Growth Patterns of Microscopic Brain Tumors

Details Growth Patterns of Microscopic Brain Tumors Growth Patterns of Microscopic Brain Tumors

2002-06-18

arxiv.org/abs/physics/0206066v1

Physics

Biological Physics

21 pages 5 figures

Scientific paper

10.1103/PhysRevE.66.051901

Highly malignant brain tumors such as Glioblastoma Multiforme (GBM) form complex growth patterns in vitro in which invasive cells organize in tenuous branches. Here, we formulate a chemotaxis 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. We investigate this in two ways: we show that there is an intrinsic instability in the model, which leads to branch formation. We also give a discrete description for the expansion of the invasive zone, and a continuum model for the nutrient supply. The results indicate that both, strong heterotype chemotaxis and strong homotype chemo-attraction are required for branch formation within the invasive zone. Our model thus can give a way to assess the importance of the various processes, and a way to explore and analyze transitions between different growth regimes.

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