An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias

Phase-synchronization is a manifestation of interaction between neuronal groups measurable from LFP, EEG or MEG signals, however, volume conduction can cause the coherence and the phase locking value to spuriously increase. It has been shown that the imaginary component of the coherency (ImC) cannot be spuriously increased by volume-conduction of independent sources. Recently, it was proposed that the phase lag index (PLI), which estimates to what extent the phase leads and lags between signals from two sensors are nonequiprobable, improves on the ImC. Compared to ImC, PLI has the advantage of being less influenced by phase delays. However, sensitivity to volume-conduction and noise, and capacity to detect changes in phase-synchronization, is hindered by the discontinuity of the PLI, as small perturbations turn phase lags into leads and vice versa. To solve this problem, we introduce a related index, namely the weighted phase lag index (WPLI). Differently from PLI, in WPLI the contribution of the observed phase leads and lags is weighted by the magnitude of the imaginary component of the cross-spectrum. We demonstrate two advantages of the WPLI over the PLI, in terms of reduced sensitivity to additional, uncorrelated noise sources and increased statistical power to detect changes in phase-synchronization. Another factor that can affect phase-synchronization indices is sample-size bias. We show that, when directly estimated, both PLI and the magnitude of the ImC have typically positively biased estimators. To solve this problem, we develop an unbiased estimator of the squared PLI, and a debiased estimator of the squared WPLI.