What is the well-stirred model formula for hepatic clearance?

• A. ClH = Q × fu × CLint
• B. ClH = Q × fu × CLint / (Q + fu × CLint)
• C. ClH = (Q × fu × CLint) / (Q + fu × CLint)
• D. ClH = (Q + fu × CLint) / (Q × fu × CLint)

Answer: (C)

In the well-stirred model, the liver is treated as a single, well-mixed compartment through which blood flows at rate Q. The drug must be unbound in plasma (fraction fu) to be available for metabolism, and CLint represents the liver’s intrinsic ability to clear the drug when not limited by flow. Combining these factors, hepatic clearance is determined by both how much drug reaches the liver and how quickly the liver can metabolize it, giving the equation ClH = (Q × fu × CLint) / (Q + fu × CLint).

This form shows the balance between flow and capacity: if fu × CLint is much larger than Q, clearance becomes flow-limited and approaches Q. If fu × CLint is much smaller than Q, clearance is capacity-limited and approaches fu × CLint. A convenient way to view it is to think of CLint′ = fu × CLint, so ClH = (Q × CLint′) / (Q + CLint′).