title: Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study.
abstract: 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.
authors.affiliation: Systems Pharmacology, Division of Pharmacology, LACDR, Leiden University, Leiden, The Netherlands.
authors.forename: S
authors.initials: S
authors.lastname: Bakshi
authors.affiliation: Systems Pharmacology, Division of Pharmacology, LACDR, Leiden University, Leiden, The Netherlands.
authors.forename: E C
authors.initials: EC
authors.lastname: de Lange
authors.affiliation: Systems Pharmacology, Division of Pharmacology, LACDR, Leiden University, Leiden, The Netherlands.|Certara QSP, Canterbury Innovation House, Canterbury, United Kingdom.
authors.forename: P H
authors.initials: PH
authors.lastname: van der Graaf
authors.affiliation: Systems Pharmacology, Division of Pharmacology, LACDR, Leiden University, Leiden, The Netherlands.
authors.forename: M
authors.initials: M
authors.lastname: Danhof
authors.affiliation: Mathematical Institute, Leiden University, Leiden, The Netherlands.
authors.forename: L A
authors.initials: LA
authors.lastname: Peletier
mesh_terms: D032882:Comprehension; D004305:Dose-Response Relationship, Drug; D006801:Humans; D008297:Male; D008954:Models, Biological; D008962:Models, Theoretical; D011388:Prolactin / Q000097:blood / Q000494:pharmacology*; D013597:Systems Analysis
chemical_list: D011388:Prolactin