A multiscale symbolic approach to decoding delta and ripple oscillation bands as biomarkers for epileptiform discharges.

We use a multiscale symbolic approach to study the complex dynamics of temporal lobe refractory epilepsy employing high-resolution intracranial electroencephalogram (iEEG). We consider the basal and preictal phases and meticulously analyze the dynamics across frequency bands, focusing on high-frequency oscillations up to 240 Hz. Our results reveal significant periodicities and critical time scales within neural dynamics across frequency bands. By bandpass filtering neural signals into delta, theta, alpha, beta, gamma, and ripple high-frequency bands (HFO), each associated with specific neural processes, we examine the distinct nonlinear dynamics. Our method introduces a reliable approach to pinpoint intrinsic time lag scales τ within frequency bands of the basal and preictal signals, which are crucial for the study of refractory epilepsy. Using metrics such as permutation entropy (H), Fisher information (F), and complexity (C), we explore nonlinear patterns within iEEG signals. We reveal the intrinsic τmax that maximize complexity within each frequency band, unveiling the nonlinear subtle patterns of the temporal structures within the basal and preictal signal. Examining the H×F and C×F values allows us to identify differences in the delta band and a band between 200 and 220 Hz (HFO 6) when comparing basal and preictal signals. Differences in Fisher information in the delta and HFO 6 bands before seizures highlight their role in capturing important system dynamics. This offers new perspectives on the intricate relationship between delta oscillations and HFO waves in patients with focal epilepsy, highlighting the importance of these patterns and their potential as biomarkers.

High-frequency oscillations in the ripple bands and amplitude information coding: Toward a biomarker of maximum entropy in the preictal signals.

Intracranial electroencephalography (iEEG) can directly record local field potentials (LFPs) from a large set of neurons in the vicinity of the electrode. To search for possible epileptic biomarkers and to determine the epileptogenic zone that gives rise to seizures, we investigated the dynamics of basal and preictal signals. For this purpose, we explored the dynamics of the recorded time series for different frequency bands considering high-frequency oscillations (HFO) up to 240 Hz. We apply a Hilbert transform to study the amplitude and phase of the signals. The dynamics of the different frequency bands in the time causal entropy-complexity plane, H × C, is characterized by comparing the dynamical evolution of the basal and preictal time series. As the preictal states evolve closer to the time in which the epileptic seizure starts, the, H × C, dynamics changes for the higher frequency bands. The complexity evolves to very low values and the entropy becomes nearer to its maximal value. These quasi-stable states converge to equiprobable states when the entropy is maximal, and the complexity is zero. We could, therefore, speculate that in this case, it corresponds to the minimization of Gibbs free energy. In this case, the maximum entropy is equivalent to the principle of minimum consumption of resources in the system. We can interpret this as the nature of the system evolving temporally in the preictal state in such a way that the consumption of resources by the system is minimal for the amplitude in frequencies between 220-230 and 230-240 Hz.