Incorporating Mechanics Into the Cellular Potts Model

Abstract

Lattice-based computational models such as the cellular Potts model (CPM) display a versatility capable of representing systems on both the tissue and cellular level, yet fail to incorporate mechanical interactions crucial for understanding the mechanisms of cell growth and movement. In contrast, the reference map technique (RMT) based on a fixed regular lattice uses a special reference map field that tracks deformations and mechanical stresses to simulate solid mechanics. In this project, I couple the cellular Potts model with the RMT to understand the mechanical behavior of multicellular entities in a dynamically changing environment. This hybrid model allows the CPM to take into account the complex mechanics of the deformation and strain of the material around the cells, while expanding the mechanical model to encompass multicellular effects. To do so, I use the Hamiltonian energy function in the CPM to influence cellular growth and movement. To account for mechanical forces, I model the system as a global continuum field in which cells placed on top of the material should apply a force to the underlying material while also being affected by the material. From a computational perspective, this technique can serve as a generalizable framework for future studies of mechanical interactions between cells.