Mathematically modeling the biological properties of gliomas: A review

Nikolay L. Martirosyan, Erica M. Rutter, Wyatt L. Ramey, Eric Kostelich, Yang Kuang, Mark C. Preul

Research output: Contribution to journalReview articlepeer-review

25 Scopus citations


Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be diffcult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the in-filtrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their inuence on the surrounding anatomical structures in the brain.

Original languageEnglish (US)
Pages (from-to)879-905
Number of pages27
JournalMathematical Biosciences and Engineering
Issue number4
StatePublished - Aug 1 2015


  • Biomathematical modeling
  • Forecasting
  • Glioma
  • Invasion
  • Proliferation
  • Tumor growth simulation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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