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Assessment of the Kochak-Benet Equation for Hepatic Clearance for the Parallel-Tube Model: Relevance of Classic Clearance Concepts in PK and PBPK

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Abstract

This report reviews concepts related to operation of the classic parallel-tube model (PTM) for hepatic disposition and examines two recent proposals of a newly derived equation to describe hepatic clearance (CLH). It is demonstrated that the proposed equation is identical to a re-arrangement of an earlier relationship from Pang and Rowland and provides a means of calculation of intrinsic clearance (CLint,PTM) rather than CLH as posed. We further demonstrate how classic hepatic clearance models with an assumed CLint, while subject to numerous limitations, remain highly useful and necessary in both traditional pharmacokinetics (PK) and physiologically based pharmacokinetic (PBPK) modeling.

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Notes

  1. Interestingly, the lowest CLH values are often less than CLint,PTM. It is commonly expected that CLH approaches CLint,PTM when the latter becomes very small. However, this requires that QH >  > CLint,PTM as can be found with Eq. 2. A similar phenomenon occurs with the WSM. Of course, adding fub will usually produce lower values of fub x CLint,PTM operative in the more complete models of hepatic clearance. This type of behavior was demonstrated previously in simulations by Winkler et al. (5).

  2. Benet et al. (10) pose that amount eliminated per unit of time/systemic concentration is the “one valid definition of CL.” While this is a correct and mechanistically operative relationship for hepatic metabolism, perhaps a more general definition of a clearance process is velocity/substrate concentration as long appreciated (5). The latter is more useful in recognizing clearance processes (viz. Eq. 1 versus 2), allows for relationships such as Eq. 6, and helps in designation of transport and flow/permeability distribution clearances versus elimination clearances.

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Acknowledgements

WJJ acknowledges that he was a reviewer for the Benet et al. (10) publication and regrets that he did not catch the indicated problems at that time. The authors appreciate review comments by Dr. Yoo-Seong Jeong.

Funding

This work was supported by NIH Grant R35 GM131800.

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  1. Department of Pharmaceutical Sciences, State University of New York at Buffalo, 404 Pharmacy Building, Buffalo, New York, 14214, USA

    William J. Jusko & Xiaonan Li

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  1. William J. Jusko
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WJJ performed most of the literature assessment and writing while XL provided calculations and manuscript revisions.

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Correspondence to William J. Jusko.

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Jusko, W.J., Li, X. Assessment of the Kochak-Benet Equation for Hepatic Clearance for the Parallel-Tube Model: Relevance of Classic Clearance Concepts in PK and PBPK. AAPS J 24, 5 (2022). https://doi.org/10.1208/s12248-021-00656-z

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