Noise amplification precedes extreme epileptic events on human EEG

Extreme events are rare and sudden abnormal deviations of the system's behavior from a typical state. Statistical analysis reveals that if the time series contains extreme events, its distribution has a heavy tail. In dynamical systems, extreme events often occur due to developing instability preceded by noise amplification. Here, we apply this theory to analyze generalized epileptic seizures in the human brain. First, we demonstrate that the time series of electroencephalogram (EEG) spectral power in a frequency band of 1–5 Hz obeys a heavy-tailed distribution, confirming the presence of extreme events. Second, we report that noise on EEG signals gradually increases before the seizure onset. Thus, we hypothesize that generalized epileptic seizures in humans are the extreme events emerging from instability accompanied by preictal noise amplification similar to other dynamical systems.

Figure 1

Wavelet power. (a) The fragment of the EEG signal registered from the frontal electrode, Fp2, representing epileptic seizure. (b) The time-frequency evolution of the WP during the seizure. The vertical dashed line shows the seizure onset, and a solid curve follows the frequency with the highest WP (a wavelet skeleton). (c) NWP corresponding to the epileptic seizure and the baseline. Data are shown as the group $\mathrm{mean}\pm \mathrm{SE}$ (Standard Error). (d) The pairwise difference distribution between NWP in the frequency bands of 1–5 Hz and 5–10 Hz. The dashed line corresponds to the equality of the NWP in these frequency bands. The circles and squares reflect the individual subjects' NWP for the seizure and the baseline. (e) The time series illustrate the WP evolution in the 5–10 Hz frequency band in the course of the experiment. The sharp peaks reflect the seizures and are considered extreme events.

Figure 2

(a) The PDF of the local maxima of NWP in the 1–5 Hz frequency band and its Weibull approximation. Data are shown for a single subject. The Weibull parameters of the seizure and baseline: (b) localization parameter $loc$ [mean $\pm$ standard deviation (SD), $p=0.74$, Wilcoxon test], (c) exponentiation parameter $a$ (mean $\pm$ SD, $p=0.005$, Wilcoxon test) and (d) its pairwise differences distribution, (e) shape parameter $c$ ($\mathrm{mean}\pm \mathrm{SD}$, $p=0.005$, Wilcoxon test) and (f) its pairwise differences distribution, and (g) scaling parameter $scale$ ($\mathrm{mean}\pm \mathrm{SD}$, $p=0.005$, Wilcoxon test) and (h) its pairwise differences distribution. The dashed line in (d), (f), and (h) reflects the Weibull parameter's equality for the seizure and baseline. Points to the right of this line indicate that the Weibull parameter is higher during the seizure, and vice versa.

Figure 3

(a) The set of EEG signals, including the preictal period and the onset of the epileptic seizure (vertical solid line). The four horizontal lines, $T_1,\cdots ,T_4$, show positions of the time windows used for the noise intensity estimation. Each window's length is equal to 30 s. (b) The noise intensity (mean $\pm$ 95% confidence interval and individual values) estimated for these time windows, $F(3,27)=3.48$, $p=0.0029$ via one-way analysis of variance (ANOVA). (c) The regression plot: colored dots correspond to each participant's data, lines have a similar slope, $r=0.52$ estimated for these participants via correlation analysis with repeated measures ($p=0.002$). (d) The signal variance (mean $\pm$ 95% confidence interval and individual values) calculated for these time windows, $F(3,27)=1.64$, $p=0.207$ via one-way ANOVA. (e) The regression plot: colored dots correspond to each participant's data, lines have a similar slope, $r=0.38$ estimated for these participants via correlation analysis with repeated measures ($p=0.031$).

Figure 4

The regression plot: colored dots correspond to each participant's data (noise intensity and signal variance); lines have a similar slope, reflecting a strong positive correlation ($r=0.809$) between the noise intensity and signal variance estimated for these participants via correlation analysis with repeated measures.