519.65

computer modeling, statistical estimation methods, vector of stationary random sequences, electrocardiogram signal, heart rhythm.

The article is devoted to a computer modeling method of electrocardiogram rhythm based on a mathematically justified model in the form of a vector of stationary random sequences. The developed computer modeling method allows for generating realizations of vector electrocardiogram rhythm signal (vector components of stationary random sequences) for different types of electrocardiogram signals, both normal and with various types of rhythm pathologies. The modeling of electrocardiogram rhythms was carried out based on the obtained statistical information in the form of estimates of the mathematical expectation and variance of the components of the vector of stationary random sequences. It has been shown that the obtained estimates of statistical characteristics of the modeled vector components (components that describe the electrocardiogram rhythm) are within confidence intervals, which is an indication of the correctness of the experiments conducted using the developed computer simulation method. The accuracy of the computer simulation method for generating realizations of the vector components of stationary random sequences has been investigated, and the error of the computer simulation does not exceed 13% for the investigated vector components.

1. Paul van Gent, Haneen Farah, Nicole van Nes, Bart van Arem, HeartPy. A novel heart rate algorithm for the analysis of noisy signals, Transportation Research Part F: Traffic Psychology and Behaviour. Vol. 66. 2019. P. 368–378. URL: https://doi.org/10.1016/j.trf.2019.09.015.
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4. Hernâni Gonçalves, Tiago Henriques-Coelho, João Bernardes, Ana Paula Rocha, Ana Brandão-Nogueira, Adelino Leite-Moreira, Analysis of heart rate variability in a rat model of induced pulmonary hypertension. Medical Engineering & Physics. Vol. 32. Issue 7. 2010. P. 746–752. URL: https://doi.org/10.1016/j. medengphy.2010.04.018.
5. Arman Kilic, Artificial Intelligence and Machine Learning in Cardiovascular Health Care, The Annals of Thoracic Surgery 109. 2020. Р. 1323–1329. Doi: 10.1016/j.athoracsur.2019.09.042.
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7. Soile Tapio, Mark P. Little, Jan Christian Kaiser, Nathalie Impens, Nobuyuki Hamada, Alexandros G. Georgakilas, David Simar, Sisko Salomaa, Ionizing radiation-induced circulatory and metabolic diseases. Environment International. 146. 2021. Doi: 10.1016/j.envint.2020.106235.
8. Lupenko S., Lytvynenko I., Sverstiuk A., Horkunenko A., Shelestovskyi B. Software for statistical processing and modeling of a set of synchronously registered cardio signals of different physical nature. CEUR Workshop Proceedings. 2021. 2864. P. 194–205.
9. Lupenko S. A., Lytvynenko I. V., Stadnyk N. B., Zozulia A. M., Sverstiuk A. S. Conditional cyclic random process of a discrete argument as a generalized mathematic model of cyclic signals with double stochasticity. Journal of Computing and Information Technology. 2020. 39. P. 60–69.
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15. Haritopoulos M., Capdessus C., Nandi A. K. Foetal PQRST extraction from ECG recordings using cyclostationarity-based source separation method. in Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. (EMBC). Aug. 2010. P. 1910–1913.
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18. Shaolin R., Xian L., Beizhen Z., Yinuo J., Xiaoyun Y., Cheng C., Label correlation embedding guided network for multi-label ECG arrhythmia diagnosis, Knowledge-Based Systems, Volume 270, 21 June 2023, 110545. URL: https://doi.org/10.1016/j.knosys.2023.110545.
19. Litvinenko Ia., Lupenko S., Oniskiv P., Trysnyuk V., Zozulia A. Mathematical model of rhythmocardiosignal in vector view of stationary and stationary-related case sequences. Advanced Information Systems. National Technical University “Kharkiv Polytechnic Institute”. 2020. Vol. 4. No. 2. P. 42–46.
20. Lytvynenko I. V., Lupenko S. A., Onyskiv P. A., Trysniuk V. M., Zozulia A. M. Metody statystychnoho opratsiuvannia rytmokardiosyhnalu iz pidvyshchenoiu rozdilnoiu zdatnistiu na osnovi yoho modeli u vyhliadi vektora statsionarnykh vypadkovykh poslidovnostei  Informatsiini tekhnolohii. Systemy upravlinnia, navihatsii ta zviazku, Natsionalnyi universytet ”Poltavska politekhnika imeni Yuriia Kondratiuka”. 2020. Vypusk 2 (60). Р. 75–84. Doi: 10.26906/SUNZ.2020.2.075. [In Ukraine].
21. I. V. Lytvynenko, S. A. Lupenko, P. A. Onyskiv, V. M. Trysniuk, A. M. Zozulia. Prohramnyi kompleks dlia avtomatyzovanoho analizu sertsevoho rytmu na osnovi vektornoho rytmokardiosyhnalu. Matematychne modeliuvannia v ekonomitsi. No. 1. 2020. ISSN 2409-8876. P. 27–38. [In Ukraine].
22. Method of Evaluation of Discrete Rhythm Structure of Cyclic Signals with the Help of Adaptive Interpolation. Lytvynenko, I., Lupenko, S., Onyskiv, P. 2020 IEEE 15th International Scientific and Technical Conference on Computer Sciences and Information Technologies, CSIT 2020. Proceedings, 2020. 1. P. 155–158. 9321878. Doi: 10.1109/CSIT49958.2020.9321878.
23. I. V. Lytvynenko, S. A. Lupenko, P. A. Onyskiv, V. M. Trysniuk, A. M. Zozulia. Prohramnyi kompleks dlia avtomatyzovanoho analizu sertsevoho rytmu na osnovi vektornoho rytmokardiosyhnalu. Matematychne modeliuvannia v ekonomitsi. No. 1. 2020. ISSN 2409-8876. P. 27–38. [In Ukraine].

1. Paul van Gent, Haneen Farah, Nicole van Nes, Bart van Arem, HeartPy. A novel heart rate algorithm for the analysis of noisy signals, Transportation Research Part F: Traffic Psychology and Behaviour. Vol. 66. 2019. P. 368–378. URL: https://doi.org/10.1016/j.trf.2019.09.015.
2. Afifah Nurrosyidah, Faizal Mahananto, Mahendrawathi ER, Tomohiko Igasaki, Toshitaka Yamakawa, Heart Rate Variability Analysis by Multiscale Entropy for Autonomic Nervous System Identification. Procedia Computer Science. Volume 161. 2019. P. 630–637. URL: https://doi.org/10.1016/j.procs. 2019.11.166.
3. Alona Ben-Tal, Sophie S. Shamailov, Julian F.R. Paton, Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: New insights from mathematical modeling, Mathematical Biosciences. Vol. 255. 2014. P. 71–82. URL: https://doi.org/10.1016/j.mbs.2014.06.015.
4. Hernâni Gonçalves, Tiago Henriques-Coelho, João Bernardes, Ana Paula Rocha, Ana Brandão-Nogueira, Adelino Leite-Moreira, Analysis of heart rate variability in a rat model of induced pulmonary hypertension. Medical Engineering & Physics. Vol. 32. Issue 7. 2010. P. 746–752. URL: https://doi.org/10.1016/j. medengphy.2010.04.018.
5. Arman Kilic, Artificial Intelligence and Machine Learning in Cardiovascular Health Care, The Annals of Thoracic Surgery 109. 2020. Р. 1323–1329. Doi: 10.1016/j.athoracsur.2019.09.042.
6. Pan Ma, Shigong Wang, Ji Zhou, Tanshi Li, Xingang Fan, Jin Fan, Siyi Wang, Meteorological rhythms of respiratory and circulatory diseases revealed by Harmonic Analysis. Heliyon 6. 2020. Doi: 10.1016/ j.heliyon.2020.e04034.
7. Soile Tapio, Mark P. Little, Jan Christian Kaiser, Nathalie Impens, Nobuyuki Hamada, Alexandros G. Georgakilas, David Simar, Sisko Salomaa, Ionizing radiation-induced circulatory and metabolic diseases. Environment International. 146. 2021. Doi: 10.1016/j.envint.2020.106235.
8. Lupenko S., Lytvynenko I., Sverstiuk A., Horkunenko A., Shelestovskyi B. Software for statistical processing and modeling of a set of synchronously registered cardio signals of different physical nature. CEUR Workshop Proceedings. 2021. 2864. P. 194–205.
9. Lupenko S. A., Lytvynenko I. V., Stadnyk N. B., Zozulia A. M., Sverstiuk A. S. Conditional cyclic random process of a discrete argument as a generalized mathematic model of cyclic signals with double stochasticity. Journal of Computing and Information Technology. 2020. 39. P. 60–69.
10. W. A. Gardner, Cyclostationarity. Half a century of research. Signal Processing. 86. 2006. Р. 639–697. Doi:10.1016/j.sigpro.2005.06.016.
11. W. A. Gardner Exploitation of cyclostationarity for identifying the Volterra kernels of non–linear systems. IEEE Transactions on Information Theory. 39. 1993. Р. 535–542. Doi:10.1109/18.212283.
12. W. A. Gardner Fraction–of–time probability for time–series that exhibit cyclostationarity. Signal Processing. 23. 1991. Р. 273–292. Doi:10.1016/0165-1684(91)90005-4.
13. W. A. Gardner, C. M. Spooner Higher–order cyclostationarity, in: International Symposium on Information Theory and Applications, ISITA '90, Honolulu, HI, 1990. P. 355–358.
14. Fonseca N. G., Aleman, M. N. Cardiac arrhythmia classication based on the RMS signal and cyclostationarity. IEEE Latin Amer. Trans. Vol. 19. No. 4. P. 584–591, Apr. 2021.W. A. Gardner,
    C. M. Spooner The cumulant theory of cyclostationary time-series. II. Development and applications. IEEE Transactions on Signal Processing. 42. 1994. Р. 3409–3429. Doi:10.1109/78.340776.
15. Haritopoulos M., Capdessus C., Nandi A. K. Foetal PQRST extraction from ECG recordings using cyclostationarity-based source separation method. in Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. (EMBC). Aug. 2010. P. 1910–1913.
16. Minschole A., Camps J., Lyon A., Rodriges B., Machine learning in the electrocardiogram, Journal of Electrocardiology. Vol. 57. Supplement. November–December 2019. P. S61–S64. URL: https://doi.org/ 10.1016/j.jelectrocard.2019.08.008.
17. Zekai W., Stavros S., Bing Y., Hierarchical deep learning with Generative Adversarial Network for automatic cardiac diagnosis from ECG signals. Computers in Biology and Medicine. Vol. 155. March 2023. 106641. https://doi.org/10.1016/j.compbiomed.2023.106641
18. Shaolin R., Xian L., Beizhen Z., Yinuo J., Xiaoyun Y., Cheng C., Label correlation embedding guided network for multi-label ECG arrhythmia diagnosis, Knowledge-Based Systems, Volume 270, 21 June 2023, 110545. URL: https://doi.org/10.1016/j.knosys.2023.110545.
19. Litvinenko Ia., Lupenko S., Oniskiv P., Trysnyuk V., Zozulia A. Mathematical model of rhythmocardiosignal in vector view of stationary and stationary-related case sequences. Advanced Information Systems. National Technical University “Kharkiv Polytechnic Institute”. 2020. Vol. 4. No. 2. P. 42–46.
20. Lytvynenko I. V., Lupenko S. A., Onyskiv P. A., Trysniuk V. M., Zozulia A. M. Metody statystychnoho opratsiuvannia rytmokardiosyhnalu iz pidvyshchenoiu rozdilnoiu zdatnistiu na osnovi yoho modeli u vyhliadi vektora statsionarnykh vypadkovykh poslidovnostei  Informatsiini tekhnolohii. Systemy upravlinnia, navihatsii ta zviazku, Natsionalnyi universytet ”Poltavska politekhnika imeni Yuriia Kondratiuka”. 2020. Vypusk 2 (60). Р. 75–84. Doi: 10.26906/SUNZ.2020.2.075. [In Ukraine].
21. I. V. Lytvynenko, S. A. Lupenko, P. A. Onyskiv, V. M. Trysniuk, A. M. Zozulia. Prohramnyi kompleks dlia avtomatyzovanoho analizu sertsevoho rytmu na osnovi vektornoho rytmokardiosyhnalu. Matematychne modeliuvannia v ekonomitsi. No. 1. 2020. ISSN 2409-8876. P. 27–38. [In Ukraine].
22. Method of Evaluation of Discrete Rhythm Structure of Cyclic Signals with the Help of Adaptive Interpolation. Lytvynenko, I., Lupenko, S., Onyskiv, P. 2020 IEEE 15th International Scientific and Technical Conference on Computer Sciences and Information Technologies, CSIT 2020. Proceedings, 2020. 1. P. 155–158. 9321878. Doi: 10.1109/CSIT49958.2020.9321878.
23. I. V. Lytvynenko, S. A. Lupenko, P. A. Onyskiv, V. M. Trysniuk, A. M. Zozulia. Prohramnyi kompleks dlia avtomatyzovanoho analizu sertsevoho rytmu na osnovi vektornoho rytmokardiosyhnalu. Matematychne modeliuvannia v ekonomitsi. No. 1. 2020. ISSN 2409-8876. P. 27–38. [In Ukraine].