Modelling and Simulation of Cell Migration in Heterogeneous Media

We present a framework for the modelling of cell motility in heterogeneous environments. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of forces that act normal to the surface. The biochemistry is modelled through partial differential equations posed on the cell membrane. For the mechanics, we propose a force balance on the surface, including external forces to model inhomogeneities in the medium such as other cells, adhesion to a substrate and obstacles. We employ a computational method based on evolving surface finite elements for the simulation of the model and report on a number of simulation results illustrating the applications of the approach.