The paper describes the method of determining direction and frequency content of the brain activity flow. The method was formulated in the framework of the AR model. The transfer function matrix was found for multichannel EEG process. Elements of this matrix, properly normalized, appeared to be good estimators of the propagation direction and spectral properties of the investigated signals. Simulation experiments have shown that the estimator proposed by us unequivocally reveals the direction of the signal flow and is able to distinguish between direct and indirect transfer of information. The method was applied to the signals recorded in the brain structures of the experimental animals and also to the human normal and epileptic EEG. The sensitivity of the method and its usefulness in the neurological and clinical applications was demonstrated.

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Performance of different estimators describing propagation of electroencephalogram (EEG) activity, namely: Granger causality, directed transfer function (DTF), direct DTF (dDTF), short-time DTF (SDTF), bivariate coherence, and partial directed coherence are compared by means of simulations and on the examples of experimental signals. In particular, the differences between pair-wise and multichannel estimates are studied. The results show unequivocally that in most cases, the pair-wise estimates are incorrect and a complete set of signals involved in a given process has to be used to obtain the correct pattern of EEG flows. Different performance of multivariate estimators of propagation depending on their normalization is discussed. Advantages of multivariate autoregressive model are pointed out.

The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented.

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The multivariate versus bivariate measures of Granger causality were considered. Granger causality in the application to multivariate physiological time series has the meaning of the information flow between channels. It was shown by means of simulations and by the example of experimental electroencephalogram signals that bivariate estimates of directionality in case of mutually interdependent channels give erroneous results, therefore multivariate measures such as directed transfer function should be used for determination of the information flow.

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