Applied Biofluid Mechanics, Second Edition

1 Review of Basic Fluid Mechanics Concepts<br/>1.1 A Brief History of Biomedical Fluid Mechanics<br/>1.2 Fluid Characteristics and Viscosity<br/>1.2.1 Displacement and Velocity<br/>1.2.2 Shear Stress and Viscosity<br/>1.2.3 Example Problem: Shear Stress<br/>1.2.4 Viscosity<br/>1.2.5 Clinical Feature: Polycythemia<br/>1.3 Fundamental Method for Measuring Viscosity<br/>1.3.1 Example Problem: Viscosity Measurement<br/>1.4 Introduction to Pipe Flow<br/>1.4.1 Reynolds Number<br/>1.4.2 Example Problem: Reynolds Number<br/>1.4.3 Poiseuille’s Law<br/>1.4.4 Flow Rate<br/>1.5 Bernoulli Equation<br/>1.6 Conservation of Mass<br/>1.6.1 Venturi Meter Example<br/>1.7 Fluid Statics<br/>1.7.1 Example Problem: Fluid Statics<br/>1.8 The Womersley Number α—A Frequency Parameter for Pulsatile Flow<br/>1.8.1 Example Problem: Womersley Number<br/>Review Problems<br/>Bibliography<br/>2 Cardiovascular Structure and Function<br/>2.1 Introduction<br/>2.2 Clinical Features<br/>2.3 Functional Anatomy<br/>2.4 The Heart as a Pump<br/>2.5 Cardiac Muscle<br/>2.5.1 Biopotential in Myocardium<br/>2.5.2 Excitability<br/>2.5.3 Automaticity<br/>2.6 Electrocardiograms<br/>2.6.1 Electrocardiogram Leads<br/>2.6.2 Mean Electrical Axis<br/>2.6.3 Example Problem: Mean Electrical Axis<br/>2.6.4 Unipolar versus Bipolar and Augmented Leads<br/>2.6.5 Electrocardiogram Interpretations<br/>2.6.6 Clinical Feature: Near Maximal Exercise Stress Test<br/>2.7 Heart Valves<br/>2.7.1 Clinical Features<br/>2.8 Cardiac Cycle<br/>2.8.1 Pressure–Volume Diagrams<br/>2.8.2 Changes in Contractility<br/>2.8.3 Ventricular Performance<br/>2.8.4 Cardiac Output (CO) Curves and Cardiac Function Curves<br/>2.8.5 Clinical Feature: Congestive Heart Failure<br/>2.8.6 Pulsatility Index<br/>2.8.7 Example Problem: Pulsatility Index<br/>2.9 Heart Sounds<br/>2.9.1 Clinical Features<br/>2.9.2 Factors Influencing Flow and Pressure<br/>2.10 Coronary Circulation<br/>2.10.1 Control of Coronary Circulation<br/>2.10.2 Clinical Features<br/>2.11 Microcirculation<br/>2.11.1 Capillary Structure<br/>2.11.2 Capillary Wall Structure<br/>2.11.3 Pressure Control in Microvasculature<br/>2.11.4 Diffusion in Capillaries<br/>2.11.5 Venules<br/>2.12 Lymphatic Circulation<br/>Review Problems<br/>Bibliography<br/>3 Pulmonary Anatomy, Pulmonary Physiology, and Respiration<br/>3.1 Introduction<br/>3.1.1 Clinical Features: Hyperventilation<br/>3.2 Alveolar Ventilation<br/>3.2.1 Tidal Volume<br/>3.2.2 Residual Volume<br/>3.2.3 Expiratory Reserve Volume<br/>3.2.4 Inspiratory Reserve Volume<br/>3.2.5 Functional Residual Capacity<br/>3.2.6 Inspiratory Capacity<br/>3.2.7 Total Lung Capacity<br/>3.2.8 Vital Capacity<br/>3.3 Ventilation-Perfusion Relationships<br/>3.4 Mechanics of Breathing<br/>3.4.1 Muscles of Inspiration<br/>3.4.2 Muscles of Expiration<br/>3.4.3 Compliance of the Lung and Chest Wall<br/>3.4.4 Elasticity, Elastance, and Elastic Recoil<br/>3.4.5 Example Problem: Compliance<br/>3.5 Work of Breathing<br/>3.5.1 Clinical Features—Respiratory Failure<br/>3.6 Airway Resistance<br/>3.6.1 Example Problem: Reynolds Number<br/>3.7 Gas Exchange and Transport<br/>3.7.1 Diffusion<br/>3.7.2 Diffusing Capacity<br/>3.7.3 Oxygen Dissociation Curve<br/>3.7.4 Example Problem: Oxygen Content<br/>3.7.5 Clinical Feature<br/>3.8 Pulmonary Pathophysiology<br/>3.8.1 Bronchitis<br/>3.8.2 Emphysema<br/>3.8.3 Asthma<br/>3.8.4 Pulmonary Fibrosis<br/>3.8.5 Chronic Obstructive Pulmonary Disease<br/>3.8.6 Heart Disease<br/>3.8.7 Comparison of Pulmonary Pathologies<br/>3.9 Respiration in Extreme Environments<br/>3.9.1 Barometric Pressure<br/>3.9.2 Partial Pressure of Oxygen<br/>3.9.3 Hyperventilation and the Alveolar Gas Equation<br/>3.9.4 Alveolar-Arterial Gradient<br/>3.9.5 Alkalosis<br/>3.9.6 Acute Mountain Sickness<br/>3.9.7 High-Altitude Pulmonary Edema<br/>3.9.8 High-Altitude Cerebral Edema<br/>3.9.9 Acclimatization<br/>3.9.10 Drugs Stimulating Red Blood Cell Production<br/>3.9.11 Example Problem: Alveolar Gas Equation<br/>Review Problems<br/>Bibliography<br/>4 Hematology and Blood Rheology<br/>4.1 Introduction<br/>4.2 Elements of Blood<br/>4.3 Blood Characteristics<br/>4.3.1 Types of Fluids<br/>4.3.2 Viscosity of Blood<br/>4.3.3 Fåhræus–Lindqvist Effect<br/>4.3.4 Einstein’s Equation<br/>4.4 Viscosity Measurement<br/>4.4.1 Rotating Cylinder Viscometer<br/>4.4.2 Measuring Viscosity Using Poiseuille’s Law<br/>4.4.3 Viscosity Measurement by a Cone and Plate Viscometer<br/>4.5 Erythrocytes<br/>4.5.1 Hemoglobin<br/>4.5.2 Clinical Features—Sickle Cell Anemia<br/>4.5.3 Erythrocyte Indices<br/>4.5.4 Abnormalities of Blood<br/>4.5.5 Clinical Feature—Thalassemia<br/>4.6 Leukocytes<br/>4.6.1 Neutrophils<br/>4.6.2 Lymphocytes<br/>4.6.3 Monocytes<br/>4.6.4 Eosinophils<br/>4.6.5 Basophils<br/>4.6.6 Leukemia<br/>4.6.7 Thrombocytes<br/>4.7 Blood Types<br/>4.7.1 Rh Blood Groups<br/>4.7.2 M and N Blood Group System<br/>4.8 Plasma<br/>4.8.1 Plasma Viscosity<br/>4.8.2 Electrolyte Composition of Plasma<br/>4.9 Blood pH<br/>4.9.1 Clinical Features—Acid–Base Imbalance<br/>Review Problems<br/>Bibliography<br/>5 Anatomy and Physiology of Blood Vessels<br/>5.1 Introduction<br/>5.2 General Structure of Arteries<br/>5.2.1 Tunica Intima<br/>5.2.2 Tunica Media<br/>5.2.3 Tunica Externa<br/>5.3 Types of Arteries<br/>5.3.1 Elastic Arteries<br/>5.3.2 Muscular Arteries<br/>5.3.3 Arterioles<br/>5.4 Mechanics of Arterial Walls<br/>5.5 Compliance<br/>5.5.1 Compliance Example<br/>5.5.2 Clinical Feature—Arterial Compliance and Hypertension<br/>5.6 Pulse Wave Velocity and the Moens–Korteweg Equation<br/>5.6.1 Applications Box—Fabrication of Arterial Models<br/>5.6.2 Pressure–Strain Modulus<br/>5.6.3 Example Problem—Modulus of Elasticity<br/>5.7 Vascular Pathologies<br/>5.7.1 Atherosclerosis<br/>5.7.2 Stenosis<br/>5.7.3 Aneurysm<br/>5.7.4 Clinical Feature—Endovascular Aneurysm Repair<br/>5.7.5 Thrombosis<br/>5.8 Stents<br/>5.8.1 Clinical Feature—“Stent Wars”<br/>5.9 Coronary Artery Bypass Grafting<br/>5.9.1 Arterial Grafts<br/>Review Problems<br/>Bibliography<br/>6 Mechanics of Heart Valves<br/>6.1 Introduction<br/>6.2 Aortic and Pulmonic Valves<br/>6.2.1 Clinical Feature—Percutaneous Aortic Valve Implantation<br/>6.3 Mitral and Tricuspid Valves<br/>6.4 Pressure Gradients across a Stenotic Heart Valve<br/>6.4.1 The Gorlin Equation<br/>6.4.2 Example Problem—Gorlin Equation<br/>6.4.3 Energy Loss across a Stenotic Valve<br/>6.4.4 Example Problem—Energy Loss Method<br/>6.4.5 Cardiac Output Using Echocardiography<br/>6.5 Prosthetic Mechanical Valves<br/>6.5.1 Clinical Feature—Performance of On-X Valve<br/>6.5.2 Case Study—The Björk-Shiley Convexo-Concave Heart Valve<br/>6.6 Prosthetic Tissue Valves<br/>Review Problems<br/>Bibliography<br/>7 Pulsatile Flow in Large Arteries<br/>7.1 Introduction<br/>7.2 Fluid Kinematics<br/>7.3 Continuity<br/>7.4 Complex Numbers<br/>7.5 Fourier Series Representation<br/>7.6 Navier–Stokes Equations<br/>7.7 Pulsatile Flow in Rigid Tubes; Womersley Solution<br/>7.8 Pulsatile Flow in Rigid Tubes; Fry Solution<br/>7.9 Instability in Pulsatile Flow<br/>Review Problems<br/>Bibliography<br/>8 Flow and Pressure Measurement<br/>8.1 Introduction<br/>8.2 Indirect Pressure Measurements<br/>8.2.1 Indirect Pressure Gradient Measurements Using Doppler Ultrasound<br/>8.3 Direct Pressure Measurement<br/>8.3.1 Intravascular; Strain Gauge— Tipped Pressure Transducer<br/>8.3.2 Extravascular; Catheter–Transducer Measuring System<br/>8.3.3 Electrical Analog of the Catheter Measuring System<br/>8.3.4 Characteristics for an Extravascular Pressure Measuring System<br/>8.3.5 Example Problem—Characteristics of an Extravascular Measuring System<br/>8.3.6 Case 1: The Undamped Catheter Measurement System<br/>8.3.7 Case 2: The Undriven, Damped Catheter Measurement System<br/>8.3.8 Pop Test—Measurement of Transient Step Response<br/>8.4 Flow Measurement<br/>8.4.1 Indicator Dilution Method<br/>8.4.2 Fick Technique for Measuring Cardiac Output<br/>8.4.3 Fick Technique Example<br/>8.4.4 Rapid Injection Indicator-Dilution Method—Dye Dilution Technique<br/>8.4.5 Thermodilution<br/>8.4.6 Electromagnetic Flowmeters<br/>8.4.7 Continuous Wave Ultrasonic Flowmeters<br/>8.4.8 Example Problem—Continuous Wave Doppler Ultrasound<br/>8.4.9 Imaging Ultrasound<br/>8.5 Summary and Clinical Applications<br/>Review Problems<br/>Bibliography<br/>9 Modeling<br/>9.1 Introduction<br/>9.2 Theory of Models<br/>9.2.1 Dimensional Analysis and Buckingham Pi Theorem<br/>9.2.2 Synthesizing Pi Terms<br/>9.3 Geometric Similarity<br/>9.4 Dynamic Similarity<br/>9.5 Kinematic Similarity<br/>9.6 Common Dimensionless Parameters in Fluid Mechanics<br/>9.7 Modeling Example 1—Does the Flea Model the Man?<br/>9.8 Modeling Example 2<br/>9.9 Modeling Example 3<br/>Review Problems<br/>Bibliography<br/>10 Lumped Parameter Mathematical Models<br/>10.1 Introduction<br/>10.2 Electrical Analog Model of Flow in a Tube<br/>10.2.1 Nodes and Equations at Each Node<br/>10.2.2 Terminal Load<br/>10.2.3 Summary of Lumped Parameter Electrical Analog Model<br/>10.3 Modeling of Flow Through the Mitral Valve<br/>10.3.1 Model Description<br/>10.3.2 Active Ventricular Relaxation<br/>10.3.3 Meaning of Convective Resistance<br/>10.3.4 Variable Area Mitral Valve Model Description<br/>10.3.5 Variable Area Mitral Valve Model Parameters<br/>10.3.6 Solving System of Differential Equations<br/>10.3.7 Model Trials<br/>10.3.8 Results<br/>10.4 Summary<br/>Review Problems<br/>Bibliography<br/>11 Biofluid Mechanics of the Kidney<br/>11.1 Body Fluid Compartments: Extracellular, Intracellular, and Edema<br/>11.1.1 Daily Loss<br/>11.1.2 Water Lost by Kidneys<br/>11.1.3 Body Fluid Compartments<br/>11.1.4 Intracellular Fluid<br/>11.1.5 Extracellular Fluid<br/>11.1.6 Measurement of a compartment volume<br/>11.2 Renal Anatomy<br/>11.2.1 Structure<br/>11.2.2 Nephron<br/>11.3 Renal Physiology<br/>11.3.1 Clinical Feature<br/>11.4 Glomerular Filtration<br/>11.4.1 Control of Glomerular Filtration Rate and Renal Blood Flow<br/>11.5 Renin-Angiotensin-Aldosterone S
ystem<br/>11.6 Tubular Reabsorption and Secretion<br/>11.7 Clearance Methods to Quantify Kidney Function<br/>11.7.1 Estimating Glomerular Filtration Rate<br/>11.7.2 Inulin clearance to measure GFR<br/>11.7.3 PAH Clearance to Measure Renal Plasma Flow<br/>11.8 Filtration Fraction<br/>Review Problems<br/>Bibliography<br/>Index