Micromechanics of Epithelial Tissue-Inspired Structures

Tejas Kulkarni, Purdue University

Abstract

Epithelial tissues, one of the four primary tissue structures found in our human body, are known to comprise of tiny cells interconnected in a unique continuous pattern. In most cases, they serve a dual purpose of protecting the internal organs from physical damage, and at the same time, enable in facilitating inter-cellular activities and prevent pathogen break ins. While the tissue mechanics and its proliferation have been scrutinized to great detail, it is their geometric uniqueness, that has remained more or less unexplored. With an intent of doing the same, this thesis identifies and explores those geometric properties/parameters that have an influence on the micro structure’s homogenized and localized response. However, it does so by extracting the microstructures profile and representing its cell edges via three dimensional beam elements - hence the name, bio-inspired structures. The analysis is carried out by first developing a staggered Representative Volume Element (RVE) using finite elements, and identifying its appropriate size. The staggered assembly aids in minimizing boundary effects from creeping in, and at the same time, provides the requisite statistical homogeneity. This is followed by the geometry study. A wide range of epithelial geometries are considered for the study, ranging from completely isotropic skin models, to in plane anisotropic cuboidal structures and out of plane anisotropic stratified geometries. The effects of orientation, relative density and edge length are extracted and studied in great detail. It is observed that cell edges initial orientation has a direct dependence on the particle distribution, whereas the change in orientation is largely dependent on the deformation the microstructure is subjected to. Relative density is documented to show a direct correlation to a materials homogenized response i.e. larger the relative density, greater is the microstructures stiffness and homogenized stress response to the same deformation. Edge length, on the other hand is observed to showcase a downward trend on the cell edge’s axial stress. On average, in any kind of distribution and any kind of deformation, smaller cell edges are known to showcase larger stresses, as compared to the larger cell edges.

Degree

M.Sc.

Advisors

Tepole, Purdue University.

Subject Area

Mechanics|Cellular biology|Developmental biology|Marketing|Mathematics|Statistics

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