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Time reversal, symbolic series and irreversibility of human heartbeat

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  • Cammarota, Camillo
  • Rogora, Enrico

Abstract

We study the time reversal properties of time series by means of a ternary coding of the differentiated series. For the symbolic series obtained in this way we show that suitable pairs of ternary words have the same probability if the time series is reversible. This provides tests in which time reversibility is rejected if the estimated probabilities are significantly different. We apply one of these tests to the human heartbeat series extracted from 24h Holter recordings of 19 healthy subjects. Data analysis shows a highly significant prevalence of irreversibility. Our symbolic approach to time reversal gives further support to the suitability of non-linear modeling of the normal heartbeat.

Suggested Citation

  • Cammarota, Camillo & Rogora, Enrico, 2007. "Time reversal, symbolic series and irreversibility of human heartbeat," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1649-1654.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:5:p:1649-1654
    DOI: 10.1016/j.chaos.2006.03.126
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    References listed on IDEAS

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    1. Cammarota, Camillo & Rogora, Enrico, 2005. "Independence and symbolic independence of nonstationary heartbeat series during atrial fibrillation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 323-335.
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    Cited by:

    1. Rong, Lei & Shang, Pengjian, 2018. "New irreversibility measure and complexity analysis based on singular value decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 913-924.
    2. Yao, Wenpo & Yao, Wenli & Wang, Jun, 2021. "A novel parameter for nonequilibrium analysis in reconstructed state spaces," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Xiong, Hui & Shang, Pengjian & Xia, Jianan & Wang, Jing, 2018. "Time irreversibility and intrinsics revealing of series with complex network approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 241-249.
    4. Alvarez-Ramirez, J. & Echeverria, J.C. & Meraz, M. & Rodriguez, E., 2017. "Asymmetric acceleration/deceleration dynamics in heart rate variability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 213-224.
    5. Olivares, Felipe & Sun, Xiaoqian & Wandelt, Sebastian & Zanin, Massimiliano, 2023. "Measuring landing independence and interactions using statistical physics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 170(C).
    6. Wu, Zhenyu & Shang, Pengjian & Xiong, Hui, 2018. "An improvement of the measurement of time series irreversibility with visibility graph approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 370-378.
    7. Huang, Yong & Yang, Dongqing & Wang, Lei & Wang, Kehong, 2020. "Classifying of welding time series based on multi-scale time irreversibility analysis and extreme learning machine," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Rong, Lei & Shang, Pengjian, 2020. "Evaluation of missing ordinal pattern and its fractional distribution entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    9. Li, Jinyang & Shang, Pengjian, 2018. "Time irreversibility of financial time series based on higher moments and multiscale Kullback–Leibler divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 248-255.
    10. Tsvetkov, V.P. & Mikheyev, S.A. & Tsvetkov, I.V., 2018. "Fractal phase space and fractal entropy of instantaneous cardiac rhythm," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 71-76.

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