Computer Modeling in Bioengineering: Theoretical Background, Examples and Software

Computer Modeling in Bioengineering......Page 4
Contents......Page 10
Contributors......Page 18
Preface......Page 20
Part I Theoretical Background of Computational Methods......Page 24
1.1 Matrix representation of mathematical objects......Page 26
1.2 Basic relations in matrix algebra......Page 27
1.3 Definition of tensors and some basic tensorial relations......Page 29
1.4 Vector and tensor differential operations and integral theorems......Page 31
1.5 Examples......Page 34
2.1.1 Stress......Page 38
2.1.2 Strain and strain rate......Page 42
2.1.3 Examples......Page 44
2.2.1 Linear elastic constitutive law......Page 49
2.2.2 Viscoelasticity......Page 52
2.2.4 Examples......Page 53
2.3.1 Formulation of the principle of virtual work......Page 60
2.3.2 Examples......Page 61
2.4 Nonlinear continuum mechanics......Page 63
2.4.1 Deformation gradient and the measures of strain and stress......Page 64
2.4.2 Nonlinear elastic constitutive relations......Page 68
2.4.3 Examples......Page 70
3.1 Heat conduction......Page 74
3.1.1 Governing relations......Page 75
3.1.2 Examples......Page 76
3.2.1 Differential equations of diffusion......Page 78
3.2.2 Examples......Page 80
3.3 Fluid flow of incompressible viscous fluid with heat and mass transfer......Page 81
3.3.1 Governing equations of fluid flow and of heat and mass transfer......Page 82
3.3.2 Examples......Page 83
3.4 Fluid flow through porous deformable media......Page 86
3.4.1 The governing equations......Page 87
3.4.2 Examples......Page 89
Part II Fundamentals of Computational Methods......Page 92
4.1 Introduction to the finite element method......Page 94
4.2.1 Truss finite element......Page 96
4.2.2 Equilibrium equations of the FE assemblage and boundary conditions......Page 101
4.2.3 Examples......Page 103
4.3.1 Element formulation......Page 104
4.3.2 Examples......Page 107
4.4 Two-dimensional (2D) isoparametric finite elements......Page 108
4.4.1 Formulation of the elements......Page 109
4.4.2 Examples......Page 112
4.5 Isoparametric shell finite element for general 3D analysis......Page 114
4.5.1 Basic assumptions about shell deformation......Page 115
4.5.2 Formulation of a four-node shell element......Page 117
4.5.3 Examples......Page 118
5.1 Introduction to dynamics of structures......Page 122
5.2 Differential equations of motion......Page 123
5.3 Integration of differential equations of motion......Page 124
5.4 System frequencies and modal shapes......Page 126
5.5 Examples......Page 127
6.1 Introduction......Page 132
6.2.1 Discrete system......Page 136
6.2.2 Principle of virtual work for a continuum......Page 137
6.2.3 Finite element model......Page 138
6.2.4 Finite element model with logarithmic strains......Page 140
6.3 Examples......Page 141
7.1 Introduction......Page 144
7.1.2 The Galerkin method......Page 145
7.2.1 The finite element equations......Page 147
7.2.2 Examples......Page 148
7.3.1 The finite element equations......Page 150
7.3.2 Examples......Page 151
7.4.1 The finite element equations......Page 152
7.4.2 Examples......Page 156
7.5.1 The ALE formulation......Page 158
7.5.2 Examples......Page 161
7.6 Solid–fluid interaction......Page 162
7.6.1 Loose coupling method......Page 163
7.6.2 Examples......Page 164
7.7.1 Finite element balance equations......Page 166
7.7.2 Examples......Page 168
8.1.1 Introduction......Page 170
8.1.2 Differential equations of motion and boundary conditions......Page 171
8.1.3 Examples......Page 173
8.2.1 Introduction to mesoscale DPD modeling......Page 174
8.2.2 Basic DPD equations......Page 175
8.2.3 Examples......Page 177
8.3.1 Introduction to multiscale modeling......Page 178
8.3.2 Basic equations and boundary conditions......Page 179
8.3.3 Examples......Page 183
8.4.2 The basic equations of the SPH method......Page 184
8.5.1 Introduction......Page 187
8.5.2 Formulation of the EFG method......Page 188
8.5.3 Examples......Page 191
Part III Computational Methods in Bioengineering......Page 194
9.1 The subject and scope of bioengineering......Page 196
9.2.1 Computational models......Page 198
9.2.2 Future advances in computer modeling......Page 200
10.1.1 The structure of bone tissue......Page 204
10.1.2 The form of bones......Page 206
10.1.3 Osteoporosis and bone density......Page 207
10.2 The mechanical properties of bone and FE modeling......Page 208
10.3.1 General considerations......Page 210
10.3.2 Fracture treatment......Page 211
10.3.3 FE modeling of femur comminuted fracture......Page 213
10.4.1 Solutions by parallel screws and by dynamic hip implant......Page 217
10.4.2 Finite element models of intracapsular fractures of the femoral neck......Page 218
11.1.1 Structure and function of biological tissue......Page 224
11.1.2 Basic experiments and mechanical models......Page 226
11.2.1 General concept of computational procedures......Page 230
11.2.2 Biaxial models of membranes, hardening and hysteretic behavior, action of surfactant......Page 232
11.2.3 Use of strain energy functions......Page 238
11.3 Examples......Page 240
12.1.1 Basic physiology of muscle mechanics......Page 250
12.1.2 Basics of muscle finite element modeling......Page 254
12.2.1 Hill’s phenomenological model......Page 257
12.2.2 Determination of stresses within muscle fiber......Page 258
12.2.3 Hill’s model which includes fatigue......Page 262
12.2.4 An extension of Hill’s model to include different fiber types......Page 265
12.3 Examples......Page 268
13.1.1 The circulatory system......Page 272
13.1.2 Blood......Page 274
13.1.3 Blood vessels......Page 278
13.2.1 Introduction......Page 279
13.2.2 Methods of blood flow modeling in large blood vessels......Page 280
13.2.3 Modeling the deformation of blood vessels......Page 283
13.2.4 Blood–blood vessel interaction......Page 284
13.3.1 Introduction......Page 285
13.3.2 Finite element model of the aorta......Page 286
13.3.3 Results and discussion......Page 287
13.4.1 Introduction......Page 288
13.4.2 Modeling of blood flow within the AAA......Page 290
13.4.3 Results......Page 291
13.5.1 Introduction......Page 293
13.5.2 Finite element model of the carotid artery bifurcation......Page 294
13.5.3 Example solutions......Page 296
13.6.1 Femoral artery anatomical and physiological considerations and endovascular solutions......Page 299
13.6.2 Analysis of the combined effects of the surrounding muscle tissue and inner blood pressure to the arterial wall with implanted stent......Page 301
13.7.1 Introduction......Page 305
13.7.2 Modeling blood flow through the veins......Page 306
13.8.1 Description of heart functioning......Page 309
13.8.2 Computational model......Page 312
14.1 Introduction......Page 318
14.2.1 The basic relations for mass transport in arteries......Page 320
14.2.2 Finite element modeling of diffusion–transport equations......Page 321
14.2.3 Examples......Page 322
14.3.1 Model description......Page 325
14.3.2 Examples......Page 327
14.4.1 General considerations......Page 329
14.4.2 Examples......Page 331
15.1 Introduction......Page 336
15.2.1 Basic physical quantities, swelling pressure and electrokinetic coupling......Page 339
15.2.2 Equations of balance......Page 341
15.3.1 Finite element balance equations......Page 343
15.4 Examples......Page 345
16.1 Introduction to mechanics of cells......Page 354
16.2.1 Stabilizing influence of CSK prestress – cellular tensegrity model......Page 357
16.2.2 Mathematical model of a six-strut tensegrity structure......Page 359
16.2.3 Biphasic models......Page 362
16.3 Examples: modeling of cell in various mechanical conditions......Page 363
17 Extracellular Mechanotransduction: Modeling Ligand Concentration Dynamics in the Lateral Intercellular Space of Compressed Airway Epithelial Cells......Page 372
17.1.1 Introduction......Page 373
17.1.2 The EGF–receptor autocrine loop in the LIS......Page 374
17.1.3 Modeling the effects of compressive stress on epithelial cells in vitro......Page 375
17.2.1 Introduction......Page 379
17.2.2 Finite element model of dynamic diffusion......Page 380
17.2.3 Exploring the parameter space of the diffusion equation......Page 382
17.3.1 Introduction......Page 385
17.3.2 Finite element model of coupled diffusion and convection......Page 386
17.3.3 Exploring the parameter space of the governing equations......Page 389
17.3.4 Rate sensitivity of extracellular mechanotransduction......Page 391
17.3.5 HB-EGF vs. TGF-alpha concentration dynamics......Page 395
17.3.6 Discussion......Page 398
18 Spider Silk: Modeling Solvent Removal during Synthetic and Nephila clavipes Fiber Spinning......Page 402
18.1.1 Introduction......Page 403
18.1.2 Numerical procedure......Page 404
18.1.3 Example......Page 409
18.2.1 Introduction......Page 411
18.2.2 Governing process during synthetic solvent removal......Page 413
18.2.3 Numerical modeling of synthetic internal solvent diffusion......Page 415
18.2.4 Example: Synthetic fiber spinning......Page 417
18.3.1 Introduction......Page 420
18.3.2 Nephila water diffusion coefficient......Page 421
18.3.3 Modeling of internal water diffusion......Page 423
18.3.4 Example: The Nephila spinning canal......Page 425
19.1 Introduction......Page 430
19.2 The transport of particulates in capillaries......Page 432
19.3 The mathematical model......Page 437
19.3.1 The governing equations......Page 438
19.3.2 The initial and boundary conditions......Page 439
19.3.3 Solution for K0 and f0......Page 440
19.3.4 Solution for K1 and f1......Page 441
19.3.5 Solution for K2......Page 442
19.3.6 The velocity distribution (effect of boundary depletion of the solvent)......Page 443
19.4 The concentration profile......Page 445
19.4.1 The mean dimensionless concentration m......Page 446
19.4.2 The local dimensionless concentration ......Page 447
19.5 Comments and discussions of the analytical models and solutions......Page 450
19.6.1 Computational procedure......Page 451
19.6.2 Example – trajectories of spherical and elliptical particles......Page 452
Index......Page 456
Plates......Page 470