ArticleJournal of mathematical biology2019
Geometric singular perturbation analysis of a dynamical target mediated drug disposition model.
Article in Journal of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Exact Formula of the Total Quasi-Steady State Approximation in Competitive Target-Mediated Drug Disposition.Computational and structural biotechnology journal · 2026Article
- On the coupling between a basic FcRn mechanism and target-mediated disposition of antibodies.Journal of pharmacokinetics and pharmacodynamics · 2025Article
- An asymptotic description of a basic FcRn-regulated clearance mechanism and its implications for PBPK modelling of large antibodies.Journal of pharmacokinetics and pharmacodynamics · 2024Article
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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.
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