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

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

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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 densitydependent 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.

Original languageEnglish (US)
Pages (from-to)1157-1172
Number of pages16
JournalMathematical Biosciences and Engineering
Issue number6
StatePublished - Dec 1 2015


  • Biomathematical modeling
  • Glioblastoma
  • Traveling waves
  • Tumor growth simulation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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