Revisiting correlation-based functional connectivity and its relationship with structural connectivity.

Raphael Liégeois,Dimitri Van De Ville,Augusto Santos,Ali H Sayed,Vincenzo Matta

doi:10.1162/netn_a_00166

Abstract

Patterns of brain structural connectivity (SC) and functional connectivity (FC) are known to be related. In SC-FC comparisons, FC has classically been evaluated from correlations between functional time series, and more recently from partial correlations or their unnormalized version encoded in the precision matrix. The latter FC metrics yield more meaningful comparisons to SC because they capture ‘direct’ statistical dependencies, that is, discarding the effects of mediators, but their use has been limited because of estimation issues. With the rise of high-quality and large neuroimaging datasets, we revisit the relevance of different FC metrics in the context of SC-FC comparisons. Using data from 100 unrelated Human Connectome Project subjects, we first explore the amount of functional data required to reliably estimate various FC metrics. We find that precision-based FC yields a better match to SC than correlation-based FC when using 5 minutes of functional data or more. Finally, using a linear model linking SC and FC, we show that the SC-FC match can be used to further interrogate various aspects of brain structure and function such as the timescales of functional dynamics in different resting-state networks or the intensity of anatomical self-connections.

Highlights

The way brain function is shaped by the underlying anatomical substrate is far from understood
We first explore the correlation between structural connectivity matrix (SC) and functional connectivity matrix (FC) evaluated from four metrics of functional magnetic resonance imaging (fMRI) time series: (i) correlation, (ii) precision, (iii) regularized precision, and (iv) autoregressive matrices
A similar trend is observed when using filtered fMRI time series or when the four FC metrics are computed from deconvolved time series

Summary

Introduction

The way brain function is shaped by the underlying anatomical substrate is far from understood. Taking advantage of the increasing amount of high-quality anatomical and functional neuroimaging data that has become available in the last decade, various models were proposed to explore this question. The functional connectivity matrix (FC), which encodes the statistical dependencies between brain function in different regions (Friston, 2011), and the structural connectivity matrix (SC), which encodes the strength of anatomical connections between brain regions, were compared without. Functional connectivity (FC): Statistical dependencies between brain function in different brain regions. Recent advances in graph signal processing (Sandryhaila & Moura, 2013; Shuman, Narang, Frossard, Ortega, & Vandergheynst, 2013) have allowed one to question this relationship from a network theory perspective by linking spectral properties of SC and FC matrices. As most studies use functional magnetic resonance imaging (fMRI) data to evaluate FC because of its high spatial resolution, other functional modalities such as electro- or magneto-encephalography were considered to explore the link between brain anatomy and function (Amico et al, 2017; Finger et al, 2016; Steinmann et al, 2018)

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Discussion

Conclusion