Advances in numerical heat transfer

Cover......Page 1
ADVANCES IN NUMERICAL HEAT TRANSFER, Volume 3......Page 4
Contents......Page 6
Preface......Page 8
Contributors......Page 9
1.1 INTRODUCTION......Page 13
1.1.1 Hyperthermia......Page 14
1.1.2 Bioheat Transfer in the Human Eye......Page 15
1.2.1 The Pennes Bioheat Equation......Page 18
1.2.2 Wulff Continuum Model......Page 19
1.2.4 Continuum Model of Chen and Holmes (CH)......Page 20
1.2.5 The Weinbaum, Jiji, and Lemons (WJL) Bioheat Equation Model......Page 23
1.2.6 The Weinbaum-Jiji Bioheat Equation Model......Page 24
1.3.1 Energy Equation......Page 25
1.3.2.1 Lumen......Page 30
1.3.2.2 Endothelium and Internal Elastic Lamina......Page 31
1.4 CONCLUSIONS......Page 32
NOMENCLATURE......Page 35
REFERENCES......Page 36
CONTENTS......Page 41
2.1 INTRODUCTION......Page 42
2.2 BASIC CONCEPTS......Page 43
2.2.1 Heat Transfer to Blood Vessels......Page 44
2.2.2 Equilibration Lengths......Page 47
2.3.2 Pennes Heat Sink Model......Page 48
2.3.3 Directed Perfusion Model......Page 49
2.3.4 Effective Conductivity Model......Page 50
2.3.5 Combination Models......Page 51
2.3.6 Parameter Values......Page 52
2.4 SOLUTIONS OF CONTINUUM MODELS......Page 53
2.4.1 Finite Difference Method......Page 54
2.4.1.1 Treatment of Boundary Conditions......Page 57
2.4.1.2 Treatment of Multimaterial Contact Problems......Page 59
2.4.2 Finite Element Method......Page 61
2.4.3 Finite Volume Method......Page 66
2.4.3.1 Linear Interpolation of Temperature......Page 69
2.4.3.2 Upwind Scheme......Page 70
2.4.3.4 Multimaterial Contact......Page 72
2.5.4 Statistical Interpretation......Page 79
2.6 CONCLUSIONS......Page 80
REFERENCES......Page 81
CONTENTS......Page 87
3.1 INTRODUCTION......Page 88
3.2.1 Probability Model for Monte Carlo Algorithm......Page 91
3.2.2 The Fixed Random Walk Formulation......Page 94
3.2.3 The Absorption Formulation......Page 100
3.2.4 Monte Carlo Algorithm for Nonlinear Boundary Conditions......Page 102
3.3.1 Particularities in Modeling of Bioheat Transfer with Phase Change......Page 104
3.3.3 Dual-Reciprocity Boundary Element Method (BEM) Formulation......Page 108
3.3.4 Phase Change Cases Based on 3D Simulation......Page 111
3.4.1 Particularities of Laser Heating of Tissues......Page 117
3.4.2 Monte Carlo Formulation for Light Propagation......Page 118
3.4.3 Conjugated Model for Heat and Flow Transport......Page 122
3.5 CONCLUSIONS......Page 126
ACKNOWLEDGMENT......Page 127
REFERENCES......Page 128
CONTENTS......Page 133
4.1.1 Bioheat Model......Page 134
4.2.1 Introduction......Page 135
4.2.2 Conductive Heat Transfer in Tissue......Page 136
4.2.3.3 Convective Heat Transfer by Blood Flow......Page 138
4.2.3.4 Interaction between Vessel and Tissue......Page 139
4.2.4 Convective Heat Transfer by a Vessel Network......Page 141
4.2.5.1 Blood Flow in the Vessels Is Known......Page 144
4.2.5.3 Discrepancies between Flow and Perfusion Data......Page 145
4.2.6 Artificial Generation of Vessels for Thermal Calculations......Page 146
4.3 VALIDATION......Page 147
4.4.1 Patient-Specific Temperature Distribution during Regional Hyperthermia......Page 149
4.4.2 Safety Guidelines for Radiofrequency Exposure......Page 151
4.4.3 Evaluation of High-Intensity Focused Ultrasound (HIFU) Scan Strategies......Page 155
4.5 CONCLUSIONS......Page 156
REFERENCES......Page 157
5.1 INTRODUCTION......Page 160
5.2 TUMOR CHARACTERISTICS......Page 161
5.3 THERMAL IMAGING OF TUMORS......Page 164
5.4 THERMALLY TARGETED DRUG DELIVERY......Page 168
5.5 TUMOR TREATMENT PLANNING AND ASSESSMENT......Page 175
5.5.1 High-Temperature Treatment......Page 177
5.5.2 Cryosurgery......Page 179
5.5.3 Alternate Cold and Heat Treatment......Page 184
5.5.4.1 Tissue Damage Model......Page 186
5.5.4.2 Cellular Damage Model......Page 187
5.5.4.3 Vascular Damage......Page 190
5.6 CONCLUSIONS......Page 191
NOMENCLATURE......Page 192
REFERENCES......Page 194
6.1 INTRODUCTION......Page 207
6.2.1 Body Temperature Distribution......Page 210
6.2.3 Numerical Method of Solving Equation (6.7)......Page 213
6.3 RESULTS......Page 214
6.4 DISCUSSION......Page 223
GREEK SYMBOLS......Page 226
REFERENCES......Page 227
7.1 INTRODUCTION......Page 230
7.2.1 Phantom Study......Page 232
7.2.2 In Vitro Tissue Study......Page 235
7.3 NUMERICAL MODELING......Page 237
7.4.1.1 Phantom Experiments......Page 240
7.4.1.2 In Vitro Tissue Experiments......Page 249
7.4.2 Numerical Results......Page 256
ACKNOWLEDGMENT......Page 262
REFERENCES......Page 263
CONTENTS......Page 266
8.1 INTRODUCTION......Page 267
8.2 EVOLUTION OF HUMAN THERMAL MODELS......Page 269
8.3 MODEL STRUCTURE......Page 271
8.3.1 Geometry......Page 272
8.3.2 Composition......Page 273
8.4.1 Regulation of Blood Flow to Muscle......Page 274
8.4.2.1 Measurement of Skin Blood Flow......Page 276
8.4.3 Algorithm for Computing Skin Blood Flow......Page 277
8.4.3.2 Active Vasodilation: The Effect of Exercise......Page 278
8.4.3.3 Active Vasodilation: Other Factors......Page 281
8.4.3.5 Effect of Ts on Skin Blood Flow (SkBF) (CVCL)......Page 282
8.4.3.7 Combination of AVD, CVCL, CVCM, and CVCE to Define qs......Page 284
8.4.3.8 Comparison of Computed and Measured Forearm Blood Flow (FBF) Data......Page 285
8.4.4 Regulation of Sweating......Page 286
8.4.4.1 Measurement of Sweat Rate......Page 287
8.4.4.2 An Algorithm for Computing the Sweat Rate......Page 288
8.4.4.3 Effect of Acclimation to Heat and Fitness on Sweating......Page 291
8.4.4.4 Effect of Exercise on Sweating......Page 293
8.4.4.5 Hidromeiosis......Page 294
8.4.4.6 Comparison of Computed and Measured Whole-Body Sweat Rates......Page 296
8.4.5.1 An Algorithm for Computing the Rate of Shivering Metabolism......Page 297
8.5 MODEL PERFORMANCE......Page 299
8.5.1 Passive Exposure to Heat......Page 301
8.5.2 Exercise at Three Intensities and Two Temperatures......Page 302
8.5.3 Passive Exposure to Cold Air......Page 305
8.5.4 Immersion in Cold Water......Page 307
8.6 CONCLUSIONS......Page 309
REFERENCES......Page 310
CONTENTS......Page 316
9.1 INTRODUCTION......Page 317
9.2 CONTROL SYSTEM IMPLEMENTATION......Page 318
9.3.1 Image Processing......Page 320
9.3.2 Geometry Processing......Page 322
9.4 GOVERNING EQUATIONS......Page 323
9.4.1 Discretization of Equations......Page 325
9.4.1.1 Time Stepping......Page 326
9.4.1.2 Adjoint Gradient......Page 327
9.4.2 Calibration Results......Page 330
9.5.1 Heating Protocol......Page 336
9.5.2 Cell Study Results......Page 337
9.6 CELL DAMAGE MODELS......Page 339
9.6.1 Two-State Cell Damage Model......Page 341
9.6.2 Parameter Estimation......Page 342
9.6.3 Model Comparison between the Arrhenius Model and the Two-State Model......Page 344
9.7 SENSITIVITY STUDY......Page 345
9.8 CONCLUSIONS AND FUTURE DIRECTIONS......Page 349
REFERENCES......Page 350
10.1 INTRODUCTION......Page 354
10.1.1 Previous Modeling Efforts......Page 357
10.1.2 Factors Influencing Model Accuracy......Page 358
10.2 TEMPERATURE MEASUREMENTS IN HUMAN SUBJECTS......Page 359
10.3 THE MATHEMATICAL MODEL......Page 360
10.3.2 Blood Perfusion Values......Page 362
10.4 STUDIES IN TISSUE-EQUIVALENT PHANTOM GEL......Page 364
10.5 PREDICTION OF INTERSTITIAL TEMPERATURES IN HUMAN SUbJECTS......Page 366
10.6.1 Prostate......Page 371
10.7 EXTENSION OF THE MODEL TO ACCOUNT FOR PHASE CHANGE......Page 373
10.8 CONCLUSIONS......Page 377
GREEK SYMBOLS......Page 378
REFERENCES......Page 379