title: A data-motivated density-dependent diffusion model of in vitro glioblastoma growth.
abstract: 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.
authors.affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, United States. email:tstepien@asu.edu.
authors.forename: Tracy L
authors.initials: TL
authors.lastname: Stepien
authors.forename: Erica M
authors.initials: EM
authors.lastname: Rutter
authors.forename: Yang
authors.initials: Y
authors.lastname: Kuang
mesh_terms: D001932:Brain Neoplasms / Q000473:pathology* / Q000503:physiopathology; D002452:Cell Count; D002465:Cell Movement; D049109:Cell Proliferation; D003198:Computer Simulation; D005909:Glioblastoma / Q000473:pathology* / Q000503:physiopathology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological