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

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

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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
Issue number3
StatePublished - 2018


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

ASJC Scopus subject areas

  • Applied Mathematics


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