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Related Experiment Video

Updated: Sep 22, 2025

Glioblastoma Relapse Post-Resection Model for Therapeutic Hydrogel Investigations
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Tracking glioblastoma progression after initial resection with minimal reaction-diffusion models.

Duane C Harris1, Giancarlo Mignucci-Jiménez2, Yuan Xu2

  • 1School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA.

Mathematical Biosciences and Engineering : MBE
|May 23, 2022
PubMed
Summary

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Mathematical modeling for glioblastoma treatment: scenario generation and validation for clinical patient counseling.

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Go-or-grow-or-die as a framework for the mathematical modeling of glioblastoma dynamics.

Mathematical biosciences·2025

This study models glioblastoma multiforme (a brain cancer) progression using two reaction-diffusion models. The models successfully simulated tumor growth in 9 out of 10 patients, aiding treatment understanding.

Area of Science:

  • Computational biology
  • Mathematical oncology
  • Biophysics

Background:

  • Glioblastoma multiforme is an aggressive brain cancer.
  • Modeling tumor progression is crucial for effective treatment strategies, especially after recurrence.
  • Current models require refinement to accurately predict tumor behavior.

Purpose of the Study:

  • To develop and validate reaction-diffusion models for glioblastoma multiforme growth.
  • To simulate tumor progression in patients with recurrent glioblastoma.
  • To assess model parameter variability and predictive accuracy.

Main Methods:

  • Utilized Fisher-Kolmogorov and a novel 2-population reaction-diffusion model.
  • Simulated models on 3D brain geometries from MRI scans of 10 patients.
Keywords:
Fisher-Kolmogorov modelensemble predictionglioblastoma multiformemagnetic resonance imagingparameter estimationreaction-diffusion equations

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  • Employed Taguchi sampling for parameter variability analysis across 144 parameter sets.

    • Main Results:

    • Successfully identified model parameters for 9 out of 10 patients.
    • Simulated tumors matched at least 40% of observed tumor volume in successful cases.
    • Demonstrated significant tumor progression over 1-3 months in patient data.

    Conclusions:

    • Preliminary models show promise in simulating recurrent glioblastoma growth.
    • Model parameterization and initialization require further investigation for improved accuracy.
    • This approach offers a foundation for personalized glioblastoma treatment planning.