Phase synchrony in multivariate Gaussian data with applications to cortical networks

Phase relationships between neuronal sources are often quantified by the phase locking value (PLV). Since the PLV is a bivariate measure and computed pairwise between sources, it cannot differentiate between direct and indirect connections in a multidimensional network. Schelter described a non-parametric partial phase synchronization index by extending sample PLV to the multivariate case by analogy to the relationship between full and partial network correlations. Here we derive an analytical expression for partial PLV for a multivariate circular Gaussian model and show that a partial PLV can be computed from partial coherence. We demonstrate our method in simulations with Roessler oscillators and experimental data of multichannel local field potentials from a macaque monkey. We show that the multivariate non-parametric and circular complex Gaussian based models suggest similar synchronization networks while the latter has a lower variance.