A cartesian time--frequency approach to reveal brain interaction dynamics.

The study of large-scale interactions from magnetoencephalographic data based on the magnitude of the complex coherence computed at channel level is a widely used method to track the coupling between neural signals. Traditionally, a measure based on the magnitude of the complex coherence estimated by Fourier analysis, has been used under the assumption that the neural signals are stationary. Here, we split the complex coherence in its real and imaginary parts and focus on the latter with the advantage that the imaginary part is insensitive to spurious connectivity resulting from volume conducted "self interaction". Furthermore, interacting sources alone contribute to a non-vanishing imaginary part of the complex coherence whereas the contribute of non-interacting sources is also mapped from the magnitude of the complex coherence. Since it has been extensively shown that non-stationary stochastic processes contribute to the generation of neural signals, it is fundamental to be able to define interaction measures that are able to follow the temporal variations in the coupling between neural signals. To this purpose time-frequency domain techniques to estimate the magnitude of the complex coherence have been developed in the past decades. Similarly, we extend the analysis of the imaginary part of complex coherence to the time-frequency domain, by using the short-time Fourier transform to analyze the complex coherence as a function of time. In this way, it is possible to get an indication about the dynamic of the underlying source interaction pattern by looking at channel level interactions without the bias introduced by artifactual self-interaction by volume conduction or by the contribute of non-interacting sources. Furthermore, the corresponding imaginary part of the cross-spectrogram can be used to estimate interactions on a source level by localizing pools of sources interacting at a given frequency and by characterizing their dynamics. The method has been applied to magnetoencephalographic data from a cross-modal visual auditory stimulation and provided evidence for the involvement of temporal and occipital areas in the integrated information processing for simultaneous audio-visual stimulation. Furthermore, the source interaction pattern shows a variation in time that reflects a dynamical synchronization of the involved brain sources in the frequency bands of interest.