Active Vertex Model for cell-resolution description of epithelial tissue mechanics
Fig 2
(a) Two coordinate representations dual to each other. In the AVM we track particles that correspond to cell centres (red dots). Particles form a Delaunay triangulation (red lines) and their positions are labeled with vectors carrying Latin indices. The dual of the Delaunay triangulation is a Voronoi tessellation, with each Voronoi cell (a shaded polygon) representing an actual cell. Cell edges are marked by blue lines. Positions of the vertices (blue dots) of the dual mesh are denoted by Greek indices. (b) Position of the circumcenter rμ of the triangle with corners ri, rj and rk. (c) The edge flip move is at the core of the equiangulation procedure. If the sum of the angles opposite to the red edge exceeds α + β > 180° the edge is “flipped”. As the result, the sum of the angles opposite to the new edge is less than 180°, i.e., γ + δ < 180°. Note that this edge flip is local and only affects one Voronoi edge (i.e., cell junction). Therefore, edge flips can only affect the local connectivity of four cells (see also, Fig 5).