Epileptiform activity and seizure risk follow long-term non-linear attractor dynamics

Many biological systems display circadian and slow multi-day rhythms, such as hormonal and cardiac cycles. In patients with epilepsy, these cycles also manifest as slow cyclical fluctuations in seizure propensity. However, such fluctuations in symptoms are consequences of the complex interactions between the underlying physiological, pathophysiological, and external causes. Therefore, identifying an accurate model of the underlying system that governs the multi-day rhythms allows for a more reliable seizure risk forecast and targeted interventions. To achieve this goal, we adopt the Hankel alternative view of Koopman (HAVOK) analysis to approximate a linear representation of nonlinear seizure propensity dynamics. The HAVOK framework leverages Koopman theory and delay-embedding to decompose chaotic dynamics into a linear system of leading delay-embedded coordinates driven by the low-energy coordinate (i.e., forcing). Our findings reveal the topology of attractors underlying multi-day seizure cycles, showing that seizures tend to occur in regions of the manifold with strongly nonlinear dynamics. Moreover, we demonstrate that the identified system driven by forcings with short periods up to a few days accurately predicts patients slower multi-day rhythms, which improves seizure risk forecasting.