Question

You inject (intravenously) a 70 Kg patient with 30 mg of drug that has a Vd of 5 L/Kg and an elimination half life of 3 hr.

Assuming that this is a loading dose, what would be your predicted steady state plasma drug concentration?

Answer 1

The predicted steady state plasma drug concentration for a 70 kg patient injected with 30 mg of drug having a Vd of 5 L/kg and a half-life of 3 hours is 85.7 μg/L.

Step-by-step explanation:

If a 70 kg patient is injected intravenously with 30 mg of a drug that has a volume of distribution (Vd) of 5 L/kg and an elimination half-life of 3 hours, we can predict the steady state plasma drug concentration using the formula:

Css = Dose / (Vd × Weight)

where 'Css' is the steady state concentration, 'Dose' is the drug amount in mg, 'Vd' is the volume of distribution, and 'Weight' is the patient's weight in kg.

Calculation:

Weight = 70 kg

Vd = 5 L/kg

Dose = 30 mg

Therefore:

Css = 30 mg / (5 L/kg × 70 kg) = 30 mg / 350 L = 0.0857 mg/L or 85.7 μg/L

This predicted concentration is achieved shortly after the loading dose and maintained if the drug is given subsequent doses at a rate equal to the rate of elimination.