Fractal structure in the volumetric contrast enhancement of malignant gliomas as a marker of oxidative metabolic pathway gene expression

Kai J. Miller*, Sharon Berendsen, Tatjana Seute, Kristen Yeom, Melanie H. Gephardt, Gerald A. Grant, Pierre A. Robe

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Background: Fractal structure is found throughout many processes in nature, and often arises from sets of simple rules. We examined MRI contrast enhancement patterns from glioblastoma patients for evidence of fractal structure and correlated these with gene expression patterns. Methods: For 39 glioblastoma patients, volumetric T1-post-contrast MRI scans were obtained before surgical resection. We calculated the fractal dimension of each tumor's contrast enhancement using a box-counting (cubic scaling) approach. RNA expression microarray data from resected tissue were explored by gene set enrichment analysis (GSEA), and vascular endothelial growth factor (VEGF) expression was determined by immunostaining of resected tissue. Results: We found robust evidence for fractal structure in the contrast enhancement pattern, with an average fractal dimension of 2.17±0.10, and a visually apparent split at 2.10. GSEA analysis showed a clear association between high fractal dimension (χ > 2.10) and decreased gene expression in 6 gene sets (of 4,080), all 6 of which are linked to mitochondrial respiration/ATP production pathways. On a protein level, high fractal dimension was correlated with increased VEGF. Conclusions: There is fractal structure in the volumetric enhancement pattern of glioblastomas. Variation in the fractal dimension, and therefore the complexity of contrast enhancement it reflects, is specifically associated with genetic correlates of a shift to glycolytic metabolism in tumor cells and VEGF. Drugs that restore oxidative metabolism have recently been identified as independent therapeutic agents as well as sensitizing agents for irradiation. Therefore, a radiogenomic marker of glucose metabolism, such as this fractal structure in enhancement, might help to guide individualized therapy.

Original languageEnglish
Pages (from-to)1275-1282
Number of pages8
JournalTranslational Cancer Research
Issue number6
Publication statusPublished - 1 Dec 2017


  • Contrast enhancement
  • Fractal
  • Glioblastoma
  • Oxidative metabolism
  • Radiogenomics


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