Linking Functional Connectivity and Structural Connectivity Quantitatively: A Comparison of Methods.

Structural connectivity in the brain is the basis of functional connectivity. Quantitatively linking the two, however, remains a challenge. For a pair of regions of interest (ROIs), anatomical connections derived from diffusion-weighted imaging are often quantified by fractional anisotropy (FA) or edge weight, whereas functional connections, derived from resting-state functional magnetic resonance imaging, can be characterized by non-time-series measures such as zero-lag cross correlation and partial correlation, as well as by time-series measures such as coherence and Granger causality. In this study, we addressed the question of linking structural connectivity and functional connectivity quantitatively by considering two pairs of ROIs, one from the default mode network (DMN) and the other from the central executive network (CEN), using two different data sets. Selecting (1) posterior cingulate cortex and medial prefrontal cortex of the DMN as the first pair of ROIs and (2) left dorsal lateral prefrontal cortex and left inferior parietal lobule of the CEN as the second pair of ROIs, we show that (1) zero-lag cross correlation, partial correlation, and pairwise Granger causality were not significantly correlated with either mean FA or edge weight and (2) conditional Granger causality (CGC) was significantly correlated with edge weight but not with mean FA. These results suggest that (1) edge weight may be a more appropriate measure to quantify the strength of the anatomical connection between ROIs and (2) CGC, which statistically removes common input and the indirect influences between a given ROI pair, may be a more appropriate measure to quantify the strength of the functional interaction enabled by the fibers linking the two ROIs.