Speaker: Steffen Eikenberry
Department of Mathemtics and Statistics
Arizona State University

Title: Infiltrative Growth and Treatment in a 3-D Mathematical Model of Glioblastoma Invasion

Abstract: Glioblastomas are aggressive primary brain cancers characterized by extensive infiltration of the brain and are highly resistant to treatment. A continuous mathematical model of glioblastoma invasion is formulated using partial differential equations and a heterogeneous three-dimensional brain geometry. This model is then extended to consider stochastic effects within the framework of the discretized PDE, and methods for simulating treatment are developed. The model is solved numerically, and the results of multiple stochastic simulations are averaged to generate a spatial probability distribution of tumor cells. Biologically, the model predicts that glioblastoma invasiveness is governed largely by the ability of glioblastoma cells to degrade and migrate in the extracellular matrix and the ability of single migrating cells to form colonies. The model also predicts that upon surgical treatment the margins and geometry of resection significantly determine the extent and pattern of post-operative recurrence; there is a nonlinear benefit to increasing resection margins, and radiotherapy works synergistically with greater resection margins to reduce recurrence. In an actual clinical case comprising several surgical interventions, the model gives good qualitative agreement between the simulated and the observed course of disease.