Multi-phase locking value: A generalized method for determining instantaneous multi-frequency phase coupling

Bhavya Vasudeva, Runfeng Tian, Dee H. Wu, Shirley A. James, Hazem H. Refai, Lei Ding, Fei He, Yuan Yang

Research output: Contribution to journalArticlepeer-review


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: mf1=nf2) 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. f1,f2,f1+f2), 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. f1,f2,f3,f4,f1+f2+f3-f4), or coupling that involves non-integer multiples of the frequencies (e.g. f1,f2,2f1/3+f2/3). 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.

Original languageEnglish (US)
Article number103492
JournalBiomedical Signal Processing and Control
StatePublished - Apr 2022
Externally publishedYes


  • Cross-frequency coupling
  • Nonlinear system
  • Phase coupling
  • Signal processing
  • Time delay

ASJC Scopus subject areas

  • Signal Processing
  • Health Informatics


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