Which expression correctly derives bioavailability (F) from AUC measurements for PO and IV dosing?

• A. F = (AUC_po × Dose_iv) / (AUC_iv × Dose_po)
• B. F = (AUC_iv × Dose_po) / (AUC_po × Dose_iv)
• C. F = AUC_po / AUC_iv
• D. F = Dose_po / Dose_iv

Answer: (A)

Bioavailability is the fraction of the oral dose that reaches systemic circulation. Using the PK relationship AUC = F × Dose / Clearance, compare oral and IV routes: AUC_po = F × Dose_po / CL and AUC_iv = Dose_iv / CL (since F for IV is 1). Taking the ratio AUC_po / AUC_iv cancels the clearance and gives AUC_po / AUC_iv = F × Dose_po / Dose_iv. Solving for F leads to F = (AUC_po × Dose_iv) / (AUC_iv × Dose_po). This is the expression that correctly incorporates both the AUC measurements and the differences in administered doses. If the doses were the same, it would simplify to F = AUC_po / AUC_iv.