Conditional correlation as a measure of mediated interactivity in fMRI and MEG/EEG

Many measures have been proposed so far to extract brain functional interactivity from functional magnetic resonance imaging (fMRI) and magnetoencephalography/electroencephalography (MEG/EEG) data sets. Unfortunately, none has been able to provide a relevant, self-contained, and common definition of brain interaction. In this paper, we propose a first step in this direction. We first introduce a common terminology together with a cross-modal definition of interaction. In this setting, we investigate the commonalities shared by some measures of interaction proposed in the literature. We show that temporal correlation, nonlinear correlation, mutual information, generalized synchronization, phase synchronization, coherence, and phase locking value (PLV) actually measure the same quantity (namely correlation) when one is investigating linear interactions between independently and identically distributed Gaussian variables. We also demonstrate that these data-driven measures can only partly account for the interaction patterns that can be expressed by the effective connectivity of structural equation modeling (SEM) . To bridge this gap, we suggest the use of conditional correlation, which is shown to be related to mediated interaction.