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

On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy. (English) Zbl 07088739

Appl. Math., Praha 64, No. 2, 253-277 (2019).
Summary: 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.

Cited in 1 Review
Cited in 1 Document

MSC:

92C50 Medical applications (general)
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
34A34 Nonlinear ordinary differential equations and systems
65F60 Numerical computation of matrix exponential and similar matrix functions
65K10 Numerical optimization and variational techniques

Keywords:

pharmacotherapy; pharmacodynamic modelling; constrained optimization; parameter estimation

Software:

UFO; Celldesigner; ODEPACK; Matlab
PDF BibTeX XML Cite
\textit{J. Duintjer Tebbens} et al., Appl. Math., Praha 64, No. 2, 253--277 (2019; Zbl 07088739)
Full Text: DOI

References:

[1] D’Argenio, D. Z.; Schumitzky, A.; Wang, X., ADAPT 5 User’s Guide: Pharmacokinetic/Pharmacodynamic Systems Analysis Software, Biomedical Simulations Resource, Los Angeles (2009), Available at https://bmsr.usc.edu/software/adapt/users-guide/
[2] Dhillon, S.; Kostrzewski, A.; (eds.), Clinical Pharmacokinetics, Pharmaceutical Press, London (2006)
[3] Tebbens, J. Duintjer; Azar, M.; Friedmann, E.; Lanzendörfer, M.; Pávek, P., Mathematical models in the description of pregnane X receptor (PXR)-regulated cytochrome P450 enzyme induction, Int. J. Mol. Sci. 19 (2018), 1785
[4] Funahashi, A.; Morohashi, M.; Kitano, H.; Tanimura, N., CellDesigner: a process diagram editor for gene-regulatory and biochemical networks, BIOSILICO 1 (2003), 159-162
[5] The GNU Fortran compiler, Available at http://gcc.gnu.org/fortran/. Software: https://swmath.org/software/00959
[6] Hindmarsh, A. C., Large ordinary differential equation systems and software, Control Systems Magazine 2 (1982), 24-30
[7] Hindmarsh, A. C., ODEPACK, a systematized collection of ODE solvers, Scientific Computing 1982 R. S. Stepleman et al. IMACS Transactions on Scientific Computation I, North-Holland Publishing, Amsterdam (1983), 55-64
[8] Jones, H. M.; Rowland-Yeo, K., Basic Concepts in Physiologically Based Pharmacokinetic Modeling in Drug Discovery and Development, CPT: Pharmacometrics & Systems Pharmacology 2 (2013), Article ID e63, 12 pages
[9] Luke, N. S.; DeVito, M. J.; Shah, I.; El-Masri, H. A., Development of a quantitative model of pregnane X receptor (PXR) mediated xenobiotic metabolizing enzyme induction, Bull. Math. Biol. 72 (2010), 1799-1819 · Zbl 1202.92029
[10] Lukšan, L.; Tůma, M.; Matonoha, C.; Vlček, J.; Ramešová, N.; Šiška, M.; Hartman, J., UFO 2017. Interactive System for Universal Functional Optimization, Technical Report V-1252, Institute for Computer Science CAS, Praha, 2017. Available at http://www.cs.cas.cz/luksan/ufo.html
[11] Lunn, D. J.; Best, N.; Thomas, A.; Wakefield, J.; Spiegelhalter, D. J., Bayesian analysis of population PK/PD models: General concepts and software, J. Pharmacokinetics Pharmacodynamics 29 (2002), 271-307
[12] MATLAB, Mathworks, Inc., 2018. Available at https://www.mathworks.com/products/matlab.html. Software: https://swmath.org/software/00558
[13] Moler, C.; Loan, C. Van, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev. 45 (2003), 3-49 · Zbl 1030.65029
[14] Nelder, J. A.; Mead, R., A simplex method for function minimization, Computer J. 4 (1965), 308-313 · Zbl 0229.65053
[15] NONMEM 7.3, ICON, Inc., 1990-2016. Available at http://www.iconplc.com/innovation/nonmem/. Software: https://swmath.org/software/08344
[16] Petzold, L., Automatic selection of methods for solving stiff and nonstiff systems of ordinary diferential equations, SIAM J. Sci. Stat. Comput. 4 (1983), 136-148 · Zbl 0518.65051
[17] Shargel, L.; Yu, A. B. C., Applied Biopharmaceutics & Pharmacokinetics, McGraw-Hill Education, New York (2016)
[18] Simcyp simulator, Certara, 2012. Available at http://www.certara.com/software/. Software: https://swmath.org/software/23162
[19] Spruill, J. W.; Wade, W. E.; DiPiro, T. J.; Blouin, A. R.; Pruemer, M. J., Concepts in Clinical Pharmacokinetics, American Society of Health-System Pharmacists, Bethesda (2014)
[20] Zhao, P.; Rowland, M.; Huang, S.-M., Best practice in the use of physiologically based pharmacokinetic modeling and simulation to address clinical pharmacology regulatory questions, Clinical Pharmacology & Therapeutics 92 (2012), 17-20
[21] Zheng, Z.; Stewart, P. S., Penetration of rifampin through staphylococcus epidermidis biofilms, Antimicrob. Agents Chemoter 46 (2002), 900-903
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.