Nonlinear Dynamic Modeling of Physiological Systems

1. Auflage 2004
ISBN: 978-0-471-46960-5
Verlag: Wiley

Buch, Englisch, 560 Seiten, Format (B × H): 186 mm x 260 mm, Gewicht: 1161 g

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.

Autoren/Hrsg.

Marmarelis, Vasilis Z

Marmarelis, Vasilis Z.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik

Inhaltsverzeichnis

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

1.3.1 Model Specification and Estimation 10

1.3.2 Nonlinearity and Nonstationarity 12

1.3.3 Definition of the Modeling Problem 13

1.4 Types of Nonlinear Models of Physiological Systems 13

Example 1.1. Vertebrate Retina 15

Example 1.2. Invertebrate Photoreceptor 18

Example 1.3. Volterra analysis of Riccati Equation 19

Example 1.4. Glucose-Insulin Minimal Model 21

Example 1.5. Cerebral Autoregulation 22

1.5 Deductive and Inductive Modeling 24

Historical Note #1: Hippocratic and Galenic Views of 26

Integrative Physiology

2 Nonparametric Modeling 29

2.1 Volterra Models 31

2.1.1 Examples of Volterra Models 37

Example 2.1. Static Nonlinear System 37

Example 2.2. L–N Cascade System 38

Example 2.3. L–N–M “Sandwich” System 39

Example 2.4. Riccati System 40

2.1.2 Operational Meaning of the Volterra Kernels 41

Impulsive Inputs 42

Sinusoidal Inputs 43

Remarks on the Meaning of Volterra Kernels 45

2.1.3 Frequency-Domain Representation of the Volterra Models 45

2.1.4 Discrete-Time Volterra Models 47

2.1.5 Estimation of Volterra Kernels 49

Specialized Test Inputs 50

Arbitrary Inputs 52

Fast Exact Orthogonalization and Parallel-Cascade Methods 55

Iterative Cost-Minimization Methods for Non-Gaussian 55

Residuals

2.2 Wiener Models 57

2.2.1 Relation between Volterra and Wiener Models 60

The Wiener Class of Systems 62

Examples of Wiener Models 63

Comparison of Volterra/Wiener Model Predictions 64

2.2.2 Wiener Approach to Kernel Estimation 67

2.2.3 The Cross-Correlation Technique for Wiener Kernel Estimation 72

Estimation of h0 73

Estimation of h1

Über Autor(innen)

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.