CONTENTS

Cover

Series Page

Title Page

Dedication

Preface

About the Companion Website

Chapter 1: Introduction

1.1 Preliminary Considerations
1.2 Historical Background
1.3 Systems Analysis: Fundamental Concepts
1.4 Physiological Control Systems Analysis: A Simple Example
1.5 Differences Between Engineering and Physiological Control Systems
1.6 The Science (and Art) of Modeling
1.7 “Systems Physiology” versus “Systems Biology”
Problems
Bibliography

Chapter 2: Mathematical Modeling

2.1 Generalized System Properties
2.2 Models with Combinations of System Elements
2.3 Linear Models of Physiological Systems: Two Examples
2.4 Conversions Between Electrical and Mechanical Analogs
2.5 Distributed-Parameter versus Lumped-Parameter Models
2.6 Linear Systems and the Superposition Principle
2.7 Zero-Input and Zero-State Solutions of ODEs
2.8 Laplace Transforms and Transfer Functions
2.9 The Impulse Response and Linear Convolution
2.10 State-Space Analysis
2.11 Computer Analysis and Simulation: MATLAB and SIMULINK
Problems
Bibliography

Chapter 3: Static Analysis of Physiological Systems

3.1 Introduction
3.2 Open-Loop versus Closed-Loop Systems
3.3 Determination of the Steady-State Operating Point
3.4 Steady-State Analysis Using SIMULINK
3.5 Regulation of Cardiac Output
3.6 Regulation of Glucose Insulin
3.7 Chemical Regulation of Ventilation
Problems
Bibliography

Chapter 4: Time-Domain Analysis of Linear Control Systems

4.1 Linearized Respiratory Mechanics: Open-Loop versus Closed-Loop
4.2 Open-Loop versus Closed-Loop Transient Responses: First-Order Model
4.3 Open-Loop versus Closed-Loop Transient Responses: Second-Order Model
4.4 Descriptors of Impulse and Step Responses
4.5 Open-Loop versus Closed-Loop Dynamics: Other Considerations
4.6 Transient Response Analysis Using MATLAB
4.7 SIMULINK Application 1: Dynamics of Neuromuscular Reflex Motion
4.8 SIMULINK Application 2: Dynamics of Glucose–Insulin Regulation
Problems
Bibliography

Chapter 5: Frequency-Domain Analysis of Linear Control Systems

5.1 Steady-State Responses to Sinusoidal Inputs
5.2 Graphical Representations of Frequency Response
5.3 Frequency-Domain Analysis Using MATLAB and SIMULINK
5.4 Estimation of Frequency Response From Input–Output Data
5.5 Frequency Response of a Model of Circulatory Control
Problems
Bibliography

Chapter 6: Stability Analysis: Linear Approaches

6.1 Stability and Transient Response
6.2 Root Locus Plots
6.3 Routh–Hurwitz Stability Criterion
6.4 Nyquist Criterion for Stability
6.5 Relative Stability
6.6 Stability Analysis of the Pupillary Light Reflex
6.7 Model of Cheyne–Stokes Breathing
Problems
Bibliography

Chapter 7: Digital Simulation of Continuous-Time Systems

7.1 Preliminary Considerations: Sampling and The Z-Transform
7.2 Methods for Continuous-Time to Discrete-Time Conversion
7.3 Sampling
7.4 Digital Simulation: Stability and Performance Considerations
7.5 Physiological Application: The Integral Pulse Frequency Modulation Model
Problems
Bibliography

Chapter 8: Model Identification and Parameter Estimation

8.1 Basic Problems in Physiological System Analysis
8.2 Nonparametric and Parametric Identification Methods
8.3 Problems in Parameter Estimation: Identifiability and Input Design
8.4 Identification of Closed-Loop Systems: “Opening the Loop”
8.5 Identification Under Closed-Loop Conditions: Case Studies
8.6 Identification of Physiological Systems Using Basis Functions
Problems
Bibliography

Chapter 9: Estimation and Control of Time-Varying Systems

9.1 Modeling Time-Varying Systems: Key Concepts
9.2 Estimation of Models With Time-Varying Parameters
9.3 Estimation of Time-Varying Physiological Models
9.4 Adaptive Control of Physiological Systems
Problems
Bibliography

Chapter 10: Nonlinear Analysis of Physiological Control Systems

10.1 Nonlinear Versus Linear Closed-Loop Systems
10.2 Phase-Plane Analysis
10.3 Nonlinear Oscillators
10.4 The Describing Function Method
10.5 Models of Neuronal Dynamics
10.6 Nonparametric Identification of Nonlinear Systems
Problems
Bibliography

Chapter 11: Complex Dynamics in Physiological Control Systems

11.1 Spontaneous Variability
11.2 Nonlinear Control Systems with Delayed Feedback
11.3 Coupled Nonlinear Oscillators: Model of Circadian Rhythms
11.4 Time-Varying Physiological Closed-Loop Systems: Sleep Apnea Model
11.5 Propagation of System Noise in Feedback Loops
Problems
Bibliography

Appendix A Commonly Used Laplace Transform Pairs

Appendix B List of MATLAB and SIMULINK Programs

B.1 How to Download the MATLAB and SIMULINK Files

Index

End User License Agreement

List of Illustrations

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

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Figure 2.10

Figure 2.11

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Figure P2.1

Figure P2.2

Figure P2.3

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Figure P2.5

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

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Figure 3.6

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Figure 3.10

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Figure P3.1

Figure P3.2

Figure P3.3

Figure P3.4

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Figure 4.2

Figure 4.3

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Figure P4.2

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Figure P4.6

Figure 5.1

Figure 5.2

Figure 5.3

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Figure P6.1

Figure P6.2

Figure 7.1

Figure 7.2

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Figure P7.1

Figure 8.1

Figure 8.2

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Figure 8.20

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Figure 8.24

Figure 9.1

Figure 9.2

Figure 9.3

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Figure 9.6

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Figure 9.10

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Figure 9.13

Figure 10.1

Figure 10.2

Figure 10.3

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Figure 10.6

Figure 10.7

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Figure 10.10

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Figure 10.20

Figure 10.21

Figure 10.22

Figure 10.23

Figure 10.24

Figure 10.25

Figure 10.26

Figure 10.27

Figure 10.28

Figure 10.29

Figure 10.30

Figure 10.31

Figure 10.32

Figure 10.33

Figure P10.1

Figure P10.2

Figure 11.1

Figure 11.2

Figure 11.3

Figure 11.4

Figure 11.5

Figure 11.6

Figure 11.7

Figure 11.8

Figure 11.9

Figure 11.10

Figure 11.11

Figure 11.12

Figure 11.13

Figure 11.14

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Figure 11.17

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Figure 11.19

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Figure 11.21

Figure 11.22

Figure 11.23

Figure 11.24

Figure 11.25

Figure 11.26

Figure 11.27

Figure 11.28

Figure 11.29

Figure 11.30

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ISBN: 978-1-119-05533-4

Preface

It has been 17 years since the publication of the original edition of this monograph. Over this period, I have taught, almost on a yearly basis, a course at the University of Southern California that is based largely on the contents of this book. This second edition incorporates much of the experience I have gained and student feedback I have received from teaching this class. I have also received input from the many instructors who have used this book for their classes. To all these readers, I am deeply appreciative of their helpful comments and questions. The primary goals of this book remain the same as in the first edition: to highlight the basic techniques employed in control theory, systems analysis, and model identification and to give the biomedical engineering student an appreciation of how these principles can be applied to better understand the processes involved in physiological regulation. As before, my assumption is that much of the contents of this second edition are suitable for use in a one-semester course on physiological control systems or physiological systems analysis taken by junior or senior undergraduates or as an introductory class on physiological systems for first-year graduate students. The more advanced parts of this book and its accompanying software may also prove to be a useful resource for biomedical engineers and interested life science or clinical researchers who have had little formal training in systems or control theory. Throughout this book, I have emphasized the physiological applications of control engineering, focusing in particular on the analysis of feedback regulation. In contrast, the basic concepts and methods of control theory are introduced with little attention paid to mathematical derivations or proofs. For this reason, I would recommend the inclusion of a more traditional, engineering-oriented control theory course as a supplement to the material covered in this volume.

One of the main issues I have had with the first edition was the “gap” between the main concepts in systems and control that were introduced assuming continuous-time systems and some of the more advanced applications that featured discrete-time models. Chapter 7 has been introduced to bridge this gap, and to show the reader how continuous-time systems can be converted into discrete-time systems, as well as the impact of different methods of conversion on stability characteristics of the system in question. This additional background should also be useful since many physiological processes (including cardiac, respiratory, and neural) are naturally oscillatory, and models that employ a cycle-by-cycle (and hence, discrete) time base may be more suitable for characterizing longer term dynamics. In Chapter 9, I have revamped what was previously Chapter 8 to cover the essential aspects of time-varying or nonstationary systems. The chapter on physiological system identification (now Chapter 8) has been expanded to include more techniques, such as nonparametric identification using multivariable autoregressive with exogenous (ARX) models and basis function expansion. Finally, the chapter on nonlinear analysis (now Chapter 10) has been expanded to include the Volterra kernel approach to nonparametric estimation of nonlinear systems as well as an introductory discussion of other methods. I have also added material to update various other sections, as well as new problems to the end of each chapter. The MATLAB/SIMULINK files accompanying the book have also been expanded and existing programs have been updated to be compatible with release version R2016b. I see these programs to be an essential complement to the learning experience, allowing the reader to explore “first-hand” the dynamics underlying the biological mechanisms being studied. I do make the implicit assumption that the reader has some basic familiarity with MATLAB/SIMULINK. For the reader who has not used MATLAB or SIMULINK, it is fortunate that there are currently many “primers” on the subject that can be easily found online or in any academic bookstore.

The completion of this second edition has taken much longer than I had anticipated when I took on the project (and I am quite embarrassed to disclose how long ‘long’ is!). I thank Wiley-IEEE Press for giving me the opportunity to produce this second edition, editor Mary Hatcher for her infinite patience, and my friend Metin Akay, the book series editor, for his constant encouragement. This second edition would not have been possible without the feedback and insights gained through my interactions with my past and present Ph.D. students over the years. In particular, I am most grateful to my former student and current research associate, P. “Sang” Chalacheva, who so generously gave her spare time and effort to help with the development of the new MATLAB files and the editing of all parts of this second edition. I would be remiss if I did not also mention the supportive environment provided by the NIH-NIBIB-funded Biomedical Simulations Resource (BMSR), which has funded my research on physiological control and modeling for the past three decades. The modeling activities of my colleagues in the BMSR, David D'Argenio, Vasilis Marmarelis, and Ted Berger, have been a great source of intellectual stimulation over the years. I cannot help but end these remarks by citing my favorite line from the writings of the late Professor Fred Grodins, who recruited me to USC many many moons ago:

“There is nothing magic about Models (or is there?)!”

Michael C.K. Khoo

Giancarlo Fortino	Andreas Molisch	Linda Shafer
David Alan Grier	Saeid Nahavandi	Mohammad Shahidehpour
Donald Heirman	Ray Perez	Sarah Spurgeon
Xiaoou Li	Jeffrey Reed	Ahmet Murat Tekalp

Analysis, Simulation, and Estimation