Index
533
Mooney-Rivlin strain-energy density function,
137
Morphogenesis
early heart development, 440–455
early lung development, 487–490
epithelial, 402–406
gastrulation, 430–440
intestinal development, 483–487
linear theory, 409–430
mechanical regulation (see Mechanical
regulation, morphogenesis)
mechanisms, 408
mesenchymal, 500–504
neural development, 455–483
Morphogens, 8
Morphomechanical laws, 492–493, 496
Murray-Oster theory
constitutive relations, 502
equation of motion, 502
mass balance, 500–501
mixture of cells, 500
pattern forming mechanism, 502–503
Muscle, 12
Muscle cells, 308, 309
Muscle growth laws
heart muscle, 306–309
skeletal muscle, 306–308
Myoblasts, 13
Myocardial growth, 449–450
Myocardial infarction, 232
Myocardial ischemia, 232
Myocardium, 10
Myofibrils, 210
Myogenic response/Bayliss phenomenon, 316
Myosin, 6
Myotubes, 13
N
Nanson’s formula, 90
Neo-Hookean material, 261, 417, 494
Neo-Hookean strain-energy density function,
355
Nervous tissue, 7
Neural development
cerebral cortex, folding, 478–483
early brain development, 463–469
eye development, 457–463
neural tube, 455–457
Neural plate (NP), 406, 440–442, 455
Neural tube (NT), 10, 455–457
Neurons, 11
Neurulation, 10, 11
3D models, 457
2D models, 456
Neutral equilibrium, 469, 471, 473
Nonlinear elasticity, 155
Nonlinearity
geometric, 52
material, 52
Non-muscle cells, 309
Notation
direct, 20, 35, 41, 42, 47
dyadic, 28
indicial, 20
NP, see Neural plate (NP)
NT, see Neural tube (NT)
Nucleus, 6, 15
O
OC, see Optic cup (OC)
Omphalomesenteric veins (OVs), 447, 448,
451–454
Opening angles and residual stress, 329–331,
371–378
Optic cup (OC)
finite-element model, 459–461
mechanism, 461
Optic stalk (OS), 458, 459, 461
Optic vesicles (OVs), 457–459, 464
Organelles, 6, 7, 15
Organogenesis, 9
Organs, 7
Orthogonal coordinate systems, 37, 41
Orthogonality, 47, 523, 524
Orthogonal tensor, 33–35, 48
Orthotropy, 142–143
OS, see Optic stalk (OS)
OVs, see Omphalomesenteric veins (OVs)
P
Passive and active fiber stress tensors, 241
Pattern formation, 8, 500, 503, 510
Permutation symbol, 24
Piola-Kirchhoff stress (first, second), 94, 96,
97, 102, 125, 131, 171–173, 225,
257, 259
Placode formation, 405, 461
Plate theory, 201–203, 414–415, 420
Poisson’s ratio, 407, 414, 502
Polyads, 25
Poynting effect, 174, 188
Pressure-volume (PV) loop, 233–234
Pressure-volume relationship, 235
Principal invariants, 32
Principal strains, 84–87
533
Mooney-Rivlin strain-energy density function,
137
Morphogenesis
early heart development, 440–455
early lung development, 487–490
epithelial, 402–406
gastrulation, 430–440
intestinal development, 483–487
linear theory, 409–430
mechanical regulation (see Mechanical
regulation, morphogenesis)
mechanisms, 408
mesenchymal, 500–504
neural development, 455–483
Morphogens, 8
Morphomechanical laws, 492–493, 496
Murray-Oster theory
constitutive relations, 502
equation of motion, 502
mass balance, 500–501
mixture of cells, 500
pattern forming mechanism, 502–503
Muscle, 12
Muscle cells, 308, 309
Muscle growth laws
heart muscle, 306–309
skeletal muscle, 306–308
Myoblasts, 13
Myocardial growth, 449–450
Myocardial infarction, 232
Myocardial ischemia, 232
Myocardium, 10
Myofibrils, 210
Myogenic response/Bayliss phenomenon, 316
Myosin, 6
Myotubes, 13
N
Nanson’s formula, 90
Neo-Hookean material, 261, 417, 494
Neo-Hookean strain-energy density function,
355
Nervous tissue, 7
Neural development
cerebral cortex, folding, 478–483
early brain development, 463–469
eye development, 457–463
neural tube, 455–457
Neural plate (NP), 406, 440–442, 455
Neural tube (NT), 10, 455–457
Neurons, 11
Neurulation, 10, 11
3D models, 457
2D models, 456
Neutral equilibrium, 469, 471, 473
Nonlinear elasticity, 155
Nonlinearity
geometric, 52
material, 52
Non-muscle cells, 309
Notation
direct, 20, 35, 41, 42, 47
dyadic, 28
indicial, 20
NP, see Neural plate (NP)
NT, see Neural tube (NT)
Nucleus, 6, 15
O
OC, see Optic cup (OC)
Omphalomesenteric veins (OVs), 447, 448,
451–454
Opening angles and residual stress, 329–331,
371–378
Optic cup (OC)
finite-element model, 459–461
mechanism, 461
Optic stalk (OS), 458, 459, 461
Optic vesicles (OVs), 457–459, 464
Organelles, 6, 7, 15
Organogenesis, 9
Organs, 7
Orthogonal coordinate systems, 37, 41
Orthogonality, 47, 523, 524
Orthogonal tensor, 33–35, 48
Orthotropy, 142–143
OS, see Optic stalk (OS)
OVs, see Omphalomesenteric veins (OVs)
P
Passive and active fiber stress tensors, 241
Pattern formation, 8, 500, 503, 510
Permutation symbol, 24
Piola-Kirchhoff stress (first, second), 94, 96,
97, 102, 125, 131, 171–173, 225,
257, 259
Placode formation, 405, 461
Plate theory, 201–203, 414–415, 420
Poisson’s ratio, 407, 414, 502
Polyads, 25
Poynting effect, 174, 188
Pressure-volume (PV) loop, 233–234
Pressure-volume relationship, 235
Principal invariants, 32
Principal strains, 84–87