Nonlinear Dynamic Modeling of Physiological Systems

by Marmarelis, Vasilis Z.

• ISBN13: 9780471469605
• ISBN10: 0471469602
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-09-03
• Publisher: Wiley-IEEE Press

Summary

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.

Author Biography

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.

Table of Contents

Prologue	xiii
Introduction	1	(28)
Purpose of this Book	1	(3)
Advocated Approach	4	(2)
The Problem of System Modeling in Physiology	6	(7)
Model Specification and Estimation	10	(2)
Nonlinearity and Nonstationarity	12	(1)
Definition of the Modeling Problem	13	(1)
Types of Nonlinear Models of Physiological Systems	13	(11)
Vertebrate Retina	15	(3)
Invertebrate Photoreceptor	18	(1)
Volterra analysis of Riccati Equation	19	(2)
Glucose-Insulin Minimal Model	21	(1)
Cerebral Autoregulation	22	(2)
Deductive and Inductive Modeling	24	(5)
Historical Note #1: Hippocratic and Galenic Views of Integrative Physiology	26	(3)
Nonparametric Modeling	29	(116)
Volterra Models	31	(26)
Examples of Volterra Models	37	(1)
Static Nonlinear System	37	(1)
L--N Cascade System	38	(1)
L--N--M ``Sandwich'' System	39	(1)
Riccati System	40	(1)
Operational Meaning of the Volterra Kernels	41	(1)
Impulsive Inputs	42	(1)
Sinusoidal Inputs	43	(2)
Remarks on the Meaning of Volterra Kernels	45	(1)
Frequency-Domain Representation of the Volterra Models	45	(2)
Discrete-Time Volterra Models	47	(2)
Estimation of Volterra Kernels	49	(1)
Specialized Test Inputs	50	(2)
Arbitrary Inputs	52	(3)
Fast Exact Orthogonalization and Parallel-Cascade Methods	55	(1)
Iterative Cost-Minimization Methods for Non-Gaussian Residuals	55	(2)
Wiener Models	57	(43)
Relation between Volterra and Wiener Models	60	(2)
The Wiener Class of Systems	62	(1)
Examples of Wiener Models	63	(1)
Comparison of Volterra/Wiener Model Predictions	64	(3)
Wiener Approach to Kernel Estimation	67	(5)
The Cross-Correlation Technique for Wiener Kernel Estimation	72	(1)
Estimation of h0	73	(1)
Estimation of h1(τ)	73	(1)
Estimation of h2(τ1, τ2)	74	(1)
Estimation of h3(τ1, τ2, τ3)	75	(2)
Some Practical Considerations	77	(1)
Illustrative Example	78	(1)
Frequency-Domain Estimation of Wiener Kernels	78	(2)
Quasiwhite Test Inputs	80	(4)
CSRS and Volterra Kernels	84	(1)
The Diagonal Estimability Problem	85	(1)
An Analytical Example	86	(2)
Comparison of Model Prediction Errors	88	(1)
Discrete-Time Representation of the CSRS Functional Series	89	(1)
Pseudorandom Signals Based on m-Sequences	89	(3)
Comparative Use of GWN, PRS, and CSRS	92	(1)
Apparent Transfer Function and Coherence Measurements	93	(3)
L--N Cascade System	96	(1)
Quadratic Volterra System	97	(1)
Nonwhite Gaussian Inputs	98	(1)
Duffing System	98	(1)
Concluding Remarks	99	(1)
Efficient Volterra Kernel Estimation	100	(25)
Volterra Kernel Expansions	101	(3)
Model Order Determination	104	(3)
The Laguerre Expansion Technique	107	(5)
Illustrative Examples	112	(10)
High-Order Volterra Modeling with Equivalent Networks	122	(3)
Analysis of Estimation Errors	125	(20)
Sources of Estimation Errors	125	(2)
Estimation Errors Associated with the Cross-Correlation Technique	127	(1)
Estimation Bias	128	(2)
Estimation Variance	130	(1)
Optimization of Input Parameters	131	(3)
Noise Effects	134	(2)
Erroneous Scaling of Kernel Estimates	136	(1)
Estimation Errors Associated with Direct Inversion Methods	137	(2)
Estimation Errors Associated with Iterative Cost-Minimization Methods	139	(1)
Historical Note #2: Vito Volterra and Norbert Wiener	140	(5)
Parametric Modeling	145	(34)
Basic Parametric Model Forms and Estimation Procedures	146	(7)
The Nonlinear Case	150	(2)
The Nonstationary Case	152	(1)
Volterra Kernels of Nonlinear Differential Equations	153	(11)
The Riccati Equation	157	(1)
Apparent Transfer Functions of Linearized Models	158	(2)
Illustrative Example	160	(1)
Nonlinear Parametric Models with Intermodulation	161	(3)
Discrete-Time Volterra Kernels of NARMAX Models	164	(3)
From Volterra Kernel Measurements to Parametric Models	167	(4)
Illustrative Example	169	(2)
Equivalence Between Continuous and Discrete Parametric Models	171	(8)
Illustrative Example	175	(2)
Modular Representation	177	(2)
Modular and Connectionist Modeling	179	(86)
Modular Form of Nonparametric Models	179	(44)
Principal Dynamic Modes	180	(6)
Illustrative Examples	186	(5)
Volterra Models of System Cascades	191	(3)
The L--N--M, L--N, and N--M Cascades	194	(4)
Volterra Models of Systems with Lateral Branches	198	(2)
Volterra Models of Systems with Feedback Branches	200	(2)
Nonlinear Feedback Described by Differential Equations	202	(2)
Cubic Feedback Systems	204	(5)
Sigmoid Feedback Systems	209	(4)
Positive Nonlinear Feedback	213	(2)
Second-Order Kernels of Nonlinear Feedback Systems	215	(1)
Nonlinear Feedback in Sensory Systems	216	(4)
Concluding Remarks on Nonlinear Feedback	220	(3)
Connectionist Models	223	(23)
Equivalence between Connectionist and Volterra Models	223	(7)
Relation with PDM Modeling	230	(2)
Illustrative Examples	232	(3)
Volterra-Equivalent Network Architectures for Nonlinear System Modeling	235	(3)
Equivalence with Volterra Kernels/Models	238	(1)
Selection of the Structural Parameters of the VEN Model	238	(2)
Convergence and Accuracy of the Training Procedure	240	(4)
The Pseudomode-Peeling Method	244	(2)
Nonlinear Autoregressive Modeling (Open-Loop)	246	(1)
The Laguerre-Volterra Network	246	(14)
Illustrative Example of LVN Modeling	249	(2)
Modeling Systems with Fast and Slow Dynamic (LVN-2)	251	(4)
Illustrative Examples of LVN-2 Modeling	255	(5)
The VWM Model	260	(5)
A Practitioner's Guide	265	(20)
Practical Considerations and Experimental Requirements	265	(7)
System Characteristics	266	(1)
System Bandwidth	266	(1)
System Memory	267	(1)
System Dynamic Range	267	(1)
System Linearity	268	(1)
System Stationarity	268	(1)
System Ergodicity	268	(1)
Input Characteristics	269	(1)
Experimental Characteristics	270	(2)
Preliminary Tests and Data Preparation	272	(4)
Test for System Bandwidth	272	(1)
Test for System Memory	272	(1)
Test for System Stationarity and Ergodicity	273	(1)
Test for System Linearity	274	(1)
Data Preparation	275	(1)
Model Specification and Estimation	276	(3)
The MDV Modeling Methodology	277	(1)
The VEN/VWM Modeling Methodology	278	(1)
Model Validation and Interpretation	279	(4)
Model Validation	279	(2)
Model Interpretation	281	(1)
Interpretation of Volterra Kernels	281	(1)
Interpretation of the PDM Model	282	(1)
Outline of Step-by-Step Procedure	283	(2)
Elaboration of the Key Step #5	284	(1)
Selected Applications	285	(74)
Neurosensory Systems	286	(34)
Vertebrate Retina	287	(109)
Invertebrate Retina	396
Auditory Nerve Fibers	302	(5)
Spider Mechanoreceptor	307	(13)
Cardiovascular System	320	(13)
Renal System	333	(9)
Metabolic-Endocrine System	342	(17)
Modeling of Multiinput/Multioutput Systems	359	(48)
The Two-Input Case	360	(9)
The Two-Input Cross-Correlation Technique	362	(1)
The Two-Input Kernel-Expansion Technique	362	(2)
Volterra-Equivalent Network Models with Two Inputs	364	(2)
Illustrative Example	366	(3)
Applications of Two-Input Modeling to Physiological Systems	369	(20)
Motion Detection in the Invertebrate Retina	369	(1)
Receptive Field Organization in the Vertebrate Retina	370	(8)
Metabolic Autoregulation in Dogs	378	(2)
Cerebral Autoregulation in Humans	380	(9)
The Multiinput Case	389	(6)
Cross-Correlation-Based Method for Multiinput Modeling	390	(3)
The Kernel-Expansion Method for Multiinput Modeling	393	(1)
Network-Based Multiinput Modeling	393	(2)
Spatiotemporal and Spectrotemporal Modeling	395	(12)
Spatiotemporal Modeling of Retinal Cells	398	(3)
Spatiotemporal Modeling of Cortical Cells	401	(6)
Modeling of Neuronal Systems	407	(60)
A General Model of Membrane and Synaptic Dynamics	408	(6)
Functional Integration in the Single Neuron	414	(25)
Neuronal Modes and Trigger Regions	417	(10)
Illustrative Examples	427	(5)
Minimum-Order Modeling of Spike-Output Systems	432	(1)
The Reverse-Correlation Technique	432	(3)
Minimum-Order Wiener Models	435	(4)
Illustrative Example	439	(1)
Neuronal Systems with Point-Process Inputs	439	(24)
The Lag-Delta Representation of P--V or P--W Kernels	445	(1)
The Reduced P--V or P--W Kernels	446	(4)
Examples from the Hippocampal Formation	450	(1)
Single-Input Stimulation in Vivo and Cross-Correlation Technique	450	(5)
Single-Input Stimulation in Vitro and Laguerre-Expansion Technique	455	(2)
Dual-Input Stimulation in the Hippocampal Slice	457	(4)
Nonlinear Modeling of Synaptic Dynamics	461	(2)
Modeling of Neuronal Ensembles	463	(4)
Modeling of Nonstationary Systems	467	(22)
Quasistationary and Recursive Tracking Methods	468	(1)
Kernel Expansion Method	469	(11)
Illustrative Example	474	(1)
A Test of Nonstationarity	475	(4)
Linear Time-Varying Systems with Arbitrary Inputs	479	(1)
Network-Based Methods	480	(4)
Illustrative Examples	481	(3)
Applications to Nonstationary Physiological Systems	484	(5)
Modeling of Closed-Loop Systems	489	(6)
Autoregressive Form of Closed-Loop Model	490	(1)
Network Model Form of Closed-Loop Systems	491	(4)
Appendix I Function Expansions	495	(4)
Appendix II Gaussian White Noise	499	(4)
Appendix III Construction of the Wiener Series	503	(2)
Appendix IV Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes	505	(2)
References	507	(28)
Index	535