For IV administration, which relation describes how AUC depends on Dose and clearance?

For IV administration, which relation describes how AUC depends on Dose and clearance?

• A. AUC = Dose × Clearance
• B. AUC = Clearance / Dose
• C. AUC = 1 / (Dose × Clearance)
• D. AUC = Dose / Clearance

Answer: (D)

For IV administration, the body receives the full amount of drug, so bioavailability F equals 1. The total amount eliminated over time is tied to the product of clearance and plasma concentration, and when you account for the entire time course, the relationship becomes CL × AUC = Dose. Solving for AUC gives AUC = Dose / CL. This makes sense dimensionally too: Dose has units of mass (e.g., mg) and clearance has units of volume per time (e.g., L/h), so Dose/CL yields mg·h/L, which is the standard unit for AUC. Because IV administration uses F = 1, the general expression AUC = F × Dose / CL simplifies to Dose/CL. The other formulations would not align with the mass-balance and unit considerations; they would imply that exposure increases with clearance or produce inconsistent units.

For IV administration, the body receives the full amount of drug, so bioavailability F equals 1. The total amount eliminated over time is tied to the product of clearance and plasma concentration, and when you account for the entire time course, the relationship becomes CL × AUC = Dose. Solving for AUC gives AUC = Dose / CL. This makes sense dimensionally too: Dose has units of mass (e.g., mg) and clearance has units of volume per time (e.g., L/h), so Dose/CL yields mg·h/L, which is the standard unit for AUC.

Because IV administration uses F = 1, the general expression AUC = F × Dose / CL simplifies to Dose/CL. The other formulations would not align with the mass-balance and unit considerations; they would imply that exposure increases with clearance or produce inconsistent units.