Precise identification of seizure propagation pathways is a critical prerequisite for targeted interventions in epilepsy, such as responsive neurostimulation. However, given the highly dynamic nature of epileptic networks, traditional static or purely probabilistic connectivity measures often fail to capture the continuous temporal flow of seizure activity. To address this challenge, we introduce the Continuous Temporal Graph (CTG) framework, a novel mathematical approach designed to model the temporal evolution of seizure pathways directly from intracranial EEG (iEEG/sEEG) recordings. Unlike discrete-time methods that compress or lose fuzzy temporal information, the CTG framework represents functional interactions not as static weights, but as continuous sets of active time intervals. By employing interval algebra—specifically union and sequential composition —we strictly capture the temporal continuity of seizure spread. Within this framework, we propose a novel metric, T_bridge , which utilizes counterfactual reasoning to quantify the temporal dependency of propagation on specific functional connections. Rather than asserting the presence of permanent structural defects, T_bridge precisely identifies pathways that act as indispensable functional bridges at specific, critical moments during a seizure. Evaluated on both simulated datasets and patient iEEG recordings, the proposed framework successfully isolates time-dependent, non-redundant critical pathways that traditional statistical metrics may obscure. Ultimately, this study provides a new mathematical lens for observing temporal network dynamics, shifting the paradigm from static connectivity estimation to the analysis of continuous temporal topology in epileptic networks.
Objective: This study aims to bridge the gap between abstract network modeling and clinical iEEG recordings by developing the Continuous Temporal Graph (CTG) framework, enabling precise mathematical mapping of temporal dependencies during seizure propagation.
Method: We applied a novel Continuous Temporal Graph (CTG) framework to intracranial EEG (iEEG) recordings from patients with drug-resistant epilepsy. In this model, nodes represent individual electrodes, and edges are defined based on their continuous active time intervals during seizures. Using interval-based mathematical operators, we calculated the temporal overlaps between brain regions. Furthermore, the T_bridge metric was introduced to quantify temporal and functional dependencies, enabling the identification of critical propagation pathways.
Results: In clinical validation (5 patients, 10 seizures), the CTG framework correctly identified expert-defined bridge edges connecting the Seizure Onset Zone (SOZ) to early propagation regions in 9 out of 10 seizures. Simulation studies confirmed the model's robustness to noise, with optimal performance at a 10–50 ms temporal resolution. Furthermore, the T_bridge metric successfully distinguished critical structural pathways from redundant connections, outperforming traditional probabilistic methods such as Transfer Entropy and Granger Causality.
Discussions: The CTG framework provides a robust mathematical approach to model the continuous temporal evolution of seizure pathways directly from iEEG data. By identifying temporal and functional bottlenecks T_bridge this method offers a patient-specific mapping of critical network dependencies. These findings suggest that CTG can enhance our understanding of seizure dynamics and potentially guide more precise, temporally-informed clinical interventions, such as targeted ablation or neurostimulation.