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Physiological Control Systems: Analysis, Simulation, and Estimation, 2nd Edition

Physiological Control Systems: Analysis, Simulation, and Estimation, 2nd Edition

Michael C. K. Khoo

ISBN: 978-1-119-05878-6 April 2018 Wiley-IEEE Press 456 Pages

Description

A guide to common control principles and how they are used to characterize a variety of physiological mechanisms

The second edition of Physiological Control Systems offers an updated and comprehensive resource that reviews the fundamental concepts of classical control theory and how engineering methodology can be applied to obtain a quantitative understanding of physiological systems. The revised text also contains more advanced topics that feature applications to physiology of nonlinear dynamics, parameter estimation methods, and adaptive estimation and control. The author—a noted expert in the field—includes a wealth of worked examples that illustrate key concepts and methodology and offers in-depth analyses of selected physiological control models that highlight the topics presented.

The author discusses the most noteworthy developments in system identification, optimal control, and nonlinear dynamical analysis and targets recent bioengineering advances. Designed to be a practical resource, the text includes guided experiments with simulation models (using Simulink/Matlab). Physiological Control Systems focuses on common control principles that can be used to characterize a broad variety of physiological mechanisms. This revised resource:

  • Offers new sections that explore identification of nonlinear and time-varying systems, and provide the background for understanding the link between continuous-time and discrete-time dynamic models
  • Presents helpful, hands-on experimentation with computer simulation models
  • Contains fully updated problems and exercises at the end of each chapter

Written for biomedical engineering students and biomedical scientists, Physiological Control Systems, offers an updated edition of this key resource for understanding classical control theory and its application to physiological systems. It also contains contemporary topics and methodologies that shape bioengineering research today. 

Related Resources

Preface xiii

About the Companion Website xvii

1 Introduction 1

1.1 Preliminary Considerations, 1

1.2 Historical Background, 2

1.3 Systems Analysis: Fundamental Concepts, 4

1.4 Physiological Control Systems Analysis: A Simple Example, 6

1.5 Differences Between Engineering and Physiological Control Systems, 8

1.6 The Science (and Art) of Modeling, 11

1.7 “Systems Physiology” Versus “Systems Biology”, 12

Problems, 13

Bibliography, 15

2 Mathematical Modeling 17

2.1 Generalized System Properties, 17

2.2 Models with Combinations of System Elements, 21

2.3 Linear Models of Physiological Systems: Two Examples, 24

2.4 Conversions Between Electrical and Mechanical Analogs, 27

2.5 Distributed-Parameter Versus Lumped-Parameter Models, 29

2.6 Linear Systems and the Superposition Principle, 31

2.7 Zero-Input and Zero-State Solutions of ODEs, 33

2.8 Laplace Transforms and Transfer Functions, 34

2.8.1 Solving ODEs with Laplace Transforms, 36

2.9 The Impulse Response and Linear Convolution, 38

2.10 State-Space Analysis, 40

2.11 Computer Analysis and Simulation: MATLAB and SIMULINK, 43

Problems, 49

Bibliography, 53

3 Static Analysis of Physiological Systems 55

3.1 Introduction, 55

3.2 Open-Loop Versus Closed-Loop Systems, 56

3.3 Determination of the Steady-State Operating Point, 59

3.4 Steady-State Analysis Using SIMULINK, 63

3.5 Regulation of Cardiac Output, 66

3.5.1 The Cardiac Output Curve, 67

3.5.2 The Venous Return Curve, 69

3.5.3 Closed-Loop Analysis: Heart and Systemic Circulation Combined, 73

3.6 Regulation of Glucose Insulin, 74

3.7 Chemical Regulation of Ventilation, 78

3.7.1 The Gas Exchanger, 80

3.7.2 The Respiratory Controller, 82

3.7.3 Closed-Loop Analysis: Lungs and Controller Combined, 82

Problems, 86

Bibliography, 91

4 Time-Domain Analysis of Linear Control Systems 93

4.1 Linearized Respiratory Mechanics: Open-Loop Versus Closed-Loop, 93

4.2 Open-Loop Versus Closed-Loop Transient Responses: First-Order Model, 96

4.2.1 Impulse Response, 96

4.2.2 Step Response, 97

4.3 Open-Loop Versus Closed-Loop Transient Responses: Second-Order Model, 98

4.3.1 Impulse Responses, 98

4.3.2 Step Responses, 103

4.4 Descriptors of Impulse and Step Responses, 107

4.4.1 Generalized Second-Order Dynamics, 107

4.4.2 Transient Response Descriptors, 111

4.5 Open-Loop Versus Closed-Loop Dynamics: Other Considerations, 114

4.5.1 Reduction of the Effects of External Disturbances, 114

4.5.2 Reduction of the Effects of Parameter Variations, 115

4.5.3 Integral Control, 116

4.5.4 Derivative Feedback, 118

4.5.5 Minimizing Effect of External Disturbances by Feedforward Gain, 119

4.6 Transient Response Analysis Using MATLAB, 121

4.7 SIMULINK Application 1: Dynamics of Neuromuscular Reflex Motion, 122

4.7.1 A Model of Neuromuscular Reflex Motion, 122

4.7.2 SIMULINK Implementation, 126

4.8 SIMULINK Application 2: Dynamics of Glucose–Insulin Regulation, 127

4.8.1 The Model, 127

4.8.2 Simulations with the Model, 131

Problems, 131

Bibliography, 135

5 Frequency-Domain Analysis of Linear Control Systems 137

5.1 Steady-State Responses to Sinusoidal Inputs, 137

5.1.1 Open-Loop Frequency Response, 137

5.1.2 Closed-Loop Frequency Response, 141

5.1.3 Relationship between Transient and Frequency Responses, 143

5.2 Graphical Representations of Frequency Response, 145

5.2.1 Bode Plot Representation, 145

5.2.2 Nichols Charts, 147

5.2.3 Nyquist Plots, 148

5.3 Frequency-Domain Analysis Using MATLAB and SIMULINK, 152

5.3.1 Using MATLAB, 152

5.3.2 Using SIMULINK, 154

5.4 Estimation of Frequency Response from Input–Output Data, 156

5.4.1 Underlying Principles, 156

5.4.2 Physiological Application: Forced Oscillation Technique in Respiratory Mechanics, 157

5.5 Frequency Response of a Model of Circulatory Control, 159

5.5.1 The Model, 159

5.5.2 Simulations with the Model, 160

5.5.3 Frequency Response of the Model, 162

Problems, 164

Bibliography, 165

6 Stability Analysis: Linear Approaches 167

6.1 Stability and Transient Response, 167

6.2 Root Locus Plots, 170

6.3 Routh–Hurwitz Stability Criterion, 174

6.4 Nyquist Criterion for Stability, 176

6.5 Relative Stability, 181

6.6 Stability Analysis of the Pupillary Light Reflex, 184

6.6.1 Routh–Hurwitz Analysis, 186

6.6.2 Nyquist Analysis, 187

6.7 Model of Cheyne–Stokes Breathing, 190

6.7.1 CO2 Exchange in the Lungs, 190

6.7.2 Transport Delays, 192

6.7.3 Controller Responses, 193

6.7.4 Loop Transfer Functions, 193

6.7.5 Nyquist Stability Analysis Using MATLAB, 194

Problems, 196

Bibliography, 198

7 Digital Simulation of Continuous-Time Systems 199

7.1 Preliminary Considerations: Sampling and the Z-Transform, 199

7.2 Methods for Continuous-Time to Discrete-Time Conversion, 202

7.2.1 Impulse Invariance, 202

7.2.2 Forward Difference, 203

7.2.3 Backward Difference, 204

7.2.4 Bilinear Transformation, 205

7.3 Sampling, 207

7.4 Digital Simulation: Stability and Performance Considerations, 211

7.5 Physiological Application: The Integral Pulse Frequency Modulation Model, 216

Problems, 221

Bibliography, 224

8 Model Identification and Parameter Estimation 225

8.1 Basic Problems in Physiological System Analysis, 225

8.2 Nonparametric and Parametric Identification Methods, 228

8.2.1 Numerical Deconvolution, 228

8.2.2 Least-Squares Estimation, 230

8.2.3 Estimation Using Correlation Functions, 233

8.2.4 Estimation in the Frequency Domain, 235

8.2.5 Optimization Techniques, 237

8.3 Problems in Parameter Estimation: Identifiability and Input Design, 243

8.3.1 Structural Identifiability, 243

8.3.2 Sensitivity Analysis, 244

8.3.3 Input Design, 248

8.4 Identification of Closed-Loop Systems: “Opening the Loop”, 252

8.4.1 The Starling Heart–Lung Preparation, 253

8.4.2 Kao’s Cross-Circulation Experiments, 253

8.4.3 Artificial Brain Perfusion for Partitioning Central and Peripheral Chemoreflexes, 255

8.4.4 The Voltage Clamp, 256

8.4.5 Opening the Pupillary Reflex Loop, 257

8.4.6 Read Rebreathing Technique, 259

8.5 Identification Under Closed-Loop Conditions: Case Studies, 260

8.5.1 Minimal Model of Blood Glucose Regulation, 262

8.5.2 Closed-Loop Identification of the Respiratory Control System, 267

8.5.3 Closed-Loop Identification of Autonomic Control Using Multivariate ARX Models, 273

8.6 Identification of Physiological Systems Using Basis Functions, 276

8.6.1 Reducing Variance in the Parameter Estimates, 276

8.6.2 Use of Basis Functions, 277

8.6.3 Baroreflex and Respiratory Modulation of Heart Rate Variability, 279

Problems, 283

Bibliography, 285

9 Estimation and Control of Time-Varying Systems 289

9.1 Modeling Time-Varying Systems: Key Concepts, 289

9.2 Estimation of Models with Time-Varying Parameters, 293

9.2.1 Optimal Estimation: The Wiener Filter, 293

9.2.2 Adaptive Estimation: The LMS Algorithm, 294

9.2.3 Adaptive Estimation: The RLS Algorithm, 296

9.3 Estimation of Time-Varying Physiological Models, 300

9.3.1 Extending Adaptive Estimation Algorithms to Other Model Structures, 300

9.3.2 Adaptive Estimation of Pulmonary Gas Exchange, 300

9.3.3 Quantifying Transient Changes in Autonomic Cardiovascular Control, 304

9.4 Adaptive Control of Physiological Systems, 307

9.4.1 General Considerations, 307

9.4.2 Adaptive Buffering of Fluctuations in Arterial PCO2, 308

Problems, 313

Bibliography, 314

10 Nonlinear Analysis of Physiological Control Systems 317

10.1 Nonlinear Versus Linear Closed-Loop Systems, 317

10.2 Phase-Plane Analysis, 320

10.2.1 Local Stability: Singular Points, 322

10.2.2 Method of Isoclines, 325

10.3 Nonlinear Oscillators, 329

10.3.1 Limit Cycles, 329

10.3.2 The van der Pol Oscillator, 329

10.3.3 Modeling Cardiac Dysrhythmias, 336

10.4 The Describing Function Method, 342

10.4.1 Methodology, 342

10.4.2 Application: Periodic Breathing with Apnea, 345

10.5 Models of Neuronal Dynamics, 348

10.5.1 The Hodgkin–Huxley Model, 349

10.5.2 The Bonhoeffer–van der Pol Model, 352

10.6 Nonparametric Identification of Nonlinear Systems, 359

10.6.1 Volterra–Wiener Kernel Approach, 360

10.6.2 Nonlinear Model of Baroreflex and Respiratory Modulated Heart Rate, 364

10.6.3 Interpretations of Kernels, 367

10.6.4 Higher Order Nonlinearities and Block-Structured Models, 369

Problems, 370

Bibliography, 374

11 Complex Dynamics in Physiological Control Systems 377

11.1 Spontaneous Variability, 377

11.2 Nonlinear Control Systems with Delayed Feedback, 380

11.2.1 The Logistic Equation, 380

11.2.2 Regulation of Neutrophil Density, 384

11.2.3 Model of Cardiovascular Variability, 387

11.3 Coupled Nonlinear Oscillators: Model of Circadian Rhythms, 397

11.4 Time-Varying Physiological Closed-Loop Systems: Sleep Apnea Model, 401

11.5 Propagation of System Noise in Feedback Loops, 409

Problems, 415

Bibliography, 416

Appendix A Commonly Used Laplace Transform Pairs 419

Appendix B List of MATLAB and SIMULINK Programs 421

Index 425