Structural connectivity provides the backbone for communication between neural populations. Since axonal transmission occurs on a millisecond time scale, measures of M/EEG functional connectivity sensitive to phase synchronization, such as coherence, are expected to reflect structural connectivity. We develop a model of MEG functional connectivity whose edges are constrained by the structural connectome. The edge strengths are defined by partial coherence, a measure of conditional dependence. We build a new method—the adaptive graphical lasso (AGL)—to fit the partial coherence to perform inference on the hypothesis that the structural connectome is reflected in MEG functional connectivity. In simulations, we demonstrate that the structural connectivity’s influence on the partial coherence can be inferred using the AGL. Further, we show that fitting the partial coherence is superior to alternative methods at recovering the structural connectome, even after the source localization estimates required to map MEG from sensors to the cortex. Finally, we show how partial coherence can be used to explore how distinct parts of the structural connectome contribute to MEG functional connectivity in different frequency bands. Partial coherence offers better estimates of the strength of direct functional connections and consequently a potentially better estimate of network structure.

The relationship between structural and functional connectivity has been mostly examined in intact brains. Fewer studies have examined how differences in structure as a result of injury alters function. In this study we analyzed the relationship of structure to function across patients with stroke among whom infarcts caused heterogenous structural damage. We estimated relationships between distinct brain regions of interest (ROIs) from functional MRI in two pipelines. In one analysis pipeline, we measured functional connectivity by using correlation and partial correlation between 114 cortical ROIs. We found fMRI-BOLD partial correlation was altered at more edges as a function of the structural connectome (SC) damage, relative to the correlation. In a second analysis pipeline, we limited our analysis to fMRI correlations between pairs of voxels for which we possess SC information. We found that voxel-level functional connectivity showed the effect of structural damage that we could not see when examining correlations between ROIs. Further, the effects of structural damage on functional connectivity are consistent with a model of functional connectivity, diffusion, which expects functional connectivity to result from activity spreading over multiple edge anatomical paths. Author Summary Examining the structure to function relationship at damaged edges in the structural connectome due to lesions from stroke we find the following: • Partial correlation reflects structural connectome damage in 24% of edges tested. • Voxel-to-voxel correlation guided by structural connectivity shows the presence of SC damage in 39% of edges tested. • Edges that show modulation when using voxel-to-voxel correlation are consistent with diffusion as a model of functional connectivity. Our work provides evidence that for pairs of regions that are not directly anatomically connected due to lesions from stroke, signals must be communicated through intermediate region-to-region steps along an anatomical path.