Structural connectome constrained graphical lasso for MEG partial coherence.

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.