Dynamics of a model for brain tumors reveals a small window for therapeutic intervention

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

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Glioblastomas are the most malignant and most common glioma, a type of primary brain tumor with the unfortunate ability to recur despite extensive treatment. Even with the advent of medical imaging technology during the last two decades, successful treatment of glioblastomas has remained elusive. It has become increasingly clear that, along with the proliferative potential of these neoplasms, it is the subclinically diffuse invasion of glioblastomas that primarily contributes to their resistance to treatment. In otherwords, the inevitable recurrence of these tumors is the result of diffusely invaded but invisible tumor cells peripheral to the abnormal signal on medical imaging and to the current limits of surgical, radiological and chemical treatments. Mathematical modeling has presented itself as a viable tool for studying complex biological processes (Murray, 1993, 2002). We have developed a mathematical model that portrays the growth and extension of theoretical glioblastoma cells in a matrix that accurately describes the brain's anatomy to a resolution of 1 cu mm (Swanson, et al, 1999, 2000, 2002, 2003a, 2003b). The model assumes that only two factors need be considered for such predictions: net growth rate and infiltrative ability. The model has already provided illustrations of theoretical glioblastomas that not only closely resemble the MRIs (magnetic resonance imaging) of actual patients, but also show the distribution of the diffusely infiltrating cells.

Original languageEnglish (US)
Pages (from-to)289-295
Number of pages7
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
StatePublished - Feb 2004


  • Brain tumor
  • Invasion
  • Mathematical model

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Dynamics of a model for brain tumors reveals a small window for therapeutic intervention'. Together they form a unique fingerprint.

Cite this