Index
531
Foregut, 12, 441, 443–447, 483
Fourier coefficients, 428, 523
Fourier series, 426, 428, 432, 523–525
Fourth-order identity tensor, 43
Functional adaptation, 1–2
Fundamental growth laws hypotheses
formulation, 304
isometric exercise, 305
mechanosensitive proteins, 305
molecular deformation, 306
Fundamental growth mechanics
constrained bar, 261–265
differential growth, 266–271
unconstrained bar, 260–261
Fundamental remodeling mechanics
matrix remodeling, 344
reorganization, 344
G
Gap junction, 403
Gastrulation, 8
in Drosophila, 434–436
invagination mechanics, 430–433
in sea squirts, 438–439
in sea urchins, 436–438
Volvox, 439–440
Genes, 8
Geometric nonlinearity, 52
Glial fibers, 478, 479
Gradient
theorem, 47
velocity, 46
Gradient operator, 81, 92, 108
Cartesian coordinates, 44–47
curl formulas, 45
gradient formulas, 45
Laplacian operator, 45
metrics, 44
polar coordinates, 44–47
Gradient theorem, 47
Growth
fundamental hypotheses, 304–306
law, 259, 284, 298–309, 311, 313, 317–318
mechanical growth laws, 298–304
mechanics (see Fundamental growth
mechanics)
muscle growth laws, 306–309
ratio, 256, 259, 262, 264, 266, 289, 294,
295, 301, 302, 307, 312, 324, 332,
352, 353, 358–360, 366, 367, 384,
386, 389, 411, 449, 456, 482, 494,
496, 497
residual stress, 271–281, 288–292
sarcomeres, 254
theories (see Rodriguez, Hoger, and
McCulloch (RHM))
types
surface, 253
volumetric, 253
Growth-induced bending, beam, 505
Growth-induced residual stress, 288–292
Growth moment, 412, 413, 416, 418, 421, 426,
428, 433
Growth-rate tensor, 284
Growth tensor, 408, 435, 437, 486
Growth theory, RHM
constitutive relations, 284
growth law, 284
incompressibility, 284
kinematics, 283–284
Gut looping, 484–485
H
Haptotaxis, 501, 503, 504
Head fold (HF), 441–443
Heart development
cardiac looping, 447–455
heart tube and foregut, 443–447
Heart fields (HFs), 403, 443–446
Heart muscle, 306–309
Heart tube (HT) and foregut (FG)
morphogenesis
AIP, 444
cardiac development, 443
cardiac jelly, 444
differential growth, 446
extracellular matrix, 444
SPL, 443, 444
3D model, 445–446
Heaviside step function, 319, 350
Helmholtz free-energy function, 132
HF, see Head fold (HF)
Hill’s equation, 221
Hindbrain, 10, 457, 463, 464
Hindgut, 12
Hole-punching experiments, 441–442
Homeostatic state, 355
Homeostatic stress, 358, 491, 492, 496
Hooke’s law, 138–140, 411, 414, 502
Hoop stress, 437, 439
HR, see Hyper-restoration (HR)
Humphrey-Rajagopal remodeling theory
constitutive relations, 353
fiber volume, 346–350
survival function, 348
turnover kinematics, 350–353
531
Foregut, 12, 441, 443–447, 483
Fourier coefficients, 428, 523
Fourier series, 426, 428, 432, 523–525
Fourth-order identity tensor, 43
Functional adaptation, 1–2
Fundamental growth laws hypotheses
formulation, 304
isometric exercise, 305
mechanosensitive proteins, 305
molecular deformation, 306
Fundamental growth mechanics
constrained bar, 261–265
differential growth, 266–271
unconstrained bar, 260–261
Fundamental remodeling mechanics
matrix remodeling, 344
reorganization, 344
G
Gap junction, 403
Gastrulation, 8
in Drosophila, 434–436
invagination mechanics, 430–433
in sea squirts, 438–439
in sea urchins, 436–438
Volvox, 439–440
Genes, 8
Geometric nonlinearity, 52
Glial fibers, 478, 479
Gradient
theorem, 47
velocity, 46
Gradient operator, 81, 92, 108
Cartesian coordinates, 44–47
curl formulas, 45
gradient formulas, 45
Laplacian operator, 45
metrics, 44
polar coordinates, 44–47
Gradient theorem, 47
Growth
fundamental hypotheses, 304–306
law, 259, 284, 298–309, 311, 313, 317–318
mechanical growth laws, 298–304
mechanics (see Fundamental growth
mechanics)
muscle growth laws, 306–309
ratio, 256, 259, 262, 264, 266, 289, 294,
295, 301, 302, 307, 312, 324, 332,
352, 353, 358–360, 366, 367, 384,
386, 389, 411, 449, 456, 482, 494,
496, 497
residual stress, 271–281, 288–292
sarcomeres, 254
theories (see Rodriguez, Hoger, and
McCulloch (RHM))
types
surface, 253
volumetric, 253
Growth-induced bending, beam, 505
Growth-induced residual stress, 288–292
Growth moment, 412, 413, 416, 418, 421, 426,
428, 433
Growth-rate tensor, 284
Growth tensor, 408, 435, 437, 486
Growth theory, RHM
constitutive relations, 284
growth law, 284
incompressibility, 284
kinematics, 283–284
Gut looping, 484–485
H
Haptotaxis, 501, 503, 504
Head fold (HF), 441–443
Heart development
cardiac looping, 447–455
heart tube and foregut, 443–447
Heart fields (HFs), 403, 443–446
Heart muscle, 306–309
Heart tube (HT) and foregut (FG)
morphogenesis
AIP, 444
cardiac development, 443
cardiac jelly, 444
differential growth, 446
extracellular matrix, 444
SPL, 443, 444
3D model, 445–446
Heaviside step function, 319, 350
Helmholtz free-energy function, 132
HF, see Head fold (HF)
Hill’s equation, 221
Hindbrain, 10, 457, 463, 464
Hindgut, 12
Hole-punching experiments, 441–442
Homeostatic state, 355
Homeostatic stress, 358, 491, 492, 496
Hooke’s law, 138–140, 411, 414, 502
Hoop stress, 437, 439
HR, see Hyper-restoration (HR)
Humphrey-Rajagopal remodeling theory
constitutive relations, 353
fiber volume, 346–350
survival function, 348
turnover kinematics, 350–353