A mathematical model of glioma invasion

Yangjin Kim
Mathematical Biosciences Institute (MBI), The Ohio State University

(November 13, 2008 10:30 AM - 11:30 AM)

A mathematical model of glioma invasion

Abstract

Glioblastoma is the most common primary tumor of the brain, and has a dismal prognosis, with a mean survival of around 1 year from diagnosis. Invasion of surrounding brain tissue is one of the main hallmarks of gliomas, and is a major reason for treatment failure, because tumor cells remaining after surgical resection cause tumor recurrence. Although tumors show preferred invasion routes in the brain, at present it is not possible to predict patterns of invasion and recurrence for a given tumor. Variations are seen in the numbers of invading cells, and in the extent and patterns of migration. Cells can migrate diffusely and can also be seen as clusters of cells distinct from the main tumor mass. This kind of clustering is also evident in vitro using 3-D spheroid models of glioma invasion. This has been reported for U87 cells stably expressing the constitutively active EGFRVIII mutant receptor, often seen expressed in glioblastoma. In this case the cells migrate as clusters rather than as single cells migrating in a radial pattern seen in control wild type U87 cells. Several models have been suggested to explain the different modes of migration, but none of them, so far, has explored the important role of cell-cell adhesion. We develops a mathematical model which includes the role of adhesion and provides an explanation for the various patterns of cell migration. It is shown that, depending on critical parameters, the migration patterns exhibit a gradual shift from branching to dispersion, as has been reported experimentally.