Cellular automata as microscopic models of cell migration in heterogeneous environments.

Understanding the precise interplay of moving cells with their typically heterogeneous environment is crucial for central biological processes as embryonic morphogenesis, wound healing, immune reactions or tumor growth. Mathematical models allow for the analysis of cell migration strategies involving complex feedback mechanisms between the cells and their microenvironment. Here, we introduce a cellular automaton (especially lattice-gas cellular automaton-LGCA) as a microscopic model of cell migration together with a (mathematical) tensor characterization of different biological environments. Furthermore, we show how mathematical analysis of the LGCA model can yield an estimate for the cell dispersion speed within a given environment. Novel imaging techniques like diffusion tensor imaging (DTI) may provide tensor data of biological microenvironments. As an application, we present LGCA simulations of a proliferating cell population moving in an external field defined by clinical DTI data. This system can serve as a model of in vivo glioma cell invasion.