WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 16, 2017
Mathematical Analysis of Glioblastoma Invasion Models from in Vitro Experiment
Authors: ,
Abstract: 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.
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Keywords: Glioblastoma, 3D invasion, Tumour, radially biased motility, Collagen gel, Mathematical model, Mathematical analysis, Computer simulation, Existence of solution, N-cadherin
Pages: 62-68
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #8