Geometric singular perturbation analysis of a dynamical target mediated drug disposition model. View Full Text


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Article Info

DATE

2019-04-10

AUTHORS

Kristian Uldall Kristiansen

ABSTRACT

In this paper we present a mathematical analysis of a pharmacological ODE model for target mediated drug disposition (TMDD). It is known that solutions of this model undergo four qualitatively different phases. In this paper we provide a mathematical identification of these separate phases by viewing the TMDD model as a singular perturbed system. Our analysis is based on geometric singular perturbation theory and we believe that this approach systemizes-and sheds further light on-the scalings arguments used by previous authors. In particular, we present a novel description of the third phase through a distinguished solution of a nonlinear differential equation. We also describe the solution curve for large values of initial drug doses and recover, en route, a result by Aston et al. (J Math Biol 68(6):1453-1478, 2014) on rebounding using our alternative perturbation approach. Finally, from our main result we derive a new method for estimating the parameters of the system in the event that detailed data is available. Ideally our approach to the TMDD model should stimulate further research into applications of these methods to more complicated models in pharmacology. More... »

References to SciGraph publications

  • 2005-05. Asymptotic expansions using blow-up in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 2013-06. Dynamics of target-mediated drug disposition: how a drug reaches its target in COMPUTATIONAL GEOSCIENCES
  • 1994-09. Pharmacologic target‐mediated drug disposition in CLINICAL PHARMACOLOGY & THERAPEUTICS
  • 2015. Multiple Time Scale Dynamics in NONE
  • 2014-05. A mathematical analysis of rebound in a target-mediated drug disposition model: I.Without feedback in JOURNAL OF MATHEMATICAL BIOLOGY
  • 2015-12. Challenges in Pharmacology Modelling in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 2012-10. Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification in JOURNAL OF PHARMACOKINETICS AND PHARMACODYNAMICS
  • 2016-04. Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle in JOURNAL OF MATHEMATICAL BIOLOGY
  • 2016-06. Asymptotic Analysis of a Target-Mediated Drug Disposition Model: Algorithmic and Traditional Approaches in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2001-12. General Pharmacokinetic Model for Drugs Exhibiting Target-Mediated Drug Disposition in JOURNAL OF PHARMACOKINETICS AND PHARMACODYNAMICS
  • 2016-09. Topics in Mathematical Pharmacology in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00285-019-01354-3

    DOI

    http://dx.doi.org/10.1007/s00285-019-01354-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1113356146

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/30972439


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