# Lumping of physiologically-based pharmacokinetic models and a mechanistic derivation of classical compartmental models

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## Abstract

In drug discovery and development, classical compartment models and physiologically based pharmacokinetic (PBPK) models are successfully used to analyze and predict the pharmacokinetics of drugs. So far, however, both approaches are used exclusively or in parallel, with little to no cross-fertilization. An approach that directly links classical compartment and PBPK models is highly desirable. We derived a new mechanistic lumping approach for reducing the complexity of PBPK models and establishing a direct link to classical compartment models. The proposed method has several advantages over existing methods: Perfusion and permeability rate limited models can be lumped; the lumped model allows for predicting the original organ concentrations; and the volume of distribution at steady state is preserved by the lumping method. To inform classical compartmental model development, we introduced the concept of a minimal lumped model that allows for prediction of the venous plasma concentration with as few compartments as possible. The minimal lumped parameter values may serve as initial values for any subsequent parameter estimation process. Applying our lumping method to 25 diverse drugs, we identified characteristic features of lumped models for moderate-to-strong bases, weak bases and acids. We observed that for acids with high protein binding, the lumped model comprised only a single compartment. The proposed lumping approach established for the first time a direct derivation of simple compartment models from PBPK models and enables a mechanistic interpretation of classical compartment models.

## Keywords

Classical model Compartment PK model Physiologically based pharmacokinetics PBPK Mechanistic lumping Volume of distribution Minimal lumped model Transfer of knowledge## Notes

### Acknowledgements

The authors kindly acknowledge comments on the manuscript by Charlotte Kloft (Clinical Pharmacy, Martin-Luther-Universität Halle-Wittenberg/ Germany), Steve Kirkland (Hamilton Institute, NUIM/Ireland), Andreas Reichel (Bayer Schering Pharma) and Olaf Lichtenberger (Abbott). S.P. acknowledges financial support from the Graduate Research Training Program PharMetrX: Pharmacometrics and Computational Disease Modeling, Martin-Luther-Universität Halle-Wittenberg and Freie Universität Berlin, Germany (http://www.pharmacometrics.de).

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