Porous Media: Applications in Biological Systems and Biotechnology

9781420065428-1......Page 1
Contents......Page 4
Preface......Page 15
Editor......Page 24
List of Contributors......Page 25
1. A General Set of Bioheat Transfer Equations Based on the Volume Averaging Theory......Page 29
1.1 Introduction......Page 30
1.2 Volume Averaging Procedure......Page 32
1.3 Governing Equation for Blood Flow......Page 35
1.4.1 Related Work......Page 36
1.4.2 Two-Energy Equation Model Based on VAT......Page 37
1.4.3 Pennes Model......Page 40
1.4.4 Wulff Model and Klinger Model......Page 41
1.4.5 Chen and Holmes Model......Page 42
1.5.1 Related Work......Page 43
1.5.2 Three-Energy Equation Model Based on the Volume Averaging Theory......Page 44
1.5.3 Keller and Seiler Model......Page 47
1.5.5 Roetzel and Xuan Model......Page 48
1.5.6 Weinbaum–Jiji Model and Bejan Model......Page 49
1.6 Effect of Spatial Distribution of Perfusion Bleed-Off Rate on Total Countercurrent Heat Transfer......Page 51
1.7.1 Related Work......Page 54
1.7.2 Bioheat Equation for Cryoablation......Page 57
1.7.3 Numerical Analysis Based on Enthalpy Method......Page 58
1.7.4 Analytical Treatment Based on Integral Method......Page 60
1.7.5 Limiting Radius for Freezing a Tumor during Cryoablation......Page 64
1.8 Conclusions......Page 66
1.9 Nomenclature......Page 67
1.10 References......Page 69
2.1 Introduction......Page 73
2.2 Fundamental Aspects of Reversible Electroporation......Page 76
2.3 Mathematical Models of Ion Transport during Electroporation......Page 79
2.4 Electrical Impedance Tomography of in vivo Electroporation......Page 81
2.5 Mass Transfer in Tissue with Reversible Electroporation......Page 86
2.6 Studies on Molecular Medicine with Drug Delivery in Tissue by Electroporation......Page 92
2.7 Future Research Needs in Mathematical Modeling of the Field of Electroporation......Page 96
2.8 References......Page 97
3. Hydrodynamics in Porous Media with Applications to Tissue Engineering......Page 103
3.1 Nomenclature......Page 104
3.2 Introduction......Page 106
3.3.1 Cell Metabolism—Nutrient and Oxygen Consumption: The Michaelis–Menten Formulation......Page 108
3.3.2 Effects of Nutrient Transport......Page 111
3.3.3 Effects of Mechanical Loading: Cell and Tissue Mechanobiology......Page 112
3.3.4 Other Physicochemical Factors Affecting Cell Metabolism......Page 114
3.4 Bioreactors and Implants......Page 116
3.4.1 Different Types of Bioreactors......Page 117
3.4.2 Microarchitectural Design of Substrates......Page 119
3.5.2 Convection–Diffusion–Reaction Phenomena: Basic Equations and Characteristic Nondimensional Parameters......Page 123
3.5.3 Computational Models: Two Examples of Model-Driven Experimental Approaches......Page 128
3.6 Conclusion......Page 137
3.7 References......Page 139
4. Biomedical Implications of the Porosity of Microbial Biofilms......Page 148
4.1.1 What Is a Biofilm?......Page 149
4.1.2 Biofilms in Medicine......Page 151
4.2.1 Microbial Attachment......Page 152
4.2.2 Biofilm Growth......Page 155
4.2.3 Detachment......Page 156
4.3.1 Bacterial Biofilms......Page 157
4.3.2 Fungal Biofilms......Page 159
4.3.3 Microbial Interactions in Mixed-Species Biofilms......Page 160
4.3.4 Antimicrobial Resistance in Infectious Bacterial Biofilms......Page 161
4.3.5 Porosity and Diffusional Limitations in Biofilms......Page 164
4.4.1 Antibacterial and Antifungal Treatment Modalities of Infectious Biofilms......Page 169
4.4.2 The Impact of Porosity and Diffusional Limitations on Treatment Efficacy......Page 172
4.5 Concluding Remarks......Page 176
4.6 References......Page 177
5. Influence of Biofilms on Porous Media Hydrodynamics......Page 199
5.2 An Introduction to Biofilms......Page 200
5.2.1 Microbial Transport and Attachment......Page 202
5.2.2 Biofilm Growth......Page 203
5.2.3 Microbial Detachment and Propagation......Page 206
5.3 Experimental Systems and Techniques for the Investigation of Biofilms in Porous Media......Page 207
5.3.1 The Challenge of Imaging Biofilms in Porous Media......Page 208
5.3.2 Porous Media Biofilm Reactors......Page 209
5.4.1 The Relationship of Porous Media Hydrodynamics and Biofilm Structure......Page 212
5.4.2 Porosity......Page 215
5.4.3 Permeability......Page 216
5.4.4 Dispersion and Diffusion......Page 223
5.4.5 Constant Head versus Constant Flow......Page 224
5.5.1 Macroscopic versus Microscopic Models......Page 228
5.6 Porous Media Biofilms in Nature and Technology......Page 229
5.6.1 Subsurface Biofilm Barriers for the Control and Remediation of Contaminated Groundwater......Page 231
5.6.2 Deep Subsurface Biofilms for Enhanced Oil Recovery and Carbon Sequestration......Page 234
5.6.3 Porous Media Biofilm Reactors in Industry and Waste Treatment......Page 235
5.7 Conclusions and Outlook......Page 236
5.8 References......Page 237
6.1 Nomenclature......Page 257
6.3 Physics of Cerebral Aneurysms......Page 258
6.4.1Clinical and Experimental Studies Associated with theTreatment of Aneurysms Using StentImplantation and Coil Placement......Page 260
6.4.2 Computational Studies Associated with Combined Use of Stents and Coils for the Treatment of Cerebral Aneurysms......Page 261
6.5 Mathematical Formulations......Page 263
6.6 Construction of Brain Aneurysm Meshes from CT Scans......Page 265
6.7 Results and Discussion......Page 266
6.8 Minimum Packing Density of the Endovascular Coil......Page 268
6.9 Future Work......Page 270
6.11 References......Page 271
7. Lagrangian Particle Methods for Biological Systems......Page 277
7.1 Introduction......Page 278
7.2 DPD Modelsfor Biological Applications......Page 280
7.3 SPHs Modelsfor Biofilm Growth......Page 291
7.3.1 Model 1......Page 293
7.3.2 Model 2......Page 294
7.3.4 Numerical Results......Page 295
7.4 An SPH Model for Mineral Precipitation......Page 297
7.5 Hybrid Models for Diffusion-Reaction Systems......Page 300
7.5.1 Hybrid Formulation for Reaction-Diffusion Systems in Porous Media......Page 301
7.5.2 Pore-Scale Description and Its SPH Formulation......Page 302
7.5.3 SPH Representation of the Pore-Scale RDEs......Page 303
7.5.4 Darcy-Scale (Continuum) Description......Page 304
7.5.5 SPH Representation of Averaged Darcy-Scale RDEs......Page 305
7.5.8 Coupling of the Pore-Scale and Darcy-Scale Simulations......Page 306
7.5.9 Multiresolution Implementation of the Hybrid Algorithm......Page 307
7.5.12 Pore-Scale SPH Simulations......Page 308
7.5.13 Hybrid Simulations......Page 310
7.6 Summary......Page 311
7.7 References......Page 312
8. Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications......Page 320
8.1 Introduction......Page 321
8.2 Thermodynamic KK Equations......Page 322
8.2.1 Derivation of Phenomenological KK Equations......Page 323
8.2.2 Practical KK Equations......Page 326
8.2.3 Transport Parameters Lp, α, and ω......Page 327
8.3 Porous Membranes......Page 328
8.3.1 Homogeneous and Inhomogeneous Porous Membranes......Page 329
8.3.2 Poiseuille’s EquationforIndividual Poresand for the Membrane......Page 330
8.4 Mechanistic Equations of Membrane Transport......Page 331
8.4.1 Equation for the Volume Flux......Page 332
8.4.2 Equation for the Solute Flux......Page 333
8.4.3 Correlation Relation for Parameters Lp, α, and ωd......Page 335
8.4.5 Corrected Form of the Mechanistic Transport Equations......Page 336
8.4.6 Equivalence of KK and ME Equations......Page 337
8.5.1 KK Equations Applied to Water Exchange by Aquatic Plants......Page 339
8.5.2 Water Exchange Described by Mechanistic Equations......Page 340
8.6 Passive Transport through Cell Membranes of Human Erythrocytes......Page 342
8.6.1 Regulation of Water Exchange between Erythrocytes and Blood Plasma......Page 344
8.6.2 Distribution of Pore Sizes......Page 345
8.7 Comparison of Transport Formalisms: KK, ME, and 2P......Page 350
8.8 References......Page 352
9. Skin Electroporation: Modeling Perspectives......Page 355
9.2 Transdermal Drug Delivery......Page 356
9.3 TheSkin as a Composite......Page 357
9.5 Nondestructive Transport Modeling: The SC as a Porous Medium......Page 358
9.5.1 Brick and Mortar Models......Page 359
9.5.2 Models Based on Lipid Microstructure: Free Volume Diffusion......Page 362
9.5.3 Aqueous Pore-Membrane Models......Page 363
9.6.1 Short Pulse (Nonthermal)......Page 366
9.6.2 Long Pulse (Thermal)......Page 368
9.6.3 LTR: Experimental Observation......Page 369
9.6.4 Lipid Thermal Phase Transitions......Page 370
9.7.1 Single Bilayer Electroporation Modeling......Page 372
9.7.2 Empirical Models......Page 374
9.8 Thermodynamic Approach......Page 377
9.8.2 LTR Lipid Thermal Phase Change......Page 378
9.8.3 Transport......Page 380
9.8.4 Thermal Energy......Page 381
9.10 References......Page 383
10. Application of Porous Media Theories in Marine Biological Modeling......Page 389
10.1 Introduction......Page 390
10.2.1 BGK Model......Page 392
10.2.2 LBM for Incompressible Flows in Porous Media......Page 394
10.2.3 LBM for concentration release in porous media......Page 395
10.3.1 Shear-Stress Control at Bottom Sediment......Page 396
10.3.2 Tortuosity of Marine Sediments......Page 399
10.3.3 Oscillating Flows over a Permeable Rippled Seabed......Page 401
10.3.4 Nutrient Release from Sinking Marine Aggregates......Page 404
10.3.5 Enhanced Nutrient Exchange by Burrowing Macrozoobenthos Species......Page 411
10.5 References......Page 415
11. The Transport of Insulin-Like Growth Factor through Cartilage......Page 423
11.1 Overview......Page 424
11.2.1 Introduction......Page 428
11.2.2 Basic Solute Transport Model in Cyclically Loaded Cartilage......Page 429
11.3.1 Introduction......Page 436
11.3.2 Interaction between IGF-I and Its IGFBPs......Page 440
11.3.3 Results and Discussion......Page 443
11.4.1 Introduction......Page 447
11.4.2 Model Development for a Competitor Growth Factor......Page 449
11.5.1 Introduction......Page 458
11.5.2 Biosynthesis Model Construction......Page 459
11.5.3 Biosynthesis Model Validation and Predictions......Page 464
11.6 Summary......Page 468
11.7 References......Page 469
12. Biotechnological and Biomedical Applications of Magnetically Stabilized and Fluidized Beds......Page 478
12.1 Introduction......Page 479
12.2.1 General......Page 481
12.2.2 Biotechnology and Biomedicine......Page 482
12.3.1 Principles of MSBs and MFBs......Page 483
12.3.2 MSBs and MFBs as Porous Media......Page 486
12.4.1 MSBs and MFBs......Page 487
2.4.2 Extra Forces or Equations Usually Required When MSFBs Are Applied in Biotechnology and Medicine......Page 492
12.5.1 Particles (Beads)......Page 494
12.5.2 Applications......Page 495
2.6 Conclusion and Future Perspectives......Page 500
12.7 References......Page 501
13.1 Introduction......Page 511
13.2 BiofuelCellApplications......Page 513
13.3 Desirable Properties and Functionalities......Page 519
13.5.1 Spectroscopic Imaging Ellipsometry......Page 521
13.5.2 Quartz Crystal Microbalance......Page 531
13.5.3 X-Ray Spectroscopic Techniques......Page 537
13.5.4 Other Spectroscopic Techniques......Page 540
13.6 Future Directions......Page 542
13.7 References......Page 543
14. Spatial Pattern Formation of Motile Microorganisms: From Gravitactic Bioconvection to Protozoan Culture Dynamics......Page 556
14.1.1 Overview......Page 557
14.1.2 Review of Literature......Page 559
14.2.1 Mathematical Formulation of Gravitactic Bioconvection in a Porous Medium......Page 562
14.2.2 Diffusion State......Page 564
14.2.3 Numerical Results......Page 567
14.3.1 Introduction......Page 572
14.3.3 Geometrical and Physicobiological Parameters......Page 574
14.3.4 Key Results of Experimental Study......Page 576
14.4 Summary and Perspectives of Future Research......Page 580
14.5 Appendix: Boussinesq Approximation for the Microorganism Suspension......Page 581
14.6 Nomenclature......Page 582
14.7 References......Page 583