Introduction to Modeling in Physiology and Medicine
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Table of contents
- Cover
- CONTENTSv
- PREFACExi
- CHAPTER 1 INTRODUCTION1
- 1.1 Introduction1
- 1.2 The Book in Context2
- 1.3 The Major Ingredients3
- 1.4 Readership4
- 1.5 Organization of the Book4
- CHAPTER 2 PHYSIOLOGICAL COMPLEXITY AND THE NEED FOR MODELS7
- 2.1 Introduction7
- 2.2 Complexity9
- 2.3 Feedback10
- 2.3.1 Negative Feedback10
- 2.3.2 Positive Feedback10
- 2.3.3 Inherent Feedback11
- 2.3.4 Combining Negative and Positive Feedback11
- 2.3.5 Derivative and Integral Feedback13
- 2.3.6 Effects of Feedback on the Complexity of System Dynamics13
- 2.4 Control in Physiological Systems13
- 2.4.1 General Features13
- 2.4.2 Enzymes15
- 2.4.3 Hormones17
- 2.5 Hierarchy19
- 2.6 Redundancy20
- 2.7 Function and Behavior and their Measurement21
- 2.8 Challenges to Understanding21
- 2.9 Exercises and Assignment Questions22
- CHAPTER 3 MODELS AND THE MODELING PROCESS23
- 3.1 Introduction23
- 3.2 What is a Model?23
- 3.3 Why Model? The Purpose of Modeling25
- 3.4 How Do We Model? The Modeling Process27
- 3.5 Model Formulation27
- 3.6 Model Identification29
- 3.7 Model Validation30
- 3.8 Model Simulation32
- 3.9 Summary33
- 3.10 Exercises and Assignment Questions34
- CHAPTER 4 MODELING THE DATA35
- 4.1 Introduction35
- 4.2 The Basis of Data Modeling36
- 4.3 The Why and When of Data Models36
- 4.4 Approaches to Data Modeling36
- 4.5 Modeling a Single Variable Occurring Spontaneously38
- 4.5.1 Temperature38
- 4.5.2 Urine Potassium41
- 4.5.3 Gastro-intestinal Rhythms43
- 4.5.4 Hormonal Time Series45
- 4.6 Modeling a Single Variable in Response to a Perturbation52
- 4.6.1 Glucose Home Monitoring Data53
- 4.6.2 Response to Drug Therapy – Prediction of Bronchodilator Response54
- 4.7 Two Variables Causally Related56
- 4.7.1 Hormone/hormone and Substrate/hormone Series56
- 4.7.2 Urine Sodium Response to Water Loading58
- 4.8 Input/output Modeling for Control61
- 4.8.1 Pupil Control62
- 4.8.2 Control of Blood Glucose by Insulin63
- 4.8.3 Control of Blood Pressure by Sodium Nitroprusside66
- 4.9 Input/output Modeling: Impulse Response and Deconvolution67
- 4.9.1 Impulse Response Estimation67
- 4.9.2 The Convolution Integral69
- 4.9.3 Reconstructing the Input70
- 4.10 Summary74
- 4.11 Exercises and Assignment Questions74
- CHAPTER 5 MODELING THE SYSTEM75
- 5.1 Introduction76
- 5.2 Static Models76
- 5.3 Linear Modeling79
- 5.3.1 The Windkessel Circulatory Model80
- 5.3.2 Elimination from a Single Compartment81
- 5.3.3 Gas Exchange82
- 5.3.4 The Dynamics of a Swinging Limb83
- 5.3.5 A Model of Glucose Regulation87
- 5.4 Distributed Modeling90
- 5.4.1 Blood-tissue Exchange91
- 5.4.2 Hepatic Removal of Materials101
- 5.4.3 Renal Medulla105
- 5.5 Nonlinear Modeling110
- 5.5.1 The Action Potential Model110
- 5.5.2 Enzyme Dynamics120
- 5.5.3 Baroreceptors122
- 5.5.4 Central Nervous Control of Heart Rate124
- 5.5.5 Compartmental Modeling125
- 5.5.6 Insulin Receptor Regulation133
- 5.5.7 Insulin Action Modeling135
- 5.5.8 Thyroid Hormone Regulation138
- 5.5.9 Modeling the Chemical Control of Breathing141
- 5.6 Time-varying Modeling145
- 5.6.1 An Example in Cardiac Modeling145
- 5.7 Stochastic Modeling150
- 5.7.1 Cellular Modeling150
- 5.7.2 Insulin Secretion154
- 5.7.3 Markov Model155
- 5.8 Summary156
- 5.9 Exercises and Assignment Questions157
- CHAPTER 6 MODEL IDENTIFICATION159
- 6.1 Introduction159
- 6.2 Data for Identification160
- 6.2.1 Selection of Test Signals160
- 6.2.2 Transient Test Signals161
- 6.2.3 Harmonic Test Signals162
- 6.2.4 Random Signal Testing163
- 6.3 Errors164
- 6.4 The Way Forward166
- 6.4.1 Parameter Estimation166
- 6.4.2 Signal Estimation167
- 6.5 Summary167
- 6.6 Exercises and Assignment Questions168
- CHAPTER 7 PARAMETRIC MODELING – THE IDENTIFIABILITY PROBLEM169
- 7.1 Introduction169
- 7.2 Some Examples173
- 7.3 Definitions179
- 7.4 Linear Models: The Transfer Function Method181
- 7.5 Nonlinear Models: The Taylor Series Expansion Method184
- 7.6 Qualitative Experimental Design187
- 7.6.1 Fundamentals187
- 7.6.2 An Amino Acid Model188
- 7.7 Summary192
- 7.8 Exercises and Assignment Questions193
- CHAPTER 8 PARAMETRIC MODELS – THE ESTIMATION PROBLEM195
- 8.1 Introduction196
- 8.2 Linear and Nonlinear Parameters197
- 8.3 Regression: Basic Concepts198
- 8.3.1 The Residual199
- 8.3.2 The Residual Sum of Squares200
- 8.3.3 The Weighted Residual Sum of Squares200
- 8.3.4 Weights and Error in the Data201
- 8.4 Linear Regression203
- 8.4.1 The Problem204
- 8.4.2 Test on Residuals205
- 8.4.3 An Example207
- 8.4.4 Extension to the Vector Case208
- 8.5 Nonlinear Regression212
- 8.5.1 The Scalar Case212
- 8.5.2 Extension to the Vector Case216
- 8.5.3 Algorithms220
- 8.5.4 An Example221
- 8.6 Tests for Model Order221
- 8.7 Maximum Likelihood Estimation225
- 8.8 Bayesian Estimation227
- 8.9 Optimal Experimental Design231
- 8.10 Summary233
- 8.11 Exercises and Assignment Questions233
- CHAPTER 9 NON-PARAMETRIC MODELS – SIGNAL ESTIMATION235
- 9.1 Introduction235
- 9.2 Why is Deconvolution Important?236
- 9.3 The Problem236
- 9.4 Difficulty of the Deconvolution Problem238
- 9.5 The Regularization Method244
- 9.5.1 Fundamentals244
- 9.5.2 Choice of the Regularization Parameter246
- 9.5.3 The Virtual Grid251
- 9.6 Summary254
- 9.7 Exercises and Assignment Questions255
- CHAPTER 10 MODEL VALIDATION257
- 10.1 Introduction257
- 10.2 Model Validation and the Domain of Validity258
- 10.2.1 Validation During Model Formulation258
- 10.2.2 Validation of the Completed Model259
- 10.3 Validation Strategies261
- 10.3.1 Validation of a Single Model – Basic Approach261
- 10.3.2 Validation of a Single Model – Additional Quantitative Tools for Numerically Identified Mod262
- 10.3.3 Validation of Competing Models264
- 10.4 Good Practice in Good Modeling265
- 10.5 Summary266
- 10.6 Exercises and Assignment Questions266
- CHAPTER 11 CASE STUDIES269
- 11.1 Case Study 1: A Sum of Exponentials Tracer Disappearance Model269
- 11.2 Case Study 2: Blood Flow Modeling273
- 11.3 Case Study 3: Cerebral Glucose Modeling274
- 11.4 Case Study 4: Models of the Ligand-Receptor System276
- 11.5 Case Study 5: A Simulation Model of the Glucose-Insulin System280
- 11.5.1 Model Formulation280
- 11.5.2 Results288
- 11.6 Case Study 6: A Model of Insulin Control292
- 11.7 Case Study 7: Illustrations of Bayesian Estimation297
- 11.8 Postscript308
- REFERENCES309
- INDEX319
- A319
- B319
- C319
- D320
- E320
- F320
- G320
- H321
- I321
- J321
- L321
- M321
- N322
- O322
- P322
- Q323
- R323
- S323
- T323
- U324
- V324
- W324
This unified modeling textbook for students of biomedical engineering provides a complete course text on the foundations, theory and practice of modeling and simulation in physiology and medicine. It is dedicated to the needs of biomedical engineering and clinical students, supported by applied BME applications and examples.
• Developed for biomedical engineering and related courses: speaks to BME students at a level and in a language appropriate to their needs, with an interdisciplinary clinical/engineering approach, quantitative basis, and many applied examples to enhance learning
• Delivers a quantitative approach to modeling and also covers simulation: the perfect foundation text for studies across BME and medicine
• Extensive case studies and engineering applications from BME, plus end-of-chapter exercises and a separate Instructor’s manual
• Developed for biomedical engineering and related courses: speaks to BME students at a level and in a language appropriate to their needs, with an interdisciplinary clinical/engineering approach, quantitative basis, and many applied examples to enhance learning
• Delivers a quantitative approach to modeling and also covers simulation: the perfect foundation text for studies across BME and medicine
• Extensive case studies and engineering applications from BME, plus end-of-chapter exercises and a separate Instructor’s manual