Residual coherence and residual envelope correlation in MEG/EEG source-space connectivity analysis

Source-space coherence analysis has become a popular method to estimate functional connectivity based on MEG/EEG. One serious problem is that source-space coherence analysis can be confounded by spurious coherence caused due to the leakage properties of the inverse algorithm employed. Such spurious coherence is typically manifested as an artifactual large peak around the seed voxel, called seed blur, in the resulting coherence images. This seed blur often obscures important details of brain interactions. A novel method of computing coherence, called the residual coherence, is first proposed to remove the spurious coherence caused by the leakage of an imaging algorithm. We then present a theoretical analysis that shows the equivalence between the proposed residual coherence and corrected imaginary coherence proposed by others. We next extend the idea of residual coherence, and propose residual envelope correlation, which is suitable for estimating connectivity from high-frequency brain activities. Results from computer simulations demonstrate the effectiveness of the residual coherence and the residual envelope correlation.