Estimating Nonlinear Dynamic Systems in Pharmacology using Chaos Synchronization
Nikhil Pillai, Sorell L. Schwartz, Thang Ho, Aris Dokoumetzidis, Robert Bies, Immanuel Freedman
University at Buffalo, Georgetown University Medical Center, Vertex Pharmaceuticals, University of Athens, University at Buffalo, Immanuel Freedman, Harleysville PA
Objectives: Bridging fundamental approaches to model optimization for pharmacometricians, systems pharmacologists and statisticians is a critical issue. Currently, these fields rely primarily on Maximum Likelihood and Extended Least Squares metrics with iterative estimation of parameters. Our research utilizes chaos synchronization to estimate physiological and pharmacological systems with emergent properties by exploring methods with potentially superior performance to stochastic estimators.
Methods: We analyze the structural identifiability of the Dokoumetzidis cortisol model [1] using the DAISY software and apply adaptive chaos synchronization (ACS) according to Huang [2] to track the system and estimate its linear parameters. We compare the performance of this chaos synchronization method to non-linear least squares (NLS) regression solving the ordinary differential equations via MATLAB/ode15s.
Results: We evaluated noiseless, sparse noisy and dense noisy data. With ACS according to Huang [2, ]the input and output rate constants rapidly converged to their nominal values and the predictions tracked the system with high fidelity without appreciable offset. NLS regression was unable to provide accurate estimation of the parameters with a substantial offset that increased with noise and sparsity of sampling.
Conclusions: The analysis shows that ACS according to Huang [2] is a highly effective and robust approach to estimating a noisy and sparsely-sampled chaotic system. Moreover, ACS provided accurate estimation with less computational resource than NLS. The overall approach is systematic and relatively easy to implement.
References:
[1] Dokoumetzidis, A., A. Iliadis, and P. Macheras, Nonlinear dynamics in Clinical Pharmacology: the paradigm of cortisol secretion and suppression. British Journal of Clinical Pharmacology, 2002. 54(1): p. 21-29.
[2] Huang, D., Synchronization-based estimation of all parameters of chaotic systems from time series. Physical Review E, 2004. 69(6): p. 067201.