Rodriguez E K, Hoger A, McCulloch A D
Institute for Biomedical Engineering, University of California, San Diego, La Jolla 92093-0412.
J Biomech. 1994 Apr;27(4):455-67. doi: 10.1016/0021-9290(94)90021-3.
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.
组织中的生长和重塑可能会受到诸如应力等机械因素的调节。例如，在心肌肥大中，机械负荷变化引起的壁应力改变会导致心脏生长和重塑。因此，提出了一种用于软弹性组织有限体积生长的一般连续体公式。生长过程中未加载组织的形状变化通过类似于变形梯度张量的映射来描述。该映射被分解为局部零应力参考状态的变换和伴随的弹性变形，以确保总生长变形的相容性。残余应力由此弹性变形产生。因此，一般来说，完整的生长运动学公式需要了解组织中应力的本构定律。由于生长反过来可能会受到组织中应力的影响，因此提出了应力依赖生长定律的一般形式，作为对称生长速率张量与应力张量之间的关系。以不可压缩、各向同性超弹性材料的厚壁空心圆柱体为例，研究了左心室肥大的力学原理。结果表明，跨壁均匀的纯周向生长，可能类似于偏心心室肥大，会改变心壁中的残余应力状态。使用轴向加载骨的模型来测试一种简单的应力依赖生长定律，其中生长速率取决于加载引起的应力与预定生长平衡应力之间的差异。
