Robust EEG/MEG Based Functional Connectivity with the Envelope of the Imaginary Coherence: Sensor Space Analysis

The brain's functional connectivity (FC) estimated at sensor level from electromagnetic (EEG/MEG) signals can provide quick and useful information towards understanding cognition and brain disorders. Volume conduction (VC) is a fundamental issue in FC analysis due to the effects of instantaneous correlations. FC methods based on the imaginary part of the coherence (iCOH) of any two signals are readily robust to VC effects, but neglecting the real part of the coherence leads to negligible FC when the processes are truly connected but with zero or π-phase (modulus 2π) interaction. We ameliorate this issue by proposing a novel method that implements an envelope of the imaginary coherence (EIC) to approximate the coherence estimate of supposedly active underlying sources. We compare EIC with state-of-the-art FC measures that included lagged coherence, iCOH, phase lag index (PLI) and weighted PLI (wPLI), using bivariate autoregressive and stochastic neural mass models. Additionally, we create realistic simulations where three and five regions were mapped on a template cortical surface and synthetic MEG signals were obtained after computing the electromagnetic leadfield. With this simulation and comparison study, we also demonstrate the feasibility of sensor FC analysis using receiver operating curve analysis whilst varying the signal's noise level. However, these results should be interpreted with caution given the known limitations of the sensor-based FC approach. Overall, we found that EIC and iCOH demonstrate superior results with most accurate FC maps. As they complement each other in different scenarios, that will be important to study normal and diseased brain activity.