A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth

Cell Prolif. 1995 Jan;28(1):17-31. doi: 10.1111/j.1365-2184.1995.tb00036.x.


During the past two decades computerized tomography (CT) and magnetic resonance imaging (MRI) have permitted the detection of tumours at much earlier stages in their development than was previously possible. In spite of this earlier diagnosis the effects of earlier and more extensive treatments have been difficult to document. This failure has led to an increasing awareness of the importance of infiltration of glioma cells into surrounding grossly normal brain tissue such that recurrence still occurs. In this paper a simple mathematical model for the proliferation and infiltration of such tumours is introduced, based in part on quantitative image analysis of histological sections of a human brain glioma and especially on cross-sectional area/volume measurements of serial CT images while the patient was undergoing chemotherapy. The model parameters were estimated using optimization techniques to give the best fit of the simulated tumour area to the CT scan data. Numerical solution of the model on a two-dimensional domain, which took into account the geometry of the brain and its natural barriers to diffusion, was used to determine the effect of chemotherapy on the spatio-temporal growth of the tumour.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Antineoplastic Combined Chemotherapy Protocols / therapeutic use*
  • Brain Neoplasms / drug therapy*
  • Brain Neoplasms / pathology*
  • Brain Neoplasms / radiotherapy
  • Cell Division / drug effects
  • Cell Division / physiology
  • Cell Division / radiation effects
  • Chemotherapy, Adjuvant
  • Follow-Up Studies
  • Glioblastoma / drug therapy*
  • Glioblastoma / pathology*
  • Glioblastoma / radiotherapy
  • Humans
  • Image Processing, Computer-Assisted
  • Magnetic Resonance Imaging
  • Models, Biological
  • Neoplasm Recurrence, Local / drug therapy*
  • Neoplasm Recurrence, Local / pathology
  • Tomography, X-Ray Computed