Analysis of the Phase Locking Index for Measuring of Interdependency of Cortical Signals Recorded in the EEG

The phase locking index (PLI) was introduced to quantify in a statistical sense the phase synchronization of two signals. It has been commonly used to process biosignals. In this paper, we analyze the PLI for measuring the interdependency of cortical source signals (CSSs) recorded in the Electroencephalogram (EEG). The main focus of the analysis is the probability density function, which describes the sensitivity of the PLI to the joint noise ensemble in the CSSs. Since this function is mathematically intractable, we derive approximations and analyze them for a simple analytical model of the CSS mixture in the EEG. The accuracies of the approximate probability density functions (APDFs) are evaluated using simulations for the model. The APDFs are found sufficiently accurate and thus are applicable for practical intents and purposes. They can hence be used to determine the confidence intervals and significance levels for detection methods for interdependencies, e.g., between cortical signals recorded in the EEG.