero. Solve for the quantity in each compartment.
49. Consider the two-compartment model shown in Figure 7.15 with

K 12 ¼ 0 : 3, K 10 ¼ 0 : 7,

K 21 ¼ 3, K 20 ¼ 1, f 1 ð t Þ¼ 2dð t Þ , and f 2 ð t Þ¼ 5 u ð t Þ: Assume that the initial conditions are zero.

Solve for the quantity in each compartment.
50. Consider the two-compartment model shown in Figure 7.15 with

K 12 ¼ 0 : 2, K 10 ¼ 0 : 6,

K 21 ¼ 0 : 1, K 20 ¼ 0 : 5, f 1 ð t Þ¼ 3dð t Þ , and f 2 ð t Þ¼dð t Þþ 5 u ð t Þ: Assume that the initial conditions

are zero. Solve for the quantity in each compartment.
51. Suppose 1 g of solute is ingested into the digestive system that has a transfer rate of 1

4hr 1 :

7hr 1 into the
environment. (a) Solve for the solute concentration in the plasma. (b) When is the maximum
solute concentration observed in the plasma compartment? (c) What is the maximum solute
in the plasma compartment?

into the plasma. The plasma compartment is 3 L and has transfer rate of 0 :