Brain cognitive functions arise through the coordinated activity of several brain regions, which form complex dynamical systems operating at multiple temporal scales. The spatio-temporal characterization of these systems is of fundamental importance for a better understanding of brain processes as well as for characterizing the signatures of healthy and diseased cognition. To this aim, it is crucial to develop methods able to disclose functional connections within and between brain systems and to disentangle functional systems. Among these methods, linear and nonlinear techniques can be used for detecting interactions occurring at the same frequency or at different frequencies (i.e., cross frequency coupling) from multichannel electroencephalographic (EEG) or magnetoencephalographic (MEG) data. In this framework, a particular interest is deserved by methods characterized by the desirable property of being robust to spurious interactions arising from mixing artifacts, i.e. volume conduction or source leakage. Namely, we present a novel approach to the third order spectral analysis of EEG and MEG data for studying cross frequency functional brain connectivity that generalizes the properties of the imaginary part of coherency from the linear to the nonlinear case. Specifically, we demonstrate in simulations that the method is robust to mixing artifacts. Moreover, our simulations show that the method can be reliably be used to: i) detect the coupled systems; ii) estimate the phase difference between the interacting sources. The method performance are affected by the increasing level of noise rather than by the complexity (i.e., number of sources) in the interacting systems. The method is then applied to analyze spontaneous EEG and MEG data. Our results reveal a cross frequency coupling between brain sources at 10 Hz and 20 Hz, i.e., for alpha and beta rhythms. This interaction is then projected from signal space to source level by using a fit-based procedure, thus highlighting that the 10 to 20 Hz dominant interaction localized in an occipito-motor network.
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