Functional connectivity in resting-state fMRI: Is linear correlation sufficient?

Abstract

Functional connectivity (FC) analysis is a prominent approach to analyzing fMRI data, especially acquired under the resting state condition. The commonly used linear correlation FC measure bears an implicit assumption of Gaussianity of the dependence structure. If only the marginals, but not all the bivariate distributions are Gaussian, linear correlation consistently underestimates the strength of the dependence. To assess the suitability of linear correlation and the general potential of nonlinear FC measures, we present a framework for testing and estimating the deviation from Gaussianity by means of comparing mutual information in the data and its Gaussianized counterpart. We apply this method to 24 sessions of human resting state fMRI. For each session, matrix of connectivities between 90 anatomical parcel time series is computed using mutual information and compared to results from its multivariate Gaussian surrogate that conserves the correlations but cancels any nonlinearity. While the group-level tests confirmed non-Gaussianity in the FC, the quantitative assessment revealed that the portion of mutual information neglected by linear correlation is relatively minor—on average only about 5% of the mutual information already captured by the linear correlation. The marginality of the non-Gaussianity was confirmed in comparisons using clustering of the parcels—the disagreement between clustering obtained from mutual information and linear correlation was attributable to random error. We conclude that for this type of data, practical relevance of nonlinear methods trying to improve over linear correlation might be limited by the fact that the data are indeed almost Gaussian.

Causal density and integrated information as measures of conscious level

“…Fortunately, Gaussian approaches appear to be very powerful in neuroscience. For example, Palǔs and colleagues have shown (in theory and when applied to preictal EEG) that a Gaussian approach can distinguish different states of nonlinear chaotic attractors in ways similar to Lyapunov exponents or nonlinear entropy rates [31,32]; they also show that Gaussian descriptions are sufficient to describe resting state activity as measured by fMRI [33]. These results build on earlier work indicating the utility of linear approximations, especially for modelling large-scale interaction in neuroscience [34].…”

Regional and inter-regional effects in evolving climate networks

“…In the context of complex nonlinear systems, the use of nonlinear functional connectivity methods seems advantageous due to sensitivity to specific non-linear dependences, and has also been advocated for climate network analysis (Donges et al, 2009a, b). However, recently proposed quantification approaches presented by Hlinka et al (2011) and Hartman et al (2011) suggest that although statistically significant, the nonlinear contribution to connectivity is for many practical purposes negligible, including the analysis of temperature data from climate reanalysis data sets (Hlinka et al, 2013a). For other issues related to the choice of an appropriate dependence measure see e.g.…”

Pairwise network information and nonlinear correlations

“…Average signals from 12 regions of the fronto-parietal network were extracted using a brain atlas [38]. After preprocessing and denoising as in [39], the data were temporally concatenated. Each variable was further discretized to 2 or 3 states using equiquantal binning.…”