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Cambridge2009年Lung.Mechanics.An.Inverse.Modeling.Approach
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作者：JASON H. T. BATES University of Vermont 内容： 1 Introduction 1 1.1 The importance of lung mechanics 1 1.2 Anatomy and physiology 2 1.2.1 Gas exchange 2 1.2.2 Control of breathing 4 1.2.3 Lung mechanics 5 1.3 Pathophysiology 6 1.3.1 Obstructive lung disease 6 1.3.2 Restrictive lung disease 7 1.4 How do we assess lung mechanical function? 8 1.4.1 Inverse modeling 9 1.4.2 Forward modeling 11 1.4.3 The modeling hierarchy 12 Further reading 14 2 Collecting data 15 2.1 Measurement theory 15 2.1.1 Characteristics of transducers 15 2.1.2 Digital data acquisition 18 2.1.3 The sampling theorem and aliasing 20 2.2 Measuring pressure, flow, and volume 22 2.2.1 Pressure transducers 22 2.2.2 Measuring lateral pressure 23 2.2.3 Esophageal pressure 25 2.2.4 Alveolar pressure 27 2.2.5 Flow transducers 28 2.2.6 Volume measurement 30 2.2.7 Plethysmography 32 2.3 Experimental scenarios 34 Problems 35 viii Contents 3 The linear single-compartment model 37 3.1 Establishing the model 37 3.1.1 Model structure 37 3.1.2 The equation of motion 38 3.2 Fitting the model to data 44 3.2.1 Parameter estimation by least squares 44 3.2.2 Estimating confidence intervals 47 3.2.3 An example of model fitting 49 3.2.4 A historical note 52 3.3 Tracking model parameters that change with time 53 3.3.1 Recursive multiple linear regression 54 3.3.2 Dealing with systematic residuals 57 Problems 61 4 Resistance and elastance 62 4.1 Physics of airway resistance 62 4.1.1 Viscosity 63 4.1.2 Laminar and turbulent flow 63 4.1.3 Poiseuille resistance 65 4.1.4 Resistance of the airway tree 68 4.2 Tissue resistance 71 4.3 Lung elastance 72 4.3.1 The effect of lung size 72 4.3.2 Surface tension 73 4.4 Resistance and elastance during bronchoconstriction 75 4.4.1 Dose-response relationship 76 4.4.2 Time-course of bronchoconstriction 78 4.4.3 Determinants of airways responsiveness 79 Problems 81 5 Nonlinear single-compartment models 82 5.1 Flow-dependent resistance 82 5.2 Volume-dependent elastance 85 5.2.1 Nonlinear pressure-volume relationships 85 5.2.2 Mechanisms of elastic nonlinearity 87 5.3 Choosing between competing models 91 5.3.1 The F-ratio test 93 5.3.2 The Akaike criterion 95 Problems 95 6 Flow limitation 97 6.1 FEV1 and FVC 97 6.2 Viscous mechanisms 98 Contents ix 6.3 Bernoulli effect 99 6.4 Wave speed 101 Problems 106 7 Linear two-compartment models 108 7.1 Passive expiration 108 7.2 Two-compartment models of heterogeneous ventilation 109 7.2.1 The parallel model 111 7.2.2 The series model 114 7.2.3 Electrical analogs 116 7.3 A model of tissue viscoelasticity 117 7.4 Stress adaptation and frequency dependence 119 7.5 Resolving the model ambiguity problem 122 7.6 Fitting the two-compartment model to data 124 Problems 126 8 The general linear model 127 8.1 Linear systems theory 127 8.1.1 Linear dynamic systems 128 8.1.2 Superposition 130 8.1.3 The impulse and step responses 130 8.1.4 Convolution 133 8.2 The Fourier transform 135 8.2.1 The discrete and fast Fourier transforms 135 8.2.2 The power spectrum 140 8.2.3 The convolution theorem for Fourier transforms 140 8.3 Impedance 142 8.3.1 The forced oscillation technique 143 8.3.2 A word about complex numbers 145 8.3.3 Signal processing 146 Problems 148 9 Inverse models of lung impedance 150 9.1 Equations of motion in the frequency domain 150 9.2 Impedance of the single-compartment model 151 9.2.1 Resonant frequency and inertance 152 9.2.2 Regional lung impedance 156 9.3 Impedance of multi-compartment models 158 9.3.1 The viscoelastic model 158 9.3.2 Effects of ventilation heterogeneity 159 9.3.3 The six-element model 162 9.3.4 Transfer impedance 164 9.4 Acoustic impedance 166 Problems 168 x Contents 10 Constant phase model of impedance 169 10.1 Genesis of the constant phase model 169 10.1.1 Power-law stress relaxation 170 10.1.2 Fitting the constant phase model to lung impedance 172 10.1.3 Physiological interpretation 174 10.2 Heterogeneity and the constant phase model 175 10.2.1 Distributed constant phase models 176 10.2.2 Heterogeneity and hysteresivity 177 10.3 The fractional calculus 181 10.4 Applications of the constant phase model 183 Problems 186 11 Nonlinear dynamic models 188 11.1 Theory of nonlinear systems 188 11.1.1 The Volterra series 188 11.1.2 Block-structured nonlinear models 189 11.2 Nonlinear system identification 190 11.2.1 Harmonic distortion 191 11.2.2 Identifying Wiener and Hammerstein models 193 11.3 Lung tissue rheology 193 11.3.1 Quasi-linear viscoelasticity 194 11.3.2 Power-law stress adaptation 195 Problems 200 12 Epilogue 201 References 207 Index 218 |
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