Mathematical Modelling of Novel Treatment Strategies in Glioblastomas

Abstract: Background: Glioblastoma is a deadly brain tumour with a median survival of 15 months. Immunotherapy using immune checkpoint inhibitors (ICIs) has shown promise in other solid tumours, such as melanoma, but clinical trials in glioblastoma have thus far failed. Recent studies showed lasting benefits for those who responded to treatment, suggesting that an improved understanding of the tumour’s interactions with its immune microenvironment is needed to establish effective combination schedules. Aims: Using mathematical modelling, we sought to answer fundamental questions about how the delivery of ICIs can be individualized for maximum patient benefit, and to delineate patient-specific characteristics distinguishing responders from non-responders. Our approach allowed us to assess the effects of immunotherapies on glioblastoma in humans in a robust and non-invasive manner. Methods: We constructed a mechanistic mathematical model capturing tumour growth and key immunological features, including pro- and anti-tumoral macrophages, CD8+ T cells, and TGFbeta. To replicate patient heterogeneity, we generated a cohort of virtual patients whose predicted trajectories were validated against clinical data. We then simulated tumour evolution under treatment combining tumour resection, radiotherapy, chemotherapy, and immunotherapy in these virtual patients. Results: CD8+ T cells were found to play a crucial role in ICI responses. Other biomarkers, such as the M2:M1 macrophage ratio, also predicted treatment outcomes in virtual patients. Optimal scheduling strategies were explored based on these key features. Conclusions: Our study demonstrates that complementary modelling approaches can provide key insights into treatment successes and failures, and design effective therapeutic strategies to bring forward into the clinic.

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