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Analytical Solution and Exposure Analysis of a Pharmacokinetic Model with Simultaneous Elimination Pathways and Endogenous Production: The Case of Multiple Dosing Administration

  • Xiaotian Wu
  • Fahima Nekka
  • Jun LiEmail author
Special Issue: Mathematics to Support Drug Discovery and Development
  • 14 Downloads

Abstract

In this paper, a typical pharmacokinetic (PK) model is studied for the case of multiple intravenous bolus-dose administration. This model, of one-compartment structure, not only exhibits simultaneous first-order and Michaelis–Menten elimination, but also involves a constant endogenous production. For the PK characterization of the model, we have established the closed-form solution of concentrations over time, the existence and local stability of the steady state. Using analytical approaches and the concept of corrected concentration, we have shown that the area under the curve (\(\hbox {AUC}^{corr}_{ss,\tau }\)) at steady state is higher compared to that at the single dose (\(\hbox {AUC}^{corr}_{0-\infty }\)). Moreover, by splitting the dose and dosing interval into halves, we have revealed that it can result in a significant decrease in the steady-state average concentration. These model-based findings, which contrast with the current knowledge for linear PK, confirm the necessity to revisit drugs exhibiting nonlinear PK and to suggest a rational way of using mathematical analysis for the dosing regimen design.

Keywords

Pharmacokinetic model Simultaneous first-order and Michaelis–Menten elimination Endogenous production Area under the curve at steady state Average concentration at steady state 

Mathematics Subject Classification

92C45 92C50 34N05 37N25 

Notes

Acknowledgements

This research is supported by NSERC-Industrial Chair in Pharmacometrics—Novartis, Pfizer and Inventiv Health Clinical and FRQNT Projet d’équipe led by F. Nekka as well as NSERC and FRQNT (F.N. and J.L.). FRQNT Fellowship and NSFC (No. 11501358) hold by X.W. are also acknowledged.

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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiPeople’s Republic of China
  2. 2.Faculté de pharmacieUniversité de MontréalMontrealCanada
  3. 3.Centre de Recherches MathématiquesUniversité de MontréalMontrealCanada

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