Epileptiform Activity and Seizure Risk Follow Long-Term Non-Linear Attractor Dynamics

Area of Science:

• Neuroscience
• Dynamical Systems Theory
• Computational Biology

Background:

• Biological systems exhibit circadian and multi-day rhythms, influencing physiological and pathophysiological processes.
• Epilepsy patients show cyclical fluctuations in seizure propensity, linked to complex underlying causes.
• Accurate modeling of these rhythms is crucial for reliable seizure risk forecasting and personalized interventions.

Purpose of the Study:

• To develop a personalized strategy for inferring long-term epileptiform activity trajectories.
• To improve seizure risk forecasting for epilepsy patients using long-term electrocorticography (ECoG) data.
• To model nonlinear seizure propensity dynamics using Koopman theory.

Main Methods:

• Adopted Hankel alternative view of Koopman (HAVOK) analysis to approximate nonlinear seizure dynamics with a linear system.
• Leveraged Koopman theory and delay-embedding to decompose chaotic dynamics.
• Analyzed long-term ECoG data from implantable neurostimulation devices.

Main Results:

• Revealed the topology of attractors underlying multi-day seizure cycles.
• Demonstrated that seizures correlate with regions of strongly nonlinear dynamics.
• Showed that the HAVOK model accurately predicts multi-day rhythms using short-period forcings.

Conclusions:

• The HAVOK analysis provides a linear framework for understanding nonlinear seizure propensity dynamics.
• Accurate prediction of multi-day rhythms significantly enhances seizure risk forecasting.
• This personalized strategy offers a pathway for targeted interventions in epilepsy management.