Revisiting non-linear functional brain co-activations: directed, dynamic and delayed

The center stage of neuro-imaging is currently occupied by studies of functional correlations between brain regions. These correlations define the brain functional networks, which are the most frequently used framework to represent and interpret a variety of experimental findings. In previous work we first demonstrated that the relatively stronger BOLD activations contain most of the information relevant to understand functional connectivity and subsequent work confirmed that a large compression of the original signals can be obtained without significant loss of information. In this work we revisit the correlation properties of these epochs to define a measure of nonlinear dynamic directed functional connectivity (nldFC) across regions of interest. We show that the proposed metric provides at once, without extensive numerical complications, directed information of the functional correlations, as well as a measure of temporal lags across regions, overall offering a different perspective in the analysis of brain co-activation patterns. In this paper we provide for a proof of concept, based on replicating and completing existing results on an Autism database, to discuss the main features and advantages of the proposed strategy for the study of brain functional correlations. These results show new interpretations of the correlations found on this sample.