Simple epithelial tissues consist of tightly packed cells that form a polygonal tiling on the apical side. The structure of these tissues can be described by a two-dimensional area- and perimeter-elasticity model based on the physical features of cells and the junctions between them. In this thesis, we modify the surface energy term so as to allow the exchange of matter between neighboring cells. The thus generalized model supplemented with dynamic processes such as cell division, death, and T1 topological transitions, is numerically analyzed in the vertex representation. We compare the results with experimental data and existing models, and we verify the validity of the Lewis law and the Aboav-Weaire law. We use the area-to-perimeter ratio to describe the isometricity of cells in the tilings. We study the topological properties and the dynamics of epithelial tilings across the state diagram.
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