STRESS-DEPENDENT FINITE GROWTH IN SOFT ELASTIC TISSUES

Growth and remodeling in tissues may be modulated by mechanical factor s 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 vol umetric growth in soft elastic tissues is therefore proposed. The shap e change of an unloaded tissue during growth is described by a mapping analogous to the deformation gradient tensor. This mapping is decompo sed 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 elasti c deformation. Hence, a complete kinematic formulation for growth in g eneral 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 re lation between the symmetric growth-rate tensor and the stress tensor. With a thick-walled hollow cylinder of incompressible, isotropic hype relastic material as an example, the mechanics of left ventricular hyp ertrophy are investigated. The results show that transmurally uniform pure circumferential growth, which may be similar to eccentric ventric ular hypertrophy, changes the state of residual stress in the heart wa ll. A model of axially loaded bone is used to test a simple stress-dep endent growth law in which growth rate depends on the difference betwe en the stress due to loading and a predetermined growth equilibrium st ress.