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

## TL;DR

This study shows that a simple mathematical model can simulate glioblastoma tumor growth and treatment outcomes, helping personalize patient counseling.

## Contribution

A reaction-diffusion model is validated for generating realistic treatment scenarios for recurrent glioblastoma using clinical imaging data.

## Key findings

- The model simulated tumor volumes within 20% of observed data in 86% of cases.
- Best simulations achieved an agreement score of 0.52 and containment score of 0.69.
- The model requires modest computational resources and could support clinical decision-making.

## Abstract

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.

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.

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.

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.