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Multi-phase locking value: A generalized method for determining instantaneous multi-frequency phase coupling
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DOI：10.1016/j.bspc.2022.103492.png)
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Abstract
En 中文
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, 2f/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), 2f(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 Ro spacing diaeresis ssler 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.
Keywords:
Cross-frequency coupling
Phase coupling
Signal processing
Nonlinear system
Time delay
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