### 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 |
---|---|

Pages (from-to) | 62-68 |

Number of pages | 7 |

Journal | WSEAS Transactions on Mathematics |

Volume | 16 |

Publication status | Published - 01-01-2017 |

### Fingerprint

### 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.

}

*WSEAS Transactions on Mathematics*, vol. 16, pp. 62-68.

**Mathematical analysis of Glioblastoma invasion models from in vitro experiment.** / Kubo, Akisato; Miyata, Yuto.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Mathematical analysis of Glioblastoma invasion models from in vitro experiment

AU - Kubo, Akisato

AU - Miyata, Yuto

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85037081549&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037081549&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85037081549

VL - 16

SP - 62

EP - 68

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -