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
