Mathematical Model for Glioma Cell Invasion

Experimental observations suggest that in the vicinity of the glioma-host interaction zone glioma cells secrete MMPs that dissolve the ECM composition and disturb the balance of the brain tissue [3]. In order to restore the natural balance, healthy brain cells try and produce more ECM components as well as secreting tissue inhibitor of the MMPs (TIMPs) [12]. In this paper we present a mathematical model containing a system of partial-differential equations that describe the evolution of the glioma cells as a result of glioma-host interactions, host up-regulation of Extracellular Matrix (ECM) production and ECM and balance between the glioma secretion of matrix metalloproteinases (MMPs) and their tissue inhibitors (TIMPs) secreted by the host cells. We consider the nature of the glioma-healthy brain interactions as predicted by our model in order to test the hypothesis posed by Knott et al. [9] that up-regulated production of ECM by the host cells can either assist or impede glioma invasion on the healthy brain cells. Using numerical simulations we identify parameter regimes where host up-regulation of the ECM components has profound effect on both the speed of glioma invasion and the character of the glioma-host interface. In particular, our numerical results suggest that when glioma cells secrete large amounts of MMPs in comparison to host secreted TIMPs, regardless of the rate of ECM degradation by the MMPs, amplified host ECM production results in assisted haptotactic migration of the glioma thus enhancing glioma invasion. In contrast, when healthy cells secrete more TIMPs than glioma-secreted MMPs and when MMPs degradation of ECM is relatively weak, amplified up-regulation of host ECM production results in glioma encapsulation. Also host up-regulation of the ECM components can produce a sharper glioma-host interface, thus suggesting a less diffusive glioma. This can give a better differentiation between the glioma and the host tissue and may be useful if surgery was to be performed.