Skip to main content

Advertisement

Log in

Novel multiscale E-metric cross-sample entropy-based cardiac arrhythmia detection and its performance investigation in reference to multiscale cross-sample entropy-based analysis

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Cardiac arrhythmia is a common difficulty of human cardiovascular system and can be evaluated using cardiac rate variability. Multiscale Cross Sample Entropy (MCSEn) is used as a reference to quantify cardiac arrhythmia on the basis of complexity for double-interval series at multiple scales. This measure is failed to provide complexity with reduced scale factors for large data lengths. To hypothesize this measure for two series cardiac data by using coarse-grained process, Multiscale E-metric Cross Sample Entropy (MECSEn) has been proposed and is used to measure complexity between arrhythmia subjects, named atrial fibrillation (AF) and congestive heart failure (CHF) and healthy subjects at multiple scales. Besides short series data and undefined value, MECSEn has come up with a very new concept of banishing the use of a large number of scale factors for evaluating the complexity between two different interval series across multiple scales. It makes the proposed algorithm less time consumer. Both measures have found subjects derived from AF behave as white noise and subjects derived from CHF behave as pink noise. The t test validates MCSEn and the proposed algorithm, MECSEn by providing p < 0.00001. Moreover, MCSEn and MECSEn algorithms are compared with multiscale sample entropy algorithm (MSEn) which uses single cardiac series to evaluate complexity of healthy and arrhythmia subjects.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available in the PhysioNet repository, [https://physionet.org/].

References

  1. Benveniste, A., Nikoukhah, R., Willsky, A.S.: Multiscale system theory. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 41(1), 2–15 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chai, T., Draxler, R.R.: Root mean square error (RMSE) or mean absolute error (MAE)?—arguments against avoiding RMSE in the literature. Geosci. Model Dev. 7(3), 1247–1250 (2014)

    Article  Google Scholar 

  3. Chen, G.Y., Huang, C.M., Liu, H.L., Lee, S.H., Lee, T.M.C., Lin, C., Wu, S.C.: Depression scale prediction with cross-sample entropy and deep learning. In: 2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 120–123. IEEE (2020)

  4. Coast, D.A., Stern, R.M., Cano, G.G., Briller, S.A.: An approach to cardiac arrhythmia analysis using hidden Markov models. IEEE Trans. Biomed. Eng. 37(9), 826–836 (1990)

    Article  Google Scholar 

  5. Costa, M., Peng, C.K., Goldberger, A.L., Hausdorff, J.M.: Multiscale entropy analysis of human gait dynamics. Phys. A Stat. Mech. Appl. 330(1–2), 53–60 (2003)

    Article  MATH  Google Scholar 

  6. Costa, M., Goldberger, A.L., Peng, C.K.: Multiscale entropy analysis of biological signals. Phys. Rev. E 71(2), 021906 (2005)

    Article  MathSciNet  Google Scholar 

  7. Costa, M.D., Goldberger, A.L.: Generalized multiscale entropy (GMSE) analysis: quantifying the structure of time series’ volatility

  8. Fabris, C., De Colle, W., Sparacino, G.: Voice disorders assessed by (cross-) sample entropy of electroglottogram and microphone signals. Biomed. Signal Process. Control 8(6), 920–926 (2013)

    Article  Google Scholar 

  9. García-Martínez, B., Fernández-Caballero, A., Alcaraz, R., Martínez-Rodrigo, A.: Cross-sample entropy for the study of coordinated brain activity in calm and distress conditions with electroencephalographic recordings. Neural Comput. Appl. 33(15), 9343–9352 (2021)

    Article  Google Scholar 

  10. Huang, M.L., Wu, Y.S.: Classification of atrial fibrillation and normal sinus rhythm based on convolutional neural network. Biomed. Eng. Lett. 10(2), 183–193 (2020)

    Article  Google Scholar 

  11. Hu, J., Gao, J., Tung, W.W., Cao, Y.: Multiscale analysis of heart rate variability: a comparison of different complexity measures. Ann. Biomed. Eng. 38(3), 854–864 (2010)

    Article  Google Scholar 

  12. Jamin, A., Humeau-Heurtier, A.: (Multiscale) cross-entropy methods: a review. Entropy 22(1), 45 (2019)

    Article  MathSciNet  Google Scholar 

  13. Junaid, M., Siddiqui, A.K., Qumar, A., Naqvi, I., Khan, A., Hussain, L.: Quantification of human gait dynamics using multiscale entropy under healthy and diseased conditions. Entropy 4(2) (2017)

  14. Kamath, M.V., Watanabe, M., Upton, A. (Eds.): Heart Rate Variability (HRV) Signal Analysis: Clinical Applications (2012)

  15. Li, S., Shang, P.: Multi-moment multiscale local sample entropy and its application to complex physiological time series. Int. J. Bifurc. Chaos 32(11), 2250166 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, Y., Liu, J., Tang, C., Han, W., Zhou, S., Yang, S., He, L., Jing, D., Luo, E., Xie, K.: Multiscale entropy analysis of instantaneous frequency variation to overcome the cross-over artifact in rhythmic EEG. IEEE Access 9, 12896–12905 (2021)

    Article  Google Scholar 

  17. Lin, T.K., Huang, T.H.: Damage quantification of 3D-printed structure based on composite multiscale cross-sample entropy. Smart Mater. Struct. 30(1), 015015 (2020)

    Article  Google Scholar 

  18. Lin, T.K., Tseng, T.C., Lainez, A.G.: Three-dimensional structural health monitoring based on multiscale cross-sample entropy. Earthq. Struct. 12(6), 673–687 (2017)

    Google Scholar 

  19. Liu, L.Z., Qian, X.Y., Lu, H.Y.: Cross-sample entropy of foreign exchange time series. Phys. A Stat. Mech. Appl. 389(21), 4785–4792 (2010)

    Article  Google Scholar 

  20. Liu, W.-M., et al.: Novel application of multiscale cross-approximate entropy for assessing early changes in the complexity between systolic blood pressure and ECG RR intervals in diabetic rats. Entropy 24(4), 473 (2022)

    Article  Google Scholar 

  21. Malik, M.: Heart rate variability. Curr. Opin. Cardiol. 13(1), 36–44 (1998)

    Article  Google Scholar 

  22. Marwaha, P., Sunkaria, R.K.: Complexity quantification of cardiac variability time series using improved sample entropy (I-SampEn). Australas. Phys. Eng. Sci. Med. 39(3), 755–763 (2016)

    Article  Google Scholar 

  23. Marwaha, P., Sunkaria, R.K.: Exploring total cardiac variability in healthy and pathophysiological subjects using improved refined multiscale entropy. Med. Biol. Eng. Comput. 55(2), 191–205 (2017)

    Article  Google Scholar 

  24. McCamley, J., Denton, W., Lyden, E., Yentes, J.M.: Measuring coupling of rhythmical time series using cross sample entropy and cross recurrence quantification analysis. Comput. Math. Methods Med. (2017)

  25. McDonough, I.M., Nashiro, K.: Network complexity as a measure of information processing across resting-state networks: evidence from the Human Connectome Project. Front. Hum. Neurosci. 8, 409 (2014)

    Article  Google Scholar 

  26. Morel, C., Humeau-Heurtier, A.: Multiscale permutation entropy for two-dimensional patterns. Pattern Recogn. Lett. 150, 139–146 (2021)

    Article  Google Scholar 

  27. Pincus, S.M., Goldberger, A.L.: Physiological time-series analysis: what does regularity quantify? Am. J. Physiol. Heart Circ. Physiol. 266(4), H1643–H1656 (1994)

    Article  Google Scholar 

  28. Ramírez-Parietti, I., Contreras-Reyes, J.E., Idrovo-Aguirre, B.J.: Cross-sample entropy estimation for time series analysis: a nonparametric approach. Nonlinear Dyn. 105(3), 2485–2508 (2021)

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. Shang, D., Shang, P., Zhang, Z.: Efficient synchronization estimation for complex time series using refined cross-sample entropy measure. Commun. Nonlinear Sci. Numer. Simul. 94, 105556 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  31. Shi, W., Shang, P.: Cross-sample entropy statistic as a measure of synchronism and cross-correlation of stock markets. Nonlinear Dyn. 71(3), 539–554 (2013)

    Article  MathSciNet  Google Scholar 

  32. Ta, N., Wei, H.C., Li, M.M.: Assessment of arteriosclerosis based on multiscale cross approximate entropy of human finger pulse wave. Technol Health Care (Preprint), 1–11 (2022)

  33. Thuraisingham, R.A., Gottwald, G.A.: On multiscale entropy analysis for physiological data. Phys. A Stat. Mech. Appl. 366, 323–332 (2006)

    Article  Google Scholar 

  34. Wang, F., Zhao, W., Jiang, S.: Detecting asynchrony of two series using multiscale cross-trend sample entropy. Nonlinear Dyn. 99(2), 1451–1465 (2020)

    Article  Google Scholar 

  35. Wu H.T., Liu, C.C., Lo, M.T., Hsu, P.C., Liu, A.B., Chang, K.Y., Tang, C.J.: Multiscale cross-approximate entropy analysis as a measure of complexity among the aged and diabetic. Comput. Math. Methods Med. (2013)

  36. Wu, H.T., Lee, C.Y., Liu, C.C., Liu, A.B.: Multiscale cross-approximate entropy analysis as a measurement of complexity between ECG RR interval and PPG pulse amplitude series among the normal and diabetic subjects. Comput. Math. Methods Med. (2013)

  37. Wu, S.D., Wu, C.W., Lee, K.Y., Lin, S.G.: Modified multiscale entropy for short-term time series analysis. Phys. A Stat. Mech. Appl. 392(23), 5865–5873 (2013)

    Article  Google Scholar 

  38. Wu, H.T., Yang, C.C., Lin, G.M., Haryadi, B., Chu, S.C., Yang, C.M., Sun, C.K.: Multiscale cross-approximate entropy analysis of bilateral fingertips photoplethysmographic pulse amplitudes among middle-to-old aged individuals with or without type 2 diabetes. Entropy 19(4), 145 (2017)

    Article  Google Scholar 

  39. Wu, Y., Shang, P., Li, Y.: Multiscale sample entropy and cross-sample entropy based on symbolic representation and similarity of stock markets. Commun. Nonlinear Sci. Numer. Simul. 56, 49–61 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  40. Xiao, M.X., Wei, H.C., Xu, Y.J., Wu, H.T., Sun, C.K.: Combination of RR interval and crest time in assessing complexity using multiscale cross-approximate entropy in normal and diabetic subjects. Entropy 20(7), 497 (2018)

    Article  Google Scholar 

  41. Yan, R., Yang, Z., Zhang, T.: Multiscale cross entropy: a novel algorithm for analyzing two time series. In: 2009 Fifth International Conference on Natural Computation, vol. 1, pp. 411–413. IEEE (2009)

  42. Yin, Y., Shang, P., Feng, G.: Modified multiscale cross-sample entropy for complex time series. Appl. Math. Comput. 289, 98–110 (2016)

    MathSciNet  MATH  Google Scholar 

  43. Yoo, C.S., Yi, S.H.: On the physiological validity and the effects of detrending in the multiscale entropy analysis of heart rate variability. J. Korean Phys. Soc. 48(4), 670 (2006)

    Google Scholar 

  44. Yoon, K.H., Thap, T., Jeong, C.W., Kim, N.H., Noh, S., Nam, Y., Lee, J.: Analysis of statistical methods for automatic detection of congestive heart failure and atrial fibrillation with short RR interval time series. In: 2015 9th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, pp. 452–457. IEEE (2015)

  45. Zhang, Y., Shang, P.: Permutation entropy analysis of financial time series based on Hill’s diversity number. Commun. Nonlinear Sci. Numer. Simul. 53, 288–298 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  46. Zhang, T., Yang, Z., Coote, J.H.: 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 (2007)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful to Biomedical Signal and Image Processing Group of Dr B R Ambedkar National Institute of Technology, Jalandhar, for their interest in this work and useful comments to draft the final form of this paper. The authors greatly acknowledge the support of SERB-DST, Government of India, sponsored Research Project sanctioned vide File No. EEQ/2018/000925) Dated: March 22, 2019, to carry out this present work. We would like to thank Dr B R Ambedkar National Institute of Technology, Jalandhar, for laboratory facilities and research environment to carry out this work.

Funding

The authors declare that no funds, grants, or other supports were received during the preparation of this manuscript.

Author information

Authors and Affiliations

Authors

Contributions

Each author has equal contribution in this manuscript.

Corresponding author

Correspondence to Kanchan Sharma.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Ethical approval

Not applicable.

Consent to publish

Not applicable.

Consent to participate

Not applicable.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sharma, K., Sunkaria, R.K. Novel multiscale E-metric cross-sample entropy-based cardiac arrhythmia detection and its performance investigation in reference to multiscale cross-sample entropy-based analysis. SIViP 17, 2845–2856 (2023). https://doi.org/10.1007/s11760-023-02503-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-023-02503-4

Keywords

Navigation