Multi-phase locking value: A generalized method for determining instantaneous multi-frequency phase coupling. (April 2022) - Vasudeva, Bhavya; Tian, Runfeng; Wu, Dee H.; James, Shirley A.; Refai, Hazem H.; Ding, Lei; He, Fei; Yang, Yuan
Highlights: A generalized method for multi-frequency phase coupling. Precise estimation of phase coupling time window. Precise estimation of time lag in delayed coupling. Detection of non-integer multi-frequency coupling. Abstract: Background: Many physical, biological and neural systems behave as coupled oscillators, with characteristic phase coupling across different frequencies. Methods such as n : m phase locking value (where two coupling frequencies are linked as: mf 1 = nf 2 ) and bi-phase locking value have previously been proposed to quantify phase coupling between two resonant frequencies (e.g. f, 2 f / 3 ) and across three frequencies (e.g. f 1, f 2, f 1 + f 2 ), respectively. However, the existing phase coupling metrics have their limitations and limited applications. They cannot be used to detect or quantify phase coupling across multiple frequencies (e.g. f 1, f 2, f 3, f 4, f 1 + f 2 + f 3 - f 4 ), or coupling that involves non-integer multiples of the frequencies (e.g. f 1, f 2, 2 f 1 / 3 + f 2 / 3 ). New methods: To address the gap, this paper proposes a generalized approach, named multi-phase locking value (M-PLV), for the quantification of various types of instantaneous multi-frequency phase coupling. Different from most instantaneous phase coupling metrics that measure the simultaneous phase coupling, the proposed M-PLV method also allows the detection of delayed phase coupling and the associated time lag between coupled oscillators. Results: The M-PLV has been tested on cases where synthetic coupled signals are generated using white Gaussian signals, and a system comprised of multiple coupled Rössler oscillators, as well as a human subject dataset. Results indicate that the M-PLV can provide a reliable estimation of the time window and frequency combination where the phase coupling is significant, as well as a precise determination of time lag in the case of delayed coupling. This method has the potential to become a powerful new tool for exploring phase coupling in complex nonlinear dynamic systems.