A data-motivated density-dependent diffusion model of in vitro glioblastoma growth

Glioblastoma multiforme is an aggressive brain cancer that is extremely fatal. It is characterized by both proliferation and large amounts of migration, which contributes to the difficulty of treatment. Previous models of this type of cancer growth often include two separate equations to model proli...

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Bibliographic Details
Published inMathematical biosciences and engineering : MBE Vol. 12; no. 6; p. 1157
Main Authors Stepien, Tracy L, Rutter, Erica M, Kuang, Yang
Format Journal Article
LanguageEnglish
Published United States 01.12.2015
Subjects
Brain Neoplasms - pathology
Brain Neoplasms - physiopathology
Cell Count
Cell Movement
Cell Proliferation
Computer Simulation
Glioblastoma - pathology
Glioblastoma - physiopathology
Humans
Mathematical Concepts
Models, Biological
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Summary:Glioblastoma multiforme is an aggressive brain cancer that is extremely fatal. It is characterized by both proliferation and large amounts of migration, which contributes to the difficulty of treatment. Previous models of this type of cancer growth often include two separate equations to model proliferation or migration. We propose a single equation which uses density-dependent diffusion to capture the behavior of both proliferation and migration. We analyze the model to determine the existence of traveling wave solutions. To prove the viability of the density-dependent diffusion function chosen, we compare our model with well-known in vitro experimental data.
ISSN:1551-0018
DOI:10.3934/mbe.2015.12.1157