Abstract
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.
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