M.Sc Thesis | |

M.Sc Student | Lev Yoav |
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Subject | Studies of a New Model of Tissue Growth Based on Continuum Mechanics |

Department | Department of Civil and Environmental Engineering |

Supervisors | MR Dimitry Val |

ASSOCIATE PROF. Konstantin Volokh |

The growth phenomenon in living tissues is a process of a change of mass and configuration due to growth on the tissue surface and within the tissue volume.

An approach to modeling tissue growth employed in the work is based on a theory proposed by Volokh. The theory used a ‘thermoelastic’ formulation of simple growing materials based on an analogy between material growth and free thermal expansion, when the density of the material replaced the temperature increment. Constitutive equations of the theory were thus analogues to those of the thermoelastic formulation. Based on the concept of altering mass and configuration.

This work further develops the Volokh’s formulation as follows. First, considering material parameters from orthotropic specimens, it is shown that the material’s anisotropy leads to the existence of residual stresses throughout the growth process. Second, an established empirical relationship between the elastic modulus of cancellous bone specimens and the density of the substance is used. Thus, the change of the tissue elastic parameters due to the change of the tissue density is taken into account. Third, the work considers adaptive growth, i.e., the growth that is influenced not only by genetic information but also by epigenetic mechanisms. This leads to the coupled mass-flow/deformation problem. For this case the work also examines the density and stress/displacement fields using orthotropic parameters. Fourth, the theory is expanded to account for a nonlinear case, which considers both material and geometric nonlinearities. Results from the nonlinear analysis are compared to those from the linear analysis and limits for the use of the linear formulation are examined.

The work demonstrates the ability of continuum mechanics to deal with problems of living tissue growth, and provides qualitative explanation of the phenomenon of tissue growth.