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A Simple Phenomenological Theory of Tissue Growth

K.Y. Volokh1
Faculty of Civil and Environmental Engineering, Technion, Haifa
2000, Israel (E-mail: cvolokh@tx.technion.ac.il)

Molecular & Cellular Biomechanics 2004, 1(2), 147-160. https://doi.org/10.3970/mcb.2004.001.147

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 tosimple 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 aboundary layersolution 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.

Keywords

Tissue growth, Constitutive behavior, Biological materials

Cite This Article

Volokh, K. (2004). A Simple Phenomenological Theory of Tissue Growth. Molecular & Cellular Biomechanics, 1(2), 147–160.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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