Lung mechanics : an inverse modeling approach / Jason H.T. Bates.

Includes bibliographical references and index.

1. Introduction -- 2. Collecting data -- 3. The linear single-compartment model -- 4. Resistance and elastance -- 5. Nonlinear single-compartment models -- 6. Flow limitation -- 7. Linear two-compartment models -- 8. The general linear model -- 9. Inverse models of lung impedance -- 10. Constant phase model of impedance -- 11. Nonlinear dynamic models -- 12. Epilogue -- --

1. Introduction -- 1.1. The importance of lung mechanics -- 1.2. Anatomy and physiology -- 1.2.1. Gas exchange -- 1.2.2. Control of breathing -- 1.2.3. Lung mechanics -- 1.3. Pathophysiology -- 1.3.1. Obstructive lung disease -- 1.3.2. Restrictive lung disease -- 1.4. How do we assess lung mechanical function? -- 1.4.1. Inverse modeling -- 1.4.2. Forward modeling -- 1.4.3. The modeling hierarchy -- -- 2. Collecting data -- 2.1. Measurement theory -- 2.1.1. Characteristics of transducers -- 2.1.2. Digital data acquisition -- 2.1.3. The sampling theorem and aliasing -- 2.2. Measuring pressure, flow, and volume -- 2.2.1. Pressure transducers -- 2.2.2. Measuring lateral pressure -- 2.2.3. Esophageal pressure -- 2.2.4. Alveolar pressure -- 2.2.5. Flow transducers -- 2.2.6. Volume measurement -- 2.2.7. Plethysmography -- 2.3. Experimental scenarios -- -- 3. The linear single-compartment model -- 3.1. Establishing the model -- 3.1.1. Model structure -- 3.1.2. The equation of motion -- 3.2. Fitting the model to data -- 3.2.1. Parameter estimation by least squares -- 3.2.2. Estimating confidence intervals -- 3.2.3. An example of model fitting -- 3.2.4. A historical note -- 3.3. Tracking model parameters that change with time -- 3.3.1. Recursive multiple linear regression -- 3.3.2. Dealing with systematic residuals -- -- 4. Resistance and elastance -- 4.1. Physics of airway resistance -- 4.1.1. Viscosity -- 4.1.2. Laminar and turbulent flow -- 4.1.3. Poiseuille resistance -- 4.1.4. Resistance of the airway tree -- 4.2. Tissue resistance -- 4.3. Lung elastance -- 4.3.1. The effect of lung size -- 4.3.2. Surface tension -- 4.4. Resistance and elastance during bronchoconstriction -- 4.4.1. Dose-response relationship -- 4.4.2. Time-course of bronchoconstriction -- 4.4.3. Determinants of airways responsiveness -- -- 5. Nonlinear single-compartment models -- 5.1. Flow-dependent resistance -- 5.2. Volume-dependent elastance -- 5.2.1. Nonlinear pressure-volume relationships -- 5.2.2. Mechanisms of elastic nonlinearity -- 5.3. Choosing between competing models -- 5.3.1. The F-ratio test -- 5.3.2. The Akaike criterion -- -- 6. Flow limitation -- 6.1. FEV1 and FVC -- 6.2. Viscous mechanisms -- 6.3. Bernoulli effect -- 6.4. Wave speed -- -- 7. Linear two-compartment models -- 7.1. Passive expiration -- 7.2. Two-compartment models of heterogeneous ventilation -- 7.2.1. The parallel model -- 7.2.2. The series model -- 7.2.3. Electrical analogs -- 7.3. A model of tissue viscoelasticity -- 7.4. Stress adaptation and frequency dependence -- 7.5. Resolving the model ambiguity problem -- 7.6. Fitting the two-compartment model to data -- -- 8. The general linear model -- 8.1. Linear systems theory -- 8.1.1. Linear dynamic systems -- 8.1.2. Superposition -- 8.1.3. The impulse and step responses -- 8.1.4. Convolution -- 8.2. The Fourier transform -- 8.2.1. The discrete and fast Fourier transforms -- 8.2.2. The power spectrum -- 8.2.3. The convolution theorem for Fourier transforms -- 8.3. Impedance -- 8.3.1. The forced oscillation technique -- 8.3.2. A word about complex numbers -- 8.3.3. Signal processing -- -- 9. Inverse models of lung impedance -- 9.1. Equations of motion in the frequency domain -- 9.2. Impedance of the single-compartment model -- 9.2.1. Resonant frequency and inertance -- 9.2.2. Regional lung impedance -- 9.3. Impedance of multi-compartment models -- 9.3.1. The viscoelastic model -- 9.3.2. Effects of ventilation heterogeneity -- 9.3.3. The six-element model -- 9.3.4. Transfer impedance -- 9.4. Acoustic impedance -- -- 10. Constant phase model of impedance -- 10.1. Genesis of the constant phase model -- 10.1.1. Power-law stress relaxation -- 10.1.2. Fitting the constant phase model to lung impedance -- 10.1.3. Physiological interpretation -- 10.2. Heterogeneity and the constant phase model -- 10.2.1. Distributed constant phase models -- 10.2.2. Heterogeneity and hysteresivity -- 10.3. The fractional calculus -- 10.4. Applications of the constant phase model -- -- 11. Nonlinear dynamic models -- 11.1. Theory of nonlinear systems -- 11.1.1. The Volterra series -- 11.1.2. Block-structured nonlinear models -- 11.2. Nonlinear system identification -- 11.2.1. Harmonic distortion -- 11.2.2. Identifying Wiener and Hammerstein models -- 11.3. Lung tissue rheology -- 11.3.1. Quasi-linear viscoelasticity -- 11.3.2. Power-law stress adaptation -- -- 12. Epilogue.

"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."--Publisher's website.