Preface ...................................................... xvii
Editor ...................................................... xxvii
List of Contributors ......................................... xxix
1 A General Set of Bioheat Transfer Equations Based on
the Volume Averaging Theory .................................. 1
Akira Nakayama, Fujio Kuwahara, and Wei Liu
1.1 Introduction ............................................ 2
1.2 Volume Averaging Procedure .............................. 4
1.3 Governing Equation for Blood Flow ....................... 7
1.4 Two-Energy Equation Model for Blood Flow and Tissue ..... 8
1.4.1 Related Work ..................................... 8
1.4.2 Two-Energy Equation Model Based on VAT ........... 9
1.4.3 Pennes Model .................................... 12
1.4.4 Wulff Model and Klinger Model ................... 13
1.4.5 Chen and Holmes Model ........................... 14
1.5 Three-Energy Equation Model for Countercurrent Heat
Transfer in a Circulatory System ....................... 15
1.5.1 Related Work .................................... 15
1.5.2 Three-Energy Equation Model Based on the
Volume Averaging Theory ......................... 16
1.5.3 Keller and Seiler Model ......................... 19
1.5.4 Chato Model ..................................... 20
1.5.5 Roetzel and Xuan Model .......................... 20
1.5.6 Weinbaum-Jiji Model and Bejan Model ............. 21
1.6 Effect of Spatial Distribution of Perfusion Bleed-Off
Rate on Total Countercurrent Heat Transfer ............. 23
1.7 Application of Bioheat Equation to Cryoablation
Therapy ................................................ 26
1.7.1 Related Work .................................... 26
1.7.2 Bioheat Equation for Cryoablation ............... 29
1.7.3 Numerical Analysis Based on Enthalpy Method ..... 30
1.7.4 Analytical Treatment Based on Integral
Method .......................................... 32
1.7.5 Limiting Radius for Freezing a Tumor during
Cryoablation .................................... 36
1.8 Conclusions ............................................ 38
1.9 Nomenclature ........................................... 39
1.10 References ............................................. 41
2 Mathematical Models of Mass Transfer in Tissue for
Molecular Medicine with Reversible Electroporation .......... 45
Yair Granot and Boris Rubinsky
2.1 Introduction ........................................... 45
2.2 Fundamental Aspects of Reversible Electroporation ...... 48
2.3 Mathematical Models of Ion Transport during
Electroporation ........................................ 51
2.4 Electrical Impedance Tomography of in vivo
Electroporation ........................................ 53
2.5 Mass Transfer in Tissue with Reversible
Electroporation ........................................ 58
2.6 Studies on Molecular Medicine with Drug Delivery in
Tissue by Electroporation .............................. 64
2.7 Future Research Needs in Mathematical Modeling of the
Field of Electroporation ............................... 68
2.8 References ............................................. 69
3 Hydrodynamics in Porous Media with Applications to Tissue
Engineering ................................................. 75
C. Oddou, T. Lemaire, J. Pierre, and B. David
3.1 Nomenclature ........................................... 76
3.2 Introduction ........................................... 78
3.3 Cell and Tissue Engineering: Physicochemical
Determinants of the Development ........................ 80
3.3.1 Cell Metabolism—Nutrient and Oxygen
Consumption: The Michaelis-Menten Formulation ... 80
3.3.2 Effects of Nutrient Transport ................... 83
3.3.3 Effects of Mechanical Loading: Cell and Tissue
Mechanobiology .................................. 84
3.3.4 Other Physicochemical Factors Affecting Cell
Metabolism ...................................... 86
3.4 Bioreactors and Implants ............................... 88
3.4.1 Different Types of Bioreactors .................. 89
3.4.2 Microarchitectural Design of Substrates ......... 91
3.5 Theoretical Models of Active Porous Media .............. 95
3.5.1 Length and Time Scales of the Different
Physicochemical Phenomena ....................... 95
3.5.2 Convection-Diffusion-Reaction Phenomena: Basic
Equations and Characteristic Nondimensional
Parameters ...................................... 95
3.5.3 Computational Models: Two Examples of
Model-Driven Experimental Approaches ........... 100
3.5.3.1 Modeling of Transport Processes in
Bone Tissue-Engineered Implants ....... 100
3.5.3.2 Microfluidic Bioreactor: A Numerical
Driven Experiment for Cartilage
Culture ............................... 105
3.6 Conclusion ............................................ 109
3.7 References ............................................ 11l
4 Biomedical Implications of the Porosity of Microbial
Biofilms ................................................... 121
H. Ben-Yoav, N. Cohen-Hadar, and Amihay Freeman
4.1 Introduction .......................................... 122
4.1.1 What Is a Biofilm? ............................. 122
4.1.2 Biofilms in Medicine ........................... 124
4.2 The Life Cycle of Biofilms ............................ 125
4.2.1 Microbial Attachment ........................... 125
4.2.1.1 Substratum Effects .................... 126
4.2.1.2 Conditioning Films .................... 126
4.2.1.3 Hydrodynamics ......................... 127
4.2.1.4 Characteristics of the Contacting
Aqueous Medium ........................ 127
4.2.1.5 Cell Properties ....................... 127
4.2.2 Biofilm Growth ................................. 128
4.2.2.1 Quorum Sensing ........................ 128
4.2.3 Detachment ..................................... 129
4.3 Infectious Microbial Biofilms—Structural and
Biological Characteristics ............................ 130
4.3.1 Bacterial Biofilms ............................. 130
4.3.1.1 Biofilms Composed of Gram-Negative
Bacteria .............................. 130
4.3.1.2 Biofilms Composed of Gram-Positive
Bacteria .............................. 131
4.3.2 Fungal Biofilms ................................ 132
4.3.3 Microbial Interactions in Mixed-Species
Biofilms ....................................... 133
4.3.4 Antimicrobial Resistance in Infectious
Bacterial Biofilms ............................. 134
4.3.5 Porosity and Diffusional Limitations in
Biofilms ....................................... 137
4.4 Infectious Microbial Biofilms—Treatment Modalities
and Resistance ........................................ 142
4.4.1 Antibacterial and Antifungal Treatment
Modalities of Infectious Biofilms .............. 142
4.4.2 The Impact of Porosity and Diffusional
Limitations on Treatment Efficacy .............. 145
4.5 Concluding Remarks .................................... 149
4.6 References ............................................ 150
5 Influence of Biofilms on Porous Media Hydrodynamics ........ 173
Robin Gerlach and Alfred B. Cunningham
5.1 Introduction and Overview ............................. 174
5.2 An Introduction to Biofilms ........................... 174
5.2.1 Microbial Transport and Attachment ............. 176
5.2.2 Biofilm Growth ................................. 177
5.2.3 Microbial Detachment and Propagation ........... 180
5.3 Experimental Systems and Techniques for the
Investigation of Biofilms in Porous Media ............. 181
5.3.1 The Challenge of Imaging Biofilms in
Porous Media ................................... 182
5.3.2 Porous Media Biofilm Reactors .................. 183
5.4 Biofilms in Porous Media and Their Effect on
Hydrodynamics ......................................... 186
5.4.1 The Relationship of Porous Media
Hydrodynamics and Biofilm Structure ............ 186
5.4.2 Porosity ....................................... 189
5.4.3 Permeability ................................... 190
5.4.4 Dispersion and Diffusion ....................... 197
5.4.5 Constant Head versus Constant Flow ............. 198
5.5 A Few Notes on Modeling ............................... 202
5.5.1 Macroscopic versus Microscopic Models .......... 202
5.5.2 Mixed Domain (Hybrid) Models ................... 203
5.6 Porous Media Biofilms in Nature and Technology ........ 203
5.6.1 Subsurface Biofilm Barriers for the Control
and Remediation of Contaminated Groundwater .... 205
5.6.2 Deep Subsurface Biofilms for Enhanced Oil
Recovery and Carbon Sequestration .............. 208
5.6.3 Porous Media Biofilm Reactors in Industry and
Waste Treatment ................................ 209
5.7 Conclusions and Outlook ............................... 210
5.8 References ............................................ 211
6 Using Porous Media Theory to Determine the Coil Volume
Needed to Arrest Flow in Brain Aneurysms ................... 231
Khalil M. Khanafer and Ramon Berguer
6.1 Nomenclature .......................................... 231
6.2 Introduction .......................................... 232
6.3 Physics of Cerebral Aneurysms ......................... 232
6.4 Background
6.4.1 Clinical and Experimental Studies Associated
with the Treatment of Aneurysms Using Stent .... 234
Implantation and Coil Placement ................ 234
6.4.2 Computational Studies Associated with
Combined Use of Stents and Coils for the
Treatment of Cerebral Aneurysms ................ 235
6.5 Mathematical Formulations ............................. 237
6.6 Construction of Brain Aneurysm Meshes from CT Scans ... 239
6.7 Results and Discussion ................................ 240
6.8 Minimum Packing Density of the Endovascular Coil ...... 242
6.9 Future Work ........................................... 244
6.10 Constructions ......................................... 245
6.11 References ............................................ 245
7 Lagrangian Particle Methods for Biological Systems ......... 251
Alexandre M. Tartakovsky, Zhijie Xu, and Paul Meakin
7.1 Introduction .......................................... 252
7.2 DPD Models for Biological Applications ................ 254
7.3 SPHs Models for Biofilm Growth ........................ 265
7.3.1 Model 1 ........................................ 267
7.3.2 Model 2 ........................................ 268
7.3.3 Implementation of the SPH Model ................ 269
7.3.4 Numerical Results .............................. 269
7.4 An SPH Model for Mineral Precipitation ................ 271
7.5 Hybrid Models for Diffusion-Reaction Systems .......... 274
7.5.1 Hybrid Formulation for Reaction-Diffusion
Systems in Porous Media ........................ 275
7.5.2 Pore-Scale Description and Its SPH
Formulation .................................... 276
7.5.3 SPH Representation of the Pore-Scale RDEs ...... 277
7.5.4 Darcy-Scale (Continuum) Description ............ 278
7.5.5 SPH Representation of Averaged Darcy-Scale
RDEs ........................................... 279
7.5.6 Hybrid Formulation ............................. 280
7.5.7 Numerical Implementation of the Hybrid
Algorithm ...................................... 280
7.5.8 Coupling of the Pore-Scale and Darcy-Scale
Simulations .................................... 280
7.5.9 Multiresolution Implementation of the Hybrid
Algorithm ...................................... 281
7.5.10 Time Integration ............................... 282
7.5.11 Numerical Example .............................. 282
7.5.12 Pore-Scale SPH Simulations ..................... 282
7.5.13 Hybrid Simulations ............................. 284
7.6 Summary ............................................... 285
7.7 References ............................................ 286
8 Passive Mass Transport Processes in Cellular Membranes
and their Biophysical Implications ......................... 295
Armin Kargol and Marian Kargol
8.1 Introduction .......................................... 296
8.2 Thermodynamic KK Equations ............................ 297
8.2.1 Derivation of Phenomenological KK Equations .... 298
8.2.2 Practical KK Equations ......................... 301
8.2.3 Transport Parameters Lp, σ, and ω .............. 302
8.3 Porous Membranes ...................................... 303
8.3.1 Homogeneous and Inhomogeneous Porous
Membranes ...................................... 304
8.3.2 Poiseuille's Equation for Individual Pores
and for the Membrane ........................... 305
8.4 Mechanistic Equations of Membrane Transport ........... 306
8.4.1 Equation for the Volume Flux ................... 307
8.4.2 Equation for the Solute Flux ................... 308
8.4.2.1 Case 1 ................................ 309
8.4.2.2 Case 2 ................................ 309
8.4.3 Correlation Relation for Parameters Lp, σ,
and ωd ......................................... 310
8.4.4 2P Form of the Mechanistic Equations ........... 311
8.4.5 Corrected Form of the Mechanistic Transport
Equations ...................................... 311
8.4.6 Equivalence of KK and ME Equations ............. 312
8.5 Water Exchange between Aquatic Plants and the
Environment ........................................... 314
8.5.1 KK Equations Applied to Water Exchange by
Aquatic Plants ................................. 314
8.5.2 Water Exchange Described by Mechanistic
Equations ...................................... 315
8.5.3 Numerical Results for Nitella translucens and
Chara Corallina ................................ 317
8.6 Passive Transport through Cell Membranes of Human
Erythrocytes .......................................... 317
8.6.1 Regulation of Water Exchange between
Erythrocytes and Blood Plasma .................. 319
8.6.2 Distribution of Pore Sizes ..................... 320
8.7 Comparison of Transport Formalisms: KK, ME, and 2P .... 324
8.8 References ............................................ 327
9 Skin Electroporation: Modeling Perspectives ................ 331
S.M. Becker and A.V. Kuznetsov
9.1 Introduction .......................................... 332
9.2 Transdermal Drug Delivery ............................. 332
9.3 The Skin as a Composite ............................... 333
9.4 Stratum Corneum and the Lipid Barrier ................. 334
9.5 Nondestructive Transport Modeling: The SC as
a Porous Medium ....................................... 334
9.5.1 Brick and Mortar Models ........................ 335
9.5.2 Models Based on Lipid Microstructure: Free
Volume Diffusion ............................... 338
9.5.3 Aqueous Pore-Membrane Models ................... 339
9.6 Skin Electroporation .................................. 342
9.6.1 Short Pulse (Nonthermal) ....................... 342
9.6.2 Long Pulse (Thermal) ........................... 344
9.6.3 LTR: Experimental Observation .................. 345
9.6.4 Lipid Thermal Phase Transitions ................ 346
9.7 Skin Electroporation Models (Nonthermal) .............. 348
9.7.1 Single Bilayer Electroporation Modeling ........ 348
9.7.2 Empirical Models ............................... 350
9.8 Thermodynamic Approach ................................ 353
9.8.1 Fully Thermodynamic Approach ................... 354
9.8.2 LTR Lipid Thermal Phase Change ................. 354
9.8.3 Transport ...................................... 356
9.8.4 Thermal Energy ................................. 357
9.9 Conclusions ........................................... 359
9.10 References ............................................ 359
10 Application of Porous Media Theories in Marine Biological
Modeling ................................................... 365
Arzhang Khalili, Bo Liu, Khodayar Javadi, Mohammad R.
Morad, Kolja Kindler, Maciej Matyka, Roman Stocker, and
Zbigniew Koza
10.1 Introduction .......................................... 366
10.2 Description of the Mathematical Model ................. 368
10.2.1 BGK Model ...................................... 368
10.2.2 LBM for Incompressible Flows in Porous Media ... 370
10.2.3 LBM for Concentration Release in Porous
Media .......................................... 371
10.3 Application of Porous Media in Marine Microbiology ... 372
10.3.1 Shear-Stress Control at Bottom Sediment ........ 372
10.3.2 Tortuosity of Marine Sediments ................. 375
10.3.3 Oscillating Flows over a Permeable Rippled
Seabed ......................................... 377
10.3.4 Nutrient Release from Sinking Marine
Aggregates ..................................... 380
10.3.5 Enhanced Nutrient Exchange by Burrowing
Macrozoobenthos Species ........................ 387
10.4 Future Prospectives ................................... 391
10.5 References ............................................ 391
11 The Transport of Insulin-Like Growth Factor through
Cartilage .................................................. 399
Lihai Zhang, Bruce S. Gardiner, David W. Smith, Peter
Pivonka, and Alan J. Grodzinsky
11.1 Overview .............................................. 400
11.2 Basic Solute Transport Model in a Deforming
Articular Cartilage ................................... 404
11.2.1 Introduction ................................... 404
11.2.1.1 Modeling Cartilage Using the Theory
of Porous Media ....................... 404
11.2.2 Basic Solute Transport Model in Cyclically
Loaded Cartilage ............................... 405
11.2.2.1 Conservation of Mass .................. 406
11.2.2.2 Conservation of Linear Momentum ....... 407
11.2.2.3 Model Geometry for Radial Solute
Transport in Cartilage under
Unconfined Cyclic Compression ......... 409
11.2.2.4 Boundary Conditions ................... 411
11.2.2.5 Initial Conditions .................... 411
11.2.2.6 Numerical Method ...................... 411
11.3 The Effect of Cyclic Loading and IGF-I Binding on
IGF-I Transport in Cartilage .......................... 412
11.3.1 Introduction ................................... 412
11.3.1.1 The Effect of IGF Binding on IGF
Transport in Cartilage ................ 415
11.3.2 Interaction between IGF-I and Its IGFBPs ....... 416
11.3.2.1 Law of Mass Action .................... 416
11.3.2.2 Model of Solute Transport and
Binding in a Deformable Cartilage ..... 417
11.3.2.3 Boundary and Initial Conditions ....... 419
11.3.3 Results and Discussion ......................... 419
11.3.3.1 Free Diffusion ........................ 419
11.3.3.2 Diffusion with Cyclic Deformation
and IGF-I, IGFBP Interaction .......... 420
11.4 IGF Transport with Competitive Binding in
a Deforming Articular Cartilage ....................... 423
11.4.1 Introduction ................................... 423
11.4.1.1 Competitive Binding of IGFs to
Their IGFBPs in Cartilage ............. 424
11.4.2 Model Development for a Competitor Growth
Factor ......................................... 425
11.4.2.1 Law of Mass Action with Competitive
Binding ............................... 426
11.4.2.2 Steady-State Growth Factor Uptake ..... 427
11.4.2.3 Model Calibration ..................... 427
11.4.2.4 Competitive Binding in a Deforming
Cartilage ............................. 429
11.4.2.5 Radial IGF-I and -II Transport in
Cartilage under Unconfined Dynamic
Compression ........................... 430
11.4.2.6 Free Diffusion with Competitor ........ 431
11.4.2.7 Growth Factor Transport with
Competitor and Cyclic Deformation ..... 431
11.5 An Integrated Model of IGF-I and Mechanical-Loading-
Mediated Biosynthesis in a Deformed Articular
Cartilage ............................................. 434
11.5.1 Introduction ................................... 434
11.5.1.1 IGF-I and Mechanical-Loading-
Mediated Cartilage Biosynthesis ....... 435
11.5.2 Biosynthesis Model Construction ................ 435
11.5.2.1 IGF-I Transport and Interaction with
IGFBPs and Receptors .................. 436
11.5.2.2 Cartilage ECM Biosynthesis ............ 437
11.5.2.3 IGF-I Mediated Aggrecan
Biosynthesis .......................... 437
11.5.2.4 Mechanical-Stimuli-Mediated Aggrecan
Biosynthesis .......................... 438
11.5.2.5 Aggrecan Molecule Transport in
Cartilage ............................. 439
11.5.3 Biosynthesis Model Validation and
Predictions .................................... 440
11.6 Summary ............................................... 444
11.7 References ............................................ 445
12 Biotechnological and Biomedical Applications of
Magnetically Stabilized and Fluidized Beds ................. 455
Teresa Castelo-Grande, Paulo A. Augusto, Angel
M. Estevéz, Domingos Barbosa, Jesus Ma. Rodríguez, and
Audelino Álvaro
12 A Introduction ......................................... 456
12.2 Historical Overview of Magnetically Stabilized and
Fluidized Beds ........................................ 458
12.2.1 General ........................................ 458
12.2.2 Biotechnology and Biomedicine .................. 459
12.3 MSBs and MFBs ......................................... 460
12.3.1 Principles of MSBs and MFBs .................... 460
12.3.2 MSBs and MFBs as Porous Media .................. 463
12.4 General Supporting Theory ............................. 464
12.4.1 MSBs and MFBs ................................. 464
12.4.1.1 Magnetic Forces ...................... 464
12.4.1.2 Van der Waals Forces ................. 465
12.4.1.3 Electrostatic Forces ................. 465
12.4.1.4 Collisional Forces ................... 465
12.4.1.5 Force Balances and Parameters
Computation .......................... 466
12.4.2 Extra Forces or Equations Usually Required
When MSFBs Are Applied in Biotechnology and
Medicine ...................................... 469
12.5 Main Biotechnological and Biomedical Applications ..... 471
12.5.1 Particles (Beads) .............................. 471
12.5.2 Applications ................................... 472
12.5.2.1 Enzyme or Cell Immobilization/
Bioreactions .......................... 472
12.5.2.2 Protein Purification/Adsorption ....... 473
12.5.2.3 MSFB Chromatography ................... 474
12.5.2.4 Novel Separations ..................... 475
12.6 Conclusion and Future Perspectives .................... 477
12.7 References ............................................ 478
13 In Situ Characterizations of Porous Media for
Applications in Biofuel Cells: Issues and Challenges ....... 489
Bor Yann Liaw
13.1 Introduction .......................................... 489
13.2 Biofuel Cell Applications ............................. 491
13.3 Desirable Properties and Functionalities .............. 497
13.4 Needs for in situ Characterization: Issues and
Challenges ............................................ 499
13.5 Applicable in situ Techniques ......................... 499
13.5.1 Spectroscopic Imaging Ellipsometry ............. 499
13.5.2 Quartz Crystal Microbalance .................... 509
13.5.3 X-Ray Spectroscopic Techniques ................. 515
13.5.4 Other Spectroscopic Techniques ................. 518
13.6 Future Directions ..................................... 520
13.7 References ............................................ 521
14 Spatial Pattern Formation of Motile Microorganisms:
From Gravitactic Bioconvection to Protozoan Culture
Dynamics ................................................... 535
Tri Nguyen-Quang, Frederic Guichard, and The Hung Nguyen
14.1 Description and Literature Review of Bioconvection .... 536
14.1.1 Overview ....................................... 536
14.1.2 Review of Literature ........................... 538
14.2 Onset and Evolution of Gravitactic Bioconvection:
Linear Stability Analysis and Numerical Simulation .... 541
14.2.1 Mathematical Formulation of Gravitactic
Bioconvection in a Porous Medium ............... 541
14.2.1.1 Description and Formulation of the
Problem ............................... 541
14.2.1.2 Initial and Boundary Conditions ....... 543
14.2.2 Diffusion State ................................ 543
14.2.2.1 Nondimensional Equations .............. 544
14.2.2.2 Linearized Equations .................. 545
14.2.3 Numerical Results .............................. 546
14.2.3.1 Linear Stability Analysis ............. 546
14.2.3.2 Evolution of Bioconvection ............ 548
14.2.3.2.1 Critical Threshold and
Subcritical Regime ......... 548
14.2.3.2.2 Supercritical State ........ 549
14.3 Experimental Study of the Pattern Formation in a
Suspension of Gravitactic Microorganisms .............. 551
14.3.1 Introduction ................................... 551
14.3.2 Hele-Shaw Apparatus and Darcy's Law ............ 553
14.3.3 Geometrical and Physicobiological Parameters ... 553
14.3.4 Key Results of Experimental Study .............. 555
14.3.4.1 The Diffusion Regime .................. 555
14.3.4.2 The Stationary Convection Regime ...... 556
14.3.4.3 Unsteady Convection Regime ............ 556
14.3.4.4 Critical Threshold for the
Transition ............................ 557
14.4 Summary and Perspectives of Future Research ........... 559
14.5 Appendix: Boussinesq Approximation for the
Microorganism Suspension .............................. 560
14.6 Nomenclature .......................................... 561
14.7 References ............................................ 562
Index ......................................................... 569
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