Nonlinear Dynamic Modeling of Physiological Systems: (IEEE Press Series on Biomedical Engineering)

The study of nonlinearities in physiology has been hindered by the lack of effective ways to obtain nonlinear dynamic models from stimulus-response data in a practical context. A considerable body of knowledge has accumulated over the last thirty years in this area of research. This book summarizes that progress, and details the most recent methodologies that offer practical solutions to this daunting problem. Implementation and application are discussed, and examples are provided using both synthetic and actual experimental data.
This essential study of nonlinearities in physiology apprises researchers and students of the latest findings and techniques in the field.

Table of Contents:

Prologue xiii

1 Introduction 1
1.1 Purpose of this Book 1
1.2 Advocated Approach 4
1.3 The Problem of System Modeling in Physiology 6
1.4 Types of Nonlinear Models of Physiological Systems 13
1.5 Deductive and Inductive Modeling 24

2 Nonparametric Modeling 29
2.1 Volterra Models 31
2.2 Wiener Models 57
2.3 Efficient Volterra Kernel Estimation 100
2.4 Analysis of Estimation Errors 125

3 Parametric Modeling 145
3.1 Basic Parametric Model Forms and Estimation Procedures 146
3.2 Volterra Kernels of Nonlinear Differential Equations 153
3.3 Discrete-Time Volterra Kernels of NARMAX Models 164
3.4 From Volterra Kernel Measurements to Parametric Models 167
3.5 Equivalence Between Continuous and Discrete Parametric Models 171

4 Modular and Connectionist Modeling 179
4.1 Modular Form of Nonparametric Models 179
4.2 Connectionist Models 223
4.3 The Laguerre-Volterra Network 246
4.4 The VWM Model 260

5 A Practitioner's Guide 265
5.1 Practical Considerations and Experimental Requirements 265
5.2 Preliminary Tests and Data Preparation 272
5.3 Model Specification and Estimation 276
5.4 Model Validation and Interpretation 279
5.5 Outline of Step-by-Step Procedure 283

6 Selected Applications 285
6.2 Cardiovascular System 320
6.3 Renal System 333
6.4 Metabolic-Endocrine System 342

7 Modeling of Multiinput/Multioutput Systems 359
7.1 The Two-Input Case 360
7.2 Applications of Two-Input Modeling to Physiological Systems 369
7.3 The Multiinput Case 389
7.4 Spatiotemporal and Spectrotemporal Modeling 395

8 Modeling of Neuronal Systems 407
8.1 A General Model of Membrane and Synaptic Dynamics 408
8.2 Functional Integration in the Single Neuron 414
8.3 Neuronal Systems with Point-Process Inputs 439
8.4 Modeling of Neuronal Ensembles 463

9 Modeling of Nonstationary Systems 467
9.1 Quasistationary and Recursive Tracking Methods 468
9.2 Kernel Expansion Method 469
9.3 Network-Based Methods 480
9.4 Applications to Nonstationary Physiological Systems 484

10 Modeling of Closed-Loop Systems 489
10.1 Autoregressive Form of Closed-Loop Model 490
10.2 Network Model Form of Closed-Loop Systems 491

Appendix I Function Expansions 495
Appendix II Gaussian White Noise 499
Appendix III Construction of the Wiener Series 503
Appendix IV Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes 505

References 507
Index 535

"...a well-written methodology book...a useful addition to [researchers, engineers and graduate students']...personal libraries." (E-STREAMS, September 2005)