  Vertex models represent confluent tissue by polygonal or polyhedral tilings
of space, with the individual cell interacting via force laws that depend on
both the geometry of the cells and the topology of the tessellation. This
dependence on the connectivity of the cellular network introduces several
complications to performing molecular-dynamics-like simulations of vertex
models, and in particular makes parallelizing the simulations difficult.
cellGPU addresses this difficulty and lays the foundation for massively
parallelized, GPU-based simulations of these models. This article discusses its
implementation for a pair of two-dimensional models, and compares the typical
performance that can be expected between running cellGPU entirely on the CPU
versus its performance when running on a range of commercial and server-grade
graphics cards. By implementing the calculation of topological changes and
forces on cells in a highly parallelizable fashion, cellGPU enables researchers
to simulate time- and length-scales previously inaccessible via existing
single-threaded CPU implementations.
