The Human Respiratory System: An Analysis of the Interplay between Anatomy, Structure, Breathing and Fractal Dynamics (Series in BioEngineering)

__The Human Respiratory System__ combines emerging ideas from biology and mathematics to show the reader how to produce models for the development of biomedical engineering applications associated with the lungs and airways. Mathematically mature but in its infancy as far as engineering uses are concerned, fractional calculus is the basis of the methods chosen for system analysis and modelling. This reflects two decades’ worth of conceptual development which is now suitable for bringing to bear in biomedical engineering. The text reveals the latest trends in modelling and identification of human respiratory parameters with a view to developing diagnosis and monitoring technologies. Of special interest is the notion of fractal structure which is indicative of the large-scale biological efficiency of the pulmonary system. The related idea of fractal dimension represents the adaptations in fractal structure caused by environmental factors, notably including disease. These basics are linked to model the dynamical patterns of breathing as a whole. The ideas presented in the book are validated using real data generated from healthy subjects and respiratory patients and rest on non-invasive measurement methods. __The____Human Respiratory System__ will be of interest to applied mathematicians studying the modelling of biological systems, to clinicians with interests outside the traditional borders of medicine, and to engineers working with technologies of either direct medical significance or for mitigating changes in the respiratory system caused by, for example, high-altitude or deep-sea environments. The Human Respiratory System 3 Foreword 6 Preface 8 Acknowledgements 12 Contents 14 Acronyms 17 Nomenclature 18 Chapter 1: Introduction 23 1.1 The Concept of Fractional Signals and Systems in Biomedical Engineering 23 1.2 Short History of Fractional Calculus and Its Application to the Respiratory System 24 1.3 Emerging Tools to Analyze and Characterize the Respiratory System 28 1.3.1 Basic Concepts of Fractional Calculus 28 1.3.2 Fractional-Order Dynamical Systems 30 1.3.3 Relation Between Fractal Structure and Fractal Dimension 31 1.4 Summary 33 Chapter 2: The Human Respiratory System 34 2.1 Anatomy and Structure 34 2.2 Morphology 35 2.3 Specific Pulmonary Abnormalities 35 2.4 Structural Changes in the Lungs with Disease 40 2.5 Non-invasive Lung Function Tests 42 2.6 Summary 43 Chapter 3: The Respiratory Impedance 44 3.1 Forced Oscillation Technique Lung Function Test 44 3.2 Frequency Response of the Respiratory Tissue and Airways 46 3.3 Lumped Models of the Respiratory Impedance 48 3.3.1 Selected Parametric Models from Literature 48 3.3.2 The Volunteers 52 3.3.3 Identification Algorithm 53 3.3.4 Results and Discussion 53 3.4 Summary 58 Chapter 4: Modeling the Respiratory Tract by Means of Electrical Analogy 59 4.1 Modeling Based on a Simplified Morphology and Structure 59 4.2 Electrical Analogy 66 4.2.1 Elastic Tube Walls 69 4.2.2 Viscoelastic Tube Walls 70 4.2.3 Generic Recurrence in the Airways 71 4.3 Some Further Thoughts 72 4.4 Summary 73 Chapter 5: Ladder Network Models as Origin of Fractional-Order Models 75 5.1 Fractal Structure and Ladder Network Models 75 5.1.1 An Elastic Airway Wall 75 5.1.2 A Viscoelastic Airway Wall 81 5.2 Effects of Structural Asymmetry 84 5.3 Relation Between Model Parameters and Physiology 86 5.3.1 A Simulation Study 86 5.3.2 A Study on Measured Respiratory Impedance 90 5.4 Summarizing Thoughts 92 Chapter 6: Modeling the Respiratory Tree by Means of Mechanical Analogy 96 6.1 Basic Elements 96 6.2 Mechanical Analogue and Ladder Network Models 98 6.3 Stress-Strain Curves 103 6.3.1 Stepwise Variations of Strain 103 6.3.2 Sinusoidal Variations of Strain 105 6.4 Relation Between Lumped FO Model Parameters and Viscoelasticity 108 6.5 Implications in Pathology 115 6.6 Summary 116 Chapter 7: Frequency Domain: Parametric Model Selection and Evaluation 118 7.1 Overview of Available Models for Evaluating the Respiratory Impedance 118 7.2 FO Model Selection in Relation to Various Frequency Intervals 119 7.2.1 Relation Between Model Parameters and Physiology 120 7.2.2 Subjects 121 7.2.3 Results 122 7.3 Implications in Pathology 127 7.3.1 FOT Measurements on Adults 127 7.3.2 Healthy vs. COPD 129 7.3.3 Healthy vs. Kyphoscoliosis 133 7.3.4 FOT Measurements on Children 136 7.3.5 Healthy vs. Asthma in Children 138 7.3.6 Healthy vs. Cystic Fibrosis in Children 143 7.4 Parametric Models for Multiple Resonant Frequencies 146 7.4.1 High Frequency Range of Respiratory Impedance 146 7.4.2 Evaluation on Healthy Adults 148 7.4.3 Relation to Physiology and Pathology 154 7.5 Summarizing Thoughts 156 Chapter 8: Time Domain: Breathing Dynamics and Fractal Dimension 157 8.1 From Frequency Response to Time Response 157 8.1.1 Calculating the Impulse Response of the Lungs 157 8.1.2 Implications in Pathology 158 8.2 Mapping the Impedance Values 162 8.2.1 Multi-dimensional Scaling 162 8.2.2 Classification Ability with Pathology 166 8.3 Revealing the Hidden Information in Breathing at Rest 175 8.3.1 Pressure-Volume Loops, Work of Breathing and Fractal Dimension 175 8.3.2 Relations with Pathology 178 8.3.3 Fractal Dimension and Identification of Power-Law Trends 179 8.4 Summary 185 Chapter 9: Non-linear Effects in the Respiratory Impedance 186 9.1 The Principles of Detection of Non-linear Distortions in a Non-linear System 186 9.1.1 Reducing the Breathing Interference 186 9.1.2 Non-linear Distortions 189 9.2 Non-linear Effects from Measuring Device 192 9.3 Clinical Markers for Quantifying Non-linear Effects 195 9.4 Non-linear Effects Originated with Pathology 196 9.5 Detecting Non-linear Distortions at Low Frequencies 198 9.5.1 Prototype Device with Feedforward Compensation 198 9.5.2 Respiratory Impedance at Low Frequencies 199 9.5.3 Non-linear Distortions at Low Frequencies 203 9.5.4 Relation to the FO Model Parameters 207 9.6 Summary 210 Chapter 10: Conclusions 214 10.1 Main Results 214 10.2 Important Directions for Research 216 10.2.1 Relating the Fractional Order Parameter Values to Pathology 216 10.2.2 Low Frequency Measurements 216 Appendix: Useful Notes on Fractional Calculus 217 References 223 Subject Index 231 The Human Respiratory System combines emerging ideas from biology and mathematics to show the reader how to produce models for the development of biomedical engineering applications associated with the lungs and airways. Mathematically mature but in its infancy as far as engineering uses are concerned, fractional calculus is the basis of the methods chosen for system analysis and modelling. This reflects two decades' worth of conceptual development which is now suitable for bringing to bear in biomedical engineering. The text reveals the latest trends in modelling and identification of human respiratory parameters with a view to developing diagnosis and monitoring technologies. Of special interest is the notion of fractal structure which is indicative of the large-scale biological efficiency of the pulmonary system. The related idea of fractal dimension represents the adaptations in fractal structure caused by environmental factors, notably including disease. These basics are linked to model the dynamical patterns of breathing as a whole. The ideas presented in the book are validated using real data generated from healthy subjects and respiratory patients and rest on non-invasive measurement methods. The Human Respiratory System will be of interest to applied mathematicians studying the modelling of biological systems, to clinicians with interests outside the traditional borders of medicine, and to engineers working with technologies of either direct medical significance or for mitigating changes in the respiratory system caused by, for example, high-altitude or deep-sea environments. Front Matter....Pages I-XXV Introduction....Pages 1-11 The Human Respiratory System....Pages 13-22 The Respiratory Impedance....Pages 23-37 Modeling the Respiratory Tract by Means of Electrical Analogy....Pages 39-54 Ladder Network Models as Origin of Fractional-Order Models....Pages 55-75 Modeling the Respiratory Tree by Means of Mechanical Analogy....Pages 77-98 Frequency Domain: Parametric Model Selection and Evaluation....Pages 99-137 Time Domain: Breathing Dynamics and Fractal Dimension....Pages 139-167 Non-linear Effects in the Respiratory Impedance....Pages 169-196 Conclusions....Pages 197-199 Back Matter....Pages 201-217