Nonlinear Dynamic Modeling of Physiological Systems

1 Introduction.

1.1 Purpose of this Book.

1.2 Advocated Approach.

1.3 The Problem of System Modeling in Physiology.

1.4 Types of Nonlinear Models of Physiological Systems.

2 Nonparametric Modeling.

2.1 Volterra Models.

2.2 Wiener Models.

2.3 Efficient Volterra Kernel Estimation.

2.4 Analysis of Estimation Errors.

3 Parametric Modeling.

3.1 Basic Parametric Model Forms and Estimation Procedures.

3.2 Volterra Kernels of Nonlinear Differential Equations.

3.3 Discrete-Time Volterra Kernels of NARMAX Models.

3.4 From Volterra Kernel Measurements to Parametric Models.

3.5 Equivalence Between Continuous and Discrete Parametric Models.

4 Modular and Connectionist Modeling.

4.1 Modular Form of Nonparametric Models.

4.2 Connectionist Models.

4.3 The Laguerre-Volterra Network.

4.4 The VWM Model.

5 A Practitioner’s Guide.

5.1 Practical Considerations and Experimental Requirements.

5.2 Preliminary Tests and Data Preparation.

5.3 Model Specification and Estimation.

5.4 Model Validation and Interpretation.

5.5 Outline of Step-by-Step Procedure.

6 Selected Applications.

6.1 Neurosensory Systems.

6.2 Cardiovascular System.

6.3 Renal System.

6.4 Metabolic-Endocrine System.

7 Modeling of Multiinput/Multioutput Systems.

7.1 The Two-Input Case.

7.2 Applications of Two-Input Modeling to Physiological Systems.

7.3 The Multiinput Case.

7.4 Spatiotemporal and Spectrotemporal Modeling.

8 Modeling of Neuronal Systems.

8.1 A General Model of Membrane and Synaptic Dynamics.

8.2 Functional Integration in the Single Neuron.

8.3 Neuronal Systems with Point-Process Inputs.

8.4 Modeling of Neuronal Ensembles.

9 Modeling of Nonstationary Systems.

9.1 Quasistationary and Recursive Tracking Methods.

9.2 Kernel Expansion Method.

9.3 Network-Based Methods.

9.4 Applications to Nonstationary Physiological Systems.

10 Modeling of Closed-Loop Systems.

10.1 Autoregressive Form of Closed-Loop Model.

10.2 Network Model Form of Closed-Loop Systems.

Appendix I: Function Expansions.

Appendix II: Gaussian White Noise.

Appendix III: Construction of the Wiener Series.

Appendix IV: Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes.

References.

Index.