On the Stability of the n:m Phase Synchronization Index

Synchronization analysis of multitrial EEG or (magneto encephalogram) MEG signals is an excellent approach to detect functional connectivity between different neuronal oscillators. In our current research, the n:m phase synchronization index (n:m PSI ) is of special interest. We prove the existence of stable and unstable synchronies dependent upon the analysis frequencies and show that they lie closely together in the frequency domain. Thus, a plot of the time-frequency plane of the n:m PSI automatically violates the sampling theorem and accordingly, the method cannot be considered as a black box. A frequency-tiling approach is presented that can detect robust synchronies while ignoring the unstable ones. The improved synchrony detection is evaluated in numerical experiments on using both simulated and real-life data. It can be demonstrated that the transient synchronization events between MEG oscillations in distant frequency ranges can be detected and that compactly textured EEG synchronization patterns can be reliably characterized.