In the past, considerable effort has been devoted to the development of signal processing techniques aimed at characterizing brain connectivity from signals recorded from spatially-distributed regions during normal or pathological conditions. In this paper, three families of methods (linear and nonlinear regression, phase synchronization, and generalized synchronization) are reviewed. Their performances were evaluated according to a model-based methodology in which a priori knowledge about the underlying relationship between systems that generate output signals is available. This approach allowed us to relate the interdependence measures computed by connectivity methods to the actual values of the coupling parameter explicitly represented in various models of signal generation. Results showed that: (i) some of the methods were insensitive to the coupling parameter; (ii) results were dependent on signal properties (broad band versus narrow band); (iii) there was no "ideal" method, i.e., none of the methods performed better than the other ones in all studied situations. Nevertheless, regression methods showed sensitivity to the coupling parameter in all tested models with average or good performances. Therefore, it is advised to first apply these "robust" methods in order to characterize brain connectivity before using more sophisticated methods that require specific assumptions about the underlying model of relationship. In all cases, it is recommended to compare the results obtained from different connectivity methods to get more reliable interpretation of measured quantities with respect to underlying coupling. In addition, time-frequency methods are also recommended when coupling in specific frequency sub-bands ("frequency-locking") is likely to occur as in epilepsy.

Brain functional connectivity can be characterized by the temporal evolution of correlation between signals recorded from spatially-distributed regions. It is aimed at explaining how different brain areas interact within networks involved during normal (as in cognitive tasks) or pathological (as in epilepsy) situations. Numerous techniques were introduced for assessing this connectivity. Recently, some efforts were made to compare methods performances but mainly qualitatively and for a special application. In this paper, we go further and propose a comprehensive comparison of different classes of methods (linear and nonlinear regressions, phase synchronization, and generalized synchronization) based on various simulation models. For this purpose, quantitative criteria are used: in addition to mean square error under null hypothesis (independence between two signals) and mean variance computed over all values of coupling degree in each model, we provide a criterion for comparing performances. Results show that the performances of the compared methods are highly dependent on the hypothesis regarding the underlying model for the generation of the signals. Moreover, none of them outperforms the others in all cases and the performance hierarchy is model dependent.

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