Arizona State University
Refreshments will be provided from 4:00 - 4:30 PM in 101A Crowley Hall
Existence and Applications of Traveling Wave Solutions in Reaction Diffusion Models of Brain Cancer Growth
Glioblastoma multiforme (GBM) is an aggressive brain cancer that is extremely fatal. It is characterized by aggressive proliferation and fast migration, which contributes to the difficulty of treatment. Based on the so-called go or grow hypothesis, existing models of GBM growth often include two separate equations to model proliferation or migration processes. Motivated by an in vitro experiment data set of GBM growth, we formulate, validate, simulate, study and compare two plausible models of GBM growth. We propose first 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 the in vitro experimental data. Our second model is build on the Go or Grow hypothesis since glioma cells tend to exhibit a dichotomous behavior: a cell either primarily proliferates or primarily migrates. For this model, different solution types are examined via approximate solution of traveling wave equations and we determine conditions for various wave front forms.