How is AUC related to clearance for IV bolus administration?

• A. AUC = Dose × Cl
• B. AUC = Cl / Dose
• C. AUC = Dose / Cl
• D. AUC = Dose × Cl / F

Answer: (C)

AUC is a measure of systemic drug exposure, and for IV bolus this exposure is set by how much drug is given and how quickly the body clears it. After a single IV dose, the entire amount enters the circulation (bioavailability F = 1), and elimination follows first-order kinetics with rate constant k = Cl/Vd. The concentration-time profile is C(t) = (Dose/Vd) e^{-kt}. When you integrate C(t) from zero to infinity to get the AUC, you get AUC = (Dose/Vd) × (1/k) = Dose/Cl.

So, exposure increases with a larger dose and decreases with greater clearance. The other expressions don’t fit IV bolus kinetics: Dose × Cl would imply increasing exposure with clearance and has incompatible units; Cl ÷ Dose flips the relationship; Dose × Cl / F would only be correct for extravascular routes where F is the bioavailability factor (and for IV, F = 1, this would not equal Dose/Cl).