Traveling waves of a go-or-grow model of glioma growth

Tracy L. Stepien, Erica M. Rutter, Yang Kuang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Glioblastoma multiforme is a deadly brain cancer in which tumor cells excessively proliferate and migrate. The first mathematical models of the spread of gliomas featured reaction-diffusion equations, and later an idea emerged through experimental study called the "Go or Grow" hypothesis in which glioma cells have a dichotomous behavior: A cell either primarily proliferates or primarily migrates. We analytically investigate an extreme form of the "Go or Grow" hypothesis where tumor cell motility and cell proliferation are considered as separate processes. Different so- lution types are examined via approximate solution of traveling wave equations, and we determine conditions for various wave front forms.

Original languageEnglish (US)
Pages (from-to)1778-1801
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume78
Issue number3
DOIs
StatePublished - Jan 1 2018

Fingerprint

Traveling Wave
Tumors
Cells
Tumor
Cell
Cell proliferation
Wave equations
Cell Motility
Brain
Cell Proliferation
Mathematical models
Reaction-diffusion Equations
Wave Front
Wave equation
Experimental Study
Cancer
Approximate Solution
Extremes
Model
Mathematical Model

Keywords

  • Glioblastoma
  • Go or grow
  • Mathematical modeling
  • Traveling wave
  • Tumor growth

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Traveling waves of a go-or-grow model of glioma growth. / Stepien, Tracy L.; Rutter, Erica M.; Kuang, Yang.

In: SIAM Journal on Applied Mathematics, Vol. 78, No. 3, 01.01.2018, p. 1778-1801.

Research output: Contribution to journalArticle

Stepien, Tracy L. ; Rutter, Erica M. ; Kuang, Yang. / Traveling waves of a go-or-grow model of glioma growth. In: SIAM Journal on Applied Mathematics. 2018 ; Vol. 78, No. 3. pp. 1778-1801.
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