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Index

Acceleration Cartesians 336, 338 Convective 337 Cylindricals 339 Local 337 Sphericals 340

Actin 437 Adventitia 121, 305 Aneurysms 124, 132, 305, 571 Angiogenesis 119 Angiography 119 Angioplasty

Balloon 119, 150, 444, 615 Neuroangioplasty 293

Angular velocity 341 Anisotropy 90 Anticlastic bending 228 Apoptosis 16 Arterial grafts 444, 502 Artery 304, 309 Atherosclerosis 305, 444 Atomic force microscope 116, 236,

276

Beams Curved 268 Deflections 227 Shearibending moment diagrams

203 Straight 203-245 Stresses in 211-218

Bernoulli equation 396, 403

Bessel functions 470 Biaxial experiments 287,560 Bifurcations 515 Bingham plastics 362 Biomechanics

Definition 3, 612 Father of 3 Scope of 3, 5-8

Bioreactor 130,453,484 Blood

Cells 360 Clotting 359 Constituents 359-361 Constitutive relation 358 Viscosity 357

Body force 383 Bone

Cancellous 95 Cortical 95 Mechanobiology 154 Properties 95 Structure 94, 156

Boundary conditions Cantilever support 30, 229 Free-end 229 Free-surface 441,480 No-slip 352,431 Simple-support 229

Boundary layers 546 Buckingham Pi Theorem

519 Bulk modulus 99 Buoyant force 391

625

626 Index

Cable 30 Cardiac cycle 466 Cardiopulmonary resuscitation 268 Cartesian coordinates

Acceleration 338 Deformation gradient 272 Equilibrium 106 Hooke's Law 87 Navier-Poisson 353 Navier-Stokes 387 Vorticity 344 Shear rates 348 Strain 70

Cartilage 365, 602 . Catheters 293, 483, 486, 509 Cell

Cytoskeleton 12 ~echanics 23,115,275,613 Structure 11, 236

Cell types Blood cells 360 Endotheliel cells 427, 436 Fibroblasts 22 Platelets 357, 361

Centroids 142-147 Chordae tendineae 86,110,114 Continuum mechanics 8--11,16,24,

26 Collagen 17-19 Columns 202, 245-254 Conservation of ~ass 379,400,498 Linear momentum 379,499 Energy 379,499

Constitutive relations Bone 96 General formulation 25, 81, 351 Fung exponential 279, 285, 291 Hooke's law 87,91 ~ooney-Rivlin 328 Navier-Poisson equation 353 Neo-Hookean 298 Newtonian 351 non-Newtonian 473

Coanda effect 548 Control volume 495 Coordinate systems 28, 48, 52, 54, 72 CPR 269 Couette flow 351, 440

Couple 28 Creep 584 Curl 344 Curvatures 124, 297 Cylindrical coordinates 54

Acceleration 339 Deformation gradient 310 Equilibrium 107 Hooke's law 92 Navier-Stokes 388 Vorticity 345 Shear rates 349 Strain 72 Stress components 54-55

Cytochalasin B 437

Darcy's law 563 Deformation gradient 271,310 DEICE 25, 82, 90, 290, 351 Del operator

Cartesian 337, 370 Cylindrical 372 Spherical 375

Delamination 96 Denude 506 Design

Optimal biological 513-518 Transducer 189

Determinant 324 Diagrams

Bending 203-211 Control volume 495 Free-body 29 Shear force 203-211

Differential equations 419-421 Diffusion 493 Dilatant fluid 356, 358 Displacement 67 Displacement gradient 69-70 Divergence

Of a vector 370, 375 Theorem 373-374

Ductile 200, 226 Duffing equation 567

Elastic behavior 82 Elastin 17, 20

Elastohydrodynamics 601 Elastodynamics 571-580 Endothelial Cells 7,22,427,436 Endothelin 427 Energy equation

Differential equation 545 Pipe-flow equation 531

Entrance length 433, 546 Equilibrium 29,105 Eulerian description 338 Euler's equation 392 Experimental

Designs 188,239,287,460,518 Needs 119 Set-ups 102,411,507,538

Extracellular matrix 16-22 Eye 132,301-303

Failure (material) 45, 244 Fatigue 244 Fibroblasts 22 Finite elements 166 First law of thermodynamics 379,499,

528,543,601 Flexure formula 216 Flow

1-D, 2-D, 3-D 341 Creeping 389 Secondary 405 Separation 405 uni-directional 341 uniform 546

Fluid 331 Fourier series 466, 573 Fracture toughness 187 Free-body diagram 29 Free surface 441, 480 Friction

Belt 34-36 Coefficient of 34, 597 Factor (fluids) 532-535 Static 33

Fully developed flow 433

Gradient Del operator 372

Green strain 70

Index 627

Growth and remodeling 613-614 Growth factors 16, 22

Haversian canals 156 Heart 120, 170 Heat equation 545 Hematocrit 358 Hemodynamics 359 Hemoglobin 360 Homogeneous behavior 83 Hooke's law 87-92 Hoop stress 121 Hydraulic accumulator 549 Hydrodynamic lubrication 597 Hydrostatic pressure 306, 333, 355, 393 Hypertension 605,614 Hysteresis 83

Ideal fluid 389, 396, 535 Identity matrix 272 Incompressibility 88, 306 Incompressible flow 346, 382 Induction 25 Initial condition 419 Integrins 15 Intermediate filaments 13 Interpolation 75, 289 Invariants 97,286 Inverse of a matrix 283, 323 Inviscid fluid 355, 389 Irrotational flow 345, 395 Isotropy 84

Jacobian 323

Kinematic constraint 244 Kinetic energy 528 Kinetic energy coefficient 530 Knee 365, 597

Lagrangian description 336 Lame constants 99 Laminar flow 433, 532 Laplace's equation 464

628 Index

Laser tweezers 116 Least squares 292 Length

Entrance 434, 448 Scale 520

Lifelong learning 617 Linear momentum balance 379 Losses

Major (viscous) 531 Minor (geometric) 532 Tabulated values 534

Lubrication theory 597-602 Lungs

Basic anatomy 492-495 Pulmonary dimensions 478 Sheet flow in 525

Mach m.~mber 550 Macrophages 22 Manometer 412-414 Mass

Balance 379, 400 Density 334, 380 Scales 520

Matrix operations 321-324 Mechanobiology 4, 557 Mechanotransduction 22-24, 81, 604 Media 121, 305 Membranes

Biaxial stretching 287 Definition 287 Constitutive behavior 291 Inflation 297 Instability of 295-301

Metals 83, 97 Method of pins 37 Microgravity 453 Microscopy

Atomic force 116, 236-239, 276 Electron 170, 463 Light 235, 309

Mixture theory 583, 602 Modulus

Loss 594,610 Shear 88 Storage 594, 610 Young's 87

Mohr's circle 67

Molecular mechanics 116-118 Moment-curvature relation 215 Moment due to force 27 Moments of area

First 142-147 Second 194-197 Polar 175, 196

Mullin's effect 294 Muscle 14 Myocardium 84, 190

Navier-Poisson relations 353 Navier-Space equation 109 Navier-Stokes equation

Cartesians 387, 417 Cylindricals 388,418 Sphericals 574 Worksheets 417-418

Neuroangioplasty 293 Neutral axis 216 Newtonian fluid 353 Nitric oxide 427 Nondimensionalization 541 Non-Newtonian fluid 356,473 No-slip condition 352,431,455,462,

489

Optical tweezers 116 Orthostatic intolerance 453 Orthotropy 91 Osteoporosis 116

Papillary muscle 189-193 Parallel axis theorem 254-260 Parallel-plate flow 428 Pascal 424, 438, 461, 478 Pathline 392 Pericardium 202, 559 Permeability 559,567,603 Phase plane 570 Pitot tube 413 Plasma 357-359 Plasticity 85 Platelets 357, 361 Poise 358,461,478 Poiseuille flow 431,450

Poisson's ratio 87,89 (poly)methylmethacrylate 171,187,

604 Power 513 Power-law fluid 473 Preconditioning 279 Pressure

Absolute 390,412 Drop 485 Dynamic 451 Gauge 390, 443 Hydrostatic 306, 333 Stagnation 413

Principal values Strain 76 Stress 62-66

Prosthesis (hip) 165, 184 Proteoglycans 17,21 Pseudoelasticity 83, 278 Pseudoplastic 356 Pulley 33 Pulsatile flow 465-473

Rate-of-deformation 346-349 Receptors (cell surface) 12 Relaxation

Function 589 Spectrum 609 Stress 585

Residual stress 303-315 Resultants 209 Retardation spectrum 609 Reynolds' number 436,452,524 Rheopectic 359 Rheology 361 Right-hand rule 172 Rigid-body motion 74 Rod 202 Rotations 73-74,274,341-345 Rouleaux 357 Rubber 83, 299-301

Serum 359 Scales for nondimensionalization 520 Shaft 202 Shear modulus 88, 99 Shear-rates 348-350

Sheet flow in lungs 525 Sickle cell 363

Index 629

Sign convention 49, 55, 204, 435, 447 Skin friction 451 Smooth muscle cells 316

Constitutive behavior 317 Specific gravity 402, 422 Specific weight 402 Spherical coordinates

Acceleration 340 Divergence 375 Equilibrium 107 Navier-Stokes 575 Shear-rates 349 Strain 72 Stress components 54-55 Vorticity 345

Stability Beams 248-254 Dynamic 568 General 246-248 Inflated membranes 293-301,

571-582 Statically indeterminate 167, 184, 242 Statics 29-39 Stenosis 339 Stent 502 Stiffness 279 Streamline 392 Steady flow 337 Strain

Gauges 78-80 Green 70 Infinitesimal (or small) 71,74 Microstrain 88, 198 Plane 93 Principal 76-78 Shear 74 Transformations 76-77

St. Venant's principle 111 Strain energy 100, 285 Stress

Cauchy 47-50, 115, 148 Concentration 227 First Piola-Kirchhoff 115, 148,

283 Hydrostatic 66 Plane 93 Principal 62-66

630 Index

Relaxation 585 Residual 121, 307 Second Piola-Kirchhoff 285 States of 54 Transformations 56--60 Yield 201

Superposition 239 Surface force 283 Surface tension 552, 607 Synovial fluid 359,363 System 495

Taylor series 104 Temperature

First law of thermodynamics 543-545

Viscosity dependence on 478 Tension 291 Theory 80-81,399,411 Thixotropic 359 Time, scales 520 TIssue engineering 121, 129, 444 Torsion 169-194 Transducer design

AFM 235 Load cells 262 Torque cells 189

Trace 569 Thansformations (see strain and stress) Transpose 322 Transverse isotropy 91 Tribology 582 Trigonometric identies 58 Truss 36-37 Turbulent flow 404, 433

Uniform flow 546 Uniform stress 112 Universal solutions 114,118,123,128,

134

Vasospasm 293 Vectors

Curl 369 Divergence 369

Scalar product 368 Vector product 369

Vein grafts 119, 445, 557 Velocity 335 Velocity gradients 349 Ventricular-assist device 405 Viscoelasticity

Boltzmann model 592 Burger model 609 Characteristic behaviors 583 Kelvin-Voigt model 588-590 Maxwell model 586-588 Quasilinear model 596 Standard model 590-592

Vinculin 437 Viscometer

Cone-and-plate 366 Concentric cylinder 458-462 Descent of a sphere 458 Parallel plate 366, 368

Viscosity Absolute 11, 352, 539 Apparent 362, 473 Kinematic 539 of blood 357 of plasma 359 of water 359

Vorticity Cartesian 344 Cylindrical 345 Spherical 345

Volume 89 Volumetric flow 400

Wall shear stress 367,435,451,460 Work 528-531 Working 530 Worksheets 417-418 Womersley's number 472

Yield criterion 201 Yield stress 85, 201 Young's modulus 87

Zero-stress state 307

About the Authors

Jay D. Humphrey is a Professor of Biomedical Engineering and a Fellow of the M.E. DeBakey Institute at Texas A&M University. He received the B.S. degree from Virginia Tech and the M.S. and Ph.D. degrees from The Georgia Institute of Technology, all in Engineering Science and Mechanics, and he completed a postdoctoral fellowship in Cardiovascular Research at Johns Hopkins University. Professor Humphrey has authored a graduate textbook entitled Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, coedited a book entitled Cardiovascular Soft Tissue Biomechanics, and published over 100 journal articles and book chapters. He is Co-Editor of the international journal Biomechanics and Modeling in Mechanobiol­ogy and Fellow of the American Institute for Medical and Biological Engineering.

Sherry L. Delange is a recent graduate of Texas A&M University. An honors student, she received her B.S. degree in 2000 and her M.S. degree in 2002, both in Biomedical Engineering. Her M.S. thesis focused on the biomechanics of the lens capsule, the membrane that invests the lens of the eye and is vital to accommodation. She was the first to measure the multi­axial mechanical properties of the lens capsule and the first to show regional differences in vitro in the multiaxial finite strains.

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