Skip to main content
SpringerLink
Log in

A novel index of functional connectivity: phase lag based on Wilcoxon signed rank test

  • Research Article
  • Published:
Cognitive Neurodynamics Aims and scope Submit manuscript

Abstract

Phase synchronization has been an effective measurement of functional connectivity, detecting similar dynamics over time among distinct brain regions. However, traditional phase synchronization-based functional connectivity indices have been proved to have some drawbacks. For example, the phase locking value (PLV) index is sensitive to volume conduction, while the phase lag index (PLI) and the weighted phase lag index (wPLI) are easily affected by noise perturbations. In addition, thresholds need to be applied to these indices to obtain the binary adjacency matrix that determines the connections. However, the selection of the thresholds is generally arbitrary. To address these issues, in this paper we propose a novel index of functional connectivity, named the phase lag based on the Wilcoxon signed-rank test (PLWT). Specifically, it characterizes the functional connectivity based on the phase lag with a weighting procedure to reduce the influence of volume conduction and noise. Besides, it automatically identifies the important connections without relying on thresholds, by taking advantage of the framework of the Wilcoxon signed-rank test. The performance of the proposed PLWT index is evaluated on simulated electroencephalograph (EEG) datasets, as well as on two resting-state EEG datasets. The experimental results on the simulated EEG data show that the PLWT index is robust to volume conduction and noise. Furthermore, the brain functional networks derived by PLWT on the real EEG data exhibit a reasonable scale-free characteristic and high test–retest (TRT) reliability of graph measures. We believe that the proposed PLWT index provides a useful and reliable tool to identify the underlying neural interactions, while effectively diminishing the influence of volume conduction and noise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Bandettini PA, Bullmore E (2010) Endogenous oscillations and networks in functional magnetic resonance imaging. Hum Brain Mapp 29(7):737–739

    Article  Google Scholar 

  • Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512

    Article  PubMed  Google Scholar 

  • Bassett DS, Meyer-Lindenberg A, Achard S, Duke T, Bullmore E (2006) Adaptive reconfiguration of fractal small-world human brain functional networks. Proc Natl Acad Sci 103(51):19518–19523

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Bastos AM, Schoffelen JM (2016) A tutorial review of functional connectivity analysis methods and their interpretational pitfalls. Front Syst Neurosci 9:175

    Article  PubMed  PubMed Central  Google Scholar 

  • Biswal BB, Van KJ, Hyde JS (1997) Simultaneous assessment of flow and BOLD signals in resting-state functional connectivity maps. NMR Biomed 10(4–5):165–170

    Article  CAS  PubMed  Google Scholar 

  • Braun U, Plichta MM, Esslinger C, Sauer C, Haddad L, Grimm O, Mier D, Mohnke S, Heinz A, Erk S, Walter H (2012) Test–retest reliability of resting-state connectivity network characteristics using fMRI and graph theoretical measures. Neuroimage 59(2):1404–1412

    Article  PubMed  Google Scholar 

  • Buiza E, Rodríguez-Martínez EI, Barriga-Paulino CI, Arjona A, Gomez CM (2018) Developmental trends of theta–beta interelectrode power correlation during resting state in normal children. Cogn Neurodyn 12(3):255–269

    Article  PubMed  PubMed Central  Google Scholar 

  • Bullmore ET, Bassett DS (2011) Brain graphs: graphical models of the human brain connectome. Annu Rev Clin Psychol 7(1):113–140

    Article  PubMed  Google Scholar 

  • Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Neurosci 10(3):186–198

    Article  CAS  Google Scholar 

  • Bullmore E, Sporns O (2012) The economy of brain network organization. Nat Neurosci 13(5):336–349

    Article  CAS  Google Scholar 

  • Daffertshofer A, Stam CJ (2007) Influences of volume conduction on phase distributions. In: International congress series, pp 209–212

  • Daneshi A, Azarnoush H, Towhidkhah F, Bernardin D, Faubert J (2019) Brain activity during time to contact estimation: an EEG study. Cogn Neurodyn 14:155–168

    Article  PubMed  PubMed Central  Google Scholar 

  • Deuker L, Bullmore ET, Smith M, Christensen S, Nathan PJ, Rockstroh B, Bassett DS (2009) Reproducibility of graph metrics of human brain functional networks. Neuroimage 47(4):1460–1468

    Article  PubMed  Google Scholar 

  • Eguiluz VM, Cecchi G, Chialvo DR, Baliki M, Apkarian AV (2003) Scale-free structure of brain functional networks. Phys Rev Lett 94(2):018102

    Google Scholar 

  • Erdős P, Rényi A (1964) On the strength of connectedness of a random graph. Acta Math Hung 12(1–2):261–267

    Article  Google Scholar 

  • García-Prieto J, Bajo R, Pereda E (2017) Efficient computation of functional brain networks: towards real-time functional connectivity. Front Neuroinform 11:8

    Article  PubMed  PubMed Central  Google Scholar 

  • Gross J, Kujala J, Hämäläinen M, Timmermann L, Schnitzler A, Salmelin R (2001) Dynamic imaging of coherent sources: studying neural interactions in the human brain. Proc Natl Acad Sci 98(2):694–699

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hardmeier M, Hatz F, Bousleiman H, Schindler C, Stam CJ, Fuhr P (2014) Reproducibility of functional connectivity and graph measures based on the phase lag index (PLI) and weighted phase lag index (wPLI) derived from high resolution EEG. PLoS ONE 9(10):e108648

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Haufe S, Ewald A (2019) A simulation framework for benchmarking EEG-based brain connectivity estimation methodologies. Brain Topogr 32(4):625–642

    Article  PubMed  Google Scholar 

  • Homan RW, Herman J, Purdy P (1987) Cerebral location of international 10–20 system electrode placement. Electroencephalogr Clin Neurophysiol 66(4):376–382

    Article  CAS  PubMed  Google Scholar 

  • Imperatori LS, Betta M, Cecchetti L, Canales-Johnson A, Ricciardi E, Siclari F, Pietrini P, Chennu S, Bernardi G (2019) EEG functional connectivity metrics wPLI and wSMI account for distinct types of brain functional interactions. Sci Rep 9(1):1–15

    Article  CAS  Google Scholar 

  • Jalili M (2015) Multivariate synchronization analysis of brain electroencephalography signals: a review of two methods. Cogn Comput 7(1):3–10

    Article  Google Scholar 

  • Joudaki A, Salehi N, Jalili M, Knyazeva MG (2012) EEG-based functional brain networks: does the network size matter? PLoS ONE 7(4):e35673

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kuramoto Y (1975) Self-entrainment of a population of coupled non-linear oscillators. In: International symposium on mathematical problems in theoretical physics, pp 420–422

  • Lachaux J, Rodriguez E, Martinerie J, Varela FJ (1999) Measuring phase synchrony in brain signals. Hum Brain Mapp 8(4):194–208

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lee UC, Oh GJ, Kim S, Noh G, Choi B, Mashour GA (2010) Brain networks maintain a scale-free organization across consciousness, anesthesia, and recovery: evidence for adaptive reconfiguration. Anesthesiology 113(5):1081–1091

    Article  PubMed  Google Scholar 

  • Mora-Sánchez A, Dreyfus G, Vialatte FB (2019) Scale-free behaviour and metastable brain-state switching driven by human cognition, an empirical approach. Cogn Neurodyn 13(5):437–452

    Article  PubMed  PubMed Central  Google Scholar 

  • Nunez PL, Williamson SJ (1996) Neocortical dynamics and human EEG rhythms. Phys Today 49(4):177–178

    Article  Google Scholar 

  • Ortiz E, Stingl K, Münssinger J, Braun C, Preissl H, Belardinelli P (2012) Weighted phase lag index and graph analysis: preliminary investigation of functional connectivity during resting state in children. Comput Math Methods Med 1:186353

    Google Scholar 

  • Quiroga RQ, Kreiman G, Koch C, Fried I (2008) Sparse but not “grandmother-cell” coding in the medial temporal lobe. Trends Cogn Sci 12(3):87–91

    Article  PubMed  Google Scholar 

  • Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3):1059–1069

    Article  PubMed  Google Scholar 

  • Shoukri MM, Asyali MH, Donner A (2004) Sample size requirements for the design of reliability study: review and new results. Stat Methods Med Res 13(4):251–271

    Article  Google Scholar 

  • Shrout PE, Fleiss JL (1979) Intraclass correlations: uses in assessing rater reliability. Psychol Bull 86(2):420–428

    Article  CAS  PubMed  Google Scholar 

  • Stam CJ, de Bruin EA (2010) Scale-free dynamics of global functional connectivity in the human brain. Hum Brain Mapp 22(2):97–109

    Article  Google Scholar 

  • Stam CJ, Nolte G, Daffertshofer A (2007) Phase lag index: assessment of functional connectivity from multichannel EEG and MEG with diminished bias from common sources. Hum Brain Mapp 28(11):1178–1193

    Article  PubMed  PubMed Central  Google Scholar 

  • Strogatz SH (2000) From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143(1–4):1–20

    Article  Google Scholar 

  • Tafreshi TF, Daliri MR, Ghodousi M (2019) Functional and effective connectivity based features of EEG signals for object recognition. Cogn Neurodyn 13(6):555–566

    Article  PubMed  PubMed Central  Google Scholar 

  • Taheri SM, Hesamian G (2013) A generalization of the Wilcoxon signed-rank test and its applications. Stat Pap 54(2):457–470

    Article  Google Scholar 

  • Van den Heuvel MP, Stam CJ, Boersma M, Hulshoff Pol HE (2008) Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain. Neuroimage 43:528–539

    Article  PubMed  Google Scholar 

  • Vinck M, Oostenveld R, Van Wingerden MV, Battaglia F, Pennartz CM (2011) An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. Neuroimage 55(4):1548–1565

    Article  PubMed  Google Scholar 

  • Weir JP (2005) Quantifying test-retest reliability using the intraclass correlation coefficient and the SEM. J Strength Cond Res 19(1):231–240

    PubMed  Google Scholar 

  • Wilcoxon F (1945) Individual comparisons by ranking methods. Biom Bull 1:80–83

    Article  Google Scholar 

  • Wu Y, Gan JQ, Wang H (2017) Identifying intrinsic phase lag in EEG signals from the perspective of Wilcoxon signed-rank test. In: International conference on neural information processing (ICONIP), pp 709–717

  • Yu H, Zhu L, Cai L, Wang J, Liu C, Shi N, Liu J (2020) Variation of functional brain connectivity in epileptic seizures: an EEG analysis with cross-frequency phase synchronization. Cogn Neurodyn 14(1):35–49

    Article  PubMed  Google Scholar 

  • Zalesky A, Fornito A, Harding IH, Cocchi L, Yücel M, Pantelis C, Bullmore ET (2010) Whole-brain anatomical networks: does the choice of nodes matter? Neuroimage 50(3):970–983

    Article  PubMed  Google Scholar 

  • Zhang L, Gan JQ, Wang H (2015a) Mathematically gifted adolescents mobilize enhanced workspace configuration of theta cortical network during deductive reasoning. Neuroscience 289:334–348

    Article  CAS  PubMed  Google Scholar 

  • Zhang L, Gan JQ, Wang H (2015b) Localization of neural efficiency of the mathematically gifted brain through a feature subset selection method. Cogn Neurodyn 9(5):495–508

    Article  PubMed  PubMed Central  Google Scholar 

  • Zuo XN, Xing XX (2014) Test-retest reliabilities of resting-state fMRI measurements in human brain functional connectomics: a systems neuroscience perspective. Neurosci Biobehav Rev 45:100–118

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61773114 and the Key Research and Development Plan (Industry Foresight and Common Key Technology) of Jiangsu Province under Grant BE2017007-1.

Author information

Author notes

  1. Xuan Li, Yunqiao Wu, Mengting Wei these authors contributed equally to this work.

Authors and Affiliations

  1. Key Laboratory of Child Development and Learning Science of Ministry of Education, School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, Jiangsu, People’s Republic of China

    Xuan Li, Yunqiao Wu & Haixian Wang

  2. Institute of Psychology, Chinese Academy of Sciences, Beijing, 100101, People’s Republic of China

    Mengting Wei

  3. Qingdao Port International Company, Ltd, Qingdao, 266011, Shandong, People’s Republic of China

    Yiyun Guo

  4. College of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an, 710054, Shanxi, People’s Republic of China

    Zhenhua Yu & Zhanli Li

  5. Co-innovation Center of Shandong Colleges and Universities: Future Intelligent Computing, Shandong Technology and Business University, Yantai, 264005, Shandong, People’s Republic of China

    Hui Fan

Authors
  1. Xuan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yunqiao Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mengting Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yiyun Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhenhua Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Haixian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zhanli Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Hui Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

XL, YW, and MW incorporated the algorithm and wrote the manuscritpt. YG and ZY collected the data and revised the manuscript. HW and ZL conceived and designed the study. HF reviewed the manuscript. All authors read and approved the manuscript.

Corresponding authors

Correspondence to Haixian Wang or Zhanli Li.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All the procedures performed in the studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee as well as with the 1964 Helsinki declaration and its later amendments, or comparable ethical standards.

Informed consent

Informed consent was obtained from all the individual participants included in the study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, X., Wu, Y., Wei, M. et al. A novel index of functional connectivity: phase lag based on Wilcoxon signed rank test. Cogn Neurodyn 15, 621–636 (2021). https://doi.org/10.1007/s11571-020-09646-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11571-020-09646-x

Keywords

Search

Navigation