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.
@article{arxiv.physics/0206066,
title = {Growth Patterns of Microscopic Brain Tumors},
author = {Leonard M. Sander and Thomas S. Deisboeck},
journal= {arXiv preprint arXiv:physics/0206066},
year = {2009}
}