The evolution of mathematical modeling of glioma proliferation and invasion

Hana L P Harpold, Ellsworth C. Alvord, Kristin R. Swanson*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

241 Scopus citations


Gliomas are well known for their potential for aggressive proliferation as well as their diffuse invasion of the normal-appearing parenchyma peripheral to the bulk lesion. This review presents a history of the use of mathematical modeling in the study of the proliferative-invasive growth of gliomas, illustrating the progress made in understanding the in vivo dynamics of invasion and proliferation of tumor cells. Mathematical modeling is based on a sequence of observation, speculation, development of hypotheses to be tested, and comparisons between theory and reality. These mathematical investigations, iteratively compared with experimental and clinical work, demonstrate the essential relationship between experimental and theoretical approaches. Together, these efforts have extended our knowledge and insight into in vivo brain tumor growth dynamics that should enhance current diagnoses and treatments.

Original languageEnglish (US)
Pages (from-to)1-9
Number of pages9
JournalJournal of neuropathology and experimental neurology
Issue number1
StatePublished - Jan 2007


  • Diffusion (invasion) rate
  • Glioma growth
  • Mathematical model
  • Proliferation rate

ASJC Scopus subject areas

  • Clinical Neurology
  • Neurology
  • Cellular and Molecular Neuroscience
  • Pathology and Forensic Medicine


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