### 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.

Original language | English |
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Pages (from-to) | 62-68 |

Number of pages | 7 |

Journal | WSEAS Transactions on Mathematics |

Volume | 16 |

Publication status | Published - 01-01-2017 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Endocrinology, Diabetes and Metabolism
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Management Science and Operations Research
- Control and Optimization
- Computational Mathematics
- Applied Mathematics

### Cite this

*WSEAS Transactions on Mathematics*,

*16*, 62-68.