Mathematical formulations and approaches to the brain tumour resection problem

Brain tumors are the fifth most common tumors and the first line of treatment for a brain tumor is surgical resection. However, resecting an entire tumour mass may raise a problem when the tumour merges with healthy cells or it has formed around the brain region that is involved in 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 disruption on the brain functionality. We propose three measures, namely, global efficiency, concurrent demand satisfaction and congestion, to quantify the brain functionality. We develop critical node detection based formulation for the first and multicommodity flow based models for other measures. We develop Benders decomposition and column generation algorithms to solve the mathematical models. We compare 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.