A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks

Abstract

This study introduces a framework for the information-theoretic analysis of brain functional connectivity performed at the level of electroencephalogram (EEG) sources. The framework combines the use of common spatial patterns to select the EEG components which maximize the variance between two experimental conditions, simultaneous implementation of vector autoregressive modeling (VAR) with independent component analysis to describe the joint source dynamics and their projection to the scalp, and computation of information dynamics measures (information storage, information transfer, statistically significant network links) from the source VAR parameters. The proposed framework was tested on simulated EEGs obtained mixing source signals generated under different coupling conditions, showing its ability to retrieve source information dynamics from the scalp signals. Then, it was applied to investigate scalp and source brain connectivity in a group of children manifesting episodes of focal and generalized epilepsy; the analysis was performed on EEG signals lasting 5 s, collected in two consecutive windows preceding and one window following each ictal episode. Our results show that generalized seizures are associated with a significant decrease from pre-ictal to post-ictal periods of the information stored in the signals and of the information transferred among them, reflecting reduced self-predictability and causal connectivity at the level of both scalp and source brain dynamics. On the contrary, in the case of focal seizures the scalp EEG activity was not discriminated across conditions by any information measure, while source analysis revealed a tendency of the measures of information transfer to increase just before seizures and to decrease just after seizures. These results suggest that focal epileptic seizures are associated with a reorganization of the topology of EEG brain networks which is only visible analyzing connectivity among the brain sources. Our findings emphasize the importance of EEG modeling approaches able to deal with the adverse effects of volume conduction on brain connectivity analysis, and their potential relevance to the development of strategies for prediction and clinical treatment of epilepsy.

Keywords: EEG; common spatial patterns; epilepsy; independent component analysis; information storage; information theory; information transfer; vector autoregressive modeling.

Figure 1

Description of the methodology adopted in this work to assess information dynamics of EEG cortical sources. The EEG signals (in the number of D signals, each with length of N samples, collected over K trials during H conditions) are reduced in dimension by CSP (from D signals to Q components), and their time-lagged and instantaneous interactions are described respectively by a VAR model and by ICA; then, source dynamics are reconstructed via unmixing of the scalp signals, their interactions are retrieved through VAR modeling and solution of Yule-Walker equations, and information measures are computed from sub-models relevant to specific sources. In the figure, blue and red arrows refer to analysis steps performed on the whole dataset and on single trials, respectively. More details on the analysis are provided in the text.

Figure 2

Estimation of information dynamics for the simulated scenarios. Plots depict the distributions across 10 trials of the information storage ($S_j$, circles) and the total information transfer ($T_j$, squares), as well as the color-coded median values of the conditional information transfer ($T_{i,j\to k}$, connectivity matrices) computed for the simulated scalp signals (a,b) and for the cortical sources reconstructed using the proposed approach (c,d) in the first condition of absence of connectivity (a,c) and in the second condition with unidirectional source propagation (b,d). The filled symbols in (c,d) indicate the exact values of the information stored in each cortical source and the total information transferred to it.

Figure 3

Examples of EEG signals recorded with monopolar montage with the reference electrode placed on the ipsilateral ear at the onset of focal (a) and generalized (b) seizures. In the two cases, seizure onsets are marked with dashed lines. It can be noticed that the epileptiform discharges begin in the left frontotemporal region with later bilateral synchronization in the right frontal region in (a), and in all brain areas at the same time in (b).

Figure 4

Contribution to the total squared Riemannian distance provided by the eigenvalues ${\lambda }_j$ corresponding to each spatial filter $c_j$ ($j=1,\dots ,19$) of the CSP matrix obtained for the generalized seizures trials classified as $base$ and $pre$. Black and red dots identify the selected spatial filters and the discarded filters, respectively.

Figure 5

Information dynamics of scalp EEG signals measured during generalized seizures. Panels report the boxplot distribution and individual subject values (average over network nodes and trials) of the information storage $S_j$, total information transfer $T_j$, conditional information transfer $T_{i\to j|k}$, and number of significant links $N_{i\to j|k}$ in the three analyzed conditions $base$, $pre$, $post$. Statistically significant differences between pairs of distributions: *, p < 0.05 $base$ vs. $post$; #, p < 0.05 $pre$ vs. $post$.

Figure 6

Information dynamics of scalp EEG signals measured during focal seizures. Plots and symbols are as in Figure 5.

Figure 7

Information dynamics of source EEG signals measured during generalized seizures. Panels report the boxplot distribution and individual subject values (average over network nodes and trials) of the information storage $S_j$, total information transfer $T_j$, conditional information transfer $T_{i\to j|k}$, and number of significant links $N_{i\to j|k}$ in the three analyzed conditions $base$, $pre$, $post$. Statistically significant difference between pairs of distributions (p < 0.05) are marked with *; p-values < 0.1 are written in bold.

Figure 8

Information dynamics of source EEG signals measured during focal seizures. Plots and symbols are as in Figure 7.