Applied Biofluid Mechanics This page intentionally left blank Applied Biofluid Mechanics Lee Waite, Ph.D., P.E. Jerry Fine, Ph.D. New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this pub- lication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-150951-8 The material in this eBook also appears in the print version of this title: 0-07-147217-7. All trademarks are trademarks of their respective owners. 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DOI: 10.1036/0071472177 ABOUT THE AUTHORS LEE WAITE, PH.D., P.E., is Head of the Department of Applied Biology and Biomedical Engineering, and Director of the Guidant/Eli Lilly and Co. Applied Life Sciences Research Center, at Rose-Hulman Institute of Technology in Terre Haute, Indiana. He is also the author of Biofluid Mechanics in Cardiovascular Systems, published by McGraw-Hill. JERRY FINE, PH.D., is Associate Professor of Mechanical Engineering at Rose-Hulman Institute of Technology. Before he joined the faculty at Rose, Dr. Fine served as a patrol plane pilot in the U.S. Navy and taught at the U.S. Naval Academy. Copyright © 2007 by The McGraw-Hill Companies, Inc. Click here for terms of use. This page intentionally left blank For more information about this title, click here Contents Preface xiii Acknowledgments xv Chapter 1. Review of Basic Fluid Mechanics Concepts 1 1.1 A Brief History of Biomedical Fluid Mechanics 1 1.2 Fluid Characteristics and Viscosity 6 1.2.1 Displacement and velocity 7 1.2.2 Shear stress and viscosity 8 1.2.3 Example problem: shear stress 10 1.2.4 Viscosity 11 1.2.5 Clinical feature: polycythemia 13 1.3 Fundamental Method for Measuring Viscosity 14 1.3.1 Example problem: viscosity measurement 16 1.4 Introduction to Pipe Flow 16 1.4.1 Reynolds number 17 1.4.2 Example problem: Reynolds number 19 1.4.3 Poiseuille’s law 19 1.4.4 Flow rate 23 1.5 Bernoulli Equation 24 1.6 Conservation of Mass 24 1.6.1 Venturi meter example 26 1.7 Fluid Statics 27 1.7.1 Example problem: fluid statics 28 1.8 The Womersley Number α: A Frequency Parameter for Pulsatile Flow 29 1.8.1 Example problem: Womersley number 30 Problems 31 Bibliography 33 Chapter 2. Cardiovascular Structure and Function 35 2.1 Introduction 35 2.2 Clinical Features 36 2.3 Functional Anatomy 37 2.4 The Heart as a Pump 38 2.5 Cardiac Muscle 39 2.5.1 Biopotential in myocardium 40 vii viii Contents 2.5.2 Excitability 41 2.5.3 Automaticity 43 2.6 Electrocardiograms 43 2.6.1 Electrocardiogram leads 44 2.6.2 Mean electrical axis 45 2.6.3 Example problem: mean electrical axis 47 2.6.4 Unipolar versus bipolar and augmented leads 48 2.6.5 Electrocardiogram interpretations 49 2.6.6 Clinical feature: near maximal exercise stress test 50 2.7 Heart Valves 51 2.7.1 Clinical features 52 2.8 Cardiac Cycle 52 2.8.1 Pressure-volume diagrams 55 2.8.2 Changes in contractility 57 2.8.3 Ventricular performance 58 2.8.4 Clinical feature: congestive heart failure 58 2.8.5 Pulsatility index 59 2.8.6 Example problem: pulsatility index 59 2.9 Heart Sounds 60 2.9.1 Clinical features 61 2.9.2 Factors influencing flow and pressure 61 2.10 Coronary Circulation 63 2.10.1 Control of the coronary circulation 64 2.10.2 Clinical features 65 2.11 Microcirculation 65 2.11.1 Capillary structure 65 2.11.2 Capillary wall structure 66 2.11.3 Pressure control in the microvasculature 67 2.11.4 Diffusion in capillaries 68 2.11.5 Venules 68 2.12 Lymphatic Circulation 69 Problems 69 Bibliography 75 Chapter 3. Pulmonary Anatomy, Pulmonary Physiology, and Respiration 77 3.1 Introduction 77 3.1.1 Clinical features: hyperventilation 78 3.2 Alveolar Ventilation 79 3.2.1 Tidal volume 79 3.2.2 Residual volume 79 3.2.3 Expiratory reserve volume 80 3.2.4 Inspiratory reserve volume 80 3.2.5 Functional residual capacity 80 3.2.6 Inspiratory capacity 80 3.2.7 Total lung capacity 80 3.2.8 Vital capacity 81 3.3 Ventilation-Perfusion Relationships 81 3.4 Mechanics of Breathing 81 3.4.1 Muscles of inspiration 82 3.4.2 Muscles of expiration 83 3.4.3 Compliance of the lung and chest wall 83 Contents ix 3.4.4 Elasticity, elastance, and elastic recoil 83 3.4.5 Example problem: compliance 84 3.5 Work of Breathing 85 3.5.1 Clinical features: respiratory failure 87 3.6 Airway Resistance 88 3.6.1 Example problem: Reynolds number 91 3.7 Gas Exchange and Transport 91 3.7.1 Diffusion 92 3.7.2 Diffusing capacity 92 3.7.3 Oxygen dissociation curve 94 3.7.4 Example problem: oxygen content 95 3.7.5 Clinical feature 96 3.8 Pulmonary Pathophysiology 96 3.8.1 Bronchitis 96 3.8.2 Emphysema 96 3.8.3 Asthma 97 3.8.4 Pulmonary fibrosis 98 3.8.5 Chronics obstructive pulmonary disease (COPD) 98 3.8.6 Heart disease 98 3.8.7 Comparison of pulmonary pathologies 98 3.9 Respiration in Extreme Environments 99 3.9.1 Barometric pressure 100 3.9.2 Partial pressure of oxygen 101 3.9.3 Hyperventilation and the alveolar gas equation 102 3.9.4 Alkalosis 103 3.9.5 Acute mountain sickness 103 3.9.6 High-altitude pulmonary edema 104 3.9.7 High-altitude cerebral edema 104 3.9.8 Acclimatization 104 3.9.9 Drugs stimulating red blood cell production 105 3.9.10 Example problem: alveolar gas equation 106 Review Problems 106 Bibliography 109 Chapter 4. Hematology and Blood Rheology 111 4.1 Introduction 111 4.2 Elements of Blood 111 4.3 Blood Characteristics 111 4.3.1 Types of fluids 112 4.3.2 Viscosity of blood 113 4.3.3 Fåhræus-Lindqvist effect 114 4.3.4 Einstein’s equation 116 4.4 Viscosity Measurement 116 4.4.1 Rotating cylinder viscometer 116 4.4.2 Measuring viscosity using Poiseuille’s law 118 4.4.3 Viscosity measurement by a cone and plate viscometer 119 4.5 Erythrocytes 121 4.5.1 Hemoglobin 123 4.5.2 Clinical features—sickle cell anemia 125 4.5.3 Erythrocyte indices 125 4.5.4 Abnormalities of the blood 126 4.5.5 Clinical feature—thalassemia 127 x Contents 4.6 Leukocytes 127 4.6.1 Neutrophils 128 4.6.2 Lymphocytes 129 4.6.3 Monocytes 131 4.6.4 Eosinophils 131 4.6.5 Basophils 131 4.6.6 Leukemia 131 4.6.7 Thrombocytes 132 4.7 Blood Types 132 4.7.1 Rh blood groups 134 4.7.2 M and N blood group system 135 4.8 Plasma 135 4.8.1 Plasma viscosity 136 4.8.2 Electrolyte composition of plasma 136 4.8.3 Blood pH 137 4.8.4 Clinical features—acid–base imbalance 137 Review Problems 138 Bibliography 139 Chapter 5.