Transport in biological media / edited by Sid M. Becker, Andrey V. Kuznetsov.

Format:

Book

Contributor:

Becker, Sid.

Kuznetsov, Andrey V.

ScienceDirect (Online service)

Language:

English

Subjects (All):

Transport theory.

Tissues--Mechanical properties.

Tissues.

Cells--Mechanical properties.

Cells.

Biological transport.

Physical Description:

1 online resource (xiii, 559 pages) : illustrations

Place of Publication:

Amsterdam ; Boston : Elsevier/Academic Press, [2013]

System Details:

Mode of access: World Wide Web.

text file

Summary:

Transport in Biological Media is a solid resource of mathematical models for researchers across a broad range of scientific and engineering problems such as the effects of drug delivery, chemotherapy, or insulin intake to interpret transport experiments in areas of cutting edge biological research. A wide range of emerging theoretical and experimental mathematical methodologies are offered by biological topic to appeal to individual researchers to assist them in solving problems in their specific area of research. Researchers in biology, biophysics, biomathematics, chemistry, engineers and clinical fields specific to transport modeling will find this resource indispensible. Provides detailed mathematical model development to interpret experiments and provides current modeling practices Provides a wide range of biological and clinical applicationsIncludes physiological descriptions of models.

Contents:

1 Modeling Momentum and Mass Transport in Cellular Biological Media: From the Molecular to the Tissue Scale / George E. Kapellos Kapellos, George E., Terpsichori S. Alexiou Alexiou, Terpsichori S.

1.1 Introduction 2

1.1.1 Cellular Biological Media 2

1.1.2 Interplay Between Transport Phenomena, Structure and Function 4

1.1.3 Modeling of Transport Phenomena Across Multiple Scales 6

1.1.4 An Engineer's Perspective 6

1.2 Mechanics of Biomolecules, Subcellular Structures and Biological Cells 7

1.2.1 Biomacromolecules 8

1.2.2 Subcellular Structures 9

1.2.3 Biological Cells 11

1.3 Formulation of Balance Laws and Constitutive Equations 12

1.3.1 Single-Scale, Single-Phase Approaches 12

1.3.2 Biot's Theory of Poroelasticity 16

1.3.3 Theory of Interacting Continua 16

1.3.4 Multiscale Bottom-Up Approaches 18

1.3.5 Multiscale Computational, Equation-Free Approaches 23

1.4 Calculation of Constitutive Parameters 23

1.4.1 Generic Framework for Theoretical Calculation 23

1.4.2 Remarks on the Experimental Determination 24

1.4.3 Transport Properties of the Extracellular Phase 25

1.4.4 Mechanical Properties of Biological Cells 25

1.4.5 Mechanical Properties of Cellular Biological Media 29

1.4.6 Hydraulic Permeability of Porous Cellular Biological Media 29

1.4.7 Diffusion Coefficients in Cellular Biological Media 31

1.5 Modeling of Growth and Pattern Formation 32

1.5.1 Continuum-Based Models 33

1.5.2 Discrete-Based Models 33

Acknowledgments 36

References 37

2 Thermal Pain in Teeth: Heat Transfer, Thermomechanics and Ion Transport / Min Lin Lin, Min, Shaobao Liu Liu, Shaobao, Feng Xu Xu, Feng, Tianjian Lu Lu, Tianjian, Bofeng Bai Bai, Bofeng, Guy M. Genin Genin, Guy M.

2.1 Introduction 42

2.2 Modeling of Thermally Induced Dentinal Fluid Flow 43

2.2.1 Analysis of Thermomechanics of the Tooth 43

2.2.2 Analysis of Dentinal Fluid Flow 46

2.3 Modeling of Nociceptor Transduction 47

2.3.1 Modeling of Shear Stress 47

2.3.2 Modeling Transduction 49

2.4 Results and Discussion 51

2.4.1 Tooth Thermomechanics 51

2.4.2 The Mechanism Underlying Thermally Induced DFF 52

2.4.3 DFF and Its Implications for Tooth Thermal Pain 53

2.4.4 The Difference Between Hot and Cold Tooth Pain 54

2.5 Conclusion 56

References 56

3 Drug Release in Biological Tissue / Filippo De Monte Monte, Filippo De, Giuseppe Pontrelli Pontrelli, Giuseppe, Sid Becker Becker, Sid

3.1 Introduction 61

3.2 Continuum Modeling of Mass Transport in Porous Media 65

3.2.1 Porosity and Volume-Averaged Variables 66

3.2.2 Permeability, Darcy's Law and the Continuity Equation 68

3.2.3 Tortuosity and Fick's Law 72

3.3 Conservation of Drug Mass 73

3.3.1 Drug Mass Balance in the Fluid Phase 74

3.3.2 Drug Mass Balance in the Solid Phase 77

3.3.3 Governing Equations 78

3.4 Analytical Solutions for Local Mass Non-Equilibrium 78

3.4.1 Nusselt's Solution 79

3.4.2 Schumann's Solution 83

3.4.3 Anzelius's Solution 85

3.4.4 Recent Solutions 86

3.5 Analytical Solutions for Local Mass Equilibrium 87

3.5.1 A Worked Example 87

3.6 Applications of Porous Media to the Drug-Eluting Stent 92

3.6.1 The Fluid Wall Model: The Pure Diffusion Approximation 96

3.6.2 The Fluid Wall Model: The Advection-Reaction-Diffusion Equation 102

3.6.3 The Multi-Layered Wall Model: The Pure Diffusion Approximation 106

3.7 Conclusion 115

References 116

4 Transport of Water and Solutes Across Endothelial Barriers and Tumor Cell Adhesion in the Microcirculation / Bingmei M. Fu Fu, Bingmei M., Yang Liu Liu, Yang

4.1 Introduction 120

4.2 Microvascular Transport 122

4.2.1 Transvascular Pathways 122

4.2.2 Transport Coefficients 129

4.2.3 Permeability Measurement 130

4.2.4 Transport Models for Water and Solutes Through Interendothelial Cleft 135

4.2.5 Endothelial Surface Glycocalyx 146

4.2.6 Transport Across Fenestrated Microvessels 152

4.2.7 Transport in Tissue Space (Intetstitium) 152

4.3 Modulation of Microvascular Transport 153

4.3.1 Permeability Increase 154

4.3.2 Permeability Decrease 156

4.3.3 Permeability Increase and Decrease 158

4.3.4 Microvascular Hyperpermeability and Tumor Metastasis 158

4.4 Tumor Cell Adhesion in the Microcirculation 162

4.4.1 Tumor Cell Adhesion Under Flow 162

4.4.2 Mathematical Models for Tumor Cell Adhesion in the Microcirculation 163

4.4.3 Model Predictions for Tumor Cell Adhesion in the Microcirculation 166

4.5 Summary and Opportunities for Future Study 170

Acknowledgments 170

References 170

5 Carrier-Mediated Transport Through Biomembranes / Ranjan K. Pradhan Pradhan, Ranjan K., Kalyan C. Vinnakota Vinnakota, Kalyan C., Daniel A. Beard Beard, Daniel A., Ranjan K. Dash Dash, Ranjan K.

5.1 Introduction 182

5.2 Physicochemical Principles and Kinetic Modeling of Carrier-Mediated Transport 183

5.2.1 Thermodynamics of Solute Transport 183

5.2.2 Kinetic Treatment of a Simple Carrier 183

5.2.3 Kinetic Treatment of a Simple Pore 187

5.2.4 Membrane Potential Dependency of Solute Transport 188

5.3 Experimentally Observable Features of Carrier-Mediated Transport Phenomena 190

5.4 Kinetic Modeling of Mitochondrial Ca²⁺ Uniporter 191

5.4.1 Historical Background 191

5.4.2 Kinetic Scheme for Mitochondrial Ca²⁺ Transport via the Ca²⁺ Uniporter 193

5.4.3 Derivation of Mitochondrial Ca²⁺ Uniporter Flux Expression 195

5.4.4 ΔΨ Dependency of Mitochondrial Ca²⁺ Uniporter Flux: Free Energy Barrier Formalism 197

5.4.5 Mitochondrial Ca²⁺ Uniporter Model Parameterization and Simulations 200

5.4.6 ΔΨDependency of Mitochondrial Ca²⁺ Uniporter Flux: Alternate Formulation 201

5.4.7 Mg²⁺ Inhibition and Pi Regulation of Mitochondrial Ca²⁺ Uniporter Function 204

5.4.8 Kinetic Scheme for Mg²⁺ Inhibition of Mitochondrial Ca²⁺ Uniporter Function 204

5.4.9 Mitochondrial Ca²⁺ Uniporter Model with Mg²⁺ Inhibition 206

5.5 Other Modes of Carrier-Mediated Transport: Antiport and Cotransport 208

5.6 Summary and Conclusion 210

Acknowledgment 211

References 211

6 Blood How Through Capillary Networks / C. Pozrikidis Pozrikidis, C., J.M. Davis Davis, J.M.

6.1 Introduction 214

6.2 Equations of Steady Capillary Blood Flow 216

6.2.1 Balances at a Bifurcation 217

6.2.2 Discharge Hematocrit 217

6.2.3 Tube Hematocrit and Hematocrit Ratio 218

6.2.4 Effective Viscosity 218

6.2.5 Cell Partitioning at a Bifurcation 219

6.2.6 Converging Bifurcations 220

6.2.7 Diverging Bifurcation 220

6.2.8 Klitzman and Johnson Cell Partitioning Law 220

6.2.9 General Expression for the Cell Partitioning Law 221

6.2.10 Empirical Cell Partitioning Law 221

6.2.11 Numerical Studies of Suspension Flow Through a Bifurcation 221

6.3 Steady Flow Through Tree Networks 222

6.3.1 Geometrical Construction 222

6.3.2 Numerical Method 223

6.3.3 Results and Discussion 223

6.4 Steady Flow Through Homogeneous Networks 226

6.4.1 Theoretical Model 226

6.4.2 Geometrical Construction 228

6.4.3 Numerical Method 228

6.4.4 Flow Through a Pristine Network 228

6.4.5 Dimensions and Parameters 229

6.4.6 Effective Hydraulic Permeability 229

6.4.7 Results and Discussion 230

6.4.8 Significance of the Bifurcation Law 231

6.4.9 Significance of the Viscosity Correlation 233

6.4.10 Discussion 234

6.5 Equations of Unsteady Blood Flow 235

6.5.1 Unsteady Flow Through a Straight Capillary 235

6.5.2 Circular Capillaries 236

6.5.3 Correlations 237

6.5.4 Balances at Bifurcations 237

6.5.5 Numerical Method 238

6.5.6 Single-Node Dynamics 240

6.6 Unsteady Flow Through Tree Networks 243

6.6.1 Steady Flow for Subcritical Exponents 244

6.6.2 Unsteady Flow for Supercritical Exponents 246

6.6.3 State Space 248

6.6.4 Summary and Discussion 248

6.7 Summary and Outlook 249

References 250

7 Models of Cerebrovascular Perfusion / T. David David, T., R.G. Brown Brown, R.G.

7.1 Introduction 254

7.2 From Arteries to Cells and Back Again (Cerebral Anatomy and Physiology) 254

7.2.1 Cerebral Arterial Structure 254

7.2.2 Circle of Willis 256

7.2.3 Penetrating Arteries and the Cortex 256

7.3 Structure of Arterial Blood Vessels 257

7.4 A Simple Description of Cerebral Autoregulation 258

7.4.1 Organ Autoregulation 258

7.4.2 Local Autotegulation: 'Functional Hyperemia' 258

7.5 Vascular Trees and Their Numerical Simulation 259

7.6 Simple Models of Autoregulated Cerebral Perfusion 259

7.6.1 Blood Flow Through the Circle of Willis 259

7.6.2 Simple Models of Autotegulated Cerebral Perfusion 261

7.7 More Complex Models 264

7.7.1 Arteriolar Models of Autoregulation 264

7.7.2 Perfusion via the Capillary Bed 267

7.8 Conclusions 272

Acknowledgments 272

References 272

8 Mechanobiology of the Arterial Wall / Anne M. Robertson Robertson, Anne M., Paul N. Watton Watton, Paul N.

8.1 Introduction 276

8.2 Overview of the Arterial Wall 278

8.2.1 Brief Overview of the Architecture of the Arterial Wall 279

8.2.2 Design Requirements for the Arterial Wall 281

8.3 The Extracellular Matrix 283

8.3.1 Collagen and the Arterial Wall 283

8.3.2 Elastin in the Arterial Wall 291

8.4 Vascular Cells 292

8.4.1 Endothelial Cells 293

8.4.2 Vascular Smooth Muscle Cells 295

8.4.3 Fibroblasts 297

8.4.4 Matrix Assembly by Vascular Cells 297

8.5 Architecture of the Arterial Wall 301

8.5.1 Tunica Intima 301

8.5.2 Tunica Media 306

8.5.3 Tunica Adventitia 308

8.6 Constitutive Models for the Arterial Wall 309

8.6.1 Multiple Mechanism Models 311

8.6.2 Isotropic Mechanism 312

8.6.3 Anisotropic Mechanisms: Kinematics of Fiber Recruitment 313

8.6.4 N-Fiber Anisotropic Models 314

8.6.5 Anisotropic Models with a Distribution of Fiber Orientations 316

8.6.6 Distributions of Fiber Recruitment Stretch 317

8.6.7 Multi-Mechanism Models: Growth, Remodeling and Damage (GR&D) 319

8.7 Modeling Vascular Disease: Intracranial Aneurysms 324

8.7.1 Background 324

8.7.2 Computational Modeling of Intracranial Aneurysms 326

8.7.3 Example: Fluid-Solid-Growth Model of Aneurysm Evolution 329

8.7.4 Discussion 331

References 333

9 Shear Stress Variation and Plasma Viscosity Effect in Microcirculation / Xuewen Yin Yin, Xuewen, Junfeng Zhang Zhang, Junfeng

9.1 Introduction 350

9.2 Models and Methods 351

9.2.1 The Lattice-Boltzmann Method (LBM) for Fluid Dynamics 351

9.2.2 Red Blood Cell (RBC) Model and Membrane Mechanics 352

9.2.3 Intercellular Aggregation 353

9.2.4 The Immersed-Boundary Method (IBM) for Fluid-Membrane Interaction 354

9.2.5 Viscosity Update Algorithm 355

9.3 Algorithm Validations 356

9.3.1 The Laplace Relationship for Stationary Bubbles 356

9.3.2 The Dispersion Relationship for Capillary Waves 357

9.3.3 The Drag Coefficient for Circular Cylinders 358

9.3.4 RBC Deformation and Rotation in Shear Flows 360

9.4 WSS Variation Induced by Blood Flows in Microvessels 360

9.4.1 Single-File RBC Flows 361

9.4.2 Cell-Free Layer (CFL) and Wall Shear Stress (WSS) Variation in Multiple RBC Flows 368

9.5 Suspending Viscosity Effect 372

9.5.1 Single RBC Rotation in Shear Flows 372

9.5.2 Single RBC Migration in Channel Flows 374

9.5.3 Multiple RBC Flows in Microvessels 376

9.5.4 RBC Motion and Deformation in Bifurcated Microvessels 380

9.6 Summary 386

Acknowledgments 387

References 387

10 Targeted Drug Delivery: Multifunctional Nanoparticles and Direct Micro-Drug Delivery to Tumors / Clement Kleinstreuer Kleinstreuer, Clement, Emily Childress Childress, Emily, Andrew Kennedy Kennedy, Andrew

10.1 Introduction 392

10.2 Diagnostic Imaging and Image-Guided Drug Delivery 392

10.2.1 Imaging Techniques 392

10.2.2 Image-Guided Drug Delivery 394

10.3 Free Transport 394

10.3.1 Passive and Active Targeting 395

10.3.2 Nanodrug Carriers 395

10.3.3 Summary 400

10.4 Forced Transport 400

10.5 Direct Transport 401

10.5.1 Implementation of Optimal Targeted Drug Delivery 401

10.5.2 Applications of Optimal Micro-Drug Delivery 404

10.6 Conclusions 413

Acknowledgments 413

References 414

11 Electrotransport Across Membranes in Biological Media: Electrokinetic Theories and Applications in Drug Delivery / S. Kevin Li Li, S. Kevin, Jinsong Hao Hao, Jinsong, Mark Liddell Liddell, Mark

11.1 Introduction 418

11.2 Nernst-Planck Theory and Model Simulation Analyses 419

11.3 Electrotransport Under a Constant Electric Field Across Membrane (Symmetric Conditions) 420

11.3.1 Membrane Flux and the Modified Nernst-Planck Equation 421

11.3.2 Membrane Flux and Transference Number 424

11.3.3 Transport Lag Time 424

11.3.4 Electroosmotic Transport 425

11.4 Electrotransport Under Variable Electric Field Across Membrane (Asymmetric Conditions) 426

11.4.1 The Nernst-Planck Equation with Electroneutrality Approximation 426

11.4.2 Electrotransport Under Asymmetric Conditions with Electroosmosis 430

11.5 Electrotransport Across Multiple Barriers/Membranes 430

11.5.1 Electrotransport Across Two-Membrane Systems Under Symmetric and Asymmetric Conditions 432

11.5.2 Effects of Membrane Porosity and Applied Voltage Upon Electrotransport Across Two-Membrane Systems 436

11.6 Electrotransport Under Alternating Current 440

11.7 Electropermeabilization Effect 441

11.8 Electrokinetic Methods of Enhanced Transport Across Biological Membranes 443

11.8.1 Transdermal Iontophoresis 444

11.8.2 Transungual Iontophotesis 447

11.8.3 Transscleral Iontophoresis 448

References 450

12 Mass Transfer Phenomena in Electroporation / Alexander Golberg Golberg, Alexander, Boris Rubinsky Rubinsky, Boris

12.1 Introduction 458

12.2 Electroporation Background and Theory 459

12.3 Applications of Electroporation-Mediated Mass Transport in Biological Systems 463

12.4 Mechanisms of Pulsed Electric Field-Mediated Transport into Cells 464

12.5 Experimental Methods Used to Study Mass Transfer During Electroporation 465

12.6 Mathematical Models Describing Molecular Transport During Reversible Electroporation 467

12.6.1 Physico-Chemical Model for Electroporation 467

12.6.2 Electropermeabilization Model 470

12.6.3 Electtodiffusion Model of DNA Cluster Formation 472

12.6.4 Model of Conductivity Changes During Cell Suspension Electroporation 475

12.6.5 Model of Small Molecule Transport Kinetics Due to Electroporation 477

12.6.6 Two Compartment Pharmacokinetic Model for Molecular Uptake During Electroporation 479

12.6.7 Statistical Model for Cell Electrotransformation 481

12.6.8 A Multiscale Model for Mass Transfer of Drug Molecules in Tissue 481

12.7 Future Needs in Mathematical Modeling of Mass Transport for Electroporation Research 484

References 485

13 Modeling Cell Electroporation and Its Measurable Effects in Tissue / Nataša Pavšelj Pavšelj, Nataša, Damijan Miklavcic Miklavcic, Damijan, Sid Becker Becker, Sid

13.1 Introduction - Electroporation 493

13.2 Skin Electroporation 495

13.3 Physical Changes in Biological Tissue Following Electroporation 497

13.3.1 Electrical Conductivity Increase 497

13.3.2 Tissue Heating During Electroporation 499

13.3.3 Molecular Transport During Skin Electroporation 502

13.4 Modeling of Skin Electroporation Transport 504

13.4.1 Modeling Non-Thermal Electroporation (Short Pulses) 506

13.4.2 Modeling Thermal Electroporation (Long Pulse) 507

13.5 Conclusions 514

Acknowledgments 515

References 515

14 Modeling Intracellular Transport in Neurons / Andrey V. Kuznetsov Kuznetsov, Andrey V.

14.1 Introduction 522

14.2 A Model of Axonal Transport Drug Delivery 523

14.3 Effect of Dynein Velocity Distribution on Propagation of Positive Injury Signals in Axons 532

14.4 Simulation of Merging of Viral Concentration Waves in Retrograde Viral Transport in Axons 540

14.5 Conclusions 546.

Notes:

Description based on print version record.

Includes index.

Includes bibliographical references at the end of each chapters and index.

Other Format:

Print version: Transport in biological media.

ISBN:

1299621449

9781299621442

9780124158245

0124158242

OCLC:

847131505

Access Restriction:

Restricted for use by site license.