Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study

In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase‐planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor‐pool model with positive feedback is used to demonstrate the power of mathematical ana...

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Detalles Bibliográficos
Autores principales: Bakshi, S, de Lange, EC, van der Graaf, PH, Danhof, M, Peletier, LA
Formato: Online Artículo Texto
Lenguaje:English
Publicado: John Wiley and Sons Inc. 2016
Materias:
Tutorial
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4961077/
https://www.ncbi.nlm.nih.gov/pubmed/27405001
http://dx.doi.org/10.1002/psp4.12098
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author Bakshi, S
de Lange, EC
van der Graaf, PH
Danhof, M
Peletier, LA
author_facet Bakshi, S
de Lange, EC
van der Graaf, PH
Danhof, M
Peletier, LA
author_sort Bakshi, S
collection PubMed
description In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase‐planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor‐pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed. The analysis offers insight into model behavior and suggests useful parameter regions, which simulations alone could not.
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spelling pubmed-49610772016-08-05 Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study Bakshi, S de Lange, EC van der Graaf, PH Danhof, M Peletier, LA CPT Pharmacometrics Syst Pharmacol Tutorial In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase‐planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor‐pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed. The analysis offers insight into model behavior and suggests useful parameter regions, which simulations alone could not. John Wiley and Sons Inc. 2016-07-20 2016-07 /pmc/articles/PMC4961077/ /pubmed/27405001 http://dx.doi.org/10.1002/psp4.12098 Text en © 2016 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs (http://creativecommons.org/licenses/by-nc-nd/4.0/) License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.
spellingShingle Tutorial
Bakshi, S
de Lange, EC
van der Graaf, PH
Danhof, M
Peletier, LA
Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
title Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
title_full Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
title_fullStr Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
title_full_unstemmed Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
title_short Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
title_sort understanding the behavior of systems pharmacology models using mathematical analysis of differential equations: prolactin modeling as a case study
topic Tutorial
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4961077/
https://www.ncbi.nlm.nih.gov/pubmed/27405001
http://dx.doi.org/10.1002/psp4.12098
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