*Rutgers 16:125:590; 16:155:544:01*

**Drug Delivery Fundamentals and Applications**

*Fall 2023*

**Assignment 2**

*Submit your answers on Canvas in a single document as a pdf file. This could be generated by a word processor or by scanning hand-written solutions to the problems.*

1. Two patients are treated with the antibiotic teicoplanin for MRSA infections. Each patient receives a 200 mg dose of teicoplanin by i.v. injection. It is observed that the initial plasma concentration immediately after injection is 11 mg/L for Patient 1, yet it is only 3.1 mg/L for Patient 2. The plasma concentration profile is well described by a one-compartment model, and the half-life of the drug in each patient is 10 h.

a) What is the volume of distribution (*Vd*) for each patient?

b) What is the elimination rate constant (*ke*, h-1) for each patient?

c) The therapeutic free teicoplanin concentration in plasma is about 1.0 mg/L. At what time will each patient’s concentration reach that level?

d) What is the total drug exposure (AUC) for each patient?

e) Give a likely cause for the difference in behavior between the two patients.

2. Drug B was administered to a patient by IV injection. After varying times, urine samples were obtained as follows. Note that because successive samples are obtained, the third column represents the cumulative amount of drug excreted in the urine.

**Time (h) **

**X****u,sample (mg) **

**Xu,tot
(mg) **

0.25

160

160

0.5

140

300

1.0

200

500

2.0

250

750

4.0

188

938

6.0

46

984

a) What was the drug dose (*X*0 = *X*u,¥)?

b) What is the elimination rate constant (*k*e = *k*u) of this drug assuming that elimination is solely due to renal clearance?

c) What is the renal clearance if the volume of distribution is known to 20 L?

3. Fentanyl was given to a patient undergoing extended orthopedic surgeries. The fentanyl is supplied as a 100 µg/h infusion supplemented by a 100 µg bolus injection administered 2 hours after the start of the infusion. The volume of distribution is estimated from pharmacokinetic data to be 500 L, and the elimination half life is 8.2 h.

a) What is the concentration of fentanyl in the patient at 2 hours, just before the bolus injection is administered?

b) What is the concentration of fentanyl in the patient at 2 hours, just after the bolus injection is administered?

c) The infusion is continued after the bolus injection. What would be the steady-state fentanyl concentration?

d) Assume that fentanyl has reached its steady-state concentration. How long after stopping the infusion will it take for the concentration of fentanyl to drop to 10% of its steady-state value?

e) What is the volumetric clearance of fentanyl in this patient?

4.

The mean plasma concentration after administration of 15 mg of Drug X in an OROS capsule is graphed beside and is described well by

*C**p *(ng/mL)=12.5(*e*−0.1*t *−*e*−0.4*t *)

the equation: ,

where *t* is in hours. It is known that the volume of distribution of Drug X in plasma is 200 L.

a) Which is faster: the rate of absorption or the rate of elimination? Explain.

b) What is the initial drug concentration in the plasma?

c) What is the absorption rate constant (*ka*, h-1) for the patient?

d) What is the elimination rate constant (*ke*, h-1) for the patient?

e) What is the elimination half-life, *t*1/2, of the drug (in hours)?

f) What is the volumetric clearance (CL) for the patient?

g) What is the bioavailability of Drug X in the patient?

5.

a) What is the primary drug delivery barrier that is overcome by Doxil®? How does it do so?

b) What is the main clinical benefit achieved by Doxil®? Explain.