M.S. Thesis Presentation: MATHEMATICAL FORMULATIONS AND APPROACHES TO THE BRAIN TUMOUR RESECTION PROBLEM by Sarp Bora İlhan
Thesis Advisor: Taghi Khaniyev
Date: July 5 Thursday 2024
Time: 10:30
Place: EA-202
Abstract:
A brain tumour is a serious disease that must be removed from the brain before it causes irreversible consequences. However, resecting the entire tumour mass may raise a problem when the tumour merges with healthy cells or it has formed around the brain region that operates vital functions. Our aim is to capture the results of resecting tumourous parts in these complex situations and selecting the tumour volume that will have the least negative impact on surrounding tis- sues. We propose three measures, namely, global efficiency, concurrent demand satisfaction and congestion, to approach this problem from different angles. We develop critical node detection based formulation for the first and multicommod- ity flow based models for other measures.
We develop Benders decomposition and column generation algorithms to solve the mathematical models. We com- pare the algorithm performances with model formulations. We use a diverse range of instances to conduct detailed comparisons. Finally, we investigate the decision outputs and how they change in different cases.