Advertisement

Visibility graph analysis of temporal irreversibility in sleep electroencephalograms

  • Hui XiongEmail author
  • Pengjian Shang
  • Fengzhen Hou
  • Yan Ma
Original Paper
  • 28 Downloads

Abstract

The study of sleep has continued to garner increased attention. However, most studies assume stationarity of sleep electroencephalogram (EEG) signals, whereas they are typically nonlinear and nonstationary. Little work has focused on the time irreversibility of sleep EEG signals. Hence, the aim of this work is to reveal the temporally irreversible structures of rapid-eye-movement (REM) and non-REM sleep using a visibility algorithm, which is robust to nonstationarity and finite-size effect. Results show that the temporal structure of non-REM sleep is more irreversible than that of REM sleep. The degree of irreversibility is highest in slow-wave sleep. Moreover, statistical analysis suggests that aging is the major factor that affects the irreversibility of sleep signals, while gender and body mass index contribute insignificantly. The dominant role of slow oscillations on the irreversible structures of the sleep signals is also indicated.

Keywords

Visibility graph Time irreversibility EEG Sleep stage Empirical mode decomposition NARMA 

Notes

Acknowledgements

The authors acknowledge the financial support from the Fundamental Research Funds for the Central Universities (2017YJS207) and National Natural Science Foundation of China (61771035). H. Xiong thanks the support of China Scholarship Council (201707090024) during her visit to Harvard Medical School.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Weiss, G.: Time-reversibility of linear stochastic processes. J. Appl. Probab. 12(4), 831–836 (1975)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Lacasa, L., Nuñez, A., Roldán, É., Parrondo, J.M., Luque, B.: Time series irreversibility: a visibility graph approach. Eur. Phys. J. B 85(6), 1–11 (2012)Google Scholar
  3. 3.
    Porta, A., Casali, K.R., Casali, A.G., Gnecchi-Ruscone, T., Tobaldini, E., Montano, N., Lange, S., Geue, D., Cysarz, D., Van Leeuwen, P.: Temporal asymmetries of short-term heart period variability are linked to autonomic regulation. Am. J. Physiol. Regul. Integr. Comp. Physiol. 295(2), R550–R557 (2008)Google Scholar
  4. 4.
    Kawai, R., Parrondo, J., Van den Broeck, C.: Dissipation: the phase-space perspective. Phys. Rev. Lett. 98(8), 080602 (2007)Google Scholar
  5. 5.
    Parrondo, J.M., Van den Broeck, C., Kawai, R.: Entropy production and the arrow of time. New J. Phys. 11(7), 073008 (2009)Google Scholar
  6. 6.
    Costa, M., Goldberger, A.L., Peng, C.K.: Broken asymmetry of the human heartbeat: loss of time irreversibility in aging and disease. Phys. Rev. Lett. 95(19), 198102 (2005)Google Scholar
  7. 7.
    Costa, M.D., Peng, C.K., Goldberger, A.L.: Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures. Cardiovasc. Eng. 8(2), 88–93 (2008)Google Scholar
  8. 8.
    Kennel, M.B.: Testing time symmetry in time series using data compression dictionaries. Phys. Rev. E 69(5), 056208 (2004)MathSciNetGoogle Scholar
  9. 9.
    Daw, C., Finney, C., Kennel, M.: Symbolic approach for measuring temporal irreversibility. Phys. Rev. E 62(2), 1912 (2000)Google Scholar
  10. 10.
    Porta, A., Guzzetti, S., Montano, N., Gnecchi-Ruscone, T., Furlan, R., Malliani, A.: Time reversibility in short-term heart period variability. In: Computers in Cardiology, vol. 33, pp. 77–80. IEEE (2006)Google Scholar
  11. 11.
    Guzik, P., Piskorski, J., Krauze, T., Wykretowicz, A., Wysocki, H.: Heart rate asymmetry by poincaré plots of rr intervals. Biomedizinische Technik 51(4), 272–275 (2006)Google Scholar
  12. 12.
    Cammarota, C., Rogora, E.: Time reversal, symbolic series and irreversibility of human heartbeat. Chaos Solitons Fractals 32(5), 1649–1654 (2007)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Porporato, A., Rigby, J., Daly, E.: Irreversibility and fluctuation theorem in stationary time series. Phys. Rev. Lett. 98(9), 094101 (2007)Google Scholar
  14. 14.
    Casali, K.R., Casali, A.G., Montano, N., Irigoyen, M.C., Macagnan, F., Guzzetti, S., Porta, A.: Multiple testing strategy for the detection of temporal irreversibility in stationary time series. Phys. Rev. E 77(6), 066204 (2008)Google Scholar
  15. 15.
    Xia, J., Shang, P., Wang, J., Shi, W.: Classifying of financial time series based on multiscale entropy and multiscale time irreversibility. Physica A 400, 151–158 (2014)Google Scholar
  16. 16.
    Hou, F., Zhuang, J., Bian, C., Tong, T., Chen, Y., Yin, J., Qiu, X., Ning, X.: Analysis of heartbeat asymmetry based on multi-scale time irreversibility test. Physica A 389(4), 754–760 (2010)Google Scholar
  17. 17.
    Hou, F., Ning, X., Zhuang, J., Huang, X., Fu, M., Bian, C.: High-dimensional time irreversibility analysis of human interbeat intervals. Med. Eng. Phys. 33(5), 633–637 (2011)Google Scholar
  18. 18.
    Flanagan, R., Lacasa, L.: Irreversibility of financial time series: a graph-theoretical approach. Phys. Lett. A 380(20), 1689–1697 (2016)Google Scholar
  19. 19.
    Nuñez, A.M., Lacasa, L., Gomez, J.P., Luque, B.: Visibility algorithms: a short review. In: Zhang, Y. (ed.) New Frontiers in Graph Theory, pp. 119–152. InTech (2012).  https://doi.org/10.5772/34810
  20. 20.
    Lacasa, L., Flanagan, R.: Time reversibility from visibility graphs of nonstationary processes. Phys. Rev. E 92(2), 022817 (2015)MathSciNetGoogle Scholar
  21. 21.
    Lacasa, L., Luque, B., Ballesteros, F., Luque, J., Nuno, J.C.: From time series to complex networks: the visibility graph. Proc. Natl. Acad. Sci. 105(13), 4972–4975 (2008)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Xiong, H., Shang, P., Xia, J., Wang, J.: Time irreversibility and intrinsics revealing of series with complex network approach. Physica A 499, 241–249 (2018)MathSciNetGoogle Scholar
  23. 23.
    Jiang, S., Bian, C., Ning, X., Ma, Q.D.: Visibility graph analysis on heartbeat dynamics of meditation training. Appl. Phys. Lett. 102(25), 253702 (2013)Google Scholar
  24. 24.
    Hou, F., Li, F., Wang, J., Yan, F.: Visibility graph analysis of very short-term heart rate variability during sleep. Physica A 458, 140–145 (2016)Google Scholar
  25. 25.
    Zhu, G., Li, Y., Wen, P.P.: An efficient visibility graph similarity algorithm and its application on sleep stages classification. In: International Conference on Brain Informatics, pp. 185–195. Springer (2012)Google Scholar
  26. 26.
    Zhu, G., Li, Y., Wen, P.P.: Analysis and classification of sleep stages based on difference visibility graphs from a single-channel EEG signal. IEEE J. Biomed. Health Inform. 18(6), 1813–1821 (2014)Google Scholar
  27. 27.
    Ahmadlou, M., Adeli, H., Adeli, A.: New diagnostic EEG markers of the Alzheimers disease using visibility graph. J. Neural Transm. 117(9), 1099–1109 (2010)Google Scholar
  28. 28.
    Bhaduri, S., Ghosh, D.: Electroencephalographic data analysis with visibility graph technique for quantitative assessment of brain dysfunction. Clin. EEG Neurosci. 46(3), 218–223 (2015)Google Scholar
  29. 29.
    Gao, Z.K., Cai, Q., Yang, Y.X., Dong, N., Zhang, S.S.: Visibility graph from adaptive optimal kernel time-frequency representation for classification of epileptiform EEG. Int. J. Neural Syst. 27(04), 1750005 (2017)Google Scholar
  30. 30.
    Cai, L., Deng, B., Wei, X., Wang, R., Wang, J.: Analysis of spontaneous EEG activity in Alzheimer’s disease using weighted visibility graph. In: 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 3100–3103. IEEE (2018)Google Scholar
  31. 31.
    Zhu, G., Li, Y., Wen, P.P.: Epileptic seizure detection in EEGs signals using a fast weighted horizontal visibility algorithm. Comput. Methods Progr. Biomed. 115(2), 64–75 (2014)Google Scholar
  32. 32.
    Hobson, J.A.: A manual of standardized terminology, techniques and scoring system for sleep stages of human subjects: A. Rechtschaffen and A. kales (editors). (Public Health Service, US Government Printing Office, Washington, DC. Electroencephalogr. Clin. Neurophysiol. 26(6), 644 (1969)Google Scholar
  33. 33.
    Šušmáková, K.: Human sleep and sleep eeg. Meas. Sci. Rev. 4(2), 59–74 (2004)Google Scholar
  34. 34.
    Prerau, M.J., Brown, R.E., Bianchi, M.T., Ellenbogen, J.M., Purdon, P.L.: Sleep neurophysiological dynamics through the lens of multitaper spectral analysis. Physiology 32(1), 60–92 (2017)Google Scholar
  35. 35.
    Prinz, P.N., Vitiello, M.V., Raskind, M.A., Thorpy, M.J.: Sleep disorders and aging. N. Engl. J. Med. 323(8), 520–526 (1990)Google Scholar
  36. 36.
    Vitiello, M.V.: Sleep disorders and aging: understanding the causes. J. Gerontol. Ser. A Biol. Sci. Med. Sci. 52(4), M189–M191 (1997)Google Scholar
  37. 37.
    Rediehs, M.H., Reis, J.S., Creason, N.S.: Sleep in old age: focus on gender differences. Sleep 13(5), 410–424 (1990)Google Scholar
  38. 38.
    Redline, S., Kirchner, H.L., Quan, S.F., Gottlieb, D.J., Kapur, V., Newman, A.: The effects of age, sex, ethnicity, and sleep-disordered breathing on sleep architecture. Arch. Intern. Med. 164(4), 406–418 (2004)Google Scholar
  39. 39.
    Reyner, A., Horne, J.: Gender-and age-related differences in sleep determined by home-recorded sleep logs and actimetry from 400 adults. Sleep 18(2), 127–134 (1995)Google Scholar
  40. 40.
    Ehlers, C., Kupfer, D.: Slow-wave sleep: do young adult men and women age differently? J. Sleep Res. 6(3), 211–215 (1997)Google Scholar
  41. 41.
    Fukuda, N., Honma, H., Kohsaka, M., Kobayashi, R., Sakakibara, S., Kohsaka, S., Koyama, T.: Gender difference of slow wave sleep in middle aged and elderly subjects. Psychiatry Clin. Neurosci. 53(2), 151–153 (1999)Google Scholar
  42. 42.
    Cappuccio, F.P., Taggart, F.M., Kandala, N.B., Currie, A., Peile, E., Stranges, S., Miller, M.A.: Meta-analysis of short sleep duration and obesity in children and adults. Sleep 31(5), 619–626 (2008)Google Scholar
  43. 43.
    Knutson, K.L., Van Cauter, E.: Associations between sleep loss and increased risk of obesity and diabetes. Ann. N. Y. Acad. Sci. 1129(1), 287–304 (2008)Google Scholar
  44. 44.
    Gevins, A.S., Rémond, A.: Methods of Analysis of Brain Electrical and Magnetic Signals, vol. 1. Elsevier, Amsterdam (1987)Google Scholar
  45. 45.
    Babloyantz, A., Salazar, J., Nicolis, C.: Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys. Lett. A 111(3), 152–156 (1985)Google Scholar
  46. 46.
    Fell, J., Röschke, J., Mann, K., Schäffner, C.: Discrimination of sleep stages: a comparison between spectral and nonlinear EEG measures. Electroencephalogr. Clin. Neurophysiol. 98(5), 401–410 (1996)Google Scholar
  47. 47.
    Pereda, E., Gamundi, A., Rial, R., González, J.: Non-linear behaviour of human EEG: fractal exponent versus correlation dimension in awake and sleep stages. Neurosci. Lett. 250(2), 91–94 (1998)Google Scholar
  48. 48.
    Ferri, R., Parrino, L., Smerieri, A., Terzano, M.G., Elia, M., Musumeci, S.A., Pettinato, S., Stam, C.J.: Non-linear EEG measures during sleep: effects of the different sleep stages and cyclic alternating pattern. Int. J. Psychophysiol. 43(3), 273–286 (2002)Google Scholar
  49. 49.
    Acharya, R., Faust, O., Kannathal, N., Chua, T., Laxminarayan, S.: Non-linear analysis of EEG signals at various sleep stages. Comput. Methods Progr. Biomed. 80(1), 37–45 (2005)Google Scholar
  50. 50.
    Shen, Y., Olbrich, E., Achermann, P., Meier, P.: Dimensional complexity and spectral properties of the human sleep EEG. Clin. Neurophysiol. 114(2), 199–209 (2003)Google Scholar
  51. 51.
    Lee, J.M., Kim, D.J., Kim, I.Y., Park, K.S., Kim, S.I.: Nonlinear-analysis of human sleep EEG using detrended fluctuation analysis. Med. Eng. Phys. 26(9), 773–776 (2004)Google Scholar
  52. 52.
    Rényi, A., et al.: On measures of entropy and information. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 547–561 (1961)Google Scholar
  53. 53.
    Roldán, É., Parrondo, J.M.: Entropy production and Kullback–Leibler divergence between stationary trajectories of discrete systems. Phys. Rev. E 85(3), 031129 (2012)Google Scholar
  54. 54.
    Roldán, É., Parrondo, J.M.: Estimating dissipation from single stationary trajectories. Phys. Rev. Lett. 105(15), 150607 (2010)Google Scholar
  55. 55.
    Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In: Proceedings of the Royal Society of London A, vol. 454, pp. 903–995. The Royal Society (1998)Google Scholar
  56. 56.
    Cummings, D.A., Irizarry, R.A., Huang, N.E., Endy, T.P., Nisalak, A., Ungchusak, K., Burke, D.S.: Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand. Nature 427(6972), 344 (2004)Google Scholar
  57. 57.
    Wang, J., Shang, P., Xia, J., Shi, W.: Emd based re ned composite multiscale entropy analysis of complex signals. Physica A 421, 583–593 (2015)Google Scholar
  58. 58.
    Xiong, H., Shang, P., Bian, S.: Detecting intrinsic dynamics of traffic flow with recurrence analysis and empirical mode decomposition. Physica A 474, 70–84 (2017)Google Scholar
  59. 59.
    Hollander, M., Wolfe, D.A.: Nonparametric Statistical Methods. Wiley, New York (1999)zbMATHGoogle Scholar
  60. 60.
    Hochberg, Y., Tamhane, A.: Multiple Comparison Procedures. Wiley, New York (1987)zbMATHGoogle Scholar
  61. 61.
    Dean, D.A., Goldberger, A.L., Mueller, R., Kim, M., Rueschman, M., Mobley, D., Sahoo, S.S., Jayapandian, C.P., Cui, L., Morrical, M.G., et al.: Scaling up scientific discovery in sleep medicine: the national sleep research resource. Sleep 39(5), 1151–1164 (2016)Google Scholar
  62. 62.
    Quan, S.F., Howard, B.V., Iber, C., Kiley, J.P., Nieto, F.J., O’connor, G.T., Rapoport, D.M., Redline, S., Robbins, J., Samet, J.M., et al.: The sleep heart health study: design, rationale, and methods. Sleep 20(12), 1077–1085 (1997)Google Scholar
  63. 63.
    Sanders, M.H., Lind, B.K., Quan, S.F., Iber, C., Gottlieb, D.J., Bonekat, W.H., Rapoport, D.M., Smith, P.L., Kiley, J.P.: Methods for obtaining and analyzing unattended polysomnography data for a multicenter study. Sleep 21(7), 759–767 (1998)Google Scholar
  64. 64.
    Buckelmüller, J., Landolt, H.P., Stassen, H., Achermann, P.: Trait-like individual differences in the human sleep electroencephalogram. Neuroscience 138(1), 351–356 (2006)Google Scholar
  65. 65.
    Berry, R.B., Brooks, R., Gamaldo, C.E., Harding, S.M., Marcus, C., Vaughn, B.: The AASM manual for the scoring of sleep and associated events. Rules, Terminology and Technical Specifications, Darien, Illinois, American Academy of Sleep Medicine (2012)Google Scholar
  66. 66.
    World Health Organization. http://www.who.int/. Accessed 30 May 2018
  67. 67.
    Chatterjee, S., Hadi, A.S.: Influential observations, high leverage points, and outliers in linear regression. Stat. Sci. 1(3), 379–393 (1986)MathSciNetzbMATHGoogle Scholar
  68. 68.
    Chen, S., Billings, S.A., Luo, W.: Orthogonal least squares methods and their application to non-linear system identification. Int. J. Control 50(5), 1873–1896 (1989)zbMATHGoogle Scholar
  69. 69.
    Billings, S.A., Chen, S., Korenberg, M.J.: Identification of MIMO non-linear systems using a forward-regression orthogonal estimator. Int. J. Control 49(6), 2157–2189 (1989)zbMATHGoogle Scholar
  70. 70.
    Loh, C.H., Duh, J.Y.: Analysis of nonlinear system using NARMA models. Doboku Gakkai Ronbunshu 537, 11–21 (1996)Google Scholar
  71. 71.
    Watanabe, R.N., Kohn, A.F.: System identification of a motor unit pool using a realistic neuromusculoskeletal model. In: 2014 5th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, pp. 610–615 (2014)Google Scholar
  72. 72.
    Kadir, S.N., Tahir, N.M., Yassin, I.M., Zabidi, A.: Malaysian tourism interest forecasting using nonlinear auto-regressive moving average (NARMA) model. In: 2014 IEEE Symposium on Wireless Technology and Applications, pp. 193–198 (2014)Google Scholar
  73. 73.
    Cao, L.: Practical method for determining the minimum embedding dimension of a scalar time series. Physica D 110, 43–50 (1997)zbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceBeijing Jiaotong UniversityBeijingPeople’s Republic of China
  2. 2.Center for Dynamical Biomarkers, Beth Israel Deaconess Medical CenterHarvard Medical SchoolBostonUSA
  3. 3.Key Laboratory of Biomedical Functional MaterialsChina Pharmaceutical UniversityNanjingPeople’s Republic of China
  4. 4.Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical CenterHarvard Medical SchoolBostonUSA
  5. 5.Department of MathematicsSchool of Science, Beijing Jiaotong UniversityBeijingPeople’s Republic of China

Personalised recommendations