The Neurophysiological Biomarker Toolbox (NBT)

# Phase Lag Index

The Phase Lag Index (PLI) is a measure of asymmetry of the distribution of phase differences between two signals. Unlike similar measures of phase synchronization, such as phase coherence and the imaginary component of coherency, PLI is much less affected by the influence of common sources (volume conduction) and active reference electrodes.

PLI is an alternative measure of statistical interdependencies between time series, in that it reflects the strength of the coupling by looking for consistent, nonzero phase lag between two times series that cannot be explained by volume conduction from a single strong source. Such consistent, nonzero phase lags can be determined from the asymmetry of the distribution of instantaneous phase differences between two signals.

The central idea is to discard phase differences that center around 0 mod $\pi$, which can be done by defining an asymmetry index for the distribution of phase differences, when the distribution is centered around a phase difference of zero. If no phase coupling exists between two time series, then this distribution is expected to be flat, therefore any deviation from this flat distribution indicates phase synchronization.

An index of the asymmetry of the phase difference distribution can be obtained from a time series of phase differences $\bigtriangleup\Phi(t_k), k = 1…N$ in the following way:

$\text{PLI} = | < \text{sign}[\bigtriangleup\Phi(t_k)] > |.$

The PLI ranges between 0 and 1. A PLI of zero indicates either no coupling or coupling with a phase difference centered around 0 mod $\pi$. A PLI of 1 indicates perfect phase locking at a value of $\bigtriangleup\Phi$ different from 0 mod $\pi$. The stronger this nonzero phase locking, the larger will PLI be. Note that PLI does no longer indicate which of the two signals is leading in phase. Whenever needed, however, this information can be easily recovered, for instance, by omitting the absolute value in the expression above.

A similar measure to PLI was derived, namely the Weighted Phase Lag Index (WPLI), which has been shown to be more robust than PLI. WPLI does not overestimate the phase lag values due to volume conduction or effects of uncorrelated noise sources, therefore showing a more reliable relationship with true phase consistency.

Figure from (Ortiz et al., 2012):

Topographic group results of sensor power, coherence, and WPLI in 1.5 Hz wide frequency bands, from 3.5 to 12 Hz. A cluster of sensors with high power is detectable in the alpha band. The sensor with the highest FFT power (MLO11, indicated by a white dot) was selected as reference node for the connectivity calculations (one-to-all connectivity). Note that the coherence topography is roughly uninformative across frequencies and strongly affected by volume conduction effects, while WPLI compares favorably in both criteria. Much more detail is discernible in the WPLI topography. (http://www.hindawi.com/journals/cmmm/2012/186353/)

# Phase Lag Index in NBT

The phase lag index can be calculated using the nbt_doPLI function.

# References

Cornelis J. Stam et al. (2007) Phase Lag Index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources, Human Brain Mapping, 28:1178-1193

Erick Ortiz et al. (2012) Weighted phase lag index and graph analysis: preliminary investigation of functional connectivity during resting state in children, Computational and Mathematical Methods in Medicine