Skip to main content

Advertisement

SpringerLink
Log in

Testing pattern synchronization in coupled systems through different entropy-based measures

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

An Erratum to this article was published on 03 April 2013

Abstract

Pattern synchronization (PS) can capture one aspect of the dynamic interactions between bivariate physiological systems. It can be tested by several entropy-based measures, e.g., cross sample entropy (X-SampEn), cross fuzzy entropy (X-FuzzyEn), multivariate multiscale entropy (MMSE), etc. A comprehensive comparison on their distinguishability is currently missing. Besides, they are highly dependent on several pre-defined parameters, the threshold value r in particular. Thus, their consistency also needs further elucidation. Based on the well-accepted assumption that a tight coupling necessarily leads to a high PS, we performed a couple of evaluations over several simulated coupled models in this study. All measures were compared to each other with respect to their consistency and distinguishability, which were quantified by two pre-defined criteria—degree of crossing (DoC) and degree of monotonicity (DoM). Results indicated that X-SampEn and X-FuzzyEn could only work well over coupled stochastic systems with meticulously selected r. It is thus not recommended to apply them to the intrinsic complex physiological systems. However, MMSE was suitable for both, indicating by relatively higher DoC and DoM values. Final analysis on the cardiorespiratory coupling validated our results.

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

Similar content being viewed by others

Notes

  1. With the increase of c, similar patterns are prone to occur. Thus the cross-predictability increases; hence X-SampEn and X-FuzzyEn decreases. However, an increase in c leads to an increase in long-range correlations both within- and between- channels which is consequently leads to an increase of MMSE.

References

  1. Ahmed MU, Mandic DP (2011) Multivariate multiscale entropy: a tool for complexity analysis of multichannel data. Phys Rev E 84(6):061918

    Article  Google Scholar 

  2. Ahmed MU, Mandic DP (2012) Multivariate Multiscale Entropy Analysis. IEEE Signal Process Lett 19(2):91–94

    Article  Google Scholar 

  3. Ahmed MU, Rehman N, Looney D, Rutkowski TM, Mandic DP (2012) Dynamical complexity of human responses: a multivariate data-adaptive framework. Bull Pol Ac: Tech 60(3):433–445

    Google Scholar 

  4. Ansari-Asl K, Senhadji L, Bellanger JJ, Wendling F (2006) Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals. Phys Rev E 74(3 Pt 1):031916

    Article  Google Scholar 

  5. Bartsch RP, Schumann AY, Kantelhardt JW, Penzel T, Ivanov P (2012) Phase transitions in physiologic coupling. Proc Nat Acad Sci USA 109(26):10181–10186

    Article  PubMed  CAS  Google Scholar 

  6. Castiglioni P, Di Rienzo M (2008) How the threshold “R” influences approximate entropy analysis of heart-rate variability. In: Murray A (ed) Computers in Cardiology. IEEE, Bologne, pp 561–564

    Google Scholar 

  7. Chen W, Zhuang J, Yu W, Wang Z (2009) Measuring complexity using FuzzyEn, ApEn, and SampEn. Med Eng Phys 31(1):61–68

    Article  PubMed  Google Scholar 

  8. Chon K, Scully CG, Lu S (2009) Approximate entropy for all signals. IEEE Eng Med Biol Mag 28(6):18–23

    Article  PubMed  Google Scholar 

  9. Costa M, Goldberger AL, Peng CK (2002) Multiscale entropy analysis of complex physiologic time series. Phys Rev Lett 89(6):068102

    Article  PubMed  Google Scholar 

  10. Dauwels J, Vialatte F, Musha T, Cichocki A (2010) A comparative study of synchrony measures for the early diagnosis of Alzheimer’s disease based on EEG. NeuroImage 49(1):668–693

    Article  PubMed  CAS  Google Scholar 

  11. Goldberger AL (1996) Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Lancet 347(9011):1312–1314

    Article  PubMed  CAS  Google Scholar 

  12. Goldberger AL, Amaral LA, Glass L, Hausdorff JM, Ivanov PC, Mark RG, Mietus JE, Moody GB, Peng CK, Stanley HE (2000) PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101(23):E215–E220

    Article  PubMed  CAS  Google Scholar 

  13. Hu M, Liang H (2012) Adaptive multiscale entropy analysis of multivariate neural data. IEEE Trans Biomed Eng 59(1):12–15

    Article  PubMed  Google Scholar 

  14. Hu Z, Shi P (2006) Interregional functional connectivity via pattern synchrony. In: 9th International Conference on Control, Automation, Robotics and Vision, Singapore, IEEE, pp 1–6

  15. Iyengar N, Peng CK, Morin R, Goldberger AL, Lipsitz LA (1996) Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics. Am J Physiol Heart Circ Physiol 271(4):R1078–R1084

    CAS  Google Scholar 

  16. Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45(6):3403–3411

    Article  PubMed  Google Scholar 

  17. Kreuz T, Mormann F, Andrzejak RG, Kraskov A, Lehnertz K, Grassberger P (2007) Measuring synchronization in coupled model systems: a comparison of different approaches. Physica D 225(1):29–42

    Article  Google Scholar 

  18. Li P, Liu CY, Wang XP, Li B, Che WB, Liu CC (2012) Cross-sample entropy and cross-fuzzy entropy for testing pattern synchrony: how results vary with different threshold value r. In: Long M (ed) IFMBE Proceeding World Congress on medical physics and biomedical engineering. Springer, Beijing, pp 485–488

    Google Scholar 

  19. Liu CY, Liu CC, Shao P, Li LP, Sun X, Wang XP, Liu F (2011) Comparison of different threshold values r for approximate entropy: application to investigate the heart rate variability between heart failure and healthy control groups. Physiol Meas 32(2):167–180

    Article  PubMed  Google Scholar 

  20. Liu CY, Li LP, Zhao LN, Zheng DC, Li P, Liu CC (2012) A combination method of improved impulse rejection filter and template matching for identification of anomalous intervals in RR sequences. J Med Biol Eng 32(4):245–250

    Article  Google Scholar 

  21. Lu S, Chen X, Kanters JK, Solomon IC, Chon KH (2008) Automatic selection of the threshold value r for approximate entropy. IEEE Trans Biomed Eng 55(8):1966–1972

    Article  PubMed  Google Scholar 

  22. Molina-Pico A, Cuesta-Frau D, Aboy M, Crespo C, Miro-Martinez P, Oltra-Crespo S (2011) Comparative study of approximate entropy and sample entropy robustness to spikes. Artif Intell Med 53(2):97–106

    Article  PubMed  Google Scholar 

  23. Pincus SM (1991) Approximate entropy as a measure of system complexity. Proc Nat Acad Sci USA 88(6):2297–2301

    Article  PubMed  CAS  Google Scholar 

  24. Quian Quiroga R, Kreuz T, Grassberger P (2002) Event synchronization: a simple and fast method to measure synchronicity and time delay patterns. Phys Rev E 66(4):041904

    Article  CAS  Google Scholar 

  25. Richman JS, Moorman JR (2000) Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol Heart Circ Physiol 278(6):H2039–H2049

    PubMed  CAS  Google Scholar 

  26. Rosenblum MG, Pikovsky AS, Kurths J (1996) Phase Synchronization of Chaotic Oscillators. Phys Rev Lett 76(11):1804–1807

    Article  PubMed  CAS  Google Scholar 

  27. Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HDI (1995) Generalized synchronization of chaos in directionally coupled chaotic systems. Phys Rev E 51(2):980–994

    Article  Google Scholar 

  28. Schiff SJ, So P, Chang T, Burke RE, Sauer T (1996) Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. Phys Rev E 54(6):6708–6724

    Article  CAS  Google Scholar 

  29. Vakorin VA, Ross B, Krakovska O, Bardouille T, Cheyne D, McIntosh AR (2010) Complexity analysis of source activity underlying the neuromagnetic somatosensory steady-state response. NeuroImage 51(1):83–90

    Article  PubMed  Google Scholar 

  30. Wagner CD, Persson PB (1998) Chaos in the cardiovascular system: an update. Cardiovasc Res 40(2):257–264

    Article  PubMed  CAS  Google Scholar 

  31. Xie H, Guo J, Zheng Y (2010) A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures. Biol Cybern 102(2):123–135

    Article  PubMed  Google Scholar 

  32. Xie H, Zheng Y, Guo J, Chen X (2010) Cross-fuzzy entropy: a new method to test pattern synchrony of bivariate time series. Inform Sciences 180(9):1715–1724

    Article  Google Scholar 

  33. Zhang T, Yang Z, Coote JH (2007) Cross-sample entropy statistic as a measure of complexity and regularity of renal sympathetic nerve activity in the rat. Exp Physiol 92(4):659–669

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

We would like to thank Prof. Danilo P. Mandic and Dr. Mosabber U. Ahmed from Imperial College for fruitful discussions. Also we thank Miss. Xinning Liu from School of Foreign Languages and Literature, Shandong University for her help in polishing this paper. We are also grateful to the anonymous reviewers for their insightful comments which helped us improving the quality of this paper.

This work is supported by the Graduate Independent Innovation Foundation of Shandong University (GIIFSDU, yzc12082), the National Natural Science Foundation of China (61201049), the Excellent Young Scientist Awarded Foundation of Shandong Province (BS2012DX019) and the Independent Innovation Foundation of Shandong University (IIFSDU, 2011GN069).

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, 17923 Jingshi Road, Jinan, 250061, People’s Republic of China

    Peng Li, Chengyu Liu, Xinpei Wang, Lei Yang, Yongcai Chen & Changchun Liu

  2. Biomedical Engineering, College of Science and Technology, Shandong University of Traditional Chinese Medicine, Daxue Road, Jinan, 250355, People’s Republic of China

    Liping Li

Authors
  1. Peng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chengyu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinpei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Liping Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lei Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yongcai Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Changchun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changchun Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, P., Liu, C., Wang, X. et al. Testing pattern synchronization in coupled systems through different entropy-based measures. Med Biol Eng Comput 51, 581–591 (2013). https://doi.org/10.1007/s11517-012-1028-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-012-1028-z

Keywords

Search

Navigation