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

1 Citation (Scopus)
69 Downloads (Pure)


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
Article number103492
Number of pages8
JournalBiomedical Signal Processing and Control
Early online date7 Jan 2022
Publication statusPublished - Apr 2022

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This document is the author’s post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.


This work was supported by NIH R21HD099710 and P20GM121312, OCAST HR21-164–1 and NSF RII Track-2 FEC 1539068. B. Vasudeva received stipend from S. N. Bose Scholars Program 2019.


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

ASJC Scopus subject areas

  • Signal Processing
  • Health Informatics


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