Traveling wave speed and profile of a “go or grow” glioblastoma multiforme model

Aisha Tursynkozha, Ardak Kashkynbayev, Bibinur Shupeyeva, Erica M. Rutter, Yang Kuang

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction–diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction–diffusion GBM model based on the ‘go or grow’ hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

Original languageEnglish
Article number107008
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusPublished - Apr 2023


  • Glioblastoma
  • Go or grow
  • Partial differential equations
  • Traveling wave

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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