Hyperspherical phase synchrony measure for quantifying global synchronization in the brain

Phase synchronization has been proposed as a plausible mechanism to quantify both linear and nonlinear relationships between neuronal populations and to assess functional brain connectivity. However, bivariate phase synchrony is not sufficient for complex system analysis such as the brain where the bivariate relationships do not always reflect the underlying network structure. Recently, multivariate extensions of bivariate phase synchrony has been of interest in investigating the interactions within a group of oscillators. Current extensions are based on either averaging all possible pairwise synchrony values or eigen decomposition of a matrix of bivariate synchronization indices to estimate multivariate synchrony using the entropy of the normalized eigenvalues. All of these approaches are sensitive to the accuracy of the bivariate synchrony indices, cause loss of information, computationally complex and are indirect ways to quantify the multivariate synchrony. In this paper, we propose a novel and direct measure to estimate the multivariate phase synchrony by forming direction vectors in a multidimensional hyperspherical coordinate system. The proposed method is evaluated through application to electroencephalogram (EEG) data containing error-related negativity (ERN) related to cognitive control. We compare the new measure with existing methods and show its effectiveness in quantifying multivariate synchronization of different brain regions.