Description
Book Synopsis* Presents complex material in an easy to understand progression of ideas. * Illustrates principles by example problems taken from physiology and medicine or design problems involving biomedical devices.
Table of ContentsPreface 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
