A mathematical model of pre-diagnostic glioma growth

Marc Sturrock, Wenrui Hao, Judith Schwartzbaum, Grzegorz A. Rempala

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Due to their location, the malignant gliomas of the brain in humans are very difficult to treat in advanced stages. Blood-based biomarkers for glioma are needed for more accurate evaluation of treatment response as well as early diagnosis. However, biomarker research in primary brain tumors is challenging given their relative rarity and genetic diversity. It is further complicated by variations in the permeability of the blood brain barrier that affects the amount of marker released into the bloodstream. Inspired by recent temporal data indicating a possible decrease in serum glucose levels in patients with gliomas yet to be diagnosed, we present an ordinary differential equation model to capture early stage glioma growth. The model contains glioma-glucose-immune interactions and poses a potential mechanism by which this glucose drop can be explained. We present numerical simulations, parameter sensitivity analysis, linear stability analysis and a numerical experiment whereby we show how a dormant glioma can become malignant.

Original languageEnglish (US)
Pages (from-to)299-308
Number of pages10
JournalJournal of Theoretical Biology
StatePublished - Sep 7 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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