# Bispectral pairwise interacting source analysis for identifying systems of cross-frequency interacting brain sources from electroencephalographic or magnetoencephalographic signals

## TL;DR

The paper introduces biPISA, a novel method for identifying cross-frequency interacting brain sources from EEG/MEG data, robust against artifacts, demonstrated through simulations and real MEG recordings.

## Contribution

biPISA extends the PISA method to analyze cross-frequency interactions, enabling robust identification of interacting brain source subsystems from EEG/MEG signals.

## Key findings

- biPISA accurately estimates phase differences in simulated data.
- The method successfully identifies interacting sources in real MEG recordings.
- Performance is affected more by noise level than the number of source pairs.

## Abstract

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.