528
Index
Blastocoel, 430, 438, 498
Blastoderm, 440–443
Blastula, 8, 9, 403, 430, 434, 436, 438, 499
Body forces, 93
Bone, 12, 195
Boundary value problem in continuum
mechanics
Cartesian coordinates, 145
principal coordinates, 146–148
tensor form, 144
Brain development, 11, 12, 463–469, 490
Brain folding, 480
Brain tube (BT)
cerebral hemispheres, 467–469
mechanical feedback, 466
morphogenesis, 466
vesicles, 463–467
Brain tumor, 292–297
Branching, 487, 488
BT, see Brain tube (BT)
Buckling
bifurcation diagram, 471
elastic beam, 471–472
growing beam, 509
on elastic foundation, 476–478
growth-induced, 469
neutral equilibrium, 469
restoring force, 469
stability, rigid bar, 469–471
structural instability, 469
wavelength, 482
C
Cardiac cycle, 244
Cardiac jelly (CJ), 444, 445, 448, 449, 451,
452, 455
Cardiac looping
heart tube bending, 448–449
heart tube twisting, 451–455
myocardial growth, 449–450
OVs, 448
Cardiac mechanics
cardiac cycle, 244
constitutive relations, 240
elastance (see Time-varying elastance)
energetics, 236–237
left ventricle model, 233, 237–239
myocardium, 232
pressure-volume
loops, 233–234
relations, 245
Cauchy-Green deformation tensor, 141
Cauchy stress, 93, 96, 100, 147, 234, 264
formula, 100
tensor, 100, 115, 226, 240, 242, 502
vector, 94
Cell adhesions, 14
Cell apex, 403, 406
Cell intercalation, 404, 405, 436, 447,
491, 493
Cell nuclei, 456
Cells, 6
Cell wedging, 406, 426, 431–433, 435, 441,
442, 456, 489, 490
Cerebral cortex, 11
cortical folding, 480–483
folding mechanisms, 478–479
gyri and sulci, 478
Cerebral hemispheres
chemomechanical growth laws, 468
hypothalamus, 468
telencephalon, 467, 468
CJ, see Cardiac jelly (CJ)
Clausius-Duhem inequality, 128
Clausius-Planck inequality, 129
C-looping, 448–455
Collagen, 12
Combined growth and contraction theory,
309–315
Connective tissue, 7–9, 361–365, 500
Constitutive relations, 199
elastic solids, 130
hyperelasticity, 131–133
incompressible material, 133–134
pseudoelasticity, 131
remodeling
hereditary integrals, 353
strain-energy, 130
density function (see Strain-energy
density function)
viscoelastic behavior, 131
Constrained mixture, 214, 346, 365, 371
Contact forces, 93, 94, 97, 111
Continuity equation, 104–107
Continuum mechanics
acceleration, 56–58
boundary value problem (see Boundary
value problem in continuum
mechanics)
time rates, change, 60–66
velocity, 56–58
Contractile element (CE), 210–214
constitutive relation
active and passive strain-energy density
function, 226, 228
Index
Blastocoel, 430, 438, 498
Blastoderm, 440–443
Blastula, 8, 9, 403, 430, 434, 436, 438, 499
Body forces, 93
Bone, 12, 195
Boundary value problem in continuum
mechanics
Cartesian coordinates, 145
principal coordinates, 146–148
tensor form, 144
Brain development, 11, 12, 463–469, 490
Brain folding, 480
Brain tube (BT)
cerebral hemispheres, 467–469
mechanical feedback, 466
morphogenesis, 466
vesicles, 463–467
Brain tumor, 292–297
Branching, 487, 488
BT, see Brain tube (BT)
Buckling
bifurcation diagram, 471
elastic beam, 471–472
growing beam, 509
on elastic foundation, 476–478
growth-induced, 469
neutral equilibrium, 469
restoring force, 469
stability, rigid bar, 469–471
structural instability, 469
wavelength, 482
C
Cardiac cycle, 244
Cardiac jelly (CJ), 444, 445, 448, 449, 451,
452, 455
Cardiac looping
heart tube bending, 448–449
heart tube twisting, 451–455
myocardial growth, 449–450
OVs, 448
Cardiac mechanics
cardiac cycle, 244
constitutive relations, 240
elastance (see Time-varying elastance)
energetics, 236–237
left ventricle model, 233, 237–239
myocardium, 232
pressure-volume
loops, 233–234
relations, 245
Cauchy-Green deformation tensor, 141
Cauchy stress, 93, 96, 100, 147, 234, 264
formula, 100
tensor, 100, 115, 226, 240, 242, 502
vector, 94
Cell adhesions, 14
Cell apex, 403, 406
Cell intercalation, 404, 405, 436, 447,
491, 493
Cell nuclei, 456
Cells, 6
Cell wedging, 406, 426, 431–433, 435, 441,
442, 456, 489, 490
Cerebral cortex, 11
cortical folding, 480–483
folding mechanisms, 478–479
gyri and sulci, 478
Cerebral hemispheres
chemomechanical growth laws, 468
hypothalamus, 468
telencephalon, 467, 468
CJ, see Cardiac jelly (CJ)
Clausius-Duhem inequality, 128
Clausius-Planck inequality, 129
C-looping, 448–455
Collagen, 12
Combined growth and contraction theory,
309–315
Connective tissue, 7–9, 361–365, 500
Constitutive relations, 199
elastic solids, 130
hyperelasticity, 131–133
incompressible material, 133–134
pseudoelasticity, 131
remodeling
hereditary integrals, 353
strain-energy, 130
density function (see Strain-energy
density function)
viscoelastic behavior, 131
Constrained mixture, 214, 346, 365, 371
Contact forces, 93, 94, 97, 111
Continuity equation, 104–107
Continuum mechanics
acceleration, 56–58
boundary value problem (see Boundary
value problem in continuum
mechanics)
time rates, change, 60–66
velocity, 56–58
Contractile element (CE), 210–214
constitutive relation
active and passive strain-energy density
function, 226, 228