  Brain cognitive functions arise through the coordinated activity of several
brain regions, which actually form complex dynamical systems operating at
multiple frequencies. These systems often consist of interacting subsystems,
whose characterization is of importance for a complete understanding of the
brain interaction processes. To address this issue, we present a technique,
namely the bispectral Pairwise Interacting Source Analysis (biPISA), for
analyzing systems of cross-frequency interacting brain sources when
multichannel electroencephalographic (EEG) or magnetoencephalographic (MEG)
data are available. Specifically, the biPISA allows to identify one or many
subsystems of cross-frequency interacting sources by decomposing the
antisymmetric components of the cross-bispectra between EEG or MEG signals,
based on the assumption that interactions are pairwise. Thanks to the
properties of the antisymmetric components of the cross-bispectra, biPISA is
also robust to spurious interactions arising from mixing artifacts, i.e. volume
conduction or field spread, which always affect EEG or MEG functional
connectivity estimates. This method is an extension of the Pairwise Interacting
Source Analysis (PISA), which was originally introduced for investigating
interactions at the same frequency, to the study of cross-frequency
interactions. The effectiveness of this approach is demonstrated in simulations
for up to three interacting source pairs, and for real MEG recordings of
spontaneous brain activity. Simulations show that the performances of biPISA in
estimating the phase difference between the interacting sources are affected by
the increasing level of noise rather than by the number of the interacting
subsystems. The analysis of real MEG data reveals an interaction between two
pairs of sources of central mu and beta rhythms, localizing in the proximity of
the left and right central sulci.

Medical Physics;Data Analysis, Statistics and Probability;Quantitative Methods