Relation between the phase-lag index and lagged coherence for assessing interactions in EEG and MEG data

Area of Science:

• Neuroscience
• Signal Processing
• Biophysics

Background:

• Numerous estimators exist for assessing brain connectivity from EEG/MEG data.
• The statistical theory and interrelationships of these estimators are not fully understood.
• Previous work suggested asymptotic equality between phase-lag index (PLI) and lagged coherence (LC) under Gaussian assumptions, but lacked rigorous proof and empirical validation.

Purpose of the Study:

• To rigorously prove the asymptotic equality of PLI and LC under Gaussian models.
• To evaluate the sampling properties and comparative performance of PLI and LC.
• To assess the validity of the Gaussian assumption in experimental EEG/MEG data and propose alternative models.

Main Methods:

• Derived the probability density of relative-phase in Gaussian models.
• Utilized power series expansions of Fourier coefficients (hypergeometric functions) for theoretical proofs.
• Conducted numerical simulations on Gaussian data and analyzed experimental EEG/MEG datasets.

Main Results:

• Provided a rigorous proof for the asymptotic equality of PLI and LC.
• Demonstrated through simulations that LC has a uniformly lower standard error than PLI across all sample sizes and parameter spaces.
• Identified deviations from Gaussianity in experimental EEG/MEG data at oscillatory resonance frequencies (delta, alpha, beta bands).

Conclusions:

• Lagged coherence is a statistically superior estimator to the phase-lag index for both Gaussian and experimental EEG/MEG data.
• The Gaussian assumption is insufficient for modeling EEG/MEG data, particularly at resonant frequencies.
• Exponential power densities offer a more appropriate modeling framework for EEG/MEG data, encompassing Gaussian and Laplace densities.