Highly malignant brain tumors such as Glioblastoma Multiforme (GBM) form
complex growth patterns in vitro in which invasive cells organize in
tenuous branches. We formulate a model for this sort of growth. A key
element controlling the pattern is homotype attraction, i.e., the tendency
for invasive cells to follow pathways previously explored. Our model can
give a way to assess the importance of various processes, and a way to
explore and analyze transitions between different growth regimes. We also
review some very recent experimental results on the formation of the
growth pathways via damage and alignment of the medium in which growth
occurs.
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