by Vasilis Z. Marmarelis, Ph.D
Nonlinear modeling of physiological systems from stimulus-response data is a long-standing problem that has substantial implications for 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.
Nonlinear 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.
This 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.
Introduction
Purpose of this Book
Advocated Approach
The Problem of System Modeling in Physiology
Types of Nonlinear Models of Physiological Systems
Deductive and Inductive Modeling
Nonparametric Modeling
Volterra Models
Wiener Models
Efficient Volterra Kernel Estimation by Michael C.K. Khoo, Ph.D.
Analysis of Estimation Errors
Parametric Modeling
Basic Parametric Model Forms and Estimation Procedures
Volterra Kernels of Nonlinear Differential Equations
Discrete-Time Volterra Kernels of NARMAX Models
From Volterra Kernel Measurements to Parametric Models
Equivalence Between Continuous and Discrete Parametric Models
Modular and Connectionist Modeling
Modular Form of Nonparametric Models
Connectionist Models
The Laguerre-Volterra Network
The VWM Model
A Practitioner's Guide
Practical Considerations and Experimental Requirements
Preliminary Tests and Data Preparation
Model Specification and Estimation
Model Validation and Interpretation
Outline of Step-by-Step Procedure
Selected Applications
Neurosensory Systems
Cardiovascular System
Renal System
Metabolic-Endocrine System
Modeling of Multiinput/Multioutput Systems
The Two-Input Case
Applications of Two-Input Modeling to Physiological Systems
The Multiinput Case
Spatiotemporal and Spectrotemporal Modeling
Modeling of Neuronal systems
A General Model of Membrane and Synaptic Dynamics
Functional Integration in the Single Neuron
Neuronal Systems with Point-Process Inputs
Modeling of Neuronal Ensembles
Modeling of Nonstationary Systems
Quasistationary and Recursive Tracking Methods
Kernel Expansion Method
Network-Based Methods
Applications to Nonstationary Physiological Systems
Modeling of Closed-Loop Systems
Autoregressive Form of Closed-Loop Model
Network Model Form of Closed-Loop Systems
