Mechanical modeling of collective cell migration: An agent-based and continuum material approach

We develop a novel modeling approach that combines a discrete agent-based model and a continuum material model to simulate collective cell migration in epithelial layers. In this approach, cells are represented as particles located at their geometrical center, but also as a polygonal body derived from the Voronoi diagram. Furthermore, we model the tissue as a continuum medium with different spatial domains that represent cell and substrate materials. In fact, the mechanical behavior of each domain is affected by the presence of cells from the discrete model. Moreover, we solve this mechanical problem using the finite element method (FEM). The forces generated by cells are projected to the FE mesh, that is created dynamically during the simulation from the discrete cell representation. After the FE resolution, we use the mesh displacements to determine the new cell positions in the agent-based model. Finally, to demonstrate the potential of this approach to model epithelial tissue mechanics, we simulate two well-studied cases of collective cell migration: durotaxis and gap closure. We use the experimental data from the literature to validate our numerical results. Therefore, the modeling strategy here presented offers a new perspective for a deeper understanding of tissue mechanics that emerge from cell dynamics in epithelial layers.