TY - JOUR
T1 - Epileptiform Activity and Seizure Risk Follow Long-Term Non-Linear Attractor Dynamics
AU - Rosch, Richard E.
AU - Scheid, Brittany
AU - Davis, Kathryn A.
AU - Litt, Brian
AU - Ashourvan, Arian
N1 - Publisher Copyright:
© 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH.
PY - 2025/6/20
Y1 - 2025/6/20
N2 - 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. The primary aim is to develop a personalized strategy for inferring long-term trajectories of epileptiform activity and, consequently, seizure risk for individual patients undergoing long-term ECoG sampling via implantable neurostimulation devices. To achieve this goal, the Hankel alternative view of Koopman (HAVOK) analysis is adopted 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). The 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, it is demonstrated 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.
AB - 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. The primary aim is to develop a personalized strategy for inferring long-term trajectories of epileptiform activity and, consequently, seizure risk for individual patients undergoing long-term ECoG sampling via implantable neurostimulation devices. To achieve this goal, the Hankel alternative view of Koopman (HAVOK) analysis is adopted 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). The 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, it is demonstrated 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.
KW - delay-embedding
KW - Hankel alternative view of Koopman (HAVOK)
KW - singular value decomposition (SVD)
UR - http://www.scopus.com/inward/record.url?scp=105002124231&partnerID=8YFLogxK
U2 - 10.1002/advs.202411829
DO - 10.1002/advs.202411829
M3 - Article
AN - SCOPUS:105002124231
SN - 2198-3844
VL - 12
JO - Advanced Science
JF - Advanced Science
IS - 23
M1 - 2411829
ER -