{"product_id":"nonlinear-dynamic-modeling-of-physiological-systems-isbn-9780471469605","title":"Nonlinear Dynamic Modeling of Physiological Systems","description":"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.\u003cbr\u003e This essential study of nonlinearities in physiology apprises researchers and students of the latest findings and techniques in the field. \u003cp\u003ePrologue xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Purpose of this Book 1\u003c\/p\u003e \u003cp\u003e1.2 Advocated Approach 4\u003c\/p\u003e \u003cp\u003e1.3 The Problem of System Modeling in Physiology 6\u003c\/p\u003e \u003cp\u003e1.3.1 Model Specification and Estimation 10\u003c\/p\u003e \u003cp\u003e1.3.2 Nonlinearity and Nonstationarity 12\u003c\/p\u003e \u003cp\u003e1.3.3 Definition of the Modeling Problem 13\u003c\/p\u003e \u003cp\u003e1.4 Types of Nonlinear Models of Physiological Systems 13\u003c\/p\u003e \u003cp\u003eExample 1.1. Vertebrate Retina 15\u003c\/p\u003e \u003cp\u003eExample 1.2. Invertebrate Photoreceptor 18\u003c\/p\u003e \u003cp\u003eExample 1.3. Volterra analysis of Riccati Equation 19\u003c\/p\u003e \u003cp\u003eExample 1.4. Glucose-Insulin Minimal Model 21\u003c\/p\u003e \u003cp\u003eExample 1.5. Cerebral Autoregulation 22\u003c\/p\u003e \u003cp\u003e1.5 Deductive and Inductive Modeling 24\u003c\/p\u003e \u003cp\u003eHistorical Note #1: Hippocratic and Galenic Views of 26\u003c\/p\u003e \u003cp\u003eIntegrative Physiology\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Nonparametric Modeling 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Volterra Models 31\u003c\/p\u003e \u003cp\u003e2.1.1 Examples of Volterra Models 37\u003c\/p\u003e \u003cp\u003eExample 2.1. Static Nonlinear System 37\u003c\/p\u003e \u003cp\u003eExample 2.2. L–N Cascade System 38\u003c\/p\u003e \u003cp\u003eExample 2.3. L–N–M “Sandwich” System 39\u003c\/p\u003e \u003cp\u003eExample 2.4. Riccati System 40\u003c\/p\u003e \u003cp\u003e2.1.2 Operational Meaning of the Volterra Kernels 41\u003c\/p\u003e \u003cp\u003eImpulsive Inputs 42\u003c\/p\u003e \u003cp\u003eSinusoidal Inputs 43\u003c\/p\u003e \u003cp\u003eRemarks on the Meaning of Volterra Kernels 45\u003c\/p\u003e \u003cp\u003e2.1.3 Frequency-Domain Representation of the Volterra Models 45\u003c\/p\u003e \u003cp\u003e2.1.4 Discrete-Time Volterra Models 47\u003c\/p\u003e \u003cp\u003e2.1.5 Estimation of Volterra Kernels 49\u003c\/p\u003e \u003cp\u003eSpecialized Test Inputs 50\u003c\/p\u003e \u003cp\u003eArbitrary Inputs 52\u003c\/p\u003e \u003cp\u003eFast Exact Orthogonalization and Parallel-Cascade Methods 55\u003c\/p\u003e \u003cp\u003eIterative Cost-Minimization Methods for Non-Gaussian 55\u003c\/p\u003e \u003cp\u003eResiduals\u003c\/p\u003e \u003cp\u003e2.2 Wiener Models 57\u003c\/p\u003e \u003cp\u003e2.2.1 Relation between Volterra and Wiener Models 60\u003c\/p\u003e \u003cp\u003eThe Wiener Class of Systems 62\u003c\/p\u003e \u003cp\u003eExamples of Wiener Models 63\u003c\/p\u003e \u003cp\u003eComparison of Volterra\/Wiener Model Predictions 64\u003c\/p\u003e \u003cp\u003e2.2.2 Wiener Approach to Kernel Estimation 67\u003c\/p\u003e \u003cp\u003e2.2.3 The Cross-Correlation Technique for Wiener Kernel Estimation 72\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e 73\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e (\u003ci\u003e𝜏\u003c\/i\u003e) 73\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e (\u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e, \u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e) 74\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e3\u003c\/sub\u003e (\u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e, \u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e, \u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e3\u003c\/sub\u003e) 75\u003c\/p\u003e \u003cp\u003eSome Practical Considerations 77\u003c\/p\u003e \u003cp\u003eIllustrative Example 78\u003c\/p\u003e \u003cp\u003eFrequency-Domain Estimation of Wiener Kernels 78\u003c\/p\u003e \u003cp\u003e2.2.4 Quasiwhite Test Inputs 80\u003c\/p\u003e \u003cp\u003eCSRS and Volterra Kernels 84\u003c\/p\u003e \u003cp\u003eThe Diagonal Estimability Problem 85\u003c\/p\u003e \u003cp\u003eAn Analytical Example 86\u003c\/p\u003e \u003cp\u003eComparison of Model Prediction Errors 88\u003c\/p\u003e \u003cp\u003eDiscrete-Time Representation of the CSRS Functional Series 89\u003c\/p\u003e \u003cp\u003ePseudorandom Signals Based on m-Sequences 89\u003c\/p\u003e \u003cp\u003eComparative Use of GWN, PRS, and CSRS 92\u003c\/p\u003e \u003cp\u003e2.2.5 Apparent Transfer Function and Coherence Measurements 93\u003c\/p\u003e \u003cp\u003eExample 2.5. L–N Cascade System 96\u003c\/p\u003e \u003cp\u003eExample 2.6. Quadratic Volterra System 97\u003c\/p\u003e \u003cp\u003eExample 2.7. Nonwhite Gaussian Inputs 98\u003c\/p\u003e \u003cp\u003eExample 2.8. Duffing System 98\u003c\/p\u003e \u003cp\u003eConcluding Remarks 99\u003c\/p\u003e \u003cp\u003e2.3 Efficient Volterra Kernel Estimation 100\u003c\/p\u003e \u003cp\u003e2.3.1 Volterra Kernel Expansions 101\u003c\/p\u003e \u003cp\u003eModel Order Determination 104\u003c\/p\u003e \u003cp\u003e2.3.2 The Laguerre Expansion Technique 107\u003c\/p\u003e \u003cp\u003eIllustrative Examples 112\u003c\/p\u003e \u003cp\u003e2.3.3 High-Order Volterra Modeling with Equivalent Networks 122\u003c\/p\u003e \u003cp\u003e2.4 Analysis of Estimation Errors 125\u003c\/p\u003e \u003cp\u003e2.4.1 Sources of Estimation Errors 125\u003c\/p\u003e \u003cp\u003e2.4.2 Estimation Errors Associated with the Cross-Correlation 127\u003c\/p\u003e \u003cp\u003eTechnique Estimation Bias 128\u003c\/p\u003e \u003cp\u003eEstimation Variance 130\u003c\/p\u003e \u003cp\u003eOptimization of Input Parameters 131\u003c\/p\u003e \u003cp\u003eNoise Effects 134\u003c\/p\u003e \u003cp\u003eErroneous Scaling of Kernel Estimates 136\u003c\/p\u003e \u003cp\u003e2.4.3 Estimation Errors Associated with Direct Inversion Methods 137\u003c\/p\u003e \u003cp\u003e2.4.4 Estimation Errors Associated with Iterative 139\u003c\/p\u003e \u003cp\u003eCost-Minimization Methods Historical Note #2: Vito Volterra and Norbert Wiener 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Parametric Modeling 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Basic Parametric Model Forms and Estimation Procedures 146\u003c\/p\u003e \u003cp\u003e3.1.1 The Nonlinear Case 150\u003c\/p\u003e \u003cp\u003e3.1.2 The Nonstationary Case 152\u003c\/p\u003e \u003cp\u003e3.2 Volterra Kernels of Nonlinear Differential Equations 153\u003c\/p\u003e \u003cp\u003eExample 3.1. The Riccati Equation 157\u003c\/p\u003e \u003cp\u003e3.2.1 Apparent Transfer Functions of Linearized Models 158\u003c\/p\u003e \u003cp\u003eExample 3.2. Illustrative Example 160\u003c\/p\u003e \u003cp\u003e3.2.2 Nonlinear Parametric Models with Intermodulation 161\u003c\/p\u003e \u003cp\u003e3.3 Discrete-Time Volterra Kernels of NARMAX Models 164\u003c\/p\u003e \u003cp\u003e3.4 From Volterra Kernel Measurements to Parametric Models 167\u003c\/p\u003e \u003cp\u003eExample 3.3. Illustrative Example 169\u003c\/p\u003e \u003cp\u003e3.5 Equivalence Between Continuous and Discrete Parametric Models 171\u003c\/p\u003e \u003cp\u003eExample 3.4. Illustrative Example 175\u003c\/p\u003e \u003cp\u003e3.5.1 Modular Representation 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Modular and Connectionist Modeling 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Modular Form of Nonparametric Models 179\u003c\/p\u003e \u003cp\u003e4.1.1 Principal Dynamic Modes 180\u003c\/p\u003e \u003cp\u003eIllustrative Examples 186\u003c\/p\u003e \u003cp\u003e4.1.2 Volterra Models of System Cascades 191\u003c\/p\u003e \u003cp\u003eThe \u003ci\u003eL–N–M, L–N, \u003c\/i\u003eand \u003ci\u003eN–M\u003c\/i\u003e Cascades 194\u003c\/p\u003e \u003cp\u003e4.1.3 Volterra Models of Systems with Lateral Branches 198\u003c\/p\u003e \u003cp\u003e4.1.4 Volterra Models of Systems with Feedback Branches 200\u003c\/p\u003e \u003cp\u003e4.1.5 Nonlinear Feedback Described by Differential Equations 202\u003c\/p\u003e \u003cp\u003eExample 1. Cubic Feedback Systems 204\u003c\/p\u003e \u003cp\u003eExample 2. Sigmoid Feedback Systems 209\u003c\/p\u003e \u003cp\u003eExample 3. Positive Nonlinear Feedback 213\u003c\/p\u003e \u003cp\u003eExample 4. Second-Order Kernels of Nonlinear 215\u003c\/p\u003e \u003cp\u003eFeedback Systems Nonlinear Feedback in Sensory Systems 216\u003c\/p\u003e \u003cp\u003eConcluding Remarks on Nonlinear Feedback 220\u003c\/p\u003e \u003cp\u003e4.2 Connectionist Models 223\u003c\/p\u003e \u003cp\u003e4.2.1 Equivalence between Connectionist and Volterra Models 223\u003c\/p\u003e \u003cp\u003eRelation with PDM Modeling 230\u003c\/p\u003e \u003cp\u003eIllustrative Examples 232\u003c\/p\u003e \u003cp\u003e4.2.2 Volterra-Equivalent Network Architectures for Nonlinear 235\u003c\/p\u003e \u003cp\u003eSystem Modeling Equivalence with Volterra Kernels\/Models 238\u003c\/p\u003e \u003cp\u003eSelection of the Structural Parameters of the VEN Model 238\u003c\/p\u003e \u003cp\u003eConvergence and Accuracy of the Training Procedure 240\u003c\/p\u003e \u003cp\u003eThe Pseudomode-Peeling Method 244\u003c\/p\u003e \u003cp\u003eNonlinear Autoregressive Modeling (Open-Loop) 246\u003c\/p\u003e \u003cp\u003e4.3 The Laguerre-Volterra Network 246\u003c\/p\u003e \u003cp\u003eIllustrative Example of LVN Modeling 249\u003c\/p\u003e \u003cp\u003eModeling Systems with Fast and Slow Dynamic (LVN-2) 251\u003c\/p\u003e \u003cp\u003eIllustrative Examples of LVN-2 Modeling 255\u003c\/p\u003e \u003cp\u003e4.4 The VWM Model 260\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 A Practitioner’s Guide 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Practical Considerations and Experimental Requirements 265\u003c\/p\u003e \u003cp\u003e5.1.1 System Characteristics 266\u003c\/p\u003e \u003cp\u003eSystem Bandwidth 266\u003c\/p\u003e \u003cp\u003eSystem Memory 267\u003c\/p\u003e \u003cp\u003eSystem Dynamic Range 267\u003c\/p\u003e \u003cp\u003eSystem Linearity 268\u003c\/p\u003e \u003cp\u003eSystem Stationarity 268\u003c\/p\u003e \u003cp\u003eSystem Ergodicity 268\u003c\/p\u003e \u003cp\u003e5.1.2 Input Characteristics 269\u003c\/p\u003e \u003cp\u003e5.1.3 Experimental Characteristics 270\u003c\/p\u003e \u003cp\u003e5.2 Preliminary Tests and Data Preparation 272\u003c\/p\u003e \u003cp\u003e5.2.1 Test for System Bandwidth 272\u003c\/p\u003e \u003cp\u003e5.2.2 Test for System Memory 272\u003c\/p\u003e \u003cp\u003e5.2.3 Test for System Stationarity and Ergodicity 273\u003c\/p\u003e \u003cp\u003e5.2.4 Test for System Linearity 274\u003c\/p\u003e \u003cp\u003e5.2.5 Data Preparation 275\u003c\/p\u003e \u003cp\u003e5.3 Model Specification and Estimation 276\u003c\/p\u003e \u003cp\u003e5.3.1 The MDV Modeling Methodology 277\u003c\/p\u003e \u003cp\u003e5.3.2 The VEN\/VWM Modeling Methodology 278\u003c\/p\u003e \u003cp\u003e5.4 Model Validation and Interpretation 279\u003c\/p\u003e \u003cp\u003e5.4.1 Model Validation 279\u003c\/p\u003e \u003cp\u003e5.4.2 Model Interpretation 281\u003c\/p\u003e \u003cp\u003eInterpretation of Volterra Kernels 281\u003c\/p\u003e \u003cp\u003eInterpretation of the PDM Model 282\u003c\/p\u003e \u003cp\u003e5.5 Outline of Step-by-Step Procedure 283\u003c\/p\u003e \u003cp\u003e5.5.1 Elaboration of the Key Step # 5 284\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Selected Applications 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Neurosensory Systems 286\u003c\/p\u003e \u003cp\u003e6.1.1 Vertebrate Retina 287\u003c\/p\u003e \u003cp\u003e6.1.2 Invertebrate Retina 396\u003c\/p\u003e \u003cp\u003e6.1.3 Auditory Nerve Fibers 302\u003c\/p\u003e \u003cp\u003e6.1.4 Spider Mechanoreceptor 307\u003c\/p\u003e \u003cp\u003e6.2 Cardiovascular System 320\u003c\/p\u003e \u003cp\u003e6.3 Renal System 333\u003c\/p\u003e \u003cp\u003e6.4 Metabolic-Endocrine System 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Modeling of Multiinput\/Multioutput Systems 359\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Two-Input Case 360\u003c\/p\u003e \u003cp\u003e7.1.1 The Two-Input Cross-Correlation Technique 362\u003c\/p\u003e \u003cp\u003e7.1.2 The Two-Input Kernel-Expansion Technique 362\u003c\/p\u003e \u003cp\u003e7.1.3 Volterra-Equivalent Network Models with Two Inputs 364\u003c\/p\u003e \u003cp\u003eIllustrative Example 366\u003c\/p\u003e \u003cp\u003e7.2 Applications of Two-Input Modeling to Physiological Systems 369\u003c\/p\u003e \u003cp\u003e7.2.1 Motion Detection in the Invertebrate Retina 369\u003c\/p\u003e \u003cp\u003e7.2.2 Receptive Field Organization in the Vertebrate Retina 370\u003c\/p\u003e \u003cp\u003e7.2.3 Metabolic Autoregulation in Dogs 378\u003c\/p\u003e \u003cp\u003e7.2.4 Cerebral Autoregulation in Humans 380\u003c\/p\u003e \u003cp\u003e7.3 The Multiinput Case 389\u003c\/p\u003e \u003cp\u003e7.3.1 Cross-Correlation-Based Method for Multiinput Modeling 390\u003c\/p\u003e \u003cp\u003e7.3.2 The Kernel-Expansion Method for Multiinput Modeling 393\u003c\/p\u003e \u003cp\u003e7.3.3 Network-Based Multiinput Modeling 393\u003c\/p\u003e \u003cp\u003e7.4 Spatiotemporal and Spectrotemporal Modeling 395\u003c\/p\u003e \u003cp\u003e7.4.1 Spatiotemporal Modeling of Retinal Cells 398\u003c\/p\u003e \u003cp\u003e7.4.2 Spatiotemporal Modeling of Cortical Cells 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Modeling of Neuronal Systems 407\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 A General Model of Membrane and Synaptic Dynamics 408\u003c\/p\u003e \u003cp\u003e8.2 Functional Integration in the Single Neuron 414\u003c\/p\u003e \u003cp\u003e8.2.1 Neuronal Modes and Trigger Regions 417\u003c\/p\u003e \u003cp\u003eIllustrative Examples 427\u003c\/p\u003e \u003cp\u003e8.2.2 Minimum-Order Modeling of Spike-Output Systems 432\u003c\/p\u003e \u003cp\u003eThe Reverse-Correlation Technique 432\u003c\/p\u003e \u003cp\u003eMinimum-Order Wiener Models 435\u003c\/p\u003e \u003cp\u003eIllustrative Example 439\u003c\/p\u003e \u003cp\u003e8.3 Neuronal Systems with Point-Process Inputs 439\u003c\/p\u003e \u003cp\u003e8.3.1 The Lag-Delta Representation of \u003ci\u003eP–V\u003c\/i\u003e or \u003ci\u003eP–W\u003c\/i\u003e Kernels 445\u003c\/p\u003e \u003cp\u003e8.3.2 The Reduced \u003ci\u003eP–V\u003c\/i\u003e or \u003ci\u003eP–W\u003c\/i\u003e Kernels 446\u003c\/p\u003e \u003cp\u003e8.3.3 Examples from the Hippocampal Formation 450\u003c\/p\u003e \u003cp\u003eSingle-Input Stimulation in Vivo and Cross-Correlation  450\u003c\/p\u003e \u003cp\u003eTechnique\u003c\/p\u003e \u003cp\u003eSingle-Input Stimulation in Vitro and Laguerre-Expansion 455\u003c\/p\u003e \u003cp\u003eTechnique\u003c\/p\u003e \u003cp\u003e Dual-Input Stimulation in the Hippocampal Slice 457\u003c\/p\u003e \u003cp\u003eNonlinear Modeling of Synaptic Dynamics 461\u003c\/p\u003e \u003cp\u003e8.4 Modeling of Neuronal Ensembles 463\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Modeling of Nonstationary Systems 467\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Quasistationary and Recursive Tracking Methods 468\u003c\/p\u003e \u003cp\u003e9.2 Kernel Expansion Method 469\u003c\/p\u003e \u003cp\u003e9.2.1 Illustrative Example 474\u003c\/p\u003e \u003cp\u003e9.2.2 A Test of Nonstationarity 475\u003c\/p\u003e \u003cp\u003e9.2.3 Linear Time-Varying Systems with Arbitrary Inputs 479\u003c\/p\u003e \u003cp\u003e9.3 Network-Based Methods 480\u003c\/p\u003e \u003cp\u003e9.3.1 Illustrative Examples 481\u003c\/p\u003e \u003cp\u003e9.4 Applications to Nonstationary Physiological Systems 484\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Modeling of Closed-Loop Systems 489\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Autoregressive Form of Closed-Loop Model 490\u003c\/p\u003e \u003cp\u003e10.2 Network Model Form of Closed-Loop Systems 491\u003c\/p\u003e \u003cp\u003eAppendix I Function Expansions 495\u003c\/p\u003e \u003cp\u003eAppendix II Gaussian White Noise 499\u003c\/p\u003e \u003cp\u003eAppendix III Construction of the Wiener Series 503\u003c\/p\u003e \u003cp\u003eAppendix IV Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes 505\u003c\/p\u003e \u003cp\u003e References 507\u003c\/p\u003e \u003cp\u003eIndex 535\u003c\/p\u003e  \"...a perfect research tool, as reference book, and even as a textbook. I highly recommend it to everyone interested in nonlinear dynamics.\" (\u003ci\u003eJournal of Intelligent \u0026amp; Fuzzy Systems\u003c\/i\u003e, Vol. 16, No. 2, 2005)  \u003cp\u003e\"...a well-written methodology book...a useful addition to [researchers, engineers and graduate students']...personal libraries.\" (\u003ci\u003eE-STREAMS\u003c\/i\u003e, September 2005)\u003c\/p\u003e 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 practical approach to obtaining nonlinear dynamic models from stimulus-response data  \u003cp\u003eNonlinear modeling of physiological systems from stimulus-response data is a long-standing problem that has substantial implications for many scientific fields and associated technologies. These disciplines include biomedical engineering, signal processing, neural networks, medical imaging, and robotics and automation. Addressing the needs of a broad spectrum of scientific and engineering researchers, this book presents practicable, yet mathematically rigorous methodologies for constructing dynamic models of physiological systems.\u003c\/p\u003e \u003cp\u003eNonlinear Dynamic Modeling of Physiological Systems provides the most comprehensive treatment of the subject to date. Starting with the mathematical background upon which these methodologies are built, the book presents the methodologies that have been developed and used over the past thirty years. The text discusses implementation and computational issues and gives illustrative examples using both synthetic and experimental data. The author discusses the various modeling approaches–nonparametric, including the Volterra and Wiener models; parametric; modular; and connectionist–and clearly identifies their comparative advantages and disadvantages along with the key criteria that must guide successful practical application. Selected applications covered include neural and sensory systems, cardiovascular and renal systems, and endocrine and metabolic systems.\u003c\/p\u003e \u003cp\u003eThis lucid and comprehensive text is a valuable reference and guide for the community of scientists and engineers who wish to develop and apply the skills of nonlinear modeling to physiological systems.\u003c\/p\u003e","brand":"Wiley-IEEE Press","offers":[{"title":"Default Title","offer_id":47989695447269,"sku":"NP9780471469605","price":211.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471469605.jpg?v=1761785137","url":"https:\/\/k12savings.com\/es\/products\/nonlinear-dynamic-modeling-of-physiological-systems-isbn-9780471469605","provider":"K12savings","version":"1.0","type":"link"}