Mathematical Biosciences and Engineering, 2015, 12(6): 1157-1172. doi: 10.3934/mbe.2015.12.1157

Primary: 92C50, 35C07; Secondary: 35K57.

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A data-motivated density-dependent diffusion model of in vitro glioblastoma growth

1. School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804
2. School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281

Glioblastoma multiforme is an aggressive brain cancer that is extremely fatal. It is characterized by both proliferation and large amounts of migration, which contributes to the difficulty of treatment. Previous models of this type of cancer growth often include two separate equations to model proliferation or migration. We propose a single equation which uses density-dependent diffusion to capture the behavior of both proliferation and migration. We analyze the model to determine the existence of traveling wave solutions. To prove the viability of the density-dependent diffusion function chosen, we compare our model with well-known in vitro experimental data.
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