Kirchhoff's Laws and Hepatic Clearance, Well-Stirred Model - Is There Common Ground?

Clearance concepts are extensively applied in drug development and drug therapy. The well-stirred model (WSM) of hepatic elimination is the most widely adopted physiologic model in pharmacokinetics owing to its simplicity. A common feature of this organ model is its use to relate hepatic clearance of a compound to the physiologic variables: organ blood flow rate, binding within blood, and hepatocellular metabolic and excretory activities. Recently, Kirchhoff's laws of electrical network have been applied to organ clearance (Pachter et al., 2022; Benet and Sodhi, 2023) with the claim that they yield the same equation for hepatic clearance as the WSM, and that the equation is independent of a mechanistic model. This commentary analyzes this claim and shows that implicit in the application of Kirchhoff's approaches are the same assumptions as those of the WSM. Concern is also expressed in the interpretation of permeability or transport parameters and related equations, as well as the inappropriateness of the corresponding equation defining hepatic clearance. There is no value, and some dangers, in applying Kirchhoff's electrical laws to organ clearance. SIGNIFICANCE STATEMENT: This commentary refutes this claim by Pachter et al. (2022), and Benet and Sodhi, (2023), who suggest that the well-stirred model (WSM) of hepatic elimination, the most widely applied physiologic model of hepatic clearance, provides the same equation as Kirchhoff's laws of electrical network that is independent of a physiologic model. A careful review shows that the claim is groundless and fraught with errors. We conclude that there is no place for the application of Kirchhoff's laws to organ clearance models.