Characterizing Epileptic Network Dynamics with Koopman Operator: Toward Surgical Targeting of Seizure Onset Zones

Accurate localization of the seizure onset zone (SOZ) is essential for the surgical treatment of drug-resistant epilepsy, yet it remains challenging because seizures involve rapid and variable spatiotemporal reorganization of brain networks. In this study, we propose a Koopman-inspired dynamic graph (KDG) framework for SOZ localization from intracranial electroen cephalography (iEEG). Unlike conventional high-frequency oscillation or functional connectivity (FC) approaches that primarily characterize local events or isolated network snapshots, the proposed framework explicitly models the temporal evolution of FC graphs using an operator-based dynamical representation. The estimated evolution operator is decomposed using singular value decomposition (SVD), and the dominant singular components are mapped back to graph space to derive interpretable nodal graph descriptors, including degree variation, node strength, eigenvector centrality, and nodal global efficiency. Under leave one-subject-out (LOSO) validation in seizure-free patients, The proposed KDG features achieved an area under the receiver operating characteristic curve (AUC) of 0.84, accuracy of 0.76, sensitivity of 0.79, and specificity of 0.76 for SOZ localization. Feature importance analysis showed that earlyictal periods contributed most strongly to SOZ discrimination, suggesting that early seizure-related network reorganization contains clinically informative biomarkers for epileptogenic tissue localization. These findings demonstrate that modeling dynamic functional brain networks can provide interpretable and clinically relevant biomarkers for SOZ localization and may offer a general framework for characterizing time-varying pathological network dynamics.