Which of the following is the well-stirred model equation for hepatic clearance CLh?

• A. CLh = (Qh × Clint) / (fu + Clint)
• B. CLh = (Qh × fu × Clint) / (Qh + fu × Clint)
• C. CLh = (Qh × fu × Clint) / (Qh + Clint)
• D. CLh = (Qh × fu) / (Qh + Clint)

Answer: (B)

In the well-stirred model of hepatic clearance, the amount of drug cleared per time depends on hepatic blood flow, the fraction of drug that remains unbound in plasma, and the liver’s intrinsic ability to metabolize the drug. The correct form combines these factors as CLh = (Qh × fu × Clint) / (Qh + fu × Clint). Here, Qh is the hepatic blood flow, fu is the fraction unbound, and Clint is the intrinsic clearance of the drug by liver enzymes.

This equation reflects two key ideas. First, only the unbound portion of the drug can be cleared, so fu multiplies Clint in the numerator, representing the actual metabolic capacity available to the flowing blood. Second, the denominator Qh + fu × Clint expresses the balance between delivery to the liver and the liver’s metabolic capacity: when the intrinsic capacity (fu × Clint) is very high relative to blood flow, clearance approaches the flow limit (CLh ≈ Qh). When the intrinsic capacity is low relative to flow, clearance is limited by metabolism (CLh ≈ fu × Clint).

Why the other forms don’t fit: removing fu from the numerator ignores the fact that only unbound drug is available for metabolism. Using a denominator that doesn’t pair Qh with fu × Clint misrepresents how flow and enzymatic capacity compete to determine clearance. Likewise, omitting either the fu × Clint product in the correct place or including incorrect terms would fail to capture the flow- versus capacity-limited behavior described above.

So the well-stirred hepatic clearance equation that correctly ties together flow, unbound fraction, and intrinsic clearance is CLh = (Qh × fu × Clint) / (Qh + fu × Clint).