Nonlinear Dynamic Modeling of Physiological Systems

Abstract

Prologue. 1 Introduction. 1.1 Purpose of this Book. 1.2 Advocated Approach. 1.3 The Problem of System Modeling in Physiology. 1.4 Types of Nonlinear Models of Physiological Systems. 2 Nonparametric Modeling. 2.1 Volterra Models. 2.2 Wiener Models. 2.3 Efficient Volterra Kernel Estimation. 2.4 Analysis of Estimation Errors. 3 Parametric Modeling. 3.1 Basic Parametric Model Forms and Estimation Procedures. 3.2 Volterra Kernels of Nonlinear Differential Equations. 3.3 Discrete-Time Volterra Kernels of NARMAX Models. 3.4 From Volterra Kernel Measurements to Parametric Models. 3.5 Equivalence Between Continuous and Discrete Parametric Models. 4 Modular and Connectionist Modeling. 4.1 Modular Form of Nonparametric Models. 4.2 Connectionist Models. 4.3 The Laguerre-Volterra Network. 4.4 The VWM Model. 5 A Practitioner's Guide. 5.1 Practical Considerations and Experimental Requirements. 5.2 Preliminary Tests and Data Preparation. 5.3 Model Specification and Estimation. 5.4 Model Validation and Interpretation. 5.5 Outline of Step-by-Step Procedure. 6 Selected Applications. 6.1 Neurosensory Systems. 6.2 Cardiovascular System. 6.3 Renal System. 6.4 Metabolic-Endocrine System. 7 Modeling of Multiinput/Multioutput Systems. 7.1 The Two-Input Case. 7.2 Applications of Two-Input Modeling to Physiological Systems. 7.3 The Multiinput Case. 7.4 Spatiotemporal and Spectrotemporal Modeling. 8 Modeling of Neuronal Systems. 8.1 A General Model of Membrane and Synaptic Dynamics. 8.2 Functional Integration in the Single Neuron. 8.3 Neuronal Systems with Point-Process Inputs. 8.4 Modeling of Neuronal Ensembles. 9 Modeling of Nonstationary Systems. 9.1 Quasistationary and Recursive Tracking Methods. 9.2 Kernel Expansion Method. 9.3 Network-Based Methods. 9.4 Applications to Nonstationary Physiological Systems. 10 Modeling of Closed-Loop Systems. 10.1 Autoregressive Form of Closed-Loop Model. 10.2 Network Model Form of Closed-Loop Systems. Appendix I: Function Expansions. Appendix II: Gaussian White Noise. Appendix III: Construction of the Wiener Series. Appendix IV: Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes. References. Index.