Heat Transfer and Fluid Flow in Biological Processes (eBook)

Sid M. Becker, Andrey V. Kuznetsov (Herausgeber)

eBook Download: PDF | EPUB

2014 | 1. Auflage
428 Seiten
Elsevier Science (Verlag)
978-0-12-407900-7 (ISBN)

Infos

Heat Transfer and Fluid Flow in Biological Processes covers emerging areas in fluid flow and heat transfer relevant to biosystems and medical technology. This book uses an interdisciplinary approach to provide a comprehensive prospective on biofluid mechanics and heat transfer advances and includes reviews of the most recent methods in modeling of flows in biological media, such as CFD. Written by internationally recognized researchers in the field, each chapter provides a strong introductory section that is useful to both readers currently in the field and readers interested in learning more about these areas. Heat Transfer and Fluid Flow in Biological Processes is an indispensable reference for professors, graduate students, professionals, and clinical researchers in the fields of biology, biomedical engineering, chemistry and medicine working on applications of fluid flow, heat transfer, and transport phenomena in biomedical technology. - Provides a wide range of biological and clinical applications of fluid flow and heat transfer in biomedical technology - Covers 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

Inhalt

Front Cover 1
Heat Transfer and Fluid Flow in Biological Processes 4
Copyright 5
Contents 6
Contributors 10
Preface 12
Chapter 1: Bioheat Transfer and Thermal Heating for Tumor Treatment 14
1.1. Pennes and Other Bioheat Transfer Equations 14
1.1.1. Introduction 14
1.1.2. Pennes' Bioheat Transfer Equation 15
1.1.3. The Chen and Holmes Model 16
1.1.4. The Weinbaum and Jiji Model 17
1.1.5. The Weinbaum, Jiji, and Lemons Model 17
1.1.6. Baish et al 18
1.1.7. Others 18
1.2. Blood Flow Impacts on Thermal Lesions with Pulsation and Different Velocity Profiles 18
1.2.1. Introduction 19
1.2.2. Mathematical Model and Numerical Method 19
1.2.2.1. Velocity Profile of Pulsatile Blood Flow in a Circular Blood Vessel 19
1.2.2.2. Governing Equations and Numerical Method 21
1.2.2.3. Calculation of Thermal Dose 23
1.2.3. Results and Discussions 24
1.2.4. Conclusion 28
1.3. Thermal Relaxation Time Factor in Blood Flow During Thermal Therapy 28
1.3.1. Introduction 28
1.3.2. Mathematical Model and Numerical Method 29
1.3.2.1. Features of the Hyperbolic Heat Equation 29
1.3.2.2. Thermal Governing Equations and the Numerical Method 30
1.3.3. Results and Discussions 32
1.3.4. Conclusion 36
1.4. PBHTE with the Vascular Cooling Network Model 37
1.4.1. Thermally Significant Blood Vessel Model 37
1.4.2. Vessel Network Geometry and Fully Conjugated Blood Vessel Network Model 38
1.4.3. Discrete Vessel Modeling with Semicurved Vessel Network and Real 3D Vasculature Network 40
1.4.4. Conclusion 42
1.5. Hyperthermia Treatment Planning 42
1.5.1. Optimization with Fine Spatial Power Deposition: Based on Local Temperature Response in the Treated Region 43
1.5.2. Optimization with Lumped Power Deposition: Uniform Absorbed Power Deposition in the Treated Tumor Region 47
1.5.3. Effect of Blood Perfusion and Blood Flow Rates on the Optimization 47
1.5.4. Optimization Without Thermally Significant Blood Vessels in the Tissues 51
1.5.5. Conclusion 51
References 53
Chapter 2: Tissue Response to Short Pulse Laser Irradiation 56
2.1. Introduction 56
2.2. Mathematical Formulation 59
2.2.1. Numerical Modeling of Laser-Tissue Interactions 59
2.2.2. Continuum Model Development 60
2.2.3. Vascular Model Development 62
2.3. Experimental Methods 63
2.4. Results and Discussion 64
2.5. Conclusion 69
References 70
Chapter 3: Quantitative Models of Thermal Damage to Cells and Tissues 72
3.1. Introduction 72
3.2. Heat Transfer in Tissue 73
3.3. Reaction Rates and Temperature 74
3.4. Thermal Denaturation of Proteins 76
3.5. Cells 79
3.6. Tissue-Level Descriptions 82
3.6.1. Burns 82
3.6.2. Normalizing Hyperthermia to Time at 43C 83
3.6.3. Other Studies Addressing Clinical Response 84
3.7. Discussion 85
References 86
Chapter 4: Analytical Bioheat Transfer: Solution Development of the Pennes Model 90
4.1. Pennes' Bioheat Equation in Living Tissue Analogy 91
4.1.1. Representation of the Governing Equations 93
4.1.2. Boundary Condition Types 93
4.1.3. Temperature Shift 94
4.2. Solutions to the Transient Homogenous Bioheat Equation 95
4.2.1. Bioheat Solution in the Cartesian Coordinate System 96
4.2.1.1. Solutions to Transient Bioheat Transfer in a Slab 100
4.2.1.2. Solutions of the Bioheat in the Infinite and Semi-infinite Domains 101
Semi-infinite Domain BC1 Type II 104
Semi-infinite Domain BC1 Type III 104
Infinite Domain 104
4.2.2. Bioheat Equation in the Cylindrical and Spherical Coordinate Systems 105
4.2.2.1. Bioheat in Cylindrical Coordinates 105
4.2.2.1.1. Cylinder with a Homogenous Type I BC2 106
4.2.2.1.2. Cylinder with a Homogenous Type II BC2 106
4.2.2.2. Bioheat in Spherical Coordinates 107
4.2.2.2.1. Sphere with a Homogenous Type I BC2 107
4.2.2.2.2. Sphere with a Homogenous Type II BC2 108
4.2.2.2.3. Sphere in the Semi-infinite Domain 108
4.3. Solution Approaches to Nonhomogenous Problems 108
4.3.1. Method of Superpositioning 109
4.3.2. Green's Functions 111
4.3.2.1. Transformation of the Conduction Greens Function to the Bioheat Problem 114
4.3.2.2. Selected Green's Functions in the Cartesian Coordinate System 114
4.3.2.3. Semi-infinite and Infinite Cartesian Domains 115
4.3.2.4. Selected Green's Functions in the Cylindrical and Spherical Coordinate Systems 117
4.3.2.4.1. Radial Heat Flow in the Cylindrical Coordinate System 118
4.3.2.4.2. Cylinder with a Homogenous Type I BC2 118
4.3.2.4.3. Cylinder with a Homogenous Type II BC2 118
4.3.2.4.4. Cylindrical Semi-infinite Problem 119
4.3.2.4.5. Radial Heat Flow in the Spherical Coordinate System 119
4.3.2.4.6. Sphere with a Homogenous Type I BC2 119
4.3.2.4.7. Sphere with a Homogenous Type II BC2 119
4.3.2.4.8. Spherical Semi-infinite Problem 120
4.4. Additional Considerations 120
4.4.1. Bioheat Problem in Multidimensions 120
4.4.2. Short Time Convergence Issues and Integral Approximations 121
4.5. The Composite Bioheat Problem 121
4.5.1. Homogenization of the Composite Domain 124
4.5.1.1. Addressing the Steady Nonhomogenous Components 124
4.5.2. The Homogenous Composite Bioheat Problem 125
4.5.3. SOV in the Composite System 126
4.5.3.1. Building the Eigenfunctions and Determining the Eigenvalues 129
4.5.4. Solutions to Homogenous Transient Bioheat Transfer in a Composite Slab 132
4.5.4.0.1. Special Case Simplification 134
4.5.5. Addressing Transient Energy Generation Using Greens Functions 135
4.6. Summary Remarks 136
References 137
Chapter 5: Characterizing Respiratory Airflow and Aerosol Condensational Growth in Children and Adults Using an Imaging-C... 138
5.1. Introduction 138
5.2. Methods 140
5.2.1. Construction of Airway Models 141
5.2.2. Breathing and Wall Boundary Conditions 142
5.2.3. In Vitro Deposition Measurement 143
5.2.4. Continuous and Discrete Particle Transport Equations 143
5.2.5. Droplet Evaporation and Condensation Model 145
5.2.6. Numerical Method and Convergence Sensitivity Analysis 147
5.3. Results 147
5.3.1. Child-Adult Discrepancies 147
5.3.2. Hygroscopic Growth Model Testing 148
5.3.3. Adult Nasal Airway Model 149
5.3.3.1. Airflow, Temperature, and RH Field 149
5.3.3.2. Baseline Case: Aerosol Transport and Deposition of Inert Particles 152
5.3.3.3. Hygroscopic Behavior of Individual Particles in Equilibrium Humidity 153
5.3.3.4. Particle Growth and Deposition in Nonequilibrium Nasal Environments 154
5.3.4. Five-Year-Old Child Nose-Throat Model 156
5.3.5. Adult Mouth-Lung Model 160
5.4. Discussion 161
5.5. Conclusion 164
References 165
Chapter 6: Transport in the Microbiome 170
6.1. Introduction 170
6.2. The Human Microbiome 171
6.3. Swimming Microorganisms 173
6.3.1. Flagellar Biomechanics and Hydrodynamics 174
6.3.1.1. Prokaryotic Flagella 175
6.3.1.2. Spirochetes 179
6.3.1.3. Eukaryotic Flagella 179
6.3.1.4. Ciliates 181
6.3.1.4.1. Pushers and Pullers 183
6.3.1.5. Non-Newtonian Effects 183
6.3.2. Flow-Induced Motion 184
6.3.2.1. Boundary Effects 184
6.3.2.2. Cell-Cell Hydrodynamics 187
6.4. Continuum Descriptions 192
6.4.1. Semi-Dilute Suspensions 192
6.4.2. Cell-Cell Collisions 195
6.4.3. Coarse Graining 196
6.5. Discussion 197
References 198
Chapter 7: A Critical Review of Experimental and Modeling Research on the Leftward Flow Leading to Left-Right Symmetry Br... 202
7.1. Introduction 203
7.2. Experimental Research on the Leftward Nodal Flow and LR Symmetry Breaking 204
7.3. Modeling Research on the Nodal Flow 206
7.4. Leftward Flow or Flow Recirculation? 207
7.5. Sensing of the Flow: Mechanosensing or Chemosensing? 207
7.6. Modeling the Effect of a Ciliated Surface by Imposing a Given Vorticity at the Edge of the Ciliated Layer 209
7.7. Summary of Relevant Parameters Describing the Nodal Flow and Estimates of Their Values 213
7.8. Numerical Results Obtained Assuming a Constant Vorticity at the Edge of the Ciliated Layer 214
7.9. Conclusions 216
Acknowledgments 217
References 217
Chapter 8: Fluid-Biofilm Interactions in Porous Media 220
8.1. Microbial Biofilms in Porous Media 220
8.1.1. Historical Stepping-Stones 223
8.1.2. Of Polymers and Cells: Processes Involved in Biofilm Formation 225
8.1.3. Morphology of Biofilms in Porous Media 227
8.2. A Motivating Problem: Biofilms and the Fate of Contaminants in Soil 229
8.2.1. Impact of Biofilms on Fluid Composition 229
8.2.2. Impact of Biofilms on Fluid Mobility 230
8.3. Models of Biofilm Growth and Pattern Formation in Quiescent Fluids 231
8.3.1. Continuum-Based Models 231
8.3.2. Discrete-Based Models 233
8.4. Computational Simulation of Fluid-Biofilm Interactions in Porous Media 235
8.4.1. Generation and Initial Colonization of the Porous Structure 236
8.4.2. Cell Proliferation and EPS Spreading 236
8.4.3. Fluid-Flow and Flow-Induced Biofilm Stresses 238
8.4.4. Detachment, Migration, and Reattachment of cells and EPS 239
8.4.5. Solute Transport 239
8.5. Mechanisms of Biological Clogging in Porous Media 240
8.5.1. Experimental Observations and Conceptual Models 240
8.5.2. Single-Pore Simulations Under Two Different Flow Regimes 242
8.5.3. Detachment and Downstream Migration of Biofilms 244
8.6. Summary 247
References 247
Chapter 9: Flow Through a Permeable Tube 252
9.1. Introduction 252
9.2. Axisymmetric Stokes Flow 253
9.2.1. Stokes Stream Function 254
9.2.2. Exponential Solutions 254
9.2.3. General Solution 258
9.3. Flow Through an Infinite Permeable Tube 258
9.3.1. No-Slip Boundary Condition 258
9.3.2. Velocity Field 259
9.3.3. Flow Rate 261
9.3.4. Pressure Field 262
9.3.5. Stress Field 263
9.3.6. Solution in Terms of the Flow Rate and Pressure at the Origin 264
9.4. Starlings Equation 265
9.4.1. Starling's Equation in Terms of the Pressure 266
9.4.2. Starling's Equation in Terms of the Normal Stress 269
9.5. Flow Through a Tube with Finite Length 270
9.5.1. Solution in Terms of Entrance and Exit Flow Rates 270
9.5.2. Solution in Terms of the Entrance and Exit Pressures 274
9.5.3. Starling's Equation in Terms of the Normal Stress 275
9.5.4. Nearly Unidirectional Flow Model 275
9.6. Effect of Wall Slip 279
9.6.1. Starling's Equation 283
9.7. Summary 285
References 285
Chapter 10: Transdermal Drug Delivery and Percutaneous Absorption 286
10.1. Introduction 287
10.2. Physiological Description and Drug Transport Models 289
10.2.1. The Skin as a Composite 289
10.2.2. The SC, Its Corneocytes, and the Lipid Matrix 289
10.2.3. The Drug and the Vehicle 290
10.2.4. Diffusion–Transport Considerations 291
10.2.4.1. Diffusion 291
10.2.4.2. Evaluation of the Diffusion Coefficient 292
10.2.4.3. Partitioning 293
10.2.4.4. Evaluation of the Partition Coefficient 294
10.2.5. Adsorption 294
10.2.5.1. Slow Binding 295
10.2.5.2. Fast Binding 295
10.2.6. Metabolism and Clearance 296
10.2.7. TDD Models 297
10.2.7.1. Fickian Models 298
10.2.7.2. Non-Fickian Models 298
10.3. Review of Mathematical Methods 299
10.3.1. Laplace Transform 299
10.3.2. Finite Difference Method 300
10.3.3. Finite Element Method 300
10.3.4. Finite Volume Method 301
10.4. Modeling TDD Through a Two-Layered System 301
10.4.1. Mathematical Formulation 301
10.4.1.1. Dimensionless Equations 305
10.4.2. Method of Solution 306
10.4.2.1. Time-Dependent Solution 307
10.4.2.2. Space-Dependent Solution: The Eigenvalue Problem 307
10.4.2.3. Concentration Solution 309
10.4.3. Numerical Simulation and Results 310
10.5. Conclusions 313
References 315
Chapter 11: Mechanical Stress Induced Blood Trauma 318
11.1. Introduction 318
11.2. Mechanical Stresses Experienced by Blood 319
11.2.1. Couette Flow 320
11.2.2. Elongational Flow 320
11.2.3. Wall Shear Stress 321
11.2.4. Scalar Shear Stress 321
11.2.5. Fluid Dynamic Stresses in the Circulation 321
11.2.6. Fluid Dynamic Stresses in Blood Contacting Devices 322
11.2.6.1. Needles, Catheters, Cannulae 322
11.2.6.2. Rotary Ventricular Assist Devices 322
11.2.6.3. Displacement Ventricular Assist Devices 323
11.2.6.4. Mechanical Heart Valves 323
11.2.6.5. Membrane Oxygenators 323
11.3. Fluid Dynamic Effects on Blood Constituents 323
11.3.1. Red Blood Cells 323
11.3.1.1. Deformation of RBCs 324
11.3.1.2. Hemolysis 325
11.3.2. White Blood Cells 327
11.3.3. Platelets 329
11.3.3.1. Adhesion 329
11.3.3.2. Activation 331
11.3.4. von Willebrand factor (vWf) 333
11.3.5. Thrombosis and Emboli 333
11.4. Numerical Models of Damage to the Blood Constituents 334
11.4.1. Red Blood Cells 334
11.4.1.1. Stress-Based 334
11.4.1.2. Strain-Based 336
11.4.1.3. Conclusion 338
11.4.2. Platelets 338
11.4.3. Blood Proteins Including von Willebrand Factor 339
11.4.4. Thrombosis and Emboli 339
11.5. Summary 341
References 342
Chapter 12: Modeling of Blood Flow in Stented Coronary Arteries 348
12.1. Introduction 349
12.2. Hemodynamic Quantities of Interest 351
12.2.1. Introduction 351
12.2.2. Near-Wall Quantities 351
12.2.3. Flow Stasis Quantities 353
12.2.4. Bulk Flow Quantities 354
12.3. Fluid Dynamic Models of Idealized Stented Geometries 355
12.3.1. Introduction 355
12.3.2. Coronary Bifurcation Models 355
12.4. Fluid Dynamic Models of Image-Based Stented Geometries 365
12.4.1. Introduction 365
12.4.2. CFD Studies from In Vitro Model Images 365
12.4.3. CFD Studies from Animal Models 367
12.4.4. CFD Studies from Patient Images 369
12.5. Limitations of the Current CFD Models and Future Remarks 375
12.5.1. Introduction 375
12.5.2. Heart Motion 375
12.5.3. Rigid Walls 375
12.5.4. Boundary Conditions 377
12.5.5. Accuracy of Three-Dimensional Geometrical Models 377
12.5.6. Model Validation 378
12.6. Conclusions 378
Acknowledgments 379
References 379
Chapter 13: Hemodynamics in the Developing Cardiovascular System 384
13.1. Introduction 384
13.2. The Chicken Embryo Model System 385
13.2.1. Key Stages in Cardiovascular Development 385
13.3. Relevant Fluid Mechanic Regimes 387
13.3.1. Viscous Effects Dominate in the Developing Circulation 388
13.3.2. Curvature Effects Are Minimal, Except in the Embryonic Heart 389
13.3.3. Pulsatile Effects Can Be Ignored in the Embryonic Phase 392
13.3.4. Local Flow Can Be Described Using Two Parameters Only 393
13.4. Experimental Studies 395
13.4.1. Influence of Temperature 396
13.4.2. Pressure 398
13.4.3. Cardiac Output 398
13.4.4. Flow Rate and Velocities in Blood Vessels 399
13.4.5. Whole-Field Measurements: Micro-PIV 400
13.4.6. Scanning Imaging Methods 403
13.5. Mechanotransduction 405
13.5.1. Mechanotransduction in Cardiovascular Development 405
13.5.2. Primary Cilia as Mechanosensors 407
13.5.3. Loss of Cilia Is Instrumental for Heart Valve Development 408
13.6. Hemorheology 409
13.6.1. Macroscopic Rheological Behavior of Blood 409
13.6.2. Multiphase Aspects of Blood 410
13.6.3. Endothelial Surface Layer 411
13.6.4. Human Versus Avian Blood 412
13.7. Conclusions and Outlook 413
References 414
Index 420

Textauszug

Chapter 1

Bioheat Transfer and Thermal Heating for Tumor Treatment

Huang-Wen Huanga [e-mail]; 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=ρcp∂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, ρ(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−ρbcbu⋅∇T=ρcp∂T∂t.

  (1.2)

Comparing this equation with Pennes’ equation, two extra terms have been added. The term − ρbcbu ⋅ ∇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...

Produkt-Details

• Erscheint lt. Verlag: 31.12.2014
• Sprache: englisch
• Themenwelt: Medizin / Pharmazie ► Pflege
• Themenwelt: Medizin / Pharmazie ► Physiotherapie / Ergotherapie ► Orthopädie
• Themenwelt: Naturwissenschaften ► Biologie ► Biochemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Technik ► Maschinenbau
• Themenwelt: Technik ► Medizintechnik
• ISBN-10: 0-12-407900-8 / 0124079008
• ISBN-13: 978-0-12-407900-7 / 9780124079007