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

I will present very recent article by Stepien, Rutter and Kuang in Mathematical Biosciences and Engeneering, 2015. The research concerns modelling glioblastoma multiforme, which is is an extremely fatal brain cancer. 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. Authors propose a single equation which uses density-dependent diffusion to capture the behavior of both proliferation and migration. The model is analyzed in order to determine the existence of traveling wave solutions. The viability of the density-dependent diffusion functionchosen has been done by comparison of model with in vitro experimental data.