Applications of Mathematics, Vol. 64, No. 2, pp. 253-277, 2019

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

Jurjen Duintjer Tebbens, Ctirad Matonoha, Andreas Matthios, Štěpán Papáček

Received October 16, 2018.   Published online March 20, 2019.

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
Classification MSC:  92C45, 34A34, 65F60, 65K10
DOI:  10.21136/AM.2019.0284-18

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Affiliations:   Jurjen Duintjer Tebbens, Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203, 500 05 Hradec Králové and Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Praha 8, Czech Republic, e-mail:; Ctirad Matonoha, Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Praha 8, Czech Republic, e-mail:; Andreas Matthios, Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203, 500 05 Hradec Králové, Czech Republic, e-mail:; Štěpán Papáček, Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of Waters, University of South Bohemia in České Budějovice, Zámek 136, 373 33 Nové Hrady, Czech Republic, e-mail:

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