# Mathematical analysis and drug exposure evaluation of pharmacokinetic models with endogenous production and simultaneous first-order and Michaelis–Menten elimination: the case of single dose

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## Abstract

Drugs with an additional endogenous source often exhibit simultaneous first-order and Michaelis–Menten elimination and are becoming quite common in pharmacokinetic modeling. In this paper, we investigate the case of single dose intravenous bolus administration for the one-compartment model. Relying on a formerly introduced transcendent function, we were able to analytically express the concentration time course of this model and provide the pharmacokinetic interpretation of its components. Using the concept of the corrected concentration, the mathematical expressions for the partial and total areas under the concentration time curve (AUC) were also given. The impact on the corrected concentration and AUC is discussed as well as the relative contribution of the exogenous part in presence of endogenous production. The present findings theoretically elucidate several pharmacokinetic issues for the considered drug compounds and provide guidance for the rational estimation of their pharmacokinetic parameters.

## Keywords

Pharmacokinetic model*X*function Endogenous production Simultaneous first-order and Michaelis–Menten elimination Area under the concentration time curve (AUC)

## Notes

### Acknowledgements

This work is supported by FRQNT Fellowship (X. Wu) and the NSERC-Industrial Chair in Pharmacometrics (co-funded by InVentiv Health and Pfizer) and FRQNT Projet d’équipe led by F. Nekka. X. Wu and J. Li also thank the support from NSFC (No.11501358). We thank the referees for their careful reading and valuable comments which helped improving the quality of the paper.

## Supplementary material

## References

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