Biotransport: Principles

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1 Robert J. Roselli Kenneth R. Diller Biotransport: Principles and Applications 4 i Springer

2 Contents Part I Fundamentals of How People Learn (HPL) 1 Introduction to HPL Methodology Introduction Adaptive Expertise Learning for Adaptive Expertise Principles of Effective Learning Challenge-Bused Instruction STAR.Legacy (SL) Cycle for Inquiry Learning X 1.7 Developing Innovation How to Use the Generate Ideas Model How to Use This Textbook to Develop Innovation Learning to Gain Understanding 27 References 29 Part II Fundamental Concepts in Biotransport 2 Fundamental Concepts in Biotransport Introduction The System and Its Environment Transport Scales in Time and Space Continuum Concepts Conservation Principles Transport Mechanisms Molecular Transport Mechanisms Convcctive Transport Mechanisms Macroscopic Transport Coefficients Interphase Transport Transport in Biological Systems: Some Unique Aspects Summary of Key Concepts Questions Problems 61 \i

3 xjj Contents 2.12 Challenges 64 References 66 3 Modeling and Solving Biotransport Problems Introduction Theoretical Approach Geometric Considerations Governing Equations Solution Procedures Presentation of Results Scaling: Identification of Important Dimensionless Parameters Examples of the Theoretical Approach Empirical Approach The Buckingham Pi Theorem: Dimensional Analysis Summary of Key Concepts Questions Problems Challenges 103 References 103 Part III Biofluid Transport 4 Rheology of Biological Fluids Introduction Solids and Fluids Flow Regimes: Laminar and Turbulent Flow Boundary Conditions Viscous Properties of Fluids Viscous Momentum Flux and Shear Stress Viscometers Newtonian and Non-Newtonian Fluid Models Newtonian Fluid Model Non-Newtonian Fluid Models Identification of Constitutive Model Equations Rheology of Biological Fluids Rheological Properties of Extravascular Body Fluids Blood Rheology Biorheology and Disease Summary of Key Concepts Questions Problems Challenges 165 References 166

4 Contents 5 Macroscopic Approach for BioHuid Transport Introduction Conservation of Mass Conservation of Momentum ISO 5.4 Conservation of Energy Engineering Bernoulli Equation Friction Loss in Conduits Friction Loss Factors. Flow Through Fittings Laminar Flow and Flow Resistance in Noncircular Conduits Flow in Packed Beds External Flow: Drag and Lift Blood Flow in Microvessels Steady Flow Through a Network of Rigid Conduits Compliance and Resistance of Flexible Conduits Flow in Collapsible Tubes Fluid Inertia Blood Flow in Organs Osmotic Pressure and Flow Summary of Key Concepts Questions Problems Challenges 316 References Shell Balance Approach for One-Dimensional Biottuid Transport Introduction General Approach Selecting an Appropriate Shell Fluid Mass Balance Fluid Momentum Balance Application of the Fluid Constitutive Relation to Find Fluid Velocity Examining and Applying Solutions for Shear Stress and Velocity Additional Shell Balances in Rectangular Coordinates One-Dimensional Shell Balances in Cylindrical Coordinates Flow of a Newtonian Fluid Through a Circular Cylinder Flow of a Newtonian Fluid in an Annulus with Inner Wall Moving Flow Through an Inclined Tube or Annulus Flow of a Casson Fluid Through a Circular Cylinder Osmotic Pressure and Flow in a Cylindrical Pore Unsteady-State 1-D Shell Balances Summary of Key Concepts Ml

5 xiv Contents 6.6 Questions Problems Challenges 387 References General Microscopic Approach for Biofluid Transport Introduction Conservation of Mass Conservation of Linear Momentum Moment Equations General Constitutive Relationship for a Newtonian Fluid Substantial Derivative Modified Pressure, jp Equations of Motion for Newtonian Fluids The Stream Function and Streamlines for Two-Dimensional Incompressible Flow Use of Navier-Stokes Equations in Rectangular Coordinates Hydrostatics Reduction of the Equations of Motion Navier-Stokes Equations in Cylindrical and Spherical Coordinate Systems Use of Navier-Stokes Equations in Cylindrical and Spherical Coordinates Scaling the Navier-Stokes Equation General Momentum Equations for Use with Non-Newtonian Fluids Constitutive Relationships for Non-Newtonian Fluids Power Law Fluid Bingham Fluid Casson Fluid Herschel-Bulkley Fluid Setting Up and Solving Non-Newtonian Problems Summary of Key Concepts Questions Problems Challenges 484 References 485 Part IV Bioheat Transport 8 Heat Transfer Fundamentals Introduction Conduction Thermal Resistance in Conduction 492

6 Contents ^v Convection Four Principle Characteristics of Convectivc Processes Fundamentals of Convectivc Processes Forced Convection Analysis Free Convection Processes Thermal Resistance in Convection Biot Number Thermal Radiation Three Governing Characteristics of Thermal Radiation Processes The Role of Surface Temperature in Thermal Radiation The Role of Surface Properties in Thermal Radiation The Role of Geometric Sizes. Shapes. Separation, and Orientation in Thermal Radiation Electrical Resistance Model for Radiation Common Heat Transfer Boundary Conditions Summary of Key Concepts Questions Problems Challenges 554 References Macroscopic Approach to Bioheat Transport Introduction General Macroscopic Energy Relation Steady-State Applications of the Macroscopic Energy Balance Thermal Resistances Heat Transfer Coefficients Convectivc Heat Transport Biomedical Applications of Thermal Radiation Heat Transfer with Phase Change Unsteady-State Macroscopic Heat Transfer Applications Lumped Parameter Analysis of Transient Diffusion with Convection Thermal Compartmental Analysis Multiple System Interactions 59X Convection: Multiple Well-Mixed Compartments Combined Conduction and Convection Radiation: Flame Burn Injury Human Thermoregulation Summary of Key Concepts Questions Problems 620

7 xvi Contents 9.9 Challenges 624 References Shell Balance Approach for One-Dimensional Bioheat Transport Introduction General Approach Steady-State Conduction with Heat Generation Steady-State Conduction with Heat Generation in a Slab Steady-State Conduction with Heat Generation in a Cylinder Steady-State Conduction with Heat Generation in a Sphere Steady-State One-dimensional Problems Involving Convection Internal Flow Convection with a Constant Temperature Boundary Condition Internal Flow Convection with a Constant Heat Flux Boundary Condition Heat Exchangers One-Dimensional Steady-State Heat Conduction Heat Conduction with Convection or Radiation at Extended Surfaces Heat Exchange in Tissue: Transient and Steady-State Pennes Equation Transient Diffusion Processes with Internal Thermal Gradients Symmetric Geometries: Exact and Approximate Solutions for Negligible Heat Generation Semi-Infinite Geometry Graphical Methods Summary of Key Concepts Questions Problems Challenges 719 References General Microscopic Approach for Bioheat Transport General Microscopic Formulation of Conservation of Energy Derivation of Conservation of Energy for Combined Conduction and Convection Simplifying the General Microscopic Energy Equation 726

8 Contents xvii 11.2 Numerical Methods for Transient Conduction: Finite Difference Analysis Forward Finite Difference Method Backward Finite Difference Method Thermal Injury Mechanisms and Analysis Burn Injury Therapeutic Applications of Hyperthermia Laser Irradiation of Tissue Distributed Energy Absorption 764 I Time Constant Analysis of the Transient Temperature Field Surface Cooling During Irradiation Summary of Key Concepts Questions Problems Challenges 783 References 784 Part V Biological Mass Transport 12 Mass Transfer Fundamentals Average and Local Mass and Molar Concentrations Phase Equilibrium Liquid-Gas Equilibrium Liquid-Liquid, Gas-Solid, Liquid-Solid. Solid-Solid Equilibrium Species Transport Between Phases Species Transport Within a Single Phase Species Fluxes and Velocities Diffusion Fluxes and Velocities Convective and Diffusive Transport Total Mass and Molar Fluxes Molecular Diffusion and Fick's Law of Diffusion Mass Transfer Coefficients Experimental Approach to Determining Mass Transfer Coefficients Relation Between Individual and Overall Mass Transfer Coefficients Permeability of Nonporous Materials Membrane Permeability Vessel or Hollow Fiber Permeability Comparison of Internal and External Resistances to Mass Transfer Transport of Electrically Charged Species 851

9 X V111 Contents 12.8 Chemical Reactions Hemoglobin and Blood Oxygen Transport Blood C02 Transport and ph Enzyme Kinetics Ligand-Receptor Binding Kinetics Cellular Transport Mechanisms Carrier-Mediated Transport Active Transport Mass Transfer Boundary Conditions Mass or Molar Concentration Specified at a Boundary Mass or Molar Flux Specified at a Boundary No-Flux Boundary Condition Concentration and Flux at an Interface Heterogeneous Reaction at a Surface Summary of Key Concepts Questions Problems Challenges 895 References Macroscopic Approach to Biomass Transport Introduction Species Conservation Compartmenta) Analysis Single Compartment Two Compartments Multiple Compartments Indicator Dilution Methods Stewart-Hamilton Relation for Measuring Flow Through a System Volume Measurements Permeability-Surface Area Measurements Chemical Reactions and Bioreactors Homogeneous Chemical Reactions Heterogeneous Reactions Pharmacokinetics Renal Excretion Drug Delivery to Tissue. Two Compartment Model More Complex Pharmacokinetics Models Mass Transfer Coefficient Applications Solute Flow Through Pores in Capillary Walls Small Solute Transport Large Solute Transport Through Pores 973

10 Contents X \ 13.9 Summary of Key Concepts Questions Problems Challenges 1001 References Shell Balance Approach for One-Dimensional Biomass Transport Introduction Microscopic Species Conservation One-Dimensional Steady-State Diffusion Through a Membrane D Diffusion with Homogeneous Chemical Reaction Zeroth Order Reaction First-Order Reaction Michaelis-Menten Kinetics Diffusion and Reaction in a Porous Particle Containing Immobilized Enzymes Convection and Diffusion Conduits with Constant Wall Concentration Hollow Fiber Devices Capillary Exchange of Non-Reacting Solutes Convection, Diffusion, and Chemical Reaction Transcapillary Exchange of 02 and C Tissue Solute Exchange, Krogh Cylinder Bioreactors One-Dimensional Unsteady-Stale Shell Balance Applications Diffusion to Tissue Unsteady-State ID Convection and Diffusion Summary of Key Concepts Questions Problems Challenges References I General Microscopic Approach for Biomass Transport Introduction D, Unsteady-State Species Conservation Comparison of the General Species Continuity Equation and the One-Dimensional Shell Balance Approach Diffusion I Steady-State. Multidimensional Diffusion Steady-State Diffusion and Superposition 1162

11 xx Contents Unsteady-State, Multidimensional Diffusion Diffusion and Chemical Reaction Convection and Diffusion Steady-State, Multidimensional Convection and Diffusion Convection, Diffusion, and Chemical Reaction Blood Oxygenation in a Hollow Fiber Summary of Key Concepts Questions Problems Challenges 1213 References 1214 Appendix A Nomenclature 1217 Appendix B.l Physical Constants 1236 Appendix B.2 Prefixes and Multipliers for SI units 1236 Appendix B.3 Conversion Factors 1237 Appendix C Transport Properties 1240 Appendix D Charts for Unsteady Conduction and Diffusion 1251 Index 1263

Biotransport: Principles and Applications

Biotransport: Principles and Applications . Robert J. Roselli l Kenneth R. Diller Biotransport: Principles and Applications Robert J. Roselli, Ph.D. Vanderbilt University Dept. Biomedical Engineering Nashville,