Introduction to Modeling in Physiology and Medicine

Cover......Page 1
Introduction to Modeling in Physiology and Medicine......Page 3
Copyright......Page 4
Preface to the second edition......Page 5
Preface to the first edition......Page 6
1.1 Introduction......Page 8
1.2 The book in context......Page 9
1.3 The major ingredients......Page 10
1.5 Organization of the book......Page 11
2.2 Complexity......Page 14
2.3 System dynamics......Page 16
2.3.2 The dynamic behavior of first-order linear time-invariant systems—solution by integration......Page 17
2.3.3 The classical solution for a first-order system......Page 19
2.3.4 General case of a first-order linear system......Page 21
2.4.2 Positive feedback......Page 24
2.4.4 Combining negative and positive feedback......Page 25
2.4.6 Effects of feedback on the complexity of system dynamics......Page 27
2.5.1 General features......Page 28
2.5.2 Enzymes......Page 29
2.5.3 Hormones......Page 31
2.7 Redundancy......Page 34
2.8 Function and behavior and their measurement......Page 35
2.9 Challenges to understanding......Page 36
2.10 Exercises and assignment questions......Page 37
3.2 What is a model?......Page 38
3.3 Why model? The purpose of modeling......Page 40
3.5 Model formulation......Page 42
3.6 Model identification......Page 44
3.7 Model validation......Page 46
3.8 Model simulation......Page 48
3.10 Exercises and assignment questions......Page 50
4.3 The why and when of data models......Page 51
4.4 Approaches to data modeling......Page 52
4.5 Modeling a single variable occurring spontaneously......Page 53
4.5.1 Temperature......Page 54
4.5.2 Urine potassium......Page 56
4.5.4 Hormonal time series......Page 59
4.6.1 Glucose home monitoring data......Page 68
4.6.2 Response to drug therapy—prediction of bronchodilator response......Page 69
4.7 Two variables causally related......Page 71
4.7.1 Hormone/hormone and substrate/hormone series......Page 72
4.7.2 Urine sodium response to water loading......Page 75
4.8.1 Pupil control......Page 77
4.8.2 Control of blood glucose by insulin......Page 79
4.9 Input/output modeling: impulse response and deconvolution......Page 81
4.9.1 Impulse response estimation......Page 83
4.9.2 The convolution integral......Page 85
4.9.3 Reconstructing the input......Page 86
4.10 Summary......Page 89
4.11 Exercises and assignment questions......Page 90
5.2 Static models......Page 91
5.3 Linear modeling......Page 94
5.3.1 The Windkessel circulatory model......Page 95
5.3.3 Gas exchange......Page 97
5.3.4 The dynamics of a swinging limb......Page 99
5.3.5 A model of glucose regulation......Page 102
5.4.1 Blood–tissue exchange......Page 106
5.4.1.1 The single-capillary model......Page 108
5.4.1.2 The capillary–interstitial fluid model......Page 110
5.4.1.3 The capillary–interstitial fluid-cell model......Page 112
5.4.1.4 The whole-organ model......Page 113
5.4.2 Hepatic removal of materials......Page 116
5.4.3 Renal medulla......Page 121
5.4.3.1 Model assumptions......Page 122
5.4.3.2 Principles of the mathematical formulation for the tubular structures......Page 123
5.4.3.3 Interstitial compartment......Page 124
5.4.3.4 Transmural flux......Page 125
5.5.1.1 An electrical model of the cell membrane......Page 126
5.5.1.2 The Hodgkin–Huxley model......Page 129
5.5.1.3 Potassium conductance......Page 130
5.5.1.4 Sodium conductance......Page 133
5.5.2 Enzyme dynamics......Page 136
5.5.3 Baroreceptors......Page 138
5.5.4 Central nervous control of heart rate......Page 139
5.5.5 Compartmental modeling......Page 141
5.5.5.1 The model......Page 143
5.5.6 Insulin receptor regulation......Page 149
5.5.7 Insulin action modeling......Page 151
5.5.8 Thyroid hormone regulation......Page 156
5.5.9.1 The controlled system......Page 159
Expiration......Page 161
Inspiratory time controller......Page 162
5.6.1 An example in cardiac modeling......Page 163
5.7.1.1 The conceptual model......Page 168
5.7.1.2 The mathematical model......Page 170
5.7.2 Insulin secretion......Page 172
5.7.3 Markov model......Page 173
5.8 Summary......Page 174
5.9 Exercises and assignment questions......Page 175
6.2.1 Selection of test signals......Page 176
6.2.2 Transient test signals......Page 178
6.2.3 Harmonic test signals......Page 179
6.2.4 Random signal testing......Page 180
6.3 Errors......Page 181
6.4.1 Parameter estimation......Page 183
6.6 Exercises and assignment questions......Page 184
7.1 Introduction......Page 185
7.2 Some examples......Page 189
7.3 Definitions......Page 195
7.4 Linear models: the transfer function method......Page 196
7.5 Nonlinear models: the Taylor series expansion method......Page 200
7.6.1 Fundamentals......Page 203
Stage A......Page 204
Stage B......Page 205
Two input/three output experiment......Page 207
7.8 Exercises and assignment questions......Page 208
8.1 Introduction......Page 210
8.2 Linear and nonlinear parameters......Page 212
8.3.2 The residual sum of squares......Page 213
8.3.4 Weights and error in the data......Page 215
8.4.1 The problem......Page 218
8.4.2 Test on residuals......Page 219
8.4.3 An Example......Page 222
8.4.4 Extension to the vector case......Page 224
8.5.1 The scalar case......Page 227
8.5.2 Extension to the vector case......Page 231
8.5.4 An example......Page 235
8.6 Tests for model order......Page 236
8.7 Maximum likelihood estimation......Page 238
8.8 Bayesian estimation......Page 242
8.9 Optimal experimental design......Page 245
8.11 Exercises and assignment questions......Page 248
9.2 Why is deconvolution important?......Page 249
9.3 The problem......Page 251
9.4 Difficulty of the deconvolution problem......Page 252
9.5.1 Fundamentals......Page 257
9.5.2 Choice of the regularization parameter......Page 259
9.5.3 The virtual grid......Page 261
9.7 Exercises and assignment questions......Page 266
10.2.1 Validation during model formulation......Page 268
10.2.2 Validation of the completed model......Page 269
Pragmatic......Page 270
Overall patterns of response......Page 271
Features of response......Page 272
Residuals of the mismatch between model and data......Page 273
Goodness of fit......Page 274
10.4 Good practice in good modeling......Page 275
10.6 Exercises and assignment questions......Page 277
11.1 Case study 1: a sum of exponentials tracer disappearance model......Page 278
11.2 Case study 2: blood flow modeling......Page 281
11.3 Case study 3: cerebral glucose modeling......Page 283
11.4 Case study 4: models of the ligand–receptor system......Page 284
11.5.1 The stochastic cellular model......Page 288
11.5.1.1 First-phase secretion......Page 293
11.5.1.2 Second-phase secretion......Page 294
11.5.2 The whole-body model......Page 304
11.6 Case study 6: a model of insulin control......Page 311
WARNING!!! DUMMY ENTRY......Page 0
Insulin sensitivity......Page 316
11.7.1.1 Glucose subsystem......Page 322
11.7.1.2 Insulin subsystem......Page 325
Endogenous glucose production......Page 326
Glucose rate of appearance......Page 328
Glucose utilization......Page 329
Insulin secretion......Page 330
Daily life for a normal subject......Page 331
Daily life for a subject with impaired glucose tolerance......Page 332
11.8.1 In silico artificial pancreas trials......Page 335
11.8.3 In silico inhaled insulin trials......Page 342
11.9 Case study 9: illustrations of Bayesian estimation......Page 344
11.9.2 The two-exponential model: ML versus MAP......Page 346
11.9.4 Two versus three-exponential model order choice......Page 349
11.9.5 Data-poor situation: ML versus MAP......Page 351
11.10 Postscript......Page 355
References......Page 356
Index......Page 366
Back Cover......Page 372