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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.

Introduction. Brain electrical activity signals (or EEG) by their very nature are non-stationary time series. This basically allows applying a set of mathematical-statistical analysis methods to them. One of the most common methods for signal analyzing is the construction of autoregressive mathematical models and analysis of their parameters in order to obtain additional information about the signal itself or causality between signals. In multivariate autoregressive (MVAR) modeling of EEG, the main issue is the optimal choice of model order. In this work, the approach for selecting the optimal order of MVAR models of brain electrical activity signals of subjects diagnosed with epilepsy is proposed. MVAR modeling. The autoregressive model assumes that the current sample of the discrete signal can be linearly predicted as a weighted sum of its previous samples. MVAR model extends this assumption to multiple time series so that the vector of current samples of all signals is modeled as a linear sum of their previous samples. MVAR models of EEG signals essentially are formed by solving systems of linear equations. The Yule-Walker method of linear equations systems solving is used in this paper. The accuracy of EEG modeling depends on the order of model. Each model order influenced by the amount of delay between current samples and last previous samples used to generate the model. To assess the order and quality of models the Schwarz-Bayes information criterion (SBC) is used in this work taking into account the covariance matrix of the residuals. Additionally, the quality is assessed by Pearson's correlation coefficient between the real and simulated data. In this paper, the MVAR modeling and statistical analysis of the models' optimal orders of the input signal periods before, during and after an epileptic seizure is carried out. Experimental results. Two sets of EEG data with generalized and focal epileptic seizures are used. The first group of patients with focal seizures consists of 26 people and more than 100 epileptic seizures. The second group with generalized seizures consists of 11 people and about 50 epileptic seizures. For EEG signals modeling, values of orders in a range from 1 to 22 are used. Consequently, for each investigated period of signal (before, during and after a seizure), 22 different MVAR models are constructed and compared. After modeling, the obtained models for each order value are evaluated using the SBC criterion. Conclusions. According to the results, it is recommended to choose the order of MVAR models of EEG signals in the predefined range of orders from 11 to 13. Since the sampling rate of the signals used in these experiments is 250 Hz, the specified range of order values indicates that MVAR-modelling of one signal includes information that contains all other signals with a delay of 44-52 ms. Therefore, theoretically, it is possible to allocate functional characteristics of brain electrical activity for patients with epilepsy that occur synchronously in different parts of the brain and spread at an average of 50 ms. Moreover, the ways of further research of electrical brain activity and functional connections of brain regions during epileptic activity are indicated.