Preface ...................................................... xiii
Author ......................................................... xv
Notation ..................................................... xvii
Chapter 1 Introduction ......................................... 1
1.1 Review of Units and Dimensions ............................. 1
1.1.1 Units ............................................... 1
1.1.2 Fundamental Dimensions .............................. 1
1.1.2.1 Mass and Weight ............................ 1
1.1.2.2 Temperature ................................ 4
1.1.2.3 Mole ....................................... 4
1.1.3 Derived Dimensional Quantities ...................... 5
1.1.3.1 Pressure ................................... 6
1.1.3.2 Volume ..................................... 6
1.1.3.3 Equations of State ......................... 7
1.2 Dimensional Equation ....................................... 7
1.3 Tips for Solving Engineering Problems ...................... 8
1.4 Conservation of Mass ...................................... 10
1.4.1 Law of Conservation ................................ 10
1.4.2 Chemical Reactions ................................. 12
1.4.3 Material Balances .................................. 14
Problems .................................................. 20
Chapter 2 A Review of Thermodynamic Concepts .................. 23
2.1 First Law of Thermodynamics ............................... 23
2.1.1 Closed Systems ..................................... 23
2.1.2 Steady Flow Processes .............................. 24
2.2 Second Law of Thermodynamics .............................. 25
2.2.1 Reversible Processes ............................... 26
2.3 Properties ................................................ 27
2.3.1 Heat Capacity ...................................... 27
2.3.2 Calculating the Change in Entropy .................. 28
2.3.2.1 Entropy Change of an Ideal Gas ............ 28
2.3.3 Gibbs and Helmholtz Free Energy .................... 30
2.3.3.1 Gibbs Free Energy ......................... 30
2.3.3.2 Helmholtz Free Energy ..................... 30
2.4 Fundamental Property Relations ............................ 31
2.4.1 Exact Differentials ................................ 31
2.5 Single Phase Open Systems ................................. 33
2.5.1 Partial Molar Properties ......................... 33
2.5.1.1 Binary Systems ............................ 35
2.5.1.2 Property Changes of Mixing ................ 35
2.5.1.3 Ideal Gas ................................. 35
2.5.1.4 Gibbs Free Energy of an Ideal Gas
Mixture ................................... 38
2.5.2 Pure Component Fugacity ............................ 38
2.5.2.1 Calculating the Pure Component Fugacity ... 39
2.5.3 Fugacity of a Component in a Mixture ............... 41
2.5.4 Ideal Solution ..................................... 42
2.6 Phase Equilibrium ......................................... 43
2.6.1 Pure Component Phase Equilibrium ................... 45
2.6.1.1 Fugacity of a Pure Component as a
Compressed Liquid ......................... 47
2.6.2 Excess Properties .................................. 48
2.6.3 Applications of Equilibrium Thermodynamics ......... 51
2.6.3.1 Solubility of a Solid in a Liquid
Solvent ................................... 51
2.6.3.2 Depression of the Freezing Point of a
Solvent by a Solute ....................... 56
2.6.3.3 Equilibrium between a Solid and a Gas
Phase ..................................... 57
2.6.3.4 Solubility of a Gas in a Liquid ........... 59
2.6.3.5 Osmotic Pressure .......................... 62
2.6.3.6 Distribution of a Solute between Two
Liquid Phases ............................. 65
2.6.3.7 Vapor-Liquid Equilibrium .................. 70
2.6.3.8 Flammability Limits ....................... 74
2.6.3.9 Thermodynamics of Surfaces ................ 76
2.6.3.10 Equilibrium Dialysis ...................... 79
2.6.3.11 Gibbs-Donnan Effect ....................... 84
2.6.3.12 Donnan Potential .......................... 87
2.6.3.13 Chemical Equilibrium in Ideal Aqueous
Solutions ................................. 89
Problems .................................................. 94
Chapter 3 Physical Properties of the Body Fluids and the
Cell Membrane ................................................. 101
3.1 Body Fluids .............................................. 101
3.2 Fluid Compositions ....................................... 102
3.3 Capillary Plasma Protein Retention ....................... 102
3.4 Osmotic Pressure ......................................... 104
3.4.1 Osmolarity ........................................ 105
3.4.2 Calculating the Osmotic Pressure .................. 105
3.4.3 Other Factors That May Affect the Osmotic
Pressure .......................................... 106
3.5 Formation of the Interstitial Fluid ...................... 106
3.6 Net Capillary Filtration Rate ............................ 108
3.7 Lymphatic System ......................................... 110
3.8 Solute Transport across the Capillary Endothelium ........ 110
3.9 Cell Membrane ............................................ 111
3.10 Ion Pumps ................................................ 116
Problems ................................................. 117
Chapter 4 The Physical and Flow Properties of Blood and
Other Fluids .................................................. 121
4.1 Physical Properties of Blood ............................. 121
4.2 Cellular Components ...................................... 121
4.3 Rheology ................................................. 121
4.4 Relationship between Shear Stress and Shear Rate ......... 125
4.5 Hagen-Poiseuille Equation ................................ 127
4.6 Other Useful Flow Relationships .......................... 128
4.7 Rheology of Blood ........................................ 129
4.8 Casson Equation .......................................... 131
4.9 Using the Casson Equation ................................ 132
4.10 Velocity Profile for Tube Flow of a Casson Fluid ......... 134
4.11 Tube Flow of Blood at Low Shear Rates .................... 134
4.12 Effect of Diameter at High Shear Rates ................... 134
4.13 Marginal Zone Theory ..................................... 136
4.14 Using the Marginal Zone Theory ........................... 138
4.15 Boundary Layer Theory .................................... 141
4.15.1 Flow near a Wall That is Set in Motion ............ 141
4.15.2 Laminar Flow of a Fluid along a Flat Plate ........ 146
4.16 Generalized Mechanical Energy Balance Equation ........... 151
4.17 Capillary Rise and Capillary Action ...................... 159
4.17.1 Equilibrium Capillary Rise ........................ 159
4.17.2 Dynamics of Capillary Action ...................... 161
Problems ...................................................... 164
Chapter 5 Solute Transport in Biological Systems ............. 175
5.1 Description of Solute Transport in Biological Systems .... 175
5.2 Capillary Properties ..................................... 175
5.3 Capillary Flow Rates ..................................... 175
5.4 Solute Diffusion ......................................... 177
5.4.1 Fick's First Law and Diffusivity .................. 177
5.4.2 Fick's Second Law ................................. 179
5.4.3 Solution for the Concentration Profile for
Diffusion from a Flat Plate into a Quiescent
Fluid ............................................. 180
5.4.4 Definition of the Solute Flux ..................... 181
5.4.5 Definition of the Mass Transfer Coefficient ....... 181
5.4.6 Mass Transfer in Laminar Boundary Layer Flow
over a Flat Plate ................................. 184
5.4.7 Mass Transfer from the Walls of a Tube
Containing a Fluid in Laminar Flow ................ 189
5.4.8 Mass Transfer Coefficient Correlations ............ 194
5.5 Solute Transport by Capillary Filtration ................. 198
5.6 Solute Diffusion within Heterogeneous Media .............. 203
5.6.1 Diffusion of a Solute from a Polymeric Material ... 208
5.6.1.1 A Solution Valid for Short Contact
Times .................................... 211
5.6.2 Diffusion in Blood and Tissue ..................... 213
5.7 Solute Permeability ...................................... 215
5.8 Irreversible Thermodynamics of Membrane Transport ........ 217
5.8.1 Finding Lp, Pm, and σ ............................. 219
5.8.2 Multicomponent Membrane Transport ................. 220
5.9 Transport of Solutes across the Capillary Wall ........... 221
5.10 Transport of a Solute between a Capillary and the
Surrounding Tissue Space ................................. 225
5.10.1 The Krogh Tissue Cylinder ......................... 225
5.10.2 A Model of the Krogh Tissue Cylinder .............. 226
5.10.2.1 Comparison of Convection and Diffusion
Effects .................................. 231
5.10.3 The Renkin-Crone Equation ......................... 231
5.10.3.1 Determining the Value of PmS ............. 232
5.10.4 Solute Transport in Vascular Beds, the Well-
Mixed Assumption .................................. 234
Problems ................................................. 236
Chapter 6 Oxygen Transport cansport in Biological
Systems ....................................................... 245
6.1 Diffusion of Oxygen in Multicellular Systems ............. 245
6.2 Hemoglobin ............................................... 245
6.3 Oxygen-Hemoglobin Dissociation Curve ..................... 247
6.4 Oxygen Levels in Blood ................................... 247
6.5 The Hill Equation ........................................ 248
6.6 Other Factors That Can Affect the Oxygen Dissociation
Curve .................................................... 250
6.7 Tissue Oxygenation ....................................... 250
6.8 Oxygen Transport in Bioartificial Organs and Tissue-
Engineered Constructs .................................... 255
6.9 Steady State Oxygen Transport in a Perfusion Bioreactor .. 261
6.10 Oxygen Transport in the Krogh Tissue Cylinder ............ 265
6.11 Approximate Solution for Oxygen Transport in the Krogh
Tissue Cylinder .......................................... 268
6.12 Artificial Blood ......................................... 272
Problems ...................................................... 276
Chapter 7 Pharmacokinetic Analysis ........................... 281
7.1 Terminology .............................................. 281
7.2 Entry Routes for Drugs ................................... 281
7.3 Modeling Approaches ...................................... 283
7.4 Factors Affecting Drug Distribution ...................... 284
7.4.1 Drug Distribution Volumes ......................... 284
7.4.2 Drug Metabolism ................................... 288
7.4.3 Renal Excretion of the Drug ....................... 289
7.5 Drug Clearance ........................................... 290
7.5.1 Renal Clearance ................................... 290
7.5.2 Plasma Clearance .................................. 292
7.5.3 Biological Half-Life .............................. 293
7.6 Model for Intravenous Injection of Drug .................. 293
7.7 Accumulation of Drug in the Urine ........................ 294
7.8 Constant Infusion of Drug ................................ 295
7.8.1 Application to Controlled Release of Drugs by
Osmotic Pumps ..................................... 297
7.8.2 Application to the Transdermal Delivery of Drugs .. 299
7.8.2.1 Predicting the Permeability of Skin ...... 301
7.9 First Order Drug Absorption and Elimination .............. 302
7.10 Two Compartment Model .................................... 306
7.10.1 Two Compartment Model for an Intravenous
Injection ......................................... 306
7.10.2 Two Compartment Model for First Order Absorption .. 310
Problems ...................................................... 312
Chapter 8 Extracorporeal Devices ............................. 319
8.1 Applications ............................................. 319
8.2 Contacting Schemes ....................................... 319
8.3 Membrane Solute Transport ................................ 321
8.4 Estimating the Mass Transfer Coefficients ................ 322
8.5 Estimating the Solute Diffusivity in Blood ............... 323
8.6 Hemodialysis ............................................. 325
8.6.1 Background ........................................ 325
8.6.2 Dialysate Composition ............................. 326
8.6.3 Role of Ultrafiltration ........................... 326
8.6.4 Clearance and Dialysance .......................... 328
8.6.5 Solute Transfer ................................... 329
8.6.6 Single Compartment Model of Urea Dialysis ......... 332
8.6.7 Peritoneal Dialysis ............................... 332
8.6.8 Aquapheresis ...................................... 335
8.7 Blood Oxygenators ........................................ 336
8.7.1 Background ........................................ 336
8.7.2 Operating Characteristics of Blood Oxygenators .... 336
8.7.3 Types of Oxygenators .............................. 338
8.7.4 Analysis of a Membrane Oxygenator, Oxygen
Transfer .......................................... 339
8.7.5 Analysis of a Membrane Oxygenator, Carbon
Dioxide Transfer .................................. 343
8.7.6 Example Calculations for Membrane Oxygenators ..... 346
8.8 Immobilized Enzyme Reactors .............................. 347
8.8.1 Background ........................................ 347
8.8.2 Examples of Medical Application of Immobilized
Enzymes ........................................... 347
8.8.3 Enzyme Reaction Kinetics .......................... 349
8.8.4 Reaction and Diffusion in Immobilized Enzyme
Systems ........................................... 352
8.8.5 Solving the Immobilized Enzyme Reaction-
Diffusion Model ................................... 354
8.8.6 Special Case of a First Order Reaction ............ 355
8.8.7 Observed Reaction Rate ............................ 356
8.8.8 External Mass Transfer Resistance ................. 356
8.8.9 Reactor Design Equations .......................... 357
8.8.9.1 Packed Bed Reactor ....................... 357
8.8.9.2 Well-Mixed Reactor ....................... 358
8.9 Affinity Adsorption ................................. 361
Problems ................................................. 365
Chapter 9 Tissue Engineering ................................. 369
9.1 Introduction ............................................. 369
9.2 Cell Transplantation ..................................... 369
9.3 Extracellular Matrix ..................................... 372
9.3.1 Glycosaminoglycans ................................ 373
9.3.2 Collagens ......................................... 374
9.3.3 Elastin ........................................... 374
9.3.4 Fibronectin ....................................... 374
9.3.5 Basement Membrane ................................. 374
9.4 Cellular Interactions .................................... 375
9.4.1 Cadherins ......................................... 376
9.4.2 Selectins ......................................... 376
9.4.3 Cell Adhesion Molecules ........................... 376
9.4.4 Integrins ......................................... 376
9.4.5 Cytokines and Growth Factors ...................... 377
9.5 Polymeric Support Structures ............................. 378
9.6 Biocompatibility and Initial Response to an Implant ...... 382
9.7 Tissue Ingrowth in Porous Polymeric Structures ........... 383
9.8 Measuring Blood Flow within Scaffolds Used for Tissue
Engineering .............................................. 386
9.9 Cell Transplantation into Polymeric Support Structures ... 387
9.10 Bioreactor Design for Tissue Engineering ................. 389
Problems ................................................. 392
Chapter 10 Bioartificial Organs ............................... 395
10.1 Background ............................................... 395
10.2 Some Immunology .......................................... 395
10.2.1 В Lymphocytes ..................................... 396
10.2.2 Antibodies ........................................ 396
10.2.3 T Lymphocytes ..................................... 398
10.2.4 Interaction between APCs, В Cells, and T Cells .... 399
10.2.5 Immune System and Transplanted Cells .............. 400
10.3 Immunoisolation .......................................... 401
10.4 Permeability of Immunoisolation Membranes ................ 403
10.5 Membrane Sherwood Number ................................. 406
10.6 Examples of Bioartificial Organs ......................... 406
10.6.1 Bioartificial Pancreas ............................ 407
10.6.1.1 Bioartificial Pancreas Approaches ........ 408
10.6.1.2 Intravascular Devices .................... 409
10.6.1.3 Microencapsulation ....................... 411
10.6.1.4 Macroencapsulation ....................... 413
10.6.1.5 Organoid ................................. 415
10.6.2 Number of Islets Needed ........................... 415
10.6.3 Islet Insulin Release Model ....................... 416
10.6.4 Pharmacokinetic Modeling of Glucose and
Insulin Interactions .............................. 418
10.6.5 Using the Pharmacokinetic Model to Evaluate
the Performance of a Bioartificial Pancreas ....... 421
10.7 Bioartificial Liver ...................................... 424
10.7.1 Artificial Liver Systems .......................... 425
10.7.2 Bioartificial Livers .............................. 426
10.7.3 Examples of Extracorporeal Bioartificial Livers ... 427
10.8 The Bioartificial Kidney ................................. 431
10.9 Design Considerations for Bioartificial Organs ........... 434
Problems ................................................. 435
References .................................................... 437
Index ......................................................... 451
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