With mathematical and computational models furthering our understanding of lung mechanics, function and disease, this book provides an all-inclusive introduction to the topic from a quantitative standpoint. Focusing on inverse modeling, the reader is guided through the theory in a logical progression, from the simplest models up to state-of-the-art models that are both dynamic and nonlinear. Key tools used in biomedical engineering research, such as regression theory, linear and nonlinear systems theory, and the Fourier transform, are explained. Derivations of important physical principles, such as the Poiseuille equation and the wave speed equation, from first principles are also provided. Example applications to experimental data throughout illustrate physiological relevance, whilst problem sets at the end of each chapter provide practice and test reader comprehension. This book is ideal for biomedical engineering and biophysics graduate students and researchers wishing to understand this emerging field.
Author(s): Jason H. T. Bates
Edition: 1
Publisher: Cambridge University Press
Year: 2009
Language: English
Pages: 238
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Notation......Page 15
1.1 The importance of lung mechanics......Page 19
1.2.1 Gas exchange......Page 20
1.2.2 Control of breathing......Page 22
1.2.3 Lung mechanics......Page 23
1.3.1 Obstructive lung disease......Page 24
1.3.2 Restrictive lung disease......Page 25
1.4 How do we assess lung mechanical function?......Page 26
1.4.1 Inverse modeling......Page 27
1.4.2 Forward modeling......Page 29
1.4.3 The modeling hierarchy......Page 30
Further reading......Page 32
2.1.1 Characteristics of transducers......Page 33
2.1.2 Digital data acquisition......Page 36
2.1.3 The sampling theorem and aliasing......Page 38
2.2.1 Pressure transducers......Page 40
2.2.2 Measuring lateral pressure......Page 41
2.2.3 Esophageal pressure......Page 43
2.2.4 Alveolar pressure......Page 45
2.2.5 Flow transducers......Page 46
2.2.6 Volume measurement......Page 48
2.2.7 Plethysmography......Page 50
2.3 Experimental scenarios......Page 52
Problems......Page 53
3.1.1 Model structure......Page 55
3.1.2 The equation of motion......Page 56
3.2.1 Parameter estimation by least squares......Page 62
3.2.2 Estimating confidence intervals......Page 65
3.2.3 An example of model fitting......Page 67
3.2.4 A historical note......Page 70
3.3 Tracking model parameters that change with time......Page 71
3.3.1 Recursive multiple linear regression......Page 72
3.3.2 Dealing with systematic residuals......Page 75
Problems......Page 79
4.1 Physics of airway resistance......Page 80
4.1.2 Laminar and turbulent flow......Page 81
4.1.3 Poiseuille resistance......Page 83
4.1.4 Resistance of the airway tree......Page 86
4.2 Tissue resistance......Page 89
4.3.1 The effect of lung size......Page 90
4.3.2 Surface tension......Page 91
4.4 Resistance and elastance during bronchoconstriction......Page 93
4.4.1 Dose-response relationship......Page 94
4.4.2 Time-course of bronchoconstriction......Page 96
4.4.3 Determinants of airways responsiveness......Page 97
Problems......Page 99
5.1 Flow-dependent resistance......Page 100
5.2.1 Nonlinear pressure-volume relationships......Page 103
5.2.2 Mechanisms of elastic nonlinearity......Page 105
5.3 Choosing between competing models......Page 109
5.3.1 The F-ratio test......Page 111
Problems......Page 113
6.1 FEV1 and FVC......Page 115
6.2 Viscous mechanisms......Page 116
6.3 Bernoulli effect......Page 117
6.4 Wave speed......Page 119
Problems......Page 124
7.1 Passive expiration......Page 126
7.2 Two-compartment models of heterogeneous ventilation......Page 127
7.2.1 The parallel model......Page 129
7.2.2 The series model......Page 132
7.2.3 Electrical analogs......Page 134
7.3 A model of tissue viscoelasticity......Page 135
7.4 Stress adaptation and frequency dependence......Page 137
7.5 Resolving the model ambiguity problem......Page 140
7.6 Fitting the two-compartment model to data......Page 142
Problems......Page 144
8.1 Linear systems theory......Page 145
8.1.1 Linear dynamic systems......Page 146
8.1.3 The impulse and step responses......Page 148
8.1.4 Convolution......Page 151
8.2.1 The discrete and fast Fourier transforms......Page 153
8.2.3 The convolution theorem for Fourier transforms......Page 158
8.3 Impedance......Page 160
8.3.1 The forced oscillation technique......Page 161
8.3.2 A word about complex numbers......Page 163
8.3.3 Signal processing......Page 164
Problems......Page 166
9.1 Equations of motion in the frequency domain......Page 168
9.2 Impedance of the single-compartment model......Page 169
9.2.1 Resonant frequency and inertance......Page 170
9.2.2 Regional lung impedance......Page 174
9.3.1 The viscoelastic model......Page 176
9.3.2 Effects of ventilation heterogeneity......Page 177
9.3.3 The six-element model......Page 180
9.3.4 Transfer impedance......Page 182
9.4 Acoustic impedance......Page 184
Problems......Page 186
10.1 Genesis of the constant phase model......Page 187
10.1.1 Power-law stress relaxation......Page 188
10.1.2 Fitting the constant phase model to lung impedance......Page 190
10.1.3 Physiological interpretation......Page 192
10.2 Heterogeneity and the constant phase model......Page 193
10.2.1 Distributed constant phase models......Page 194
10.2.2 Heterogeneity and hysteresivity......Page 195
10.3 The fractional calculus......Page 199
10.4 Applications of the constant phase model......Page 201
Problems......Page 204
11.1.1 The Volterra series......Page 206
11.1.2 Block-structured nonlinear models......Page 207
11.2 Nonlinear system identification......Page 208
11.2.1 Harmonic distortion......Page 209
11.3 Lung tissue rheology......Page 211
11.3.1 Quasi-linear viscoelasticity......Page 212
11.3.2 Power-law stress adaptation......Page 213
Problems......Page 218
12 Epilogue......Page 219
References......Page 225
Index......Page 236
