Virtual and real brain tumors: Using mathematical modeling to quantify glioma growth and invasion

Kristin R. Swanson, Carly Bridge, J. D. Murray, Ellsworth C. Alvord

Research output: Contribution to journalReview articlepeer-review

394 Scopus citations


Over the last 10 years increasingly complex mathematical models of cancerous growths have been developed, especially on solid tumors, in which growth primarily comes from cellular proliferation. The invasiveness of gliomas, however, requires a change in the concept to include cellular motility in addition to proliferative growth. In this article we review some of the recent developments in mathematical modeling of gliomas. We begin with a model of untreated gliomas and continue with models of polyclonal gliomas following chemotherapy or surgical resection. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have recently been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter on a geometrically complex brain domain, including sulcal boundaries, with a resolution of 1 mm3 voxels. We conclude that the velocity of expansion is linear with time and varies about 10-fold, from about 4 mm/year for low-grade gliomas to about 3 mm/month for high-grade ones.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalJournal of the neurological sciences
Issue number1
StatePublished - Dec 15 2003


  • Glioma
  • Mathematical model
  • Tumor growth
  • Tumor invasion

ASJC Scopus subject areas

  • Neurology
  • Clinical Neurology


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