Functional connectivity: studying nonlinear, delayed interactions between BOLD signals.

Correlation analysis has been widely used in the study of functional connectivity based on fMRI data. It assumes that the relevant information about the interactions of brain regions is reflected by a linear relationship between the values of two signals at the same time. However, this hypothesis has not been thoroughly investigated yet. In this work, we study in depth the information shared by BOLD signals of pairs of brain regions. In particular, we assess the amount of nonlinear and/or nonsynchronous interactions present in data. This is achieved by testing models reflecting linear, synchronous interactions against more general models, encompassing nonlinear, nonsynchronous interactions. Many factors influencing measured BOLD signals are critical for the study of connectivity, such as paradigm-induced BOLD responses, preprocessing, motion artifacts, and geometrical distortions. Interactions are also influenced by the proximity of brain regions. The influence of all these factors is taken into account and the nature of the interactions is studied using various experimental conditions such that the conclusions reached are robust with respect to variation of these factors. After defining nonlinear and/or nonsynchronous interaction models in the framework of general linear models, statistical tests are performed on different fMRI data sets to infer the nature of the interactions. Finally, a new connectivity metric is proposed which takes these inferences into account. We find that BOLD signal interactions are statistically more significant when taking into account the history of the distant signal, i.e., the signal from the interacting region, than when using a model of linear instantaneous interaction. Moreover, about 75% of the interactions are symmetric, as assessed with the proposed connectivity metric. The history-dependent part of the coupling between brain regions can explain a high percentage of the variance in the data sets studied. As these results are robust with respect to various confounding factors, this work suggests that models used to study the functional connectivity between brain areas should in general take the BOLD signal history into account.