Index
529
force-length behavior, 228
shortening velocity, 225
time-varying active modulus, 224
Contractile fiber (CF)
constitutive relation, 219, 221
contractile behavior
non-muscle cells, 220
smooth muscle, 220
tetanus, 219–220
twitch, 219–220
contractile structures, 219
cytoskeleton, 215, 218
passive and active strain-energy density
functions, 215
rule-of-mixtures, 214
shortening velocity, 220–221
stress fiber, 216
time-varying elasticity, 221–223
volume fractions, 214
Contraction
actomyosin, 209
alternative models, 232
cardiac (see Cardiac mechanics)
contractile structures, 210
cross-bridge, 209
motor proteins, 209
ratio, 211
Convergent extension, 405, 436, 441, 442, 447,
491, 493
Coordinate transformation
coefficients, 37
matrices, 38
second-order tensor, 38
Cortical folding
buckling wavelength, 482
finite-element model, 483
residual stresses, 480–481
Critical load, 471–473, 475–478
Cross-bridges, 211, 226, 232
Cross-links, 343
Cross product, 23–25
Curl, 45
Curl theorem, 47
Curvilinear coordinate system, 22, 41
Cylindrical bending, 414, 423–424,
497–498
Cylindrical polar coordinates
base vectors, 22
deformation gradient, 520
equations of motion, 520–521
vector components, 20
Cytoplasm, 6
Cytoskeleton, 6, 7, 14, 15, 403, 492
D
Deformation
deformation gradient tensor, 73–77
geometric measures
area and volume change, 88–90
deformation rate, 90–92
stretch ratio and shear, 87–88
nonlinearity, 52
principal strains, 84–87
strain tensor, 77–82
strain transformation, 83–84
tensor, 78
3D (see 3D deformation)
2D, 69–73
Deformation gradient tensor, 73–77, 87, 285,
367
Deformation rate
1D, 91
strain rates, 90
3D, 92
viscoelastic materials, 91
Developmental biology
actin, 6
blastomeres, 8
blastula, 8, 9
blood vessels, 9
bone, 12, 13
brain tube, 10, 11
cells, 6
cytoplasm, 6
cytoskeleton, 6, 7
differentiation, 8, 13
early embryonic development, 8
ECM, 7
embryos, 8
epithelial cells, 8
eukaryotic cells, 6
gastrulation, 8
gut, 12
heart, 9, 10
human brain development, 12
intermediate filaments, 7
intestinal villi, development, 12
lungs, 12, 13
mesenchyme, 8
microtubules, 6
morphogens, 8
muscle, 12–14
myosin, 6
nucleus, 6
organelles, 6, 7
organogenesis, 9
tissue, 7
types of tissue, 7
529
force-length behavior, 228
shortening velocity, 225
time-varying active modulus, 224
Contractile fiber (CF)
constitutive relation, 219, 221
contractile behavior
non-muscle cells, 220
smooth muscle, 220
tetanus, 219–220
twitch, 219–220
contractile structures, 219
cytoskeleton, 215, 218
passive and active strain-energy density
functions, 215
rule-of-mixtures, 214
shortening velocity, 220–221
stress fiber, 216
time-varying elasticity, 221–223
volume fractions, 214
Contraction
actomyosin, 209
alternative models, 232
cardiac (see Cardiac mechanics)
contractile structures, 210
cross-bridge, 209
motor proteins, 209
ratio, 211
Convergent extension, 405, 436, 441, 442, 447,
491, 493
Coordinate transformation
coefficients, 37
matrices, 38
second-order tensor, 38
Cortical folding
buckling wavelength, 482
finite-element model, 483
residual stresses, 480–481
Critical load, 471–473, 475–478
Cross-bridges, 211, 226, 232
Cross-links, 343
Cross product, 23–25
Curl, 45
Curl theorem, 47
Curvilinear coordinate system, 22, 41
Cylindrical bending, 414, 423–424,
497–498
Cylindrical polar coordinates
base vectors, 22
deformation gradient, 520
equations of motion, 520–521
vector components, 20
Cytoplasm, 6
Cytoskeleton, 6, 7, 14, 15, 403, 492
D
Deformation
deformation gradient tensor, 73–77
geometric measures
area and volume change, 88–90
deformation rate, 90–92
stretch ratio and shear, 87–88
nonlinearity, 52
principal strains, 84–87
strain tensor, 77–82
strain transformation, 83–84
tensor, 78
3D (see 3D deformation)
2D, 69–73
Deformation gradient tensor, 73–77, 87, 285,
367
Deformation rate
1D, 91
strain rates, 90
3D, 92
viscoelastic materials, 91
Developmental biology
actin, 6
blastomeres, 8
blastula, 8, 9
blood vessels, 9
bone, 12, 13
brain tube, 10, 11
cells, 6
cytoplasm, 6
cytoskeleton, 6, 7
differentiation, 8, 13
early embryonic development, 8
ECM, 7
embryos, 8
epithelial cells, 8
eukaryotic cells, 6
gastrulation, 8
gut, 12
heart, 9, 10
human brain development, 12
intermediate filaments, 7
intestinal villi, development, 12
lungs, 12, 13
mesenchyme, 8
microtubules, 6
morphogens, 8
muscle, 12–14
myosin, 6
nucleus, 6
organelles, 6, 7
organogenesis, 9
tissue, 7
types of tissue, 7