Mathematical analysis of Glioblastoma invasion models from in vitro experiment

Akisato Kubo, Yuto Miyata

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Pages (from-to)62-68
Number of pages7
JournalWSEAS Transactions on Mathematics
Publication statusPublished - 2017

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


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