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Estimating parameters of nonlinear dynamic systems in pharmacology using chaos synchronization and grid search

Authors
  • Pillai, Nikhil1
  • Schwartz, Sorell L.2
  • Ho, Thang3
  • Dokoumetzidis, Aris4
  • Bies, Robert1, 5
  • Freedman, Immanuel6
  • 1 University at Buffalo, Computational and Data-Enabled Science, Buffalo, USA , Buffalo (United States)
  • 2 Georgetown University Medical Center, Department of Pharmacology and Physiology, Georgetown, USA , Georgetown (United States)
  • 3 Vertex Pharmaceuticals, Boston, USA , Boston (United States)
  • 4 University of Athens, Department of Pharmaceutical Technology, Athens, Greece , Athens (Greece)
  • 5 University at Buffalo, Pharmaceutical Science, Buffalo, USA , Buffalo (United States)
  • 6 Freedman Patent, Harleysville, PA, 19438, USA , Harleysville (United States)
Type
Published Article
Journal
Journal of Pharmacokinetics and Pharmacodynamics
Publisher
Springer US
Publication Date
Mar 30, 2019
Volume
46
Issue
2
Pages
193–210
Identifiers
DOI: 10.1007/s10928-019-09629-4
Source
Springer Nature
Keywords
License
Green

Abstract

Bridging fundamental approaches to model optimization for pharmacometricians, systems pharmacologists and statisticians is a critical issue. These fields rely primarily on Maximum Likelihood and Extended Least Squares metrics with iterative estimation of parameters. Our research combines adaptive chaos synchronization and grid search to estimate physiological and pharmacological systems with emergent properties by exploring deterministic methods that are more appropriate and have potentially superior performance than classical numerical approaches, which minimize the sum of squares or maximize the likelihood. We illustrate these issues with an established model of cortisol in human with nonlinear dynamics. The model describes cortisol kinetics over time, including its chaotic oscillations, by a delay differential equation. We demonstrate that chaos synchronization helps to avoid the tendency of the gradient-based optimization algorithms to end up in a local minimum. The subsequent analysis illustrates that the hybrid adaptive chaos synchronization for estimation of linear parameters with coarse-to-fine grid search for optimal values of non-linear parameters can be applied iteratively to accurately estimate parameters and effectively track trajectories for a wide class of noisy chaotic systems.

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