  Understanding brain dynamics in epilepsy is critical for establishing
rigorous control objectives that enable new therapeutic methods to mitigate
seizure occurrence. In multichannel electrocorticography (ECoG) recordings
acquired in 21 subjects during a total of 94 seizures, we apply dynamical
systems stability analysis to assess the balance versus imbalance of seizure
dynamics across different timescales and brain regions. Specifically, we
consider a sliding time window multivariate autoregressive linear approximation
of the data captured by the ECoG channels, where eigendecomposition of the
estimated matrix of coefficients describes the contribution of different
regions to the spatiotemporal process (eigenvectors) associated with a
particular timescale (eigenvalues). Interestingly, we observe a pattern of
eigenvalue evolution and slowly changing (or approximately time-invariant)
eigenvectors across both seizures and subjects. The seizure-onset is marked by
an increase in high frequency spatial information to which a few regions
contribute for a long period. By contrast, the seizure termination is
characterized by a sudden, small time period change in dynamics to which many
regions contribute. As the seizure terminates, the relatively stable ictal
dynamics rapidly transition into the post-ictal regime, marked by relatively
fast-damping oscillations. Our methodology offers a subject-specific
characterization of the spatiotemporal behavior of the seizure, providing new
insights into the dynamic patterns and functional interactions between brain
regions that occur over different timescales. More generally, our approach
informs the development of engineering objectives that can be used to deploy
new control strategies to prevent seizure evolution or to hasten seizure
termination.
