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

Eric Kostelich^1*Yuan Xu²Carlos Calderon-Valero²Duane Harris^1,3Oscar Alcantar-Garibay²Gerardo Gomez-Castro²Thomas J. On²Richard Dortch²Yang Kuang¹Mark C. Preul^4*

• ¹Arizona State University School of Mathematical and Statistical Sciences, Tempe, United States
• ²Barrow Neurological Institute, Phoenix, United States
• ³Los Alamos National Laboratory Theoretical Biology and Biophysics Division, Los Alamos, United States
• ⁴Division of Neurological Surgery, Barrow Neurological Institute (BNI), Phoenix, Arizona, United States

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 in 86% of cases Kostelich et al. Mathematical Modeling for Glioblastoma (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.