Mathematical analysis of Glioblastoma invasion models from in vitro experiment

Stein et al. proposed a continuum mathematical model describing Glioblastoma invasion ob-served in their experiments on the patterns of growth and dispersion of U87MG tumour spheroids in a three-dimensional collagen-I gel. They identify and characterise discrete cellular mechanisms underlying invasive cell motility from the experimental data. However in their experiments it is observed micro-scopically that the U87MG invasive cells often exhibit more complicated and irregular behaviour than expressed by their model. We propose a mathematical model by generalising the radially biased motility term in their model based on the mechanism govering the behaviour of U87MG cell in the experiment. We show a rigorous mathematical analysis of our model and give computer simulations of the experiment based on our mathematical model.