Andrei Ciprian Macarie ¹ Szabolcs Balint Suveges ² Mohamed Okasha ³ Kismet Hossain-Ibrahim ³ J Douglas Steele ² Dumitru Trucu ^4*

• ¹ Mathematics & Medicine, University of Dundee, Dundee, United Kingdom
• ² School of Medicine, University of Dundee, Dundee, Scotland, United Kingdom
• ³ NHS Tayside, Dundee, Scotland, United Kingdom
• ⁴ Mathematics, University of Dundee, Dundee, United Kingdom

Glioblastoma multiforme (GBM), the most aggressive primary brain tumour, exhibits low survival rates due to its rapid growth, infiltrates surrounding brain tissue, and is highly resistant to treatment.One major challenge is oedema infiltration, a fluid build-up that provides a path for cancer cells to invade other areas. MRI resolution is insufficient to detect these infiltrating cells, leading to relapses despite chemotherapy and radiotherapy. In this work, we propose a new multiscale mathematical modelling method, to explore the oedema infiltration and predict tumour relapses.To address tumour relapses, we investigated several possible scenarios for the distribution of remaining GBM cells within the oedema after surgery. Furthermore, in this computational modelling investigation on tumour relapse scenarios were investigated assuming the presence of clinically relevant chemo-radio therapy, numerical results suggest that a higher concentration of GBM cells near the surgical cavity edge led to limited spread and slower progression of tumour relapse. Finally, we explore mathematical and computational avenues for reconstructing relevant shapes for the initial distributions of GBM cells within the oedema from available MRI scans. The results obtained show good overlap between our simulation and the patient's serial MRI scans taken 881 days into the treatment. While still under analytical investigation, this work paves the way for robust reconstruction of tumour relapses from available clinical data.