PROBLEMS ON IV BOLUS & INFUSION

One - c ompar t ment op e n m odel in IV b olus

1. A 70-kg volunteer is given an intravenous dose of an antibiotic, and

serum drug concentrations were determined at 2 hours and 5 hours

after administration. The drug concentrations were 1.2 and 0.3 µg/mL,

respectively. What is the biologic half-life for this drug, assuming

first- order elimination kinetics?

8

2. A 50-kg woman was given a single IV dose of an antibacterial drug at

a dose level of 6 mg/kg. Blood samples were taken at various time

intervals. The concentration of the drug (C p) was determined in the

plasma fraction of each blood sample and the following data were

obtained:

t (hr) 0.25 0.5 1 3 6 12 18

Cp(µg/mL) 8.21 7.87 7.23 5.15 3.09 1.11 0.40

a. What are the values for V D, k, and t 1/2 for this drug?

b. This antibacterial agent is not effective at a plasma concentration

of less than 2 µg/mL. What is the duration of activity for this drug?

c. How long would it take for 99.9% of this drug to be eliminated?

d. If the dose of the antibiotic were doubled exactly, what would be

the increase in duration of activity?

9

10

3. A new drug was given in a single intravenous dose of 200 mg to an 80-

kg adult male patient. After 6 hours, the plasma drug concentration of

drug was 1.5 mg/100 mL of plasma. Assuming that the apparent V D is

10% of body weight, compute the total amount of drug in the body fluids

after 6 hours. What is the half-life of this drug?

11

4. A new antibiotic drug was given in a single intravenous bolus of 4

mg/kg to five healthy male adults ranging in age from 23 to 38 years

(average weight 75 kg). The pharmacokinetics of the plasma drug

concentration–time curve for this drug fits a one-compartment model.

The equation of the curve that best fits the data is

Cp=78e-0.46t

Determine the following (assume units of µg/mL for C p and hr for t):

a. What is the t 1/2? b. What is the V D?

c. What is the plasma level of the drug after 4 hours?

d. How much drug is left in the body after 4 hours?

e. Predict what body water compartment this drug might occupy

and explain why you made this prediction.

f. Assuming the drug is no longer effective when levels decline to

less than 2 µg/mL, when should you administer the next dose?

12

13

14

5. Define the term apparent volume of distribution. What criteria are

necessary for the measurement of the apparent volume of distribution to

be useful in pharmacokinetic calculations?

15

6. A drug has an elimination t 1/2 of 6 hours and follows first-order

kinetics. If a single 200-mg dose is given to an adult male patient (68 kg)

by IV bolus injection, what percent of the dose is lost in 24 hours?

16

7. A single IV bolus injection containing 500 mg of cefamandole nafate is

given to an adult female patient (63 years, 55 kg) for a septicemic

infection. The apparent volume of distribution is 0.1 L/kg and the

elimination half-life is 0.75 hour. Assuming the drug is eliminated by

first-order kinetics and may be described by a one-compartment model,

calculate the following:

a. The C p 0

b. The amount of drug in the body 4 hours after the dose is given

c. The time for the drug to decline to 0.5 µg/mL, the minimum

inhibitory concentration for streptococci

17

8. If the amount of drug in the body declines from 100% of the dose (IV

bolus injection) to 25% of the dose in 8 hours, what is the elimination

half-life for this drug? (Assume first-order kinetics.)

9. A drug has an elimination half-life of 8 hours and follows first-order

elimination kinetics. If a single 600-mg dose is given to an adult female

patient (62 kg) by rapid IV injection, what percent of the dose is

eliminated (lost) in 24 hours assuming the apparent V D is 400 mL/kg?

What is the expected plasma drug concentration (C p) at 24 hours

postdose?

18

10. For drugs that follow the kinetics of a one-compartment open model,

must the tissues and plasma have the same drug concentration? Why?

The total drug concentration in the plasma is not usually equal to the total drug concentration in the tissues. A one-compartment model implies that the drug is rapidly equilibrated in the body (in plasma and tissues). At equilibrium, the drug concentration in the tissues may differ from the drug concentration in the body because of drug protein binding, partitioning of drug into fat, differences in pH in different regions of the body causing a different degree of ionization for a weakly dissociated electrolyte drug, an active tissue uptake process, etc.

19

Ph a r m a c o k i n etics o f d r ugs a d m i nister e d by I .V. infusion

1. Why do we use a loading dose to rapidly achieve therapeutic concentration

for a drug with a long elimination half-life, instead of increasing the rate of

drug infusion or increasing the size of the infusion dose?

1-The loading drug dose is used to rapidly attain the target drug concentration, which

is approximately the steady-state drug concentration. However, the loading dose will not

maintain the steady-state level unless an appropriate IV drug infusion rate or maintenance

dose is also used. If a larger IV drug infusion rate or maintenance dose is given, the resulting

steady-state drug concentration will be much higher and will remain sustained at the higher

level. A higher infusion rate may be administered if the initial steady-state drug level is

inadequate for the patient.

20

2. A female patient (35 years old, 65 kg) with normal renal function is to

be given a drug by IV infusion. According to the literature, the

elimination half-life of this drug is 7 hours and the apparent V D is 23.1%

of body weight. The pharmacokinetics of this drug assumes a first-order

process. The desired steady-state plasma level for this antibiotic is 10

µg/mL.

a. Assuming no loading dose, how long after the start of the IV

infusion would it take to reach 95% of the C SS?

b. What is the proper loading dose for this antibiotic?

c. What is the proper infusion rate for this drug?

d. What is the total body clearance?

e. If the patient suddenly develops partial renal failure, how long

would it take for a new steady-state plasma level to be established

(assume that 95% of the C SS is a reasonable approximation)?

f. If the total body clearance declined 50% due to partial renal

failure, what new infusion rate would you recommend to maintain

the desired steady-state plasma level of 10 µg/mL?

21

3. An antibiotic is to be given by IV infusion. How many milliliters per

minute should a sterile drug solution containing 25 mg/mL be given to a

75-kg adult male patient to achieve an infusion rate of 1 mg/kg per hour?

4. An antibiotic drug is to be given to an adult male patient (75 kg, 58

years old) by IV infusion. The drug is supplied in sterile vials containing

30 mL of the antibiotic solution at a concentration of 125 mg/mL. What

rate in milliliters per hour would you infuse this patient to obtain a

steady-state concentration of 20 µg/mL? What loading dose would you

suggest? Assume the drug follows the pharmacokinetics of a one-

compartment open model. The apparent volume of distribution of this

drug is 0.5 L/kg, and the elimination half-life is 3 hours.

22

5. According to the manufacturer, a steady-state serum concentration of

17 µg/mL was measured when the antibiotic cephradine was given by IV

infusion to 9 adult male volunteers (average weight, 71.7 kg) at a rate of

5.3 mg/kg hr for 4 hours.

a. Calculate the total body clearance for this drug.

b. When the IV infusion was discontinued, the cephradine serum

concentration decreased exponentially, declining to 1.5 µg/mL at

6.5 hours after the start of the infusion. Calculate the elimination

half-life.

c. From the information above, calculate the apparent volume of

distribution.

d. Cephradine is completely excreted unchanged in the urine, and

studies have shown that probenecid given concurrently causes

elevation of the serum cephradine concentration. What is the

probable mechanism for this interaction of probenecid with

cephradine?

23

24

7. An antibiotic is to be given to an adult male patient (58 years old, 75

kg) by IV infusion. The elimination half-life is 8 hours and the apparent

volume of distribution is 1.5 L/kg. The drug is supplied in 60-mL

ampules at a drug concentration of 15 mg/mL. The desired steady-state

drug concentration is 20 µg/mL.

a. What infusion rate, in milliliters per hour, would you

recommend for this patient?

b. What loading dose would you recommend for this patient? By

what route of administration would you give the loading dose?

When?

c. Why should a loading dose be recommended?

d. According to the manufacturer, the recommended starting

infusion rate is 15 mL/hr. Do you agree with this recommended

infusion rate for your patient? Give a reason for your answer.

e. If you were to monitor the patient's serum drug concentration,

when would you request a blood sample? Give a reason for your

answer.

f. The observed serum drug concentration is higher than

anticipated. Give two possible reasons based on sound

pharmacokinetic principles that would account for this observation.

25

26