Optimization over trained graph neural networks with an application in brain tumor resection

Abstract

Low-grade gliomas (LGGs) present a critical challenge in neurosurgical oncology due to their slow progression and the brain’s adaptive neuroplastic reorganization. While complete resection reduces recurrence risk, it may disrupt reorganized functional networks. Emerging evidence shows partial resection can preserve neurological outcomes without compromising tumor control. However, surgeons lack quantitative tools to preoperatively evaluate these tradeoffs. The absence of a computational framework to model resection trade offs leaves surgical planning reliant on subjective intraoperative assessments rather than predictive network analysis. Our research addresses this gap by formulating the brain tumor resection problem as a mathematical optimization model using graph neural networks (GNNs), where the brain is represented as a multiplex network comprising regions of interest (ROIs) with structural and spatial connectivity. In our formulation, GNNs approximate brain functionality metrics such as global efficiency and modularity, serving as surrogate objective functions within a mixed-integer programming framework. We extend this methodology to bi-objective optimization, systematically analyzing trade-offs between several brain functionality metrics. Our framework provides surgeons with data-driven strategies that balance maximal tumor control with minimal network disruption. It achieves solutions whithin 0.34% of the true optimium and efficiently approximates the Pareto frontier, enabling precision neurosurgery tailored to individual brain networks.