530
Index
Diencephalon, 10, 457, 463–466
Differential expansion, 406
Differential growth hypothesis, 449,
479
Dipodial branching, 487, 488
Direct notation, 20, 35, 41, 42, 47
Displacement gradient tensor, 75
Dissipation inequality, 128
Divergence, 45–47
Divergence theorem, 47
DM, see Dorsal mesocardium (DM)
DMB, see Diencephalon-midbrain boundary
(DMB)
Dorsal mesocardium (DM), 444, 448, 449,
451–453
Dot product, 25–27, 29, 33, 48
Double-dot product, 26
Drosophila (fruit fly)
computational models, 434
ventral furrow, 434
Drosophila embryo, 404, 490, 492
Dummy index, 21
Dyad, 25
Dyadic analysis, 47, 103
Dyadics, 25–27
E
ECM, see Extracellular matrix (ECM)
eCSF, see Embryonic cerebrospinal fluid
(eCSF)
Ectoderm, 9, 10, 403, 430, 434, 435, 437–441,
443, 455–460
Eigenvectors, 31–33
Elastance, 234
Elastic deformation, 401, 408, 420
Elastic foundation, 468, 476–477, 480, 486,
488, 506
Elastic solids, 51
Elastic strain, 305, 372, 411
Elastic stretch ratio, 356
Elastin, 7
Elementary beam theory, 409
Embryonic cerebrospinal fluid (eCSF), 459,
463, 466–468
Embryonic development, 2, 195
Embryonic epithelial cell, 403
End-diastolic pressure-volume relationship
(EDPVR), 235
End-diastolic volume (EDV), 308, 309
Endocardial cushions, 455
Endocardium, 10
Endochondral ossification, 12
Endoderm, 8
End-systolic pressure-volume relationship
(ESPVR), 235, 245
Energy balance
material form, 124–125
mechanical power, 118
1D, 119–121
spatial form, 121–124
spring-mass system, 117, 118
stress power, 125–126
thermomechanical system, 117
total kinetic energy, 117
Entropy
inequality, 126–129
irreversible process, 127
1D, 127–128
principle, 127
production, 127
reversible process, 127
3D, 128–129
Entropy input, 127
Epithelial cells, 8
Epithelial-mesenchymal transition, 403, 404
Epithelial morphogenesis (cell sheets)
bending, 406
stretching, 403–405
structure, 403
Equilibrium equation, 118, 151
Eukaryotic cells, 6
Eulerian (spatial) coordinates, 56
Eulerian stretch rate, 91
Extracellular matrix (ECM), 7, 403, 437, 444,
459, 460, 463, 503
Eye, 188, 330, 455
See also Eye development
Eye development
lens vesicle, 458, 461–463
optic cup, 457, 459–461
optic vesicle, 457–459
F
Fiber orientation changes, cyclic stretch,
387–393
Fiber volume changes
degradation-rate coefficient, 347
production and degradation, 347
survival function, 348
volume-production rate, 347
Finite-element models, 407, 419, 426,
434–436, 439, 449, 451, 455, 456,
458–464, 481–484, 486, 488, 489
First Piola-Kirchhoff stress, 94, 95, 98, 101,
102, 125, 132, 171–173
Flexural rigidity, 412, 415
Forebrain, 10, 457, 463–468
Index
Diencephalon, 10, 457, 463–466
Differential expansion, 406
Differential growth hypothesis, 449,
479
Dipodial branching, 487, 488
Direct notation, 20, 35, 41, 42, 47
Displacement gradient tensor, 75
Dissipation inequality, 128
Divergence, 45–47
Divergence theorem, 47
DM, see Dorsal mesocardium (DM)
DMB, see Diencephalon-midbrain boundary
(DMB)
Dorsal mesocardium (DM), 444, 448, 449,
451–453
Dot product, 25–27, 29, 33, 48
Double-dot product, 26
Drosophila (fruit fly)
computational models, 434
ventral furrow, 434
Drosophila embryo, 404, 490, 492
Dummy index, 21
Dyad, 25
Dyadic analysis, 47, 103
Dyadics, 25–27
E
ECM, see Extracellular matrix (ECM)
eCSF, see Embryonic cerebrospinal fluid
(eCSF)
Ectoderm, 9, 10, 403, 430, 434, 435, 437–441,
443, 455–460
Eigenvectors, 31–33
Elastance, 234
Elastic deformation, 401, 408, 420
Elastic foundation, 468, 476–477, 480, 486,
488, 506
Elastic solids, 51
Elastic strain, 305, 372, 411
Elastic stretch ratio, 356
Elastin, 7
Elementary beam theory, 409
Embryonic cerebrospinal fluid (eCSF), 459,
463, 466–468
Embryonic development, 2, 195
Embryonic epithelial cell, 403
End-diastolic pressure-volume relationship
(EDPVR), 235
End-diastolic volume (EDV), 308, 309
Endocardial cushions, 455
Endocardium, 10
Endochondral ossification, 12
Endoderm, 8
End-systolic pressure-volume relationship
(ESPVR), 235, 245
Energy balance
material form, 124–125
mechanical power, 118
1D, 119–121
spatial form, 121–124
spring-mass system, 117, 118
stress power, 125–126
thermomechanical system, 117
total kinetic energy, 117
Entropy
inequality, 126–129
irreversible process, 127
1D, 127–128
principle, 127
production, 127
reversible process, 127
3D, 128–129
Entropy input, 127
Epithelial cells, 8
Epithelial-mesenchymal transition, 403, 404
Epithelial morphogenesis (cell sheets)
bending, 406
stretching, 403–405
structure, 403
Equilibrium equation, 118, 151
Eukaryotic cells, 6
Eulerian (spatial) coordinates, 56
Eulerian stretch rate, 91
Extracellular matrix (ECM), 7, 403, 437, 444,
459, 460, 463, 503
Eye, 188, 330, 455
See also Eye development
Eye development
lens vesicle, 458, 461–463
optic cup, 457, 459–461
optic vesicle, 457–459
F
Fiber orientation changes, cyclic stretch,
387–393
Fiber volume changes
degradation-rate coefficient, 347
production and degradation, 347
survival function, 348
volume-production rate, 347
Finite-element models, 407, 419, 426,
434–436, 439, 449, 451, 455, 456,
458–464, 481–484, 486, 488, 489
First Piola-Kirchhoff stress, 94, 95, 98, 101,
102, 125, 132, 171–173
Flexural rigidity, 412, 415
Forebrain, 10, 457, 463–468