Nonlinear Dynamic Modeling of Physiological Systems

Vasilis Z. Marmarelis, PhD, received his diploma in electrical and mechanical engineering from the National Technical University of Athens and his MS in information science and PhD in engineering science (bio-information systems) from the California Institute of Technology. He is currently a professor in the faculty of the Biomedical and Electrical Engineering Departments at USC, where he served as chairman of Biomedical Engineering from 1990 to 1996. He is also Codirector of the Biomedical Simulations Resource (BMSR), a research center dedicated to modeling and simulation of physiological systems and funded by the National Institutes of Health through multimillion-dollar grants since 1985.

"...a perfect research tool, as reference book, and even as a textbook. I highly recommend it to everyone interested in nonlinear dynamics." (Journal of Intelligent & Fuzzy Systems, Vol. 16, No. 2, 2005) "...a well-written methodology book...a useful addition to [researchers, engineers and graduate students']...personal libraries." (E-STREAMS, September 2005)

• Prologue xiii1 Introduction 11.1 Purpose of this Book 11.2 Advocated Approach 41.3 The Problem of System Modeling in Physiology 61.4 Types of Nonlinear Models of Physiological Systems 131.5 Deductive and Inductive Modeling 242 Nonparametric Modeling 292.1 Volterra Models 312.2 Wiener Models 572.3 Efficient Volterra Kernel Estimation 1002.4 Analysis of Estimation Errors 1253 Parametric Modeling 1453.1 Basic Parametric Model Forms and Estimation Procedures 1463.2 Volterra Kernels of Nonlinear Differential Equations 1533.3 Discrete-Time Volterra Kernels of NARMAX Models 1643.4 From Volterra Kernel Measurements to Parametric Models 1673.5 Equivalence Between Continuous and Discrete Parametric Models 1714 Modular and Connectionist Modeling 1794.1 Modular Form of Nonparametric Models 1794.2 Connectionist Models 2234.3 The Laguerre-Volterra Network 2464.4 The VWM Model 2605 A Practitioner's Guide 2655.1 Practical Considerations and Experimental Requirements 2655.2 Preliminary Tests and Data Preparation 2725.3 Model Specification and Estimation 2765.4 Model Validation and Interpretation 2795.5 Outline of Step-by-Step Procedure 2836 Selected Applications 2856.2 Cardiovascular System 3206.3 Renal System 3336.4 Metabolic-Endocrine System 3427 Modeling of Multiinput/Multioutput Systems 3597.1 The Two-Input Case 3607.2 Applications of Two-Input Modeling to Physiological Systems 3697.3 The Multiinput Case 3897.4 Spatiotemporal and Spectrotemporal Modeling 3958 Modeling of Neuronal Systems 4078.1 A General Model of Membrane and Synaptic Dynamics 4088.2 Functional Integration in the Single Neuron 4148.3 Neuronal Systems with Point-Process Inputs 4398.4 Modeling of Neuronal Ensembles 4639 Modeling of Nonstationary Systems 4679.1 Quasistationary and Recursive Tracking Methods 4689.2 Kernel Expansion Method 4699.3 Network-Based Methods 4809.4 Applications to Nonstationary Physiological Systems 48410 Modeling of Closed-Loop Systems 48910.1 Autoregressive Form of Closed-Loop Model 49010.2 Network Model Form of Closed-Loop Systems 491Appendix I Function Expansions 495Appendix II Gaussian White Noise 499Appendix III Construction of the Wiener Series 503Appendix IV Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes 505References 507Index 535