The pharmacokinetic propeies of a new antihistamine are being studied in normal volunteers during phase I clinical trials. The clearance and half-life of the drug are determined to be 4.0 L/hour and 10 hours, respectively. Which of the following values is the approximate volume of distribution for this drug?
**Core Concept**
The volume of distribution (Vd) is a pharmacokinetic parameter that represents the theoretical volume that would be required to contain the total amount of an administered drug at the same concentration that is observed in the body. It is a crucial parameter in understanding the distribution and elimination of a drug.
**Why the Correct Answer is Right**
The clearance (Cl) of a drug is the volume of plasma from which the drug is completely removed per unit time. The half-life (t1/2) of a drug is the time required for the plasma concentration of the drug to decrease by half. The relationship between clearance, half-life, and volume of distribution can be described by the equation: Vd = Cl x t1/2 / 0.693. Given the clearance (Cl) of 4.0 L/hour and the half-life (t1/2) of 10 hours, we can calculate the volume of distribution (Vd) using this equation.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is likely a distractor with an incorrect unit. The volume of distribution should be in liters per kilogram (L/kg) or liters (L), not milliliters (mL) or grams (g).
**Option B:** This option represents an excessively high volume of distribution, which would be unusual for most drugs. A volume of distribution much greater than the total body water (approximately 60% of body weight in adults) would suggest that the drug is highly lipophilic and distributed extensively into tissues.
**Option C:** This option represents an excessively low volume of distribution, which would be unusual for most drugs. A volume of distribution much lower than the total body water (approximately 60% of body weight in adults) would suggest that the drug is highly polar and distributed primarily in the plasma.
**Clinical Pearl / High-Yield Fact**
When calculating the volume of distribution, it's essential to use the correct units and to consider the relationship between clearance, half-life, and volume of distribution. A high volume of distribution may indicate that a drug is highly lipophilic and distributed extensively into tissues, while a low volume of distribution may indicate that a drug is highly polar and distributed primarily in the plasma.
**Correct Answer:** **C. 40 L**.