Heading for data-driven measures of effective connectivity in functional MRI

A recent issue in functional magnetic resonance imaging (fMRI) data analysis has been the investigation of functional brain interactivity. Two standpoints have been considered so far. On the one hand, effective connectivity describes the influence that regions exert on each other. Yet, it requires the prior definition of a structural model that often turns out to be unknown. On the other hand, functional connectivity, based on marginal correlation, sets the framework for exploratory data-driven measures of statistical interdependency between regions. Unfortunately, one usually cannot use this knowledge to infer potential patterns of effective connectivity from the data. In this abstract, we emphasize the main reason why effective connectivity remains out of reach of functional connectivity. More precisely, we show that marginal correlation is unable to deal with mediation. Using a simple instance of structural equation modeling (SEM), we demonstrate how this model entails certain patterns of functional interaction that can be discriminated by functional connectivity and how other patterns cannot be differentiated. We then introduce conditional correlation as a way to achieve such a differentiation and show how it is related to mediated interaction.