title: Velocity of radial expansion of contrast-enhancing gliomas and the effectiveness of radiotherapy in individual patients: a proof of principle.
abstract: OBJECTIVE
  The initial aims were to use recently available observations of glioblastomas (as part of a previous study) that had been imaged twice without intervening treatment before receiving radiotherapy in order to obtain quantitative measures of glioma growth and invasion according to a new bio-mathematical model. The results were so interesting as to raise the question whether the degree of radio-sensitivity of each tumour could be estimated by comparing the model-predicted and actual durations of survival and total numbers of glioma cells after radiotherapy.
  
  
  METHODS
  The gadolinium-enhanced T1-weighted and T2-weighted magnetic resonance imaging volumes were segmented and used to calculate the velocity of radial expansion (v) and the net rates of proliferation (rho) and invasion/dispersal (D) for each patient according to the bio-mathematical model.
  
  
  RESULTS
  The ranges of the values of v, D and rho show that glioblastomas, although clustering at the high end of rates, vary widely one from the other. The effects of X-ray therapy varied from patient to patient. About half survived as predicted without treatment, indicating radio-resistance of these tumours. The other half survived up to about twice as long as predicted without treatment and could have had a corresponding loss of glioma cells, indicating some degree of radio-sensitivity. These results approach the historical estimates that radiotherapy can double survival of the average patient with a glioblastoma.
  
  
  CONCLUSIONS
  These cases are among the first for which values of v, D and rho have been calculated for glioblastomas. The results constitute a 'proof of principle' by combining our bio-mathematical model for glioma growth and invasion with pre-treatment imaging observations to provide a new tool showing that individual glioblastomas may be identified as having been radio-resistant or radio-sensitive.
authors.affiliation: Laboratory of Neuropathology, University of Washington, Harborview Medical Center, 325-9th Avenue, Seattle, WA 98104, USA. swanson@amath.washington.edu
authors.forename: K R
authors.initials: KR
authors.lastname: Swanson
authors.forename: H L P
authors.initials: HL
authors.lastname: Harpold
authors.forename: D L
authors.initials: DL
authors.lastname: Peacock
authors.forename: R
authors.initials: R
authors.lastname: Rockne
authors.forename: C
authors.initials: C
authors.lastname: Pennington
authors.forename: L
authors.initials: L
authors.lastname: Kilbride
authors.forename: R
authors.initials: R
authors.lastname: Grant
authors.forename: J M
authors.initials: JM
authors.lastname: Wardlaw
authors.forename: E C
authors.initials: EC
authors.lastname: Alvord
mesh_terms: D000328:Adult; D000368:Aged; D001932:Brain Neoplasms / Q000401:mortality / Q000473:pathology / Q000532:radiotherapy*; D003287:Contrast Media; D005260:Female; D005909:Glioblastoma / Q000401:mortality / Q000473:pathology / Q000532:radiotherapy*; D006801:Humans; D008279:Magnetic Resonance Imaging; D008297:Male; D008875:Middle Aged; D015996:Survival Rate; D047368:Tumor Burden
chemical_list: D003287:Contrast Media