A simple phenomenological theory of tissue growth.

K Y Volokh
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Abstract

A simple phenomenological framework for modeling growth of living tissues is proposed. Growth is defined as a change of mass and configuration of the tissue. Tissue is considered as an open system where mass conservation is violated and the full-scale mass balance is applied. A possible structure of constitutive equations is discussed with reference to simple growing materials. 'Thermoelastic' formulation of the simple growing material is specified. Within this framework traction free growth of cylindrical and spherical bodies is examined. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to a boundary layer solution of the governing equations. This finding proves the ability of continuum mechanics to describe surface growth. The latter is contrary to the usual use of purely kinematical theories, which do not involve balance and constitutive equations, for treating surface growth.

组织生长的简单现象学理论。
提出了一个简单的现象学框架来模拟活组织的生长。生长被定义为组织质量和结构的变化。组织被认为是一个开放的系统,质量守恒被打破,全尺寸质量平衡被应用。参考简单生长材料,讨论了本构方程的一种可能结构。指定了简单生长材料的“热弹性”配方。在这个框架内,柱体和球体的牵引自由生长进行了研究。结果表明,该理论适用于在均匀体积增长中不产生应力的情况。还发现,表面生长对应于控制方程的边界层解。这一发现证明了连续介质力学描述表面生长的能力。后者与通常使用的纯运动学理论相反,后者不涉及平衡和本构方程,用于处理表面生长。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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