Hybrid cell centred/vertex model for large tissue deformations

Abstract

Macroscopic deformations in embryonic soft tissues are due to the intra-cellular remodelling and cell intercalation. We here present a computational approach that can handle the two types of deformations, and also take into account the active cell response. The model resorts to cell-centred techniques, where particles represent cell nuclei, and to vertex models, where the vertices represent cell boundaries. This hybrid approach allows to consider separately intracellular and inter-cellular forces, and at the same time impose cell incompressibility. In the proposed model, the cell boundaries (defined by vertices) and cell nuclei (or cellcentres) networks are coupled through an interpolation scheme, which is eventually relaxed in order to smooth the cell boundaries. We show that this coupling between the two networks modifies the equilibrium equations and stabilises the vertex network. Incompressibility is implemented through a penalty method. The resulting model can be implemented in two- and three-dimensions, and is complemented with active rheological models. We apply the model to simulate the stretching and relaxation of cell monolayers, and to simulate wound healing process in the wing disc of Drosophila fly embryo. We show that the numerical results agree with the experimental measurements.