Mathematical modelling of glioblastoma tumour development: A review

Haralampos Hatzikirou, Andreas Deutsch, Carlo Schaller, Matthias Simon, Kristin Swanson

Research output: Contribution to journalArticlepeer-review

93 Scopus citations


During the past several years mathematical models have been applied to various aspects of cancer dynamics, in particular avascular and vascular tumour growth, invasion, angiogenesis, and metastasis. This paper focuses on the most common and malignant brain tumour, glioblastoma, and surveys the growing number of studies dealing with mathematical modelling of this tumour. We attempt to classify these studies by their biomedical relevance and critically analyse their results. The aim of this review is to provide a meaningful reference, to both biomedical and mathematical researchers, of the current state of the art of glioma tumour modelling. The discussion attempts to identify current open problems as well as new research perspectives in the mathematical modelling of glioblastoma growth.

Original languageEnglish (US)
Pages (from-to)1779-1794
Number of pages16
JournalMathematical Models and Methods in Applied Sciences
Issue number11
StatePublished - Nov 2005


  • Avascular tumour growth
  • Glioblastoma multiforme
  • Invasion
  • Mathematical modelling
  • Therapy

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


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