Аннотация
Growth and remodeling in tissues may be modulated by mechanical factors
such as stress. For example, in cardiac hypertrophy, alterations in wall
stress arising from changes in mechanical loading lead to cardiac growth
and remodeling. A general continuum formulation for finite volumetric
growth in soft elastic tissues is therefore proposed. The shape change
of an unloaded tissue during growth is described by a mapping analogous
to the deformation gradient tensor. This mapping is decomposed into a
transformation of the local zero-stress reference state and an
accompanying elastic deformation that ensures the compatibility of the
total growth deformation. Residual stress arises from this elastic
deformation. Hence, a complete kinematic formulation for growth in
general requires a knowledge of the constitutive law for stress in the
tissue. Since growth may in turn be affected by stress in the tissue, a
general form for the stress-dependent growth law is proposed as a
relation between the symmetric growth-rate tensor and the stress tensor.
With a thick-walled hollow cylinder of incompressible, isotropic
hyperelastic material as an example, the mechanics of left ventricular
hypertrophy are investigated. The results show that transmurally uniform
pure circumferential growth, which may be similar to eccentric
ventricular hypertrophy, changes the state of residual stress in the
heart wall. A model of axially loaded bone is used to test a simple
stress-dependent growth law in which growth rate depends on the
difference between the stress due to loading and a predetermined growth
equilibrium stress.
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