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Biomedical Mass Transport and Chemical Reaction: Physicochemical Principles and Mathematical Modeling

ISBN: 978-0-471-65632-6
656 pages
June 2016, ©2016
Biomedical Mass Transport and Chemical Reaction: Physicochemical Principles and Mathematical Modeling (0471656321) cover image

Description

Teaches the fundamentals of mass transport with a unique approach emphasizing engineering principles in a biomedical environment

  • Includes a basic review of physiology, chemical thermodynamics, chemical kinetics, mass transport, fluid mechanics and relevant mathematical methods
  • Teaches engineering principles and mathematical modelling useful in the broad range of problems that students will encounter in their academic programs as well as later on in their careers
  • Illustrates principles with examples taken from physiology and medicine or with design problems involving biomedical devices
  • Stresses the simplification of problem formulations based on key geometric and functional features that permit practical analyses of biomedical applications
  • Offers a web site of homework problems associated with each chapter and solutions available to instructors
Homework problems related to each chapter are available from a supplementary website (<http://engineering.case.edu/BMTR). These problems provide practice in basic computations, model development, and simulations using analytical and numerical methods.
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Table of Contents

Preface xvi

Guidance to Instructors xvii

Methods for Solving Model Equations xix

Acknowledgments xx

About the Companion Website xxi

Part I Introduction 1

1 Biological Structure and Function 3

1.1 Cell Energy Related to Whole-Body Function 4

1.2 Tissue and Organ Systems 8

1.3 Cell Structure and Energy Metabolism 16

2 Modeling Concepts for Biological Mass Transport 21

2.1 Representation of Biological Media 21

2.2 Mechanisms of Mass Transport 25

2.3 Formulation of Material Balances 30

2.4 Spatially Lumped and Distributed Models 32

References 39

Part II Thermodynamics of Biomedical Processes 41

3 Basics of Equilibrium Thermodynamics 43

3.1 Thermodynamic Systems and States 43

3.2 Heat, Work, and the First Law 44

3.3 Enthalpy and Heat Effects 45

3.4 Entropy and the Second Law 46

3.5 Gibbs Free Energy and Equilibrium 46

3.6 Properties of the Chemical Potential 51

References 53

4 Interfacial and Membrane Equilibria 54

4.1 Equilibrium Criterion 54

4.2 Interfacial Equilibria 56

4.3 Membrane Equilibria 62

4.4 Electrical Double Layer 71

References 75

5 Chemical Reaction Equilibrium 76

5.1 Equilibrium Criterion 76

5.2 Equilibrium Coefficients 78

5.3 Acid Dissociation 80

5.4 Ligand–Receptor Binding 83

5.5 Equilibrium Models of Blood Gas Content 90

References 101

Part III Fundamentals of Rate Processes 103

6 Nonequilibrium Thermodynamics and Transport Rates 105

6.1 Transport Velocities and Fluxes 105

6.2 Stefan–Maxwell Equation 109

6.3 Diffusion of Uncharged Substances 111

6.4 Diffusion of Electrolytes 116

6.5 Transport across Membranes 117

References 123

7 Mechanisms and Models of Diffusion 124

7.1 Transport Rates in Homogeneous Materials 125

7.2 Diffusion Coefficients in Gases 125

7.3 Diffusion Coefficients in Liquids 128

7.4 Transport in Porous Media Models of Tissue 134

7.5 Transport in Suspension Models of Tissue 144

References 151

8 Chemical Reaction Rates 152

8.1 General Kinetic Models 152

8.2 Basis of Reaction Rate Equations 154

8.3 Multi-Step Reactions 158

8.4 Ligand–Receptor Kinetics 161

8.5 Enzyme Kinetics 166

8.6 Urea Cycle as a Reaction Network 173

References 178

Part IV Transport Models in Fluids and Membranes 179

9 Unidirectional Transport 181

9.1 Unidirectional Transport Equations 181

9.2 Steady-State Diffusion 186

9.3 Diffusion with Parallel Convection 191

9.4 Diffusion with Chemical Reaction 194

9.5 Unsteady-State Diffusion 201

References 203

10 Membrane Transport I: Convection and Diffusion Processes 204

10.1 Ordinary Diffusion 204

10.2 Diffusion with Parallel Convection 211

10.3 Cell Membrane Channels 216

References 223

11 Membrane Transport II: Carrier-Mediated Processes 224

11.1 Facilitated Transport of a Single Substance 224

11.2 Cotransport of Two Substrates 227

11.3 Simulation of Tracer Experiments 230

11.4 Primary Active Transport 237

11.5 Electrical Effects on Ion Transport 242

References 244

12 Mass Transfer Coefficients and Chemical Separation Devices 245

12.1 Transport Through a Single Phase 245

12.2 Transport Through Multiple Phases 256

12.3 Design and Performance of Separation Devices 265

References 279

Part V Multidimensional Processes of Molecules and Cells 281

13 Fluid Mechanics I: Basic Concepts 283

13.2 Mechanical Properties and Rheology of Fluids 289

13.3 Model Formulation and Scaling of Fluid Flow 293

13.4 Steady Flow Through A Tube 299

References 306

14 Fluid Mechanics II: Complex Flows 307

14.1 Boundary Layer Flows 307

14.2 Creeping Flow Through a Leaky Tube 319

14.3 Periodic Flow Along a Tube 323

Reference 329

15 Mass Transport I: Basic Concepts and Nonreacting Systems 330

15.1 Three-Dimensional Mass Balances 330

15.2 Special Cases 332

15.3 One-Dimensional Transport Equations 334

15.4 Model Formulation and Scaling of Mass Transport 339

15.5 Diffusion and Convection in Nonreacting Systems 344

References 357

16 Mass Transport II: Chemical Reacting Systems 358

16.1 Single-Phase Processes 358

16.2 Multiphase Processes 368

16.3 Processes with Interfacial Reaction 380

References 387

17 Cell Population Dynamics 388

17.1 Cell Number Balances 388

17.2 Cell Transport and Fate Processes 389

17.3 Single Cell Population Dynamics 394

17.4 Multiple Cell Population Dynamics 399

Reference 409

Part VI Compartmental Modeling 411

18 Compartment Models I: Basic Concepts and Tracer Analysis 413

18.1 Compartmental Modeling Concepts 413

18.2 Multiple-Compartment Models 421

18.3 Nonideal Inputs and Moment Analysis 430

Reference 438

19 Compartment Models II: Analysis of Physiological Systems 439

19.1 Open-Loop Models 439

19.1.1 Multipool Model of Glucose Metabolism 439

19.2 Models with Feedback and Recirculation 452

References 466

Part VII Advanced Biomedical Applications 467

20 Therapies for Tissue and Organ Dysfunction 469

20.1 Dynamics of Urea Clearance in a Patient During Hemodialysis 469

20.2 Hemodialyzer Performance with Varying Filtration 474

20.3 Gas Exchange in an Intravascular Lung Device 480

20.4 Separation of Blood Components by Apheresis 486

20.5 Epidermal Regeneration in Tissue-Engineered Skin 490

References 497

21 Drug Release, Delivery, and Distribution 498

21.1 Drug Release From an Agglomerated Tablet 498

21.2 Drug Release From an Osmotic Pump Device 504

21.3 Intestinal Drug Transport 509

21.4 Drug Distribution in Ablated Tissues 515

21.5 Intracranial Drug Delivery and Distribution 520

21.6 Whole-Body Methotrexate Distribution 526

References 534

22 Diagnostics and Sensing 535

22.1 Chemical Monitoring of Tissue by Microdialysis 535

22.2 Dual-Electrode Measurement of Blood Flow and Oxygen 541

22.3 Detection of Ethanol in Blood from Exhaled Gas 546

22.4 Oxygen Uptake and Utilization in Exercising Muscle 552

22.5 Tracer Analysis with Pet Imaging 562

22.6 Cancer Cell Migration with Cell–Cell Interaction 569

References 576

Appendix A Units and Property Data 577

A.1 American National Standard for SI Units 577

A.2 Definitions of Concentration 579

A.3 Thermodynamic Properties 580

A.4 Transport Properties 583

References 586

Appendix B Representing Transport Processes in Complex Systems 587

B.1 Vector and Tensor Operations 587

B.2 Nonequilibrium Thermodynamics 592

B.3 Spatially Averaged Balances for Heterogeneous Tissue 596

B.4 Tables for Fluid Motion in Common Coordinate Systems 602

References 604

Appendix C Mathematical Methods 605

C.1 Dimensionless Forms and Scaling 605

C.2 Inversion of Square Matrices 608

C.3 Initial-value Problems 609

C.4 Laplace Transforms 613

C.5 Alternative Representation of a Point Source 614

C.6 Similarity Transform of a Partial Differential Equation 615

Nomenclature 619

Index 624

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Author Information

James S. Ultman, PhD, is a Professor Emeritus of Chemical Engineering and Biomedical Engineering at the Pennsylvania State University.

Harihara Baskaran, PhD, is a Professor of Chemical and Biomolecular Engineering at Case Western Reserve University.

Gerald M. Saidel, PhD, is a Professor of Biomedical Engineering at Case Western Reserve University.
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Professor Reviews

"The book is particularly suited to Biomedical Engineering and Biophysics courses and would provide excellent supplementary material for basic transport courses in Chemical Engineering and Mechanical Engineering. The authors are all very experienced researchers in the area of biotransport and have taught the subject matter at both the undergraduate and graduate levels for many years. Their experience is evident throughout this well- conceived textbook...Overall, there is more than enough material here to allow the creative instructor flexibility to design a unique and exciting course that moves from basic principles to modern applications." John M. Tarbell, CUNY and Wallace Coulter Distinguished Professor, Department of Biomedical Engineering, The City College of New York

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