Improved model prediction of glioma growth utilizing tissue-specific boundary effects

Joshua Jacobs, Russell C. Rockne, Andrea J. Hawkins-Daarud, Pamela R. Jackson, Sandra K. Johnston, Paul Kinahan, Kristin R. Swanson

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Kinetic parameter estimates for mathematical models of glioblastoma multiforme (GBM), derived from clinical scans, have been used to predict the occurrence of hypoxia, necrosis, response to radiation therapy, and overall survival. Modeling GBM growth in a cerebral model encounters anatomical boundaries that interfere with model calibration from clinical measurements. Methods: The effect of boundaries is examined on both spherically symmetric and anatomical models of tumor growth. This effect is incorporated into a method that updates kinetic parameters. The efficacy of this method in reproducing clinical image-derived subject data is evaluated. Results: Spherically symmetric simulations of tumor growth with simple boundaries behave predictably when in a linear phase of growth. Anatomic simulations of eleven out of twenty subjects demonstrated improved fit to subject data with the new method. When only subjects exhibiting linear growth are considered, eight out of nine subject demonstrate improved fit to the data. Conclusion: Anatomical boundaries to tumor growth measurably deflect progression and affect estimates of kinetic parameters. The presented method reliably updates kinetic parameters to fit anatomic computational models to clinically derived subject data when those data are in a linear regime.

Original languageEnglish (US)
Pages (from-to)59-66
Number of pages8
JournalMathematical Biosciences
StatePublished - Jun 2019


  • Boundary effects
  • GBM
  • Parameter estimation

ASJC Scopus subject areas

  • 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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