Inferring Functional Neural Connectivity with Phase Synchronization Analysis: A Review of Methodology
Figure 1
Schematic diagram of phase synchronization (PS) analysis. For broadband raw signals (a), a bandpass filter is first applied to extracting signal waves in specific frequency band (b). Then analytic signals of signal waves may be defined based on the Hilbert transform ((c) and (d)), and the argument of the analytic signals are defined as instantaneous phase (IP) of the corresponding signal waves. The IPs could be wrapped into the range (e). In some cases as marked by dotted rectangle in (e), the estimated analytic signal [] may be ill-defined due to noisy data and does not always rotate counterclockwise around origin in the complex plane, resulting in non-monotonic IP “jump” at the time when the trajectory of analytic signal crosses through the origin. Signals with too many IP “jumps” are not suitable for PS analysis. With the differences of IPs which are wrapped in the range , PS index (PSI), which quantifies the level of PS, could be estimated according to the distribution of IP difference (g). In addition, significance test could provide a significance threshold (the black bar in (h)) for estimated PSI. If the estimated PSI is greater than the threshold, then the corresponding signal wave pair is claimed to be in significant PS with a certain confidence level. For some cases, the amplitudes of analytic signals may be rather weakly correlated (f), but the corresponding PSI is with relatively large value. For the case in (f) and (g), the correlation coefficient between the amplitudes (i.e., versus ) of two signal waves is −0.07, while the corresponding MPC-based PSI is 0.44.
