E-Book, Englisch, 428 Seiten
Advances and Applications
E-Book, Englisch, 428 Seiten
ISBN: 978-0-12-407900-7
Verlag: Elsevier Reference Monographs
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Provides a wide range of biological and clinical applications of fluid flow and heat transfer in biomedical technologyCovers topics such as electrokinetic transport, electroporation of cells and tissue dialysis, inert solute transport (insulin), thermal ablation of cancerous tissue, respiratory therapies, and associated medical technologies Reviews the most recent advances in modeling techniques
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Heat Transfer and Fluid Flow in Biological Processes;4
3;Copyright;5
4;Contents;6
5;Contributors;10
6;Preface;12
7;Chapter 1: Bioheat Transfer and Thermal Heating for Tumor Treatment;14
7.1;1.1. Pennes and Other Bioheat Transfer Equations;14
7.1.1;1.1.1. Introduction;14
7.1.2;1.1.2. Pennes' Bioheat Transfer Equation;15
7.1.3;1.1.3. The Chen and Holmes Model;16
7.1.4;1.1.4. The Weinbaum and Jiji Model;17
7.1.5;1.1.5. The Weinbaum, Jiji, and Lemons Model;17
7.1.6;1.1.6. Baish et al;18
7.1.7;1.1.7. Others;18
7.2;1.2. Blood Flow Impacts on Thermal Lesions with Pulsation and Different Velocity Profiles;18
7.2.1;1.2.1. Introduction;19
7.2.2;1.2.2. Mathematical Model and Numerical Method;19
7.2.2.1;1.2.2.1. Velocity Profile of Pulsatile Blood Flow in a Circular Blood Vessel;19
7.2.2.2;1.2.2.2. Governing Equations and Numerical Method;21
7.2.2.3;1.2.2.3. Calculation of Thermal Dose;23
7.2.3;1.2.3. Results and Discussions;24
7.2.4;1.2.4. Conclusion;28
7.3;1.3. Thermal Relaxation Time Factor in Blood Flow During Thermal Therapy;28
7.3.1;1.3.1. Introduction;28
7.3.2;1.3.2. Mathematical Model and Numerical Method;29
7.3.2.1;1.3.2.1. Features of the Hyperbolic Heat Equation;29
7.3.2.2;1.3.2.2. Thermal Governing Equations and the Numerical Method;30
7.3.3;1.3.3. Results and Discussions;32
7.3.4;1.3.4. Conclusion;36
7.4;1.4. PBHTE with the Vascular Cooling Network Model;37
7.4.1;1.4.1. Thermally Significant Blood Vessel Model;37
7.4.2;1.4.2. Vessel Network Geometry and Fully Conjugated Blood Vessel Network Model;38
7.4.3;1.4.3. Discrete Vessel Modeling with Semicurved Vessel Network and Real 3D Vasculature Network;40
7.4.4;1.4.4. Conclusion;42
7.5;1.5. Hyperthermia Treatment Planning;42
7.5.1;1.5.1. Optimization with Fine Spatial Power Deposition: Based on Local Temperature Response in the Treated Region;43
7.5.2;1.5.2. Optimization with Lumped Power Deposition: Uniform Absorbed Power Deposition in the Treated Tumor Region;47
7.5.3;1.5.3. Effect of Blood Perfusion and Blood Flow Rates on the Optimization;47
7.5.4;1.5.4. Optimization Without Thermally Significant Blood Vessels in the Tissues;51
7.5.5;1.5.5. Conclusion;51
7.6;References;53
8;Chapter 2: Tissue Response to Short Pulse Laser Irradiation;56
8.1;2.1. Introduction;56
8.2;2.2. Mathematical Formulation;59
8.2.1;2.2.1. Numerical Modeling of Laser-Tissue Interactions;59
8.2.2;2.2.2. Continuum Model Development;60
8.2.3;2.2.3. Vascular Model Development;62
8.3;2.3. Experimental Methods;63
8.4;2.4. Results and Discussion;64
8.5;2.5. Conclusion;69
8.6;References;70
9;Chapter 3: Quantitative Models of Thermal Damage to Cells and Tissues;72
9.1;3.1. Introduction;72
9.2;3.2. Heat Transfer in Tissue;73
9.3;3.3. Reaction Rates and Temperature;74
9.4;3.4. Thermal Denaturation of Proteins;76
9.5;3.5. Cells;79
9.6;3.6. Tissue-Level Descriptions;82
9.6.1;3.6.1. Burns;82
9.6.2;3.6.2. Normalizing Hyperthermia to Time at 43C;83
9.6.3;3.6.3. Other Studies Addressing Clinical Response;84
9.7;3.7. Discussion;85
9.8;References;86
10;Chapter 4: Analytical Bioheat Transfer: Solution Development of the Pennes Model;90
10.1;4.1. Pennes' Bioheat Equation in Living Tissue Analogy;91
10.1.1;4.1.1. Representation of the Governing Equations;93
10.1.2;4.1.2. Boundary Condition Types;93
10.1.3;4.1.3. Temperature Shift;94
10.2;4.2. Solutions to the Transient Homogenous Bioheat Equation;95
10.2.1;4.2.1. Bioheat Solution in the Cartesian Coordinate System;96
10.2.1.1;4.2.1.1. Solutions to Transient Bioheat Transfer in a Slab;100
10.2.1.2;4.2.1.2. Solutions of the Bioheat in the Infinite and Semi-infinite Domains;101
10.2.1.2.1;Semi-infinite Domain BC1 Type II;104
10.2.1.2.2;Semi-infinite Domain BC1 Type III;104
10.2.1.2.3;Infinite Domain;104
10.2.2;4.2.2. Bioheat Equation in the Cylindrical and Spherical Coordinate Systems;105
10.2.2.1;4.2.2.1. Bioheat in Cylindrical Coordinates;105
10.2.2.1.1;4.2.2.1.1. Cylinder with a Homogenous Type I BC2;106
10.2.2.1.2;4.2.2.1.2. Cylinder with a Homogenous Type II BC2;106
10.2.2.2;4.2.2.2. Bioheat in Spherical Coordinates;107
10.2.2.2.1;4.2.2.2.1. Sphere with a Homogenous Type I BC2;107
10.2.2.2.2;4.2.2.2.2. Sphere with a Homogenous Type II BC2;108
10.2.2.2.3;4.2.2.2.3. Sphere in the Semi-infinite Domain;108
10.3;4.3. Solution Approaches to Nonhomogenous Problems;108
10.3.1;4.3.1. Method of Superpositioning;109
10.3.2;4.3.2. Green's Functions;111
10.3.2.1;4.3.2.1. Transformation of the Conduction Greens Function to the Bioheat Problem;114
10.3.2.2;4.3.2.2. Selected Green's Functions in the Cartesian Coordinate System;114
10.3.2.3;4.3.2.3. Semi-infinite and Infinite Cartesian Domains;115
10.3.2.4;4.3.2.4. Selected Green's Functions in the Cylindrical and Spherical Coordinate Systems;117
10.3.2.4.1;4.3.2.4.1. Radial Heat Flow in the Cylindrical Coordinate System;118
10.3.2.4.2;4.3.2.4.2. Cylinder with a Homogenous Type I BC2;118
10.3.2.4.3;4.3.2.4.3. Cylinder with a Homogenous Type II BC2;118
10.3.2.4.4;4.3.2.4.4. Cylindrical Semi-infinite Problem;119
10.3.2.4.5;4.3.2.4.5. Radial Heat Flow in the Spherical Coordinate System;119
10.3.2.4.6;4.3.2.4.6. Sphere with a Homogenous Type I BC2;119
10.3.2.4.7;4.3.2.4.7. Sphere with a Homogenous Type II BC2;119
10.3.2.4.8;4.3.2.4.8. Spherical Semi-infinite Problem;120
10.4;4.4. Additional Considerations;120
10.4.1;4.4.1. Bioheat Problem in Multidimensions;120
10.4.2;4.4.2. Short Time Convergence Issues and Integral Approximations;121
10.5;4.5. The Composite Bioheat Problem;121
10.5.1;4.5.1. Homogenization of the Composite Domain;124
10.5.1.1;4.5.1.1. Addressing the Steady Nonhomogenous Components;124
10.5.2;4.5.2. The Homogenous Composite Bioheat Problem;125
10.5.3;4.5.3. SOV in the Composite System;126
10.5.3.1;4.5.3.1. Building the Eigenfunctions and Determining the Eigenvalues;129
10.5.4;4.5.4. Solutions to Homogenous Transient Bioheat Transfer in a Composite Slab;132
10.5.4.1;4.5.4.0.1. Special Case Simplification;134
10.5.5;4.5.5. Addressing Transient Energy Generation Using Greens Functions;135
10.6;4.6. Summary Remarks;136
10.7;References;137
11;Chapter 5: Characterizing Respiratory Airflow and Aerosol Condensational Growth in Children and Adults Using an Imaging-C...;138
11.1;5.1. Introduction;138
11.2;5.2. Methods;140
11.2.1;5.2.1. Construction of Airway Models;141
11.2.2;5.2.2. Breathing and Wall Boundary Conditions;142
11.2.3;5.2.3. In Vitro Deposition Measurement;143
11.2.4;5.2.4. Continuous and Discrete Particle Transport Equations;143
11.2.5;5.2.5. Droplet Evaporation and Condensation Model;145
11.2.6;5.2.6. Numerical Method and Convergence Sensitivity Analysis;147
11.3;5.3. Results;147
11.3.1;5.3.1. Child-Adult Discrepancies;147
11.3.2;5.3.2. Hygroscopic Growth Model Testing;148
11.3.3;5.3.3. Adult Nasal Airway Model;149
11.3.3.1;5.3.3.1. Airflow, Temperature, and RH Field;149
11.3.3.2;5.3.3.2. Baseline Case: Aerosol Transport and Deposition of Inert Particles;152
11.3.3.3;5.3.3.3. Hygroscopic Behavior of Individual Particles in Equilibrium Humidity;153
11.3.3.4;5.3.3.4. Particle Growth and Deposition in Nonequilibrium Nasal Environments;154
11.3.4;5.3.4. Five-Year-Old Child Nose-Throat Model;156
11.3.5;5.3.5. Adult Mouth-Lung Model;160
11.4;5.4. Discussion;161
11.5;5.5. Conclusion;164
11.6;References;165
12;Chapter 6: Transport in the Microbiome;170
12.1;6.1. Introduction;170
12.2;6.2. The Human Microbiome;171
12.3;6.3. Swimming Microorganisms;173
12.3.1;6.3.1. Flagellar Biomechanics and Hydrodynamics;174
12.3.1.1;6.3.1.1. Prokaryotic Flagella;175
12.3.1.2;6.3.1.2. Spirochetes;179
12.3.1.3;6.3.1.3. Eukaryotic Flagella;179
12.3.1.4;6.3.1.4. Ciliates;181
12.3.1.4.1;6.3.1.4.1. Pushers and Pullers;183
12.3.1.5;6.3.1.5. Non-Newtonian Effects;183
12.3.2;6.3.2. Flow-Induced Motion;184
12.3.2.1;6.3.2.1. Boundary Effects;184
12.3.2.2;6.3.2.2. Cell-Cell Hydrodynamics;187
12.4;6.4. Continuum Descriptions;192
12.4.1;6.4.1. Semi-Dilute Suspensions;192
12.4.2;6.4.2. Cell-Cell Collisions;195
12.4.3;6.4.3. Coarse Graining;196
12.5;6.5. Discussion;197
12.6;References;198
13;Chapter 7: A Critical Review of Experimental and Modeling Research on the Leftward Flow Leading to Left-Right Symmetry Br...;202
13.1;7.1. Introduction;203
13.2;7.2. Experimental Research on the Leftward Nodal Flow and LR Symmetry Breaking;204
13.3;7.3. Modeling Research on the Nodal Flow;206
13.4;7.4. Leftward Flow or Flow Recirculation?;207
13.5;7.5. Sensing of the Flow: Mechanosensing or Chemosensing?;207
13.6;7.6. Modeling the Effect of a Ciliated Surface by Imposing a Given Vorticity at the Edge of the Ciliated Layer;209
13.7;7.7. Summary of Relevant Parameters Describing the Nodal Flow and Estimates of Their Values;213
13.8;7.8. Numerical Results Obtained Assuming a Constant Vorticity at the Edge of the Ciliated Layer;214
13.9;7.9. Conclusions;216
13.10;Acknowledgments;217
13.11;References;217
14;Chapter 8: Fluid-Biofilm Interactions in Porous Media;220
14.1;8.1. Microbial Biofilms in Porous Media;220
14.1.1;8.1.1. Historical Stepping-Stones;223
14.1.2;8.1.2. Of Polymers and Cells: Processes Involved in Biofilm Formation;225
14.1.3;8.1.3. Morphology of Biofilms in Porous Media;227
14.2;8.2. A Motivating Problem: Biofilms and the Fate of Contaminants in Soil;229
14.2.1;8.2.1. Impact of Biofilms on Fluid Composition;229
14.2.2;8.2.2. Impact of Biofilms on Fluid Mobility;230
14.3;8.3. Models of Biofilm Growth and Pattern Formation in Quiescent Fluids;231
14.3.1;8.3.1. Continuum-Based Models;231
14.3.2;8.3.2. Discrete-Based Models;233
14.4;8.4. Computational Simulation of Fluid-Biofilm Interactions in Porous Media;235
14.4.1;8.4.1. Generation and Initial Colonization of the Porous Structure;236
14.4.2;8.4.2. Cell Proliferation and EPS Spreading;236
14.4.3;8.4.3. Fluid-Flow and Flow-Induced Biofilm Stresses;238
14.4.4;8.4.4. Detachment, Migration, and Reattachment of cells and EPS;239
14.4.5;8.4.5. Solute Transport;239
14.5;8.5. Mechanisms of Biological Clogging in Porous Media;240
14.5.1;8.5.1. Experimental Observations and Conceptual Models;240
14.5.2;8.5.2. Single-Pore Simulations Under Two Different Flow Regimes;242
14.5.3;8.5.3. Detachment and Downstream Migration of Biofilms;244
14.6;8.6. Summary;247
14.7;References;247
15;Chapter 9: Flow Through a Permeable Tube;252
15.1;9.1. Introduction;252
15.2;9.2. Axisymmetric Stokes Flow;253
15.2.1;9.2.1. Stokes Stream Function;254
15.2.2;9.2.2. Exponential Solutions;254
15.2.3;9.2.3. General Solution;258
15.3;9.3. Flow Through an Infinite Permeable Tube;258
15.3.1;9.3.1. No-Slip Boundary Condition;258
15.3.2;9.3.2. Velocity Field;259
15.3.3;9.3.3. Flow Rate;261
15.3.4;9.3.4. Pressure Field;262
15.3.5;9.3.5. Stress Field;263
15.3.6;9.3.6. Solution in Terms of the Flow Rate and Pressure at the Origin;264
15.4;9.4. Starlings Equation;265
15.4.1;9.4.1. Starling's Equation in Terms of the Pressure;266
15.4.2;9.4.2. Starling's Equation in Terms of the Normal Stress;269
15.5;9.5. Flow Through a Tube with Finite Length;270
15.5.1;9.5.1. Solution in Terms of Entrance and Exit Flow Rates;270
15.5.2;9.5.2. Solution in Terms of the Entrance and Exit Pressures;274
15.5.3;9.5.3. Starling's Equation in Terms of the Normal Stress;275
15.5.4;9.5.4. Nearly Unidirectional Flow Model;275
15.6;9.6. Effect of Wall Slip;279
15.6.1;9.6.1. Starling's Equation;283
15.7;9.7. Summary;285
15.8;References;285
16;Chapter 10: Transdermal Drug Delivery and Percutaneous Absorption;286
16.1;10.1. Introduction;287
16.2;10.2. Physiological Description and Drug Transport Models;289
16.2.1;10.2.1. The Skin as a Composite;289
16.2.2;10.2.2. The SC, Its Corneocytes, and the Lipid Matrix;289
16.2.3;10.2.3. The Drug and the Vehicle;290
16.2.4;10.2.4. Diffusion–Transport Considerations;291
16.2.4.1;10.2.4.1. Diffusion;291
16.2.4.2;10.2.4.2. Evaluation of the Diffusion Coefficient;292
16.2.4.3;10.2.4.3. Partitioning;293
16.2.4.4;10.2.4.4. Evaluation of the Partition Coefficient;294
16.2.5;10.2.5. Adsorption;294
16.2.5.1;10.2.5.1. Slow Binding;295
16.2.5.2;10.2.5.2. Fast Binding;295
16.2.6;10.2.6. Metabolism and Clearance;296
16.2.7;10.2.7. TDD Models;297
16.2.7.1;10.2.7.1. Fickian Models;298
16.2.7.2;10.2.7.2. Non-Fickian Models;298
16.3;10.3. Review of Mathematical Methods;299
16.3.1;10.3.1. Laplace Transform;299
16.3.2;10.3.2. Finite Difference Method;300
16.3.3;10.3.3. Finite Element Method;300
16.3.4;10.3.4. Finite Volume Method;301
16.4;10.4. Modeling TDD Through a Two-Layered System;301
16.4.1;10.4.1. Mathematical Formulation;301
16.4.1.1;10.4.1.1. Dimensionless Equations;305
16.4.2;10.4.2. Method of Solution;306
16.4.2.1;10.4.2.1. Time-Dependent Solution;307
16.4.2.2;10.4.2.2. Space-Dependent Solution: The Eigenvalue Problem;307
16.4.2.3;10.4.2.3. Concentration Solution;309
16.4.3;10.4.3. Numerical Simulation and Results;310
16.5;10.5. Conclusions;313
16.6;References;315
17;Chapter 11: Mechanical Stress Induced Blood Trauma;318
17.1;11.1. Introduction;318
17.2;11.2. Mechanical Stresses Experienced by Blood;319
17.2.1;11.2.1. Couette Flow;320
17.2.2;11.2.2. Elongational Flow;320
17.2.3;11.2.3. Wall Shear Stress;321
17.2.4;11.2.4. Scalar Shear Stress;321
17.2.5;11.2.5. Fluid Dynamic Stresses in the Circulation;321
17.2.6;11.2.6. Fluid Dynamic Stresses in Blood Contacting Devices;322
17.2.6.1;11.2.6.1. Needles, Catheters, Cannulae;322
17.2.6.2;11.2.6.2. Rotary Ventricular Assist Devices;322
17.2.6.3;11.2.6.3. Displacement Ventricular Assist Devices;323
17.2.6.4;11.2.6.4. Mechanical Heart Valves;323
17.2.6.5;11.2.6.5. Membrane Oxygenators;323
17.3;11.3. Fluid Dynamic Effects on Blood Constituents;323
17.3.1;11.3.1. Red Blood Cells;323
17.3.1.1;11.3.1.1. Deformation of RBCs;324
17.3.1.2;11.3.1.2. Hemolysis;325
17.3.2;11.3.2. White Blood Cells;327
17.3.3;11.3.3. Platelets;329
17.3.3.1;11.3.3.1. Adhesion;329
17.3.3.2;11.3.3.2. Activation;331
17.3.4;11.3.4. von Willebrand factor (vWf);333
17.3.5;11.3.5. Thrombosis and Emboli;333
17.4;11.4. Numerical Models of Damage to the Blood Constituents;334
17.4.1;11.4.1. Red Blood Cells;334
17.4.1.1;11.4.1.1. Stress-Based;334
17.4.1.2;11.4.1.2. Strain-Based;336
17.4.1.3;11.4.1.3. Conclusion;338
17.4.2;11.4.2. Platelets;338
17.4.3;11.4.3. Blood Proteins Including von Willebrand Factor;339
17.4.4;11.4.4. Thrombosis and Emboli;339
17.5;11.5. Summary;341
17.6;References;342
18;Chapter 12: Modeling of Blood Flow in Stented Coronary Arteries;348
18.1;12.1. Introduction;349
18.2;12.2. Hemodynamic Quantities of Interest;351
18.2.1;12.2.1. Introduction;351
18.2.2;12.2.2. Near-Wall Quantities;351
18.2.3;12.2.3. Flow Stasis Quantities;353
18.2.4;12.2.4. Bulk Flow Quantities;354
18.3;12.3. Fluid Dynamic Models of Idealized Stented Geometries;355
18.3.1;12.3.1. Introduction;355
18.3.2;12.3.2. Coronary Bifurcation Models;355
18.4;12.4. Fluid Dynamic Models of Image-Based Stented Geometries;365
18.4.1;12.4.1. Introduction;365
18.4.2;12.4.2. CFD Studies from In Vitro Model Images;365
18.4.3;12.4.3. CFD Studies from Animal Models;367
18.4.4;12.4.4. CFD Studies from Patient Images;369
18.5;12.5. Limitations of the Current CFD Models and Future Remarks;375
18.5.1;12.5.1. Introduction;375
18.5.2;12.5.2. Heart Motion;375
18.5.3;12.5.3. Rigid Walls;375
18.5.4;12.5.4. Boundary Conditions;377
18.5.5;12.5.5. Accuracy of Three-Dimensional Geometrical Models;377
18.5.6;12.5.6. Model Validation;378
18.6;12.6. Conclusions;378
18.7;Acknowledgments;379
18.8;References;379
19;Chapter 13: Hemodynamics in the Developing Cardiovascular System;384
19.1;13.1. Introduction;384
19.2;13.2. The Chicken Embryo Model System;385
19.2.1;13.2.1. Key Stages in Cardiovascular Development;385
19.3;13.3. Relevant Fluid Mechanic Regimes;387
19.3.1;13.3.1. Viscous Effects Dominate in the Developing Circulation;388
19.3.2;13.3.2. Curvature Effects Are Minimal, Except in the Embryonic Heart;389
19.3.3;13.3.3. Pulsatile Effects Can Be Ignored in the Embryonic Phase;392
19.3.4;13.3.4. Local Flow Can Be Described Using Two Parameters Only;393
19.4;13.4. Experimental Studies;395
19.4.1;13.4.1. Influence of Temperature;396
19.4.2;13.4.2. Pressure;398
19.4.3;13.4.3. Cardiac Output;398
19.4.4;13.4.4. Flow Rate and Velocities in Blood Vessels;399
19.4.5;13.4.5. Whole-Field Measurements: Micro-PIV;400
19.4.6;13.4.6. Scanning Imaging Methods;403
19.5;13.5. Mechanotransduction;405
19.5.1;13.5.1. Mechanotransduction in Cardiovascular Development;405
19.5.2;13.5.2. Primary Cilia as Mechanosensors;407
19.5.3;13.5.3. Loss of Cilia Is Instrumental for Heart Valve Development;408
19.6;13.6. Hemorheology;409
19.6.1;13.6.1. Macroscopic Rheological Behavior of Blood;409
19.6.2;13.6.2. Multiphase Aspects of Blood;410
19.6.3;13.6.3. Endothelial Surface Layer;411
19.6.4;13.6.4. Human Versus Avian Blood;412
19.7;13.7. Conclusions and Outlook;413
19.8;References;414
20;Index;420
Chapter 1 Bioheat Transfer and Thermal Heating for Tumor Treatment
Huang-Wen Huanga hhw402@mail.tku.edu.tw; Tzyy-Leng Horngb a Tamkang University, Taipei, Taiwan
b Feng Chia University, Taichung, Taiwan Abstract
Hyperthermia (or thermal ablation) is a tumor treatment which uses thermal energy deposited to damage and kill cancer cells (i.e., coagulation necrosis) in a living, human body, with minimal injury to normal tissue. The treatment involves several heat transfer modes and blood flow cooling biological processes. The objective of this chapter is to introduce bioheat transfer models and those blood flow impacting processes used during thermal heating for tumor treatment. Heat transfer modes and blood flow are interrelated during thermal heating. Blood flow in thermally significant blood vessels, blood perfusion rate, and heat transfer modes (conduction and convection) will be presented. Some difficulties during heating for tumor treatments will also be addressed. Keywords Hyperthermia Thermal ablation Thermal modeling Heat transfer Blood perfusion rate Thermally significant blood vessels Outline 1.1 Pennes’ and Other Bioheat Transfer Equations 1 1.2 Blood Flow Impacts on Thermal Lesions with Pulsation and Different Velocity Profiles 5 1.3 Thermal Relaxation Time Factor in Blood Flow During Thermal Therapy 15 1.4 PBHTE with the Vascular Cooling Network Model 24 1.5 Hyperthermia Treatment Planning 29 1.1 Pennes’ and Other Bioheat Transfer Equations
1.1.1 Introduction
The investigation of heat transfer and fluid flow in biological processes requires accurate mathematical models. Biological processes basically involve two phases—solid and liquid (fluid). During the past 50 years, through development of thermal modeling in biological processes, heat transfer processes have been established that include the impact of fluid flow which is due to blood. Table 1.1 shows the significance of thermal transport modes in typical components of biothermal systems, as our subject of discussion refers to cancer treatments using heat. For example, thermal diffusion plays a dominant transport mode in tissues, and convection is less significant as blood perfuses in solid tissues at capillary level vessels (which are small in size and slow in blood motion). Table 1.1 Significance of Thermal Transport Modes in Typical Components of Biothermal Systems Tissues Significant Less significant Insignificant Bones Significant Insignificant Insignificant Blood vessels Less significant Significant Insignificant Skins Insignificant Significant Significant Thermal ablation therapy is an application of heat transfer and fluid flow in biological processes. Temperature plays a significant role with tissue interactions (e.g., coagulation necrosis). To give readers a picture of temperature treatments with tissue (and terminology), Table 1.2 shows temperature ranges with their tissue interactions in biological processes. A thermal model that satisfied the following three criteria was needed to predict temperatures in a perfused tissue: (1) the model satisfied conservation of energy; (2) the heat transfer rate from blood vessels to tissue was modeled without following a vessel path; and (3) the model applied to any unheated and heated tissue. To meet these criteria, many research groups around the world have proposed mathematical models in an attempt to properly describe the heat transfer and fluid flow in biological processes in a heated, vascularized, finite tissue by making a few simplifying assumptions. We will highlight some of the key models and some models considering the impact of large blood vessel(s) by starting with Pennes’ model. Table 1.2 Temperature Ranges with Their Tissue Interactions in Biological Processes Temperature range (°C) Interaction and terminology with tissues 35-40 Normothermia 42-46 Hyperthermia 46-48 Irreversible cellular damage at 45 min 50-52 Coagulation necrosis, 4-6 min 60-100 Near instantaneous coagulation necrosis > 110 Tissue vaporization 1.1.2 Pennes’ Bioheat Transfer Equation
The Pennes’ [1] bioheat transfer equation (PBHTE) has been a standard model for predicting temperature distributions in living tissues for more than a half century. The equation was established by conducting a sequence of experiments measuring temperatures of tissue and arterial blood in the resting human forearm. The equation includes a special term that describes the heat exchange between blood flow and solid tissues. The blood temperature is assumed to be constant arterial blood temperature. In 1948, Pennes [1] performed a series of experiments that measured temperatures on human forearms of volunteers and derived a thermal energy conservation equation: the well-known bioheat transfer equation (BHTE) or the traditional BHTE. Tissue matrix thermal equations can be explained most succinctly by considering the PBHTE as the most general formulation. It is written as: ·k?T+qp+qm-WcbT-Ta=?cp?T?t, (1.1) where T(°C) is the local tissue temperature, Ta(°C) is the arterial temperature, cb(J/kg/°C) is the blood specific heat, cp(J/kg/°C) is the tissue specific heat, W(kg/m3/s) is the local tissue-blood perfusion rate, k(w/m/°C) is the tissue thermal conductivity, ?(kg/m3) is the tissue density, qp(w/m3) is the energy deposition rate, and qm(w/m3) is the metabolism, which is usually very small compared to the external power deposition term qp [2]. The term Wcb(T - Ta), which accounts for the effects of blood perfusion, can be the dominant form of energy removal when considering heating processes. It assumes that the blood enters the control volume at some arterial temperature Ta, and then comes to equilibrium at the tissue temperature. Thus, as the blood leaves the control volume it carries away the energy, and hence acts as an energy sink in hyperthermia treatment. Because Pennes’ equation is an approximation equation and does not have a physically consistent theoretical basis, it is surprising that this simple mathematical formulation predicted temperature fields well in many applications. The reasons why PBHTE has been widely used in the hyperthermia modeling field are twofold: (1) its mathematical simplicity; and (2) its ability to predict the temperature field reasonably well in application. Nevertheless, the equation does have some limitations. It does not, nor was it ever intended to, handle several physical effects. The most significant problem is that it does not consider the effect of the directionality of blood flow, and hence does not describe any convective heat transfer mechanism. 1.1.3 The Chen and Holmes Model
Several investigators have developed alternative formulations to predict temperatures in living tissues. In 1980, Chen and Holmes (CH) [3] derived one with a very strong physical and physiological basis. The equation can be written as: ·k+kp?T+qp+qm-WcbT-Ta-?bcbu·?T=?cp?T?t. (1.2) Comparing this equation with Pennes’ equation, two extra terms have been added. The term - ?bcbu · ?T is the convective heat transfer term, which accounts for the thermal interactions between blood vessels and tissues. The term ? · kp?T accounts for the enhanced tissue conductive heat transfer due to blood perfusion term in tissues, where kp is called the perfusion conductivity, and is a function of the blood perfusion rate. The blood perfusion term - Wcb(T - Ta), shown in the CH model, accounts for the effects of the large number of capillary structures whose individual dimensions are small relative to the macroscopic phenomenon under their study. Relatively, the CH model has a more solid physical basis than Pennes’ model. However, it requires...
