A Three-Dimensional Morphogenesis Simulation of Epithelial Monolayers Using a Cell-Centered Model

Understanding morphogenesis in epithelial tissues requires both biological and mechanical insights. Complex processes such as cell division and apical contraction control tissue shape changes, but how local behaviors influence global deformations, especially on curved surfaces, remains unclear. While the cell-centered model is computationally efficient by representing cells only at their centers, it struggles to account for anisotropic cell shapes and oriented cell divisions in curved surfaces, which are crucial for morphogenesis. In the case of curved surfaces, traditional methods such as Delaunay triangulation or Voronoi diagrams cannot be directly applied, requiring a more complex approach to reconstruct cell shapes.

To address these limitations, we developed a novel cell-centered model effective for three-dimensional deformations on curved surfaces. By reconstructing cell shapes using triangular centroids in a triangular mesh, the model efficiently simulates cell division, rearrangement, and apical contraction. Simulation results matched previous studies and accurately represented deformations on curved surfaces, validating the mechanical accuracy and robustness of the model.