POROUS
MEDIAApplications in
Biological Systemsand Biotechnology
Edited by
KAMBIZ VAFAI
CRC PressTaylor & Francis CroupBoca Raton London New York
CRC Press Is an imprint of the
Taylor 6t Francis Croup, an Informa business
Contents
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
v
vi Contents
1.7.4 Analytical Treatment Based on Integral Method .. .32
1.7.5 Limiting Radius for Freezing a Tumor duringCryoablation 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 Rubinsky2.1 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: PhysicochemicalDeterminants of the Development 80
3.3.1 Cell Metabolism—Nutrient and OxygenConsumption: 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
Contents vii
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 Microfiuidic Bioreactor:
A Numerical Driven Experimentfor Cartilage Culture 105
3.6 Conclusion 109
3.7 References Ill
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 ContactingAqueous 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 BiologicalCharacteristics 130
4.3.1 Bacterial Biofilms 130
4.3.1.1 Biofilms Composed of Gram-NegativeBacteria 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
viii Contents
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. Cunningham5.1 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 Investigationof 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 Hydrodynamicsand 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 Berguer6.1 Nomenclature 231
6.2 Introduction 232
6.3 Physics of Cerebral Aneurysms 232
Contents ix
6.4 Background 234
6.4.1 Clinical and Experimental Studies Associated with
the Treatment of Aneurysms Using Stent
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 Conclusions 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-ScaleRDEs 279
7.5.6 Hybrid Formulation 280
7.5.7 Numerical Implementation of the HybridAlgorithm 280
7.5.8 Coupling of the Pore-Scale and Darcy-ScaleSimulations 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
X Contents
8 Passive Mass Transport Processes in Cellular Membranes
and their Biophysical Implications 295
Armin Kargol and Marian Kargol8.1 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, cr, and u 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, cr, and Ud 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 byAquatic Plants 314
8.5.2 Water Exchange Described by Mechanistic
Equations 315
8.5.3 Numerical Results for Nitella translucens and
Chora 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
Contents xi
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: Pree
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, B,oman 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 BurrowingMacrozoobenthos Species 387
10.4 Future Prospectives 391
10.5 References 391
xii Contents
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 Introchiction 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 DeformingArticular 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 CompetitiveBinding 426
11.4.2.2 Steady-State Growth Factor Uptake 427
11.4.2.3 Model Calibration 427
Contents xiii
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. Estevez,
Domingos Barbosa, Jesus M1, Rodriguez, and Audelino Alvaro12.1 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
xiv Contents
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
Bar 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 Nguyen14.1 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
Contents xv
14.2.2 Diffusion State 543
14.2.2.1 Non-dimensional 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
