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Applications of Mathematics

, Volume 64, Issue 2, pp 253–277 | Cite as

On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy

  • Jurjen Duintjer TebbensEmail author
  • Ctirad MatonohaEmail author
  • Andreas MatthiosEmail author
  • Štěpán PapáčekEmail author
Article
  • 16 Downloads

Abstract

A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter on the solution of the model’s system of ordinary differential equations is given and it is pointed out that some ingredients of the analysis might be useful for more general pharmacodynamic models. Numerical experiments are presented to illustrate the performance of related parameter estimation procedures based on least-squares minimization.

Keywords

pharmacotherapy pharmacodynamic modelling constrained optimization parameter estimation 

MSC 2010

92C45 34A34 65F60 65K10 

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Notes

Acknowledgement

We would like to thank Prof. Petr Pávek for the laboratory experiments described in this manuscript; they were performed under his supervision and in his laboratory at the Faculty of Pharmacy of Charles university in Hradec Králové.

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Copyright information

© Mathematical Institute, Academy of Sciences of Cz 2019

Authors and Affiliations

  1. 1.Faculty of Pharmacy in Hradec KrálovéCharles UniversityHradec KrálovéCzech Republic
  2. 2.Institute of Computer ScienceCzech Academy of SciencesPraha 8Czech Republic
  3. 3.Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of WatersUniversity of South Bohemia in České BudějoviceNové HradyCzech Republic

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