532
Index
Hyperelasticity, 131–133
Hyper-restoration (HR)
bars, 509
cylindrical bending, plate, 497–498
hypothesis, 491–492
sea urchin gastrulation, 498–499
Hyper-restoration (HR) hypothesis, 491–492
Hypothalamus, 463–465, 467, 468
Hysteresis loop, 131
I
Identity tensor, 31, 34, 43
Incompressible material, 133–134
Indicial notation, 20
Interkinetic nuclear migration, 406, 456
Intestinal development
chick embryo, 484
gut looping, 484–485
villus formation, 485–487
Intramembranous ossification, 12
Invagination mechanics
cell wedging, 431
Fourier series, 432
Invariants, 19, 26, 32, 33
Inverse method, 155
Inverse tensor, 31
Isotropy, 136–140, 195
K
Kinematics, 175–177, 182–183, 190–191,
196–198, 410–411
Kronecker delta, 24, 25
L
Lagrange multiplier, 134, 147, 243
Lagrangian (material) coordinates, 56
Lagrangian strain, 67, 71, 72, 103
Lagrangian strain tensor, 77–79, 81, 83, 87,
131, 239
Laplace’s law, 307, 308, 467, 468
Laplacian operator, 45
Left ventricle (LV) model, 307
myocardium, 238
thick-walled cylindrical tube, 237
Lens, 458, 459
Lens vesicle (LV), 458
apical contraction, 461
development, 461
finite-element model, 462–463
placode formation, invagination and
closure, 461
programmed cell death/apoptosis, 462
Linear growth theory
beam, 409–414
growth-strain, 416, 417
plate, 414–415
Linear momentum
1D, 109–110
principle, 109
3D
material form, 113–114
spatial form, 111–112
2D, 110–111
Linear strain tensor, 502
Looping
cardiac looping (see Cardiac looping)
gut, 484–485
Lung development
branching, 487, 488
bud formation
finite-element model, 488–489
dipodial branching, 487, 488
monopodial branching, 487
LV, see Lens vesicle (LV)
M
Mandel stress tensor, 284
Material (Lagrangian) coordinates, 56
Material nonlinearity, 52, 358
Material time derivative, 61
Mathematical modeling in biology, 3–6
Mechanical feedback, 433, 466, 467, 490, 492
See also Growth
Mechanical regulation, morphogenesis
feedback, 490
HR
hypothesis, 491–492
morphomechanical laws, 492–493
Mechanobiological instability, 302
Mechanotransduction, 14–15
Mesenchymal cells, 8, 403, 430, 455, 485,
500
Mesenchymal-epithelial transition, 403, 404
Mesenchymal morphogenesis
Murray-Oster theory, 500–503
pattern formation, 500
positional information hypothesis, 500
vasculogenesis, 503–504
Mesenchyme, 8
Mesoderm, 8, 430, 434–436, 440, 443–446
Metric, 44
Microtubules, 6
Midbrain, 10, 457, 463–466
Monopodial branching, 487
Index
Hyperelasticity, 131–133
Hyper-restoration (HR)
bars, 509
cylindrical bending, plate, 497–498
hypothesis, 491–492
sea urchin gastrulation, 498–499
Hyper-restoration (HR) hypothesis, 491–492
Hypothalamus, 463–465, 467, 468
Hysteresis loop, 131
I
Identity tensor, 31, 34, 43
Incompressible material, 133–134
Indicial notation, 20
Interkinetic nuclear migration, 406, 456
Intestinal development
chick embryo, 484
gut looping, 484–485
villus formation, 485–487
Intramembranous ossification, 12
Invagination mechanics
cell wedging, 431
Fourier series, 432
Invariants, 19, 26, 32, 33
Inverse method, 155
Inverse tensor, 31
Isotropy, 136–140, 195
K
Kinematics, 175–177, 182–183, 190–191,
196–198, 410–411
Kronecker delta, 24, 25
L
Lagrange multiplier, 134, 147, 243
Lagrangian (material) coordinates, 56
Lagrangian strain, 67, 71, 72, 103
Lagrangian strain tensor, 77–79, 81, 83, 87,
131, 239
Laplace’s law, 307, 308, 467, 468
Laplacian operator, 45
Left ventricle (LV) model, 307
myocardium, 238
thick-walled cylindrical tube, 237
Lens, 458, 459
Lens vesicle (LV), 458
apical contraction, 461
development, 461
finite-element model, 462–463
placode formation, invagination and
closure, 461
programmed cell death/apoptosis, 462
Linear growth theory
beam, 409–414
growth-strain, 416, 417
plate, 414–415
Linear momentum
1D, 109–110
principle, 109
3D
material form, 113–114
spatial form, 111–112
2D, 110–111
Linear strain tensor, 502
Looping
cardiac looping (see Cardiac looping)
gut, 484–485
Lung development
branching, 487, 488
bud formation
finite-element model, 488–489
dipodial branching, 487, 488
monopodial branching, 487
LV, see Lens vesicle (LV)
M
Mandel stress tensor, 284
Material (Lagrangian) coordinates, 56
Material nonlinearity, 52, 358
Material time derivative, 61
Mathematical modeling in biology, 3–6
Mechanical feedback, 433, 466, 467, 490, 492
See also Growth
Mechanical regulation, morphogenesis
feedback, 490
HR
hypothesis, 491–492
morphomechanical laws, 492–493
Mechanobiological instability, 302
Mechanotransduction, 14–15
Mesenchymal cells, 8, 403, 430, 455, 485,
500
Mesenchymal-epithelial transition, 403, 404
Mesenchymal morphogenesis
Murray-Oster theory, 500–503
pattern formation, 500
positional information hypothesis, 500
vasculogenesis, 503–504
Mesenchyme, 8
Mesoderm, 8, 430, 434–436, 440, 443–446
Metric, 44
Microtubules, 6
Midbrain, 10, 457, 463–466
Monopodial branching, 487