Mathematical analysis of Glioblastoma invasion models from in vitro experiment

Stein et al. proposed a continuum mathematical model describing Glioblastoma invasion observed 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 microscopically 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. Key–Words: Glioblastoma, 3D invasion, Tumour, radially biased motility, Collagen gel, Mathematical model, Mathematical analysis, Computer simulation, Existence of solution, N-cadherin.