PHARMACOKINETICS PROBLEMS

1. Assuming first order kinetics what fraction of an IV drug dose remains in the body after 4 half-lives?
2. The t_1/2 of a drug is 6 hours. What fraction is left in the body at 21h post drug administration?
3. Twenty percent of a drug dose remains in the body at t=10hours. What is the half-life of the drug?
4. The plasma concentration of a drug administered by IV bolus injection may be described by the following equation:

C_t = 0.92e ^-0.35t

where C_t is in units of mg/L and the time (t) is in hours.

If the dose is 50mg calculate the following:

• The plasma concentration at 6.5h post dosing.
• The plasma half-life.
• The volume of distribution.
• The area under the plasma concentration versus time curve.
• The total clearance.

 

5. Drug X is administered as an IV bolus dose of 100mg and the following plasma concentrations were obtained with time:

Time (h)	0.25	0.5	1.0	3.0	5.0	7.0	10.0
Plasma Concentration (mg/L)	2.6	2.4	2.1	1.2	0.75	0.45	0.2

Calculate the volume of distribution, plasma half-life and clearance of X.

X was subsequently administered via the oral route at a dose of 200mg as both an aqueous solution and as a formulated product. The measured areas under the plasma concentration time curves were 14.3 mg/L.h and 12.6 mg/L.h for the solution dose and formulated product respectively.

 

Using this data calculate the relative and absolute bioavailability of X.

6. Drug W on IV administration to an experimental animal at a dose of 10mg/kg (animal weight 2.3kg) gave the following plasma concentrations with time:

Time (h)	0.1	0.25	0.5	0.75	1.0	1,5	2.0	3.0	4.0
Plasma Concentration (mg/L)	4.2	3.2	2.3	1.8	1.5	1.2	1.09	0.88	0.71

 

Using the above data:

• Draw a diagram of a compartmental model that describes the plasma disposition of the drug and indicate any relevant rate constants.
• Write an equation describing the plasma concentration versus time curve (use numbers rather than symbols as much as possible).
• Calculate the values of the rate constants you have indicated in part (a).
• What is the terminal half-life of drug W?
• What is the volume of distribution of W and what is the initial dilution volume (volume of the central compartment)?
• Calculate the area under the plasma concentration versus time curve and compare this value with that obtained using the trapezoidal method.

 

7. Drug Y is administered orally to a patient at a dose of 100mg and the following plasma concentrations were obtained with time:

Time (h)	0.2	0.4	1.0	2.0	3.0	4.0	6.0	8.0	10.0
Plasma Concentration (mg/L)	0.33	1.0	1.8	2.02	2.0	1.6	1.0	0.6	0.38

 

Calculate the absorption and elimination rate constants, the volume of distribution and clearance of Y assuming that F, the bioavailability, is equal to 0.75.

If the 100mg oral dose is repeated at 8 hourly intervals calculate the maximum, minimum and average steady-state plasma concentrations.

8. Drug A is administered IV to a patient according to the following table:

 

Day	Time	Dose (mg)
1	4.00pm	80
	11.00pm	160
2	7.00am	120
	1.30pm	80

 

At 4.00pm on day 2 a plasma sample was analysed for A and a concentration of 6mg/L was obtained.

Is this measured concentration consistent with the expected value?

Volume of distribution of A is 14.5L and clearance is 40mL/min.