Topological Phase Transitions in Functional Brain Networks: A Robust, Explainable Precursor to Epileptic Seizures

Background : Epileptic seizure forecasting has evolved from linear univariate measures to complex Deep Learning (DL) models. However, the black-box nature of DL limits clinical trust, and inter-patient variability remains a significant hurdle. Methods: We propose a transparent, network-based biomarker—the Canonical Dimension (Φ)—derived from the zeroth-order persistent homology of functional connectivity networks. Instead of using real EEG recordings, we generate fully synthetic multichannel signals and construct simulated functional networks that reproduce key statistical properties and recording conditions inspired by the CHB-MIT (pediatric) and TUH (adult) cohorts. Unlike threshold-based graph metrics, Φ integrates topological features across all filtration scales. We evaluate Φ across two simulated cohorts (24 pediatric-inspired and 45 adult-inspired virtual subjects) with heterogeneous seizure profiles and noise conditions. Results: Across all simulations, Φ consistently identified pre-ictal transitions with an average lead time of 32 seconds (AUROC = 0.94). Sensitivity analysis showed robustness against signal-to-noise ratios as low as 5dB. Statistical significance was confirmed via Benjamini–Hochberg FDR correction (padj < 0.001). Conclusion: Our findings indicate that simulated seizure onsets are preceded by a topological collapse—a generic earlywarning mechanism analogous to critical slowing down in dynamical systems. The Canonical Dimension Φ provides a computationally efficient (12ms/epoch) and fully explainable alternative to opaque neural networks, offering a principled target for future validation on real EEG datasets.