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

Authors

• Eric J. Kostelich, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, United States.
• Yuan Xu, The Loyal & Edith Davis Neurosurgical Research Laboratory, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, United States.Follow
• Carlos Calderón-Valero, The Loyal & Edith Davis Neurosurgical Research Laboratory, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, United States.
• Duane C. Harris, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, United States.
• Oscar Alcantar-Garibay, The Loyal & Edith Davis Neurosurgical Research Laboratory, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, United States.
• Gerardo Gomez-Castro, The Loyal & Edith Davis Neurosurgical Research Laboratory, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, United States.
• Thomas J. On, The Loyal & Edith Davis Neurosurgical Research Laboratory, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, United States.
• Richard D. Dortch, Barrow Neuroimaging Innovation Center, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, United States.
• Yang Kuang, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, United States.
• Mark C. Preul, The Loyal & Edith Davis Neurosurgical Research Laboratory, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, United States.

Document Type

Article

Abstract

INTRODUCTION: Glioblastoma (GBM) is an aggressive primary brain tumor. Despite standard treatment, recurrence is common, and patient counseling remains challenging. Mathematical modeling offers a potential strategy to simulate tumor behavior and personalize care. This study evaluates whether a simple reaction-diffusion model can generate realistic scenarios of treatment outcomes for individual patients with recurrent GBM using clinical imaging data. METHODS: We retrospectively analyzed 132 MRI intervals from 46 patients who underwent treatment for recurrent GBM. T1 post-contrast and T2/FLAIR images were co-registered and manually segmented to identify enhancing tumor and edema. Using a systematic parameter sampling design, tumor growth between successive scans was simulated 18 times with a reaction-diffusion equation, the "ASU-Barrow" model, to generate realistic ranges of tumor response to treatment, as evaluated by clinical imaging. RESULTS: Model-generated scenarios for changes in tumor volumes well approximated the observed ranges in the patient data. In 86% of the imaging intervals, at least one scenario yielded a simulated tumor volume that agreed to within 20% of the observed one (and to within 10% in 65% of the cases). Spatial accuracy was assessed using agreement and containment scores, indicating how well the predicted tumor matched the real one. The best simulations achieved an agreement of 0.52 and a containment score of 0.69. These results suggest that a simple model can generate a realistic range of outcomes, over intervals of two or three months, in a majority of patient cases. CONCLUSION: This reaction-diffusion model simulates likely ranges of GBM progression under treatment with reasonable accuracy and modest computational needs and may yield a clinically practical tool to support patient counseling. Incorporating advanced imaging, such as perfusion MRI, may further improve accuracy. With further development, our approach could provide personalized scenarios of treatment outcomes that could aid in patient counseling.

Publication Date

1-1-2025

Publication Title

Frontiers in oncology

ISSN

2234-943X

Volume

15

First Page

1647144

PubMed ID

41089515

Digital Object Identifier (DOI)

10.3389/fonc.2025.1647144

Recommended Citation

Kostelich, Eric J.; Xu, Yuan; Calderón-Valero, Carlos; Harris, Duane C.; Alcantar-Garibay, Oscar; Gomez-Castro, Gerardo; On, Thomas J.; Dortch, Richard D.; Kuang, Yang; and Preul, Mark C., "Mathematical modeling for glioblastoma treatment: scenario generation and validation for clinical patient counseling" (2025). Neurosurgery. 2338.
https://scholar.barrowneuro.org/neurosurgery/2338