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Approximate entropy profile: a novel approach to comprehend irregularity of short-term HRV signal

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Abstract

Kolmogorov–Sinai entropy-based irregularity measures such as approximate entropy (ApEn), sample entropy and fuzzy entropy are widely used for short-term heart rate variability analysis. These entropy statistics are estimated for a specific value of the tolerance parameter (r) that is mostly chosen from a common recommended range. Entropy measurement on short-term signals is highly sensitive to the choice of r. An incorrect selection of r results in an inaccurate entropy value, thereby leading to unreliable information retrieval. By addressing this inaccuracy due to r selection, the quality and reliability of information retrieval can be improved. Thus, we hypothesize that generating a complete entropy profile using all potential r values will give a more complete and useful information about signal irregularity in contrast to the case of finding entropy at a single selected value of r. In order to do so, one must be able to accurately select all potential r candidates. In this paper, we use a data-driven algorithm based on cumulative histograms to automatically select potential r values for an individual signal based on its dynamics. An appropriate set of r values is designated by the algorithm for generating a series of ApEn values (ApEn profile) instead of a single value of ApEn. ApEn profile- based secondary measures such as TotalApEn and SDApEn have been used as features to classify sets of synthetic and physiologic data. Our study proves that secondary measures obtained from an ApEn profile are more efficient in indicating irregularity levels in comparison with the traditional measure of ApEn evaluated at a single r value, specially in the case of short length data.

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References

  1. Heart rate variability: standards of measurement, physiological interpretation and clinical use. task force of the European society of cardiology and the north American society of pacing and electrophysiology. Circulation 93(5), 1043–1065 (1996)

  2. Acharya, U.R., Joseph, K.P., Kannathal, N., Lim, C.M., Suri, J.S.: Heart rate variability: a review. Med. Biol. Eng. Comput. 44(12), 1031–1051 (2006)

    Article  Google Scholar 

  3. Acharya, U.R., Kannathal, N., Ong Wai, S., Luk Yi, P., TjiLeng, C.: Heart rate analysis in normal subjects of various age groups. Biomed. Eng. Online 3, 24–28 (2004)

    Article  Google Scholar 

  4. Ahmed, M.U., Mandic, D.P.: Multivariate multiscale entropy: a tool for complexity analysis of multichannel data. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 84(6 Pt 1), 061918 (2011)

    Article  Google Scholar 

  5. Boskovic, A., Loncar-Turukalo, T., Japundzic-Zigon, N., Bajic, D.: The flip-flop effect in entropy estimation. In: 2011 IEEE 9th International Symposium on Intelligent Systems & Informatics (SISY) p. 227 (2011)

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

  7. Castiglioni, P., Zurek, S., Piskorski, J., Kosmider, M., Guzik, P., Ce, E., Rampichini, S., Merati, G.: Assessing sample entropy of physiological signals by the norm component matrix algorithm: application on muscular signals during isometric contraction. In: 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) p. 5053 (2013)

  8. Chen, W., Zhuang, J., Yu, W., Wang, Z.: Measuring complexity using fuzzyen, apen, and sampen. Med. Eng. Phys. 31, 61–68 (2009)

    Article  Google Scholar 

  9. Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–656 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  10. Goldberger, A.L.: Is the normal heartbeat chaotic or homeostatic? News Physiol. Sci. Int. J. Physiol. Prod. Jointly Int. Union Physiol. Sci. Am. Physiol. Soc. 6, 87–91 (1991)

    Google Scholar 

  11. Goldberger, A.L., Luis, A.N.A., Hausdorff, J.M., Plamen, ChI, Peng, C.-K., Stanley, H.E.: Fractal dynamics in physiology: alterations with disease and aging. Proc. Natl. Acad. Sci. USA 99(3), 2466 (2002)

    Article  Google Scholar 

  12. Goldberger, A.L., West, B.J.: Applications of nonlinear dynamics to clinical cardiology. Ann. N.Y. Acad. Sci. 504, 195–213 (1987)

    Article  Google Scholar 

  13. Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Phys. D Nonlinear Phenom. 9, 189–208 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hegger, R., Kantz, H., Schreiber, T.: Practical implementation of nonlinear time series methods: the tisean package. Chaos 9(2), 413 (1999)

    Article  MATH  Google Scholar 

  15. Iyengar, N., Peng, C.K., Morin, R., Goldberger, A.L., Lipsitz, L.A.: Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics. Am. J. Physiol. 271(4), 1078 (1996)

    Google Scholar 

  16. Kaplan, D.T., Furman, M.I., Pincus, S.M., Ryan, S.M., Lipsitz, L.A., Goldberger, A.L.: Aging and the complexity of cardiovascular dynamics. Biophys. J. 59(4), 945–949 (1991)

    Article  Google Scholar 

  17. Lake, D.E., Richman, J.S., Griffin, M.P., Moorman, J.R., Mosconi, G., Carnevali, O., Habibi, H.: Sample entropy analysis of neonatal heart rate variability. Am. J. Physiol. 283(3), 789 (2002)

    Google Scholar 

  18. Li, P., Liu, C., Li, K., Zheng, D., Liu, C., Hou, Y.: Assessing the complexity of short-term heartbeat interval series by distribution entropy. Med. Biol. Eng. Comput. 53(1), 77–87 (2015)

    Article  Google Scholar 

  19. Li, P., Liu, C., Wang, X., Li, B., Che, W., Liu, C.: Cross-sample entropy and cross-fuzzy entropy for testing pattern synchrony: How results vary with different threshold value r. In: IFMBE Proceedings, Medical Physics and Biomedical Engineering, vol. 39, pp. 485–488 (2013)

  20. Li, P., Liu, C., Wang, X., Li, L., Yang, L., Chen, Y., Liu, C.: Testing pattern synchronization in coupled systems through different entropy-based measures. Med. Biol. Eng. Comput. 51(5), 581–591 (2013)

    Article  Google Scholar 

  21. Lipsitz, L.A., Goldberger, A.L.: Loss of ’complexity’ and aging: potential applications of fractals and chaos theory to senescence. J. Am. Med. Assoc. 267(13), 1806 (1992)

    Article  Google Scholar 

  22. Liu, C., Li, K., Zhao, L., Liu, F., Zheng, D., Liu, C., Liu, S.: Analysis of heart rate variability using fuzzy measure entropy. Comput. Biol. Med. 43(2), 100–108 (2013)

    Article  Google Scholar 

  23. Liu, C., Liu, C., Shao, P., Li, L., Sun, X., Wang, X., Liu, F.: 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 (2011)

    Article  Google Scholar 

  24. Lu, S., Chen, X., Kanters, J.K., Solomon, I.C., Chon, K.H.: Automatic selection of the threshold value for approximate entropy. IEEE Trans. Biomed. Eng. 55(8), 1966–1972 (2008)

    Article  Google Scholar 

  25. Maestri, R., Pinna, G.D., Porta, A., Balocchi, R., Sassi, R., Signorini, M.G., Dudziak, M., Raczak, G.: Assessing nonlinear properties of heart rate variability from short-term recordings: are these measurements reliable? Physiol. Meas. 28(9), 1067–1077 (2007)

    Article  Google Scholar 

  26. Mayer, C.C., Bachler, M., Hörtenhuber, M., Stocker, C., Holzinger, A., Wassertheurer, S.: Selection of entropy-measure parameters for knowledge discovery in heart rate variability data. BMC Bioinform. 15(Suppl 6), S2 (2014)

    Article  Google Scholar 

  27. Moody, G.: Rr interval time series modeling: the physionet/computers in cardiology challenge 2002. In: Computers in Cardiology, vol. 29, pp. 125–128 (2002)

  28. Nemati, S., Edwards, B.A., Lee, J., Pittman-Polletta, B., Butler, J.P., Malhotra, A.: Respiration and heart rate complexity: effects of age and gender assessed by band-limited transfer entropy. Respir. Physiol. Neurobiol. 189, 27–33 (2013)

    Article  Google Scholar 

  29. Nunan, D., Sandercock, G.R., Brodie, D.A.: A quantitative systematic review of normal values for short-term heart rate variability in healthy adults nunan, et al. review of short-term hrv values. Pacing Clin. Electrophysiol. 33(11), 1407–1417 (2010)

    Article  Google Scholar 

  30. Orphanidou, C., Fleming, S., Shah, S., Tarassenko, L.: Data fusion for estimating respiratory rate from a single-lead ecg. Biomed. Signal Process. Control 8, 98–105 (2013)

    Article  Google Scholar 

  31. Pincus, S.: Approximate entropy (apen) as a complexity measure. Chaos 5(1), 110 (1995)

    Article  MathSciNet  Google Scholar 

  32. Pincus, S.M.: Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA 88(6), 2297–2301 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  33. Pincus, S.M., Gladstone, I.M., Ehrenkranz, R.A.: A regularity statistic for medical data analysis. J. Clin. Monit. 7(4), 335–345 (1991)

    Article  Google Scholar 

  34. Pincus, S.M., Goldberger, A.L.: Physiological time-series analysis: what does regularity quantify? Am. J. Physiol. 266, H1643–H1643 (1994)

    Google Scholar 

  35. Pincus, S.M., Huang, W.: Approximate entropy: statistical properties and applications. Commun. Stat. Theory Methods 21(11), 3061 (1992)

    Article  MATH  Google Scholar 

  36. Pincus, S.M., Viscarello, R.R.: Approximate entropy: a regularity measure for fetal heart rate analysis. Obstet. Gynecol. 79(2), 249–255 (1992)

    Google Scholar 

  37. Rajendra Acharya, U., Paul Joseph, K., Kannathal, N., Lim, C.M., Suri, J.S.: Heart rate variability: a review. Med. Biol. Eng. Comput. 44(12), 1031–1051 (2006)

    Article  Google Scholar 

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

    Google Scholar 

  39. Ryan, S.M., Goldberger, A.L., Pincus, S.M., Mietus, J., Lipsitz, L.A.: Gender- and age-related differences in heart rate dynamics: are women more complex than men? J. Am. Coll. Cardiol. 24(7), 1700–1707 (1994)

    Article  Google Scholar 

  40. Voss, A., Heitmann, A., Schroeder, R., Peters, A., Perz, S.: Short-term heart rate variability-age dependence in healthy subjects. Physiol. Meas. 33(8), 1289–1311 (2012)

    Article  Google Scholar 

  41. Voss, A., Schroeder, R., Heitmann, A., Peters, A., Perz, S.: Short term heart rate variability influence of gender and age in healthy subjects. PLoS One 10(3), 1–33 (2015)

    Google Scholar 

  42. Voss, A., Schulz, S., Schroeder, R., Baumert, M., Caminal, P.: Methods derived from nonlinear dynamics for analysing heart rate variability. Philos. Trans. Math. Phys. Eng. Sci. 367(1887), 277–296 (2009)

    Article  MATH  Google Scholar 

  43. Xie, H.B., Chen, W.T., He, W.X., Liu, H.: Complexity analysis of the biomedical signal using fuzzy entropy measurement. Appl. Soft Comput. J. 11(2), 2871–2879 (2011)

  44. Xie, H.B., He, W.X., Liu, H.: Measuring time series regularity using nonlinear similarity-based sample entropy. Phys. Lett. A 372, 7140–7146 (2008)

    Article  MATH  Google Scholar 

  45. Yentes, J.M., Hunt, N., Schmid, K.K., Kaipust, J.P., McGrath, D., Stergiou, N.: The appropriate use of approximate entropy and sample entropy with short data sets. Ann. Biomed. Eng. 41(2), 349–365 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC, 3010, Australia

    Radhagayathri K. Udhayakumar, Chandan Karmakar & Marimuthu Palaniswami

  2. Centre for Pattern Recognition and Data Analytics (PRaDA), Deakin University, Geelong, VIC, 3220, Australia

    Chandan Karmakar

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  1. Radhagayathri K. Udhayakumar
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Correspondence to Chandan Karmakar.

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Udhayakumar, R.K., Karmakar, C. & Palaniswami, M. Approximate entropy profile: a novel approach to comprehend irregularity of short-term HRV signal. Nonlinear Dyn 88, 823–837 (2017). https://doi.org/10.1007/s11071-016-3278-z

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