Topological biomarkers for seizure state transitions

Detecting critical state transitions in noisy, high-dimensional neural recordings remains a challenge in nonlinear dynamics. We apply a geometric, persistent-homology-based analysis to sliding-window reconstructions of multichannel neurophysiological signals. From the resulting time-varying persistence diagrams, we evaluate two topological biomarkers: a finite-difference persistence derivative to quantify the rate of topological change of the underlying attractor and the total persistence to measure the state's topological complexity. Across iEEG/EEG/MEG datasets, the derivative robustly aligns with seizure onset and termination, while total persistence provides a statistically significant distinction between ictal and interictal periods. This work provides an interpretable topological framework for analyzing state transitions in complex neurophysiological dynamics.