1. A drug was present in the plasma shortly after IV administration at a concentration of 300 µg/ml. Eight hours later, the plasma concentration was determined at 75 µg/ml. Assuming first order kinetics, the half-life of the drug is approximately:
    1. 30 minutes
    2. 60 minutes
    3. 2 hours
    4. 4 hours
    5. 6 hours

    75 µg/ml is one-quarter the concentration of 300 µg/ml

    That means 2 half-lives have passed in 8 hours, so the half life is 4 hours.

  2. A drug is administered intravenously in a dose of 200 mg to an 80 kg male patient. After 4 hours the plasma concentration was 1.5 mg/ml. Assume that the apparent volume of distribution is 10% of body weight. The total amount of drug in body fluids at 4 hours is approximately:
    1. 15 mg
    2. 30 mg
    3. 60 mg
    4. 90 mg
    5. 120 mg

    In my haste to post some practice problems last Friday, I didn't double check that this was a good problem. I think there is an error, although I haven't figured out what the mistake is.

     

     

  3. A single dose of a drug is given to an 85 kg female patient. The drug is known to have an apparent volume of distribution of 20% of body weight and elimination half-life of 2 hours. The total body clearance of this drug is:
    1. 20 ml/min
    2. 50 ml/min
    3. 100 ml/min
    4. 170 ml/min
    5. 340 ml/min

    Vd = .2 X 85 = 17 L = 17000 ml

    T1/2 = 2 hours = 120 min

    Clp = ?

    Clp = (0.693 * Vd) / T1/2 = 100 ml/min

     

  4. Drug X is administered via constant infusion at a rate of 150 µg/min. The half life of drug X is 15 hours, the elimination constant (ke) is 0.046/hr, the volume of distribution is 40 L. What is the steady state concentration?
    1. 0.082 µg/ml
    2. 4.89 µg/ml
    3. 4.89 mg/ml
    4. 9.8 µg/ml
    5. 0.0489

    Css = ?

    Css = Q / ke * Vd where:

    Q = 150 mg/min

    ke = 0.046/hr

    and Vd = 40 L

    so

    Css = 150 mg/min /((0.046/60min)*40,000ml)

    notice how the units are consistent: hr in

    ke changed to min to match Q (mg/min) and 40 L is

    represented as 40,000 ml

    Answer: Css = 4.89 mg/ml

  5. In order to attain a steady-state concentration of 25 µg/ml, at what infusion rate must drug X be administered via constant infusion if the half-life of drug X is 15 hours, the elimination constant (ke) is 0.046/hr, and the volume of distribution is 40 L?
    1. 25 µg/min
    2. 300 µg/min
    3. 600 µg/min
    4. 760 µg/min
    5. 0.019 µg/min

    Q = ?

    Css = Q / ke * Vd where:

    Css = 25 ug/ml

    Q = ? m g/min

    ke = 0.046/hr

    and Vd = 40 L

    25 ug/ml = Q / ((0.046/60 min) * 40,000 ml)

    Answer: Q = 760 ug/min

  6. Use the graph below to calculate some key pharmacokinetic parameters. The dose is 200 mg. Calculate Ke, Clp, T1/2 , and Vd. State if drug Q is bound to plasma proteins.

Determine Ke first:

log 25 µg/ml = log Co -(Ke/2.303) X 5 hours

log 17.4 µg/ml = log Co - (Ke/2.303) X 15 hours

Rearrange to:

log 25 µg/ml + (Ke/2.303) X 5 = log 17.4 µg/ml + (Ke/2.303) X 15

solving for Ke = 0.036

T 1/2 = 0.693/0.036 = 19 hours

Vd = 200 / 30 = 6.7 L (extrapolate line back to t=0 to get Co)

Clp = (0.693 X 6700 ml) / 1140 min = 4 ml/min

Since Vd = 6.7 L, the drug is highly bound to plasma proteins