Index
535
2D, 94–99
(traction) vector, 96
Stress-dependent growth, 466, 467, 483
Stretching morphogenesis
actomyosin contraction, 405
cell intercalation, 404, 405
convergent extension, 405
mechanisms, 403, 404
Stretch ratio, 67, 71, 87–88
Striated muscles, 210, 306
Summation convention, 20–21, 27, 41
Surface growth, 253
Surface tractions, 170–171
Survival function, 348, 354, 358, 362, 370,
374, 389, 393, 394
T
Telencephalon, 10, 457, 463–468
Tensor product, 26
Tensors
components, 20
determinant, 28–31
eigenvalues, 31–33
eigenvectors, 31–33
formulas, 27, 28
identity, 31
inverse, 31
notation, 20–21
orthogonal, 33–35
rotation, 34
second-order, 19, 27
trace, 28–31
transpose, 28–31
Theory of elasticity, 51
Thermomechanical system, 117, 125
3D continuum, 58–60
Tight junctions, 403
Time rates of change
acceleration, 63–65
convective rate, 63
local rate, 63
material time derivative, 61
spatial description, 61, 63
velocity, 60, 62–64
Time-varying elastance
EDPVR, 235
ESPVR, 235
PVR, 235
stress-stretch curves, 236
Time-varying elasticity
active force-length curves, 222
isometric contraction, 221
material properties, 223
over-stretch ratio, 223
stress-stretch curves, 223
Torsion, 181–188, 204, 226, 239, 242, 250,
413, 448, 449, 451, 453, 455
Traction vectors, 96
Transverse isotropy, 140–141
Tube, 174–181, 288–292, 443–447, 455–457,
Turnover, 344–347, 349, 350–353, 358–360,
364, 375–377, 383, 386–388, 391,
393
U
Uniaxial extension, 143, 158–161–163, 203,
225, 354, 396, 493–497
Unstable equilibrium, 469, 471
V
Vasculogenesis, 503–504
Vectors
base vectors, 22–23
column/row, 29, 30
components, 19–20
cross product, 23–25
dot product, 23–25
formulas, 27, 28
tensor product, 25, 26
Velocity, 56–58, 66
gradient, 66, 92, 125
Ventral furrow, 434–437
Vesicle formation, 463–467
Villus formation, 485–487
Viscoelastic behavior, 131
Vitelline membrane (VM), 434, 435, 440–443
VM, see Vitelline membrane (VM)
Volume ratio, 88
Volumetric growth, 253
Volvox, 439–440
W
Windkessel model, 119
Wolff’s law, 341
Wound healing, 462
Y
Young’s modulus, 411, 502
Z
Zero-stress state (ZSS), 210, 256, 368
ZSS, see Zero-stress state (ZSS)
535
2D, 94–99
(traction) vector, 96
Stress-dependent growth, 466, 467, 483
Stretching morphogenesis
actomyosin contraction, 405
cell intercalation, 404, 405
convergent extension, 405
mechanisms, 403, 404
Stretch ratio, 67, 71, 87–88
Striated muscles, 210, 306
Summation convention, 20–21, 27, 41
Surface growth, 253
Surface tractions, 170–171
Survival function, 348, 354, 358, 362, 370,
374, 389, 393, 394
T
Telencephalon, 10, 457, 463–468
Tensor product, 26
Tensors
components, 20
determinant, 28–31
eigenvalues, 31–33
eigenvectors, 31–33
formulas, 27, 28
identity, 31
inverse, 31
notation, 20–21
orthogonal, 33–35
rotation, 34
second-order, 19, 27
trace, 28–31
transpose, 28–31
Theory of elasticity, 51
Thermomechanical system, 117, 125
3D continuum, 58–60
Tight junctions, 403
Time rates of change
acceleration, 63–65
convective rate, 63
local rate, 63
material time derivative, 61
spatial description, 61, 63
velocity, 60, 62–64
Time-varying elastance
EDPVR, 235
ESPVR, 235
PVR, 235
stress-stretch curves, 236
Time-varying elasticity
active force-length curves, 222
isometric contraction, 221
material properties, 223
over-stretch ratio, 223
stress-stretch curves, 223
Torsion, 181–188, 204, 226, 239, 242, 250,
413, 448, 449, 451, 453, 455
Traction vectors, 96
Transverse isotropy, 140–141
Tube, 174–181, 288–292, 443–447, 455–457,
Turnover, 344–347, 349, 350–353, 358–360,
364, 375–377, 383, 386–388, 391,
393
U
Uniaxial extension, 143, 158–161–163, 203,
225, 354, 396, 493–497
Unstable equilibrium, 469, 471
V
Vasculogenesis, 503–504
Vectors
base vectors, 22–23
column/row, 29, 30
components, 19–20
cross product, 23–25
dot product, 23–25
formulas, 27, 28
tensor product, 25, 26
Velocity, 56–58, 66
gradient, 66, 92, 125
Ventral furrow, 434–437
Vesicle formation, 463–467
Villus formation, 485–487
Viscoelastic behavior, 131
Vitelline membrane (VM), 434, 435, 440–443
VM, see Vitelline membrane (VM)
Volume ratio, 88
Volumetric growth, 253
Volvox, 439–440
W
Windkessel model, 119
Wolff’s law, 341
Wound healing, 462
Y
Young’s modulus, 411, 502
Z
Zero-stress state (ZSS), 210, 256, 368
ZSS, see Zero-stress state (ZSS)
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