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An overview of principles and mathematical models of biological pattern formation is presented. One can distinguish preformation, optimization, topological and self-organization principles. Combinations of such principles are responsible for shape and tissue formation, differentiation, regeneration, morphogenetic motion, cell division and even malignant patterns, e.g. in tumor growth. Mathematical modeling allows for a systematic analysis of the pattern-formation potential of morphogenetic principles....
Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous
cell proliferation and motility rates. The interplay of proliferation and migration
dynamics plays an important role in the invasion of these malignant tumors. We analyze the
regulation of proliferation and migration processes with a lattice-gas cellular automaton
(LGCA). We study and characterize the influence of the migration/proliferation dichotomy
(also known...
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