A mathematical model of dynamic glioma–host interactions: receptor-mediated invasion and local proteolysis

We present a mathematical model of glioma spread based on cellular movement by receptor-mediated haptotaxis, local proteolysis of healthy tissue components by glioma-derived proteinases, malignant proliferative enhancement and host up-regulation of specific key extracellular matrix (ECM) components in response to the invading glioma. We subsequently consider the nature of glioma–host interactions as predicted by our model in order to test the hypothesis given in (Knott et al. (1998) that production of adhesive ECM components by the brain in response to the invading glioma may have the counter-intuitive effect of enhancing glioma invasion by assisting haptotactic migration. We suggest that host production of certain adhesive ECM chemicals can have a profound effect on both glioma invasion speed and the character of the glioma–host interface. In particular, we conclude that up-regulation of host ECM production in the vicinity of the glioma may produce a less diffuse glioma, providing clearer demarcation between glioma and healthy tissue, and thus improving the possibility of surgical resection within reasonable bounds.