# PHARMACOKINETICS PROBLEMS

1. Assuming first order kinetics what fraction of an IV drug dose remains in the body after 4 half-lives?
2. The t1/2 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:

Ct = 0.92e -0.35t

where Ct 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.

1. 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 3 5 7 10 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.

1. 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 1,5 2 3 4 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.

1. 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.

1. 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.