Practice Problems

The chapter contains a number of practice problems, for which step-to-step answers are provided in Appendix I. Many of the problems are based on experimental data that have been extracted from original research publications. However, in all cases, the original data have been modified in order to emphasize the teaching on pharmacokinetics and the mathematics and models applied. The aim is to help the student understand the rather abstract mammillary model and how it can be applied in the development of pharmaceutical products.

Keywords

Bioavailability; clearance; kinetic rate constants; pharmaceutical availability; protein binding; sustained release; urinary data

Some of the following problems are based on experimental data extracted from original research publications in international peer-reviewed journals. In all cases, the data have been modified from the original data, and thus do not show the normal experimental variations.

7.1

Scopolamine was administered to 12 healthy men (31.0±4.5 years, 78.2±7.2 kg) as nasal spray (IN), oral tablet (PO), and intravenous (IV) bolus injection [1]. The dose was, in all three cases, 0.40 mg (D₀=0.40 mg). Blood samples were collected and the plasma scopolamine concentration (C_P) determined at various time points (t).

Time (h)	C_P (pg/ml)^a
Time (h)	IV	IN	PO
0.1	4,500	90	–
0.2	2,650	750	60
0.3	1,900	1,400	80
0.4	1,500	1,240	–
0.5	1,250	1,135	100
0.8	985	1,000	–
1.0	900	900	85
2.0	650	650	60
4.0	360	360	23
5.0	260	260	–
6.0	190	190	–
7.0	138	140	–
8.0	100	100	–

^a One picogram (pg) is 1.0·10⁻⁹ mg or 1.0·10⁻¹² gram (g).

A. Calculate k, k₁₂, k₂₁, and t_1/2 after IV bolus administration.

B. Calculate k_a after IN administration.

C. Calculate k and k_a after PO administration.

D. Determine scopolamine bioavailability from the tablets. Determine scopolamine bioavailability from the nasal spray.

E. Determine the total body clearance (Cl_T).

F. On average, 6% of the drug was eliminated unmetabolized in urine after IV administration. Determine the renal clearance (Cl_R).

G. The minimum effective concentration (MEC) is 40 pg/ml. Determine the duration of activity after the IN administration of scopolamine.

7.2

Phenytoin follows nonlinear pharmacokinetics at the therapeutic dosing range. The patient (70 kg) received phenytoin as IV bolus injections at dosing rates (R) of 4.3 and 5.0 mg/kg/day that gave steady-state plasma concentration (C_SS) of 8.0 and 20 µg/ml, respectively.

A. Determine V_max and K_m in this patient.

B. The therapeutic window of phenytoin is between 10 and 20 µg/ml (see Figure 5.1). Determine the dosing rate that gives a C_SS of 15 µg/ml.

C. Determine the Cl_T of phenytoin in this patient when C_SS is 15 µg/ml.

7.3

Itraconazole follows the two-compartment open model after administration of oral itraconazole solution [2]. Six healthy male volunteers received itraconazole (D₀=40 mg) as an oral solution under both fed () and fasting () conditions. Blood samples were collected and the average itraconazole plasma concentration determined up to 72 h after administration of the drug. The obtained ln C_P versus time profile is shown below.