Brain Topography

, Volume 31, Issue 2, pp 186–201 | Cite as

Permutation Mutual Information: A Novel Approach for Measuring Neuronal Phase-Amplitude Coupling

  • Ning Cheng
  • Qun Li
  • Sitong Wang
  • Rubin Wang
  • Tao Zhang
Original Paper


Cross-frequency phase-amplitude coupling (PAC) in neuronal oscillations network plays an important functional role in large scale neuronal communication and neuronal encoding. In the present study, a novel approach named permutation mutual information (PMI) was applied in measuring PAC. It is derived from the permutation entropy based on the mutual information theory, by which the mutual information of permutations of two time series can be evaluated. In order to verify the ability of PMI, a numerical test was performed by using both simulation data and experimental data. The performances of PMI were compared with that of two well-known methods, which were the mean vector length (MVL) and the modulation index (MI). It was found that the performance of PMI was similar to that of MI when measuring PAC intensity, but the coupling sensitivity of PMI was the highest among all these three approaches. Moreover, there was the lowest sensitivity in the MVL measurement, suggesting that MVL was a more conservative approach in detecting the existence of PAC. In addition, an ROC analysis showed that PMI performed better in measuring PAC compared to that of others. Furthermore, the experimental data, obtained from rats’ hippocampal CA3 regions, were analyzed by using the three approaches. The result was essentially in line with that of the simulation performances. In a word, the results suggest that PMI is a better choice for assessing PAC under the certain conditions.


Permutation mutual information Neuronal oscillations Phase-amplitude coupling (PAC) Local field potentials (LFPs) Rats 



This work was supported by grants from the National Natural Science Foundation of China (11232005, 31771148), 111 Project (B08011), the State Key Laboratory of Medicinal Chemical Biology and the Ph.D. Candidate Research Innovation Fund of Nankai University (63163004).

Compliance with Ethical Standards

Conflict of interest

There is not a conflict of interest for all authors.

Supplementary material

10548_2017_599_MOESM1_ESM.docx (2 mb)
Supplementary material 1 (DOCX 2013 KB)


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Ning Cheng
    • 1
  • Qun Li
    • 1
  • Sitong Wang
    • 1
  • Rubin Wang
    • 2
  • Tao Zhang
    • 1
  1. 1.College of Life Sciences and Key Laboratory of Bioactive Materials Ministry of EducationNankai UniversityTianjinPeople’s Republic of China
  2. 2.Institute for Cognitive NeurodynamicsEast China University of Science and TechnologyShanghaiPeople’s Republic of China

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