519.246

modeling, heart rhythm analysis, rhythm cardiogram, electrocardiosignal, segmentation methods.

The method of automatic formation of rhythm cardiogram with increased resolution by means of already-registered electrocardiogram processing has been substantiated and used in the paper for the first time. This method enables the process of heart rhythm analysis based on rhythmcardiogram with the increased resolution be fully automated in the automatic computer-based systems of functional diagnostics of human heart condition and it is more informative in comparison with the conventional methods of heart rhythm analysis based on the classic cardiointervalogram. The methods of statistical processing of cardiointervalogram have been implemented on the basis of the mathematical model in the form of a conditional cyclic random process which is the most complete and adequate description of the model within the stochastic approach. The formation of rhythmcardiogram with the increased resolution is carried out in three stages. On the first stage the phases of the same type are supposed to be detected corresponding to the limits of zones in all heart cycles of the registered cardiogram. On the second stage the phases of the same type within the limits of the determined zones which correspond to the waves’ extreme are supposed to be detected. On the third stage the differences between the determined time moments are calculated that correspond to the detected phases of the same type in all the neighboring cycles of the electrocardiosignal. The conventional segmentation methods were used in the paper to determine the limits of the segments namely, the method, which is based on the Brodsky-Darhovsky statistics and the method based on difference function of the first order. The structure of the method of rhythmcardiogram with increased resolution formation has been described in the article. Moreover, the analysis of the obtained results of relative errors of rhythmcardiogram with the increased resolution has been performed by the applied segmentation methods.

1. Brandão G. S. et al., “Analysis of heart rate variability in the measurement of the activity of the autonomic nervous system: technical note”. Manual Therapy, Posturology & Rehabilitation Journal. 2014. 12. Р. 243–251.
2. Kotel’nikov S. A. et al. “Cardiac rhythm variability: approaches to mechanisms”. Human Physiology. 2002. 28. Р. 114–127.
3. Carvalho J. L., Rocha A. F., Oliveira F. A. Nascimento Development of a Matlab Software for Analysis of Heart Rate Variability: 6th International Conf. Signal Processing, ICSP’02: proc. conf. Beijing, China, 2002. Vol. 2. Р. 1488–1491.
4. Lupenko S., Lutsyk N., Yasniy O. and Sobaszek Ł. “Statistical analysis of human heart with increased informativeness”. Аcta mechanica et automatic. Vol. 12. 2018. Р. 311–315.
5. Lupenko S., Lutsyk N., Yasniy O., Zozulia A. The Modeling and Diagnostic Features in the Computer Systems of the Heart Rhythm Analysis with the Increased Informativeness: 9th International Conference on Advanced Computer Information Technologies (ACIT). IEEE, 2019. Р. 121–124.
6. Christov I. I. Real time electrocardiogram QRS detection using combined adaptive threshold. BioMed. 2004. Vol. 3. No. 28. 9 p. URL: http://www.biomedical-engineering-online.com/content/3/1/28.
7. Pan J., Tomhins W. J. A real-time QRS detection algorithm. IEEE Trans. Biomed. Eng. 1985. V. 32. P. 230–236.
8. Hamilton P. S., Tompkins W. J. Quantitative investigation of QRS detection rules using the MIT/BIH Arryhthmia database. IEEE Transactions on Biomed. Eng. 1986. Vol. 33. Р. 1157–1165.
9. De Chazazl P., Celler B. Automatic measurement of the QRS onset and offset in individual ECG leads. IEEE Engineering in Medicine and Biology Society. 1996. Vol. 4. P. 1399–1403.
10. Khaled Daqrouq, Ibrahim N. AbuIsbeih, Abdel-Rahman Al-Qawasmi QRS Complex Detection Based on Symmlets Wavelet Function: 5th International MultiConference on Systems, Signals and Devices. 2008.
11. Santanu Sahoo, Prativa Biswal, Tejaswini Das, Sukanta Sabut. De-noising of ECG Signal and QRS Detection Using Hilbert Transform and Adaptive Thresholding. Procedia Technology. Vol. 25. 2016.
    P. 68–75. URL: https://doi.org/10.1016/j.protcy.2016.08.082.
12. Semchyshyn O. V., Leshchyshyn Yu. Z., Zabytivskyi V. P. Alhorytm vydilennia RR-intervaliv kardiosyhnalu dlia zadachi analizu variabelnosti sertsevoho rytmu v systemi realnoho chasu. Visnyk Khmelnytskoho natsionalnoho universytetu. 2007. T. 1. № 6. Р. 130–136.
13. Darrington J. Towards real time QRS detection: A fast method using minimal pre-processing. Biomedical Signal Processing and Control. Elsevier inc. 2006. Vol. 1. Р. 169–176.
14. Friesen G. M., Jannett T. C., Jadallah M. A. et al A comparison of the noise sensitivity of nine QRS detection algorithms. IEEE Transactions on BME. January 1990: proc. conf. 1990. Vol. 37. No. 1. Р. 85–98.
15. Christov I. I. Real time electrocardiogram QRS detection using combined adaptive threshold. BioMed. 2004. Vol. 3. No. 28. 9 p. URL: http://www.biomedical-engineering-online.com/content/3/1/28.
16. Ferdi Y., Herbeuval J. P., Charef A., Boucheham B. R wave detection using fractional digital differentiation. ITBM-RBM. Elsevier Inc. 2003. Vol. 24. Р. 273–280.
17. Chen S.-W., Chen H.-C., Chan H.-L. H.-L. A real-time QRS detection method based on moving-averaging incorporating with wavelet denoising. Computer Methods and Programs in Biomedicine. Elsevier Inc. 2006. Vol. 82. Р. 187–195.
18. Xue Q., Hu Y. H., Tompkins W. J. Neural-network- based adaptive matched filtering for QRS detection. IEEE Trans. Biomed. Eng. 1992. Vol. 39 (4). Р. 317–329.
19. Li C., Zheng C., Tai C. Detection of ECG characteristic points using the wavelet transform. IEEE Trans. Biomed. Eng. 1995. Vol. 42. Р. 21–28.
20. Hamilton P. S., Tompkins W. J. Quantitative investigation of QRS detection rules using the MIT/BIH Arryhthmia database. IEEE Transactions on Biomed. Eng. 1986. Vol. 33. Р. 1157–1165.
21. Pan J., Tompkins W. J. A real-time QRS detection algorithm. IEEE Trans. Biomed. Eng. 1985. Vol. 32.
    No. 3. Р. 230–236.
22. Lupenko S., Lutsyk N., Lapusta Y. Cyclic Linear Random Process As A Mathematical Model Of Cyclic Signals. Acta mechanica et automatic. 2015. № 9 (4). Р. 219–224.
23. Lupenko S., Orobchuk O., Stadnik N., Zozulya A. Modeling and signals processing using cyclic random functions: 13th IEEE International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT) (Lviv, September 11–14. 2018.). Lviv, 2018. T. 1. Р. 360–363. ISBN 978-1-5386-6463-6. IEEE Catalog Number: CFP18D36-PRT.
24. Lupenko S., Zozulia A., Sverstiuk A., Stadnyk N. Matematychne modeliuvannia ta metody opratsiuvannia syhnaliv sertsia na bazi tsyklichnykh vypadkovykh protsesiv ta vektoriv. Sciences and Education a New Dimension. Natural and Technical Sciences. VI (20). ISSUE 172. Budapest, 2018. P. 47–54.
25. Lupenko S., Sverstiuk A., Lutsyk N., Stadnyk N., Zozulia A. Umovnyi tsyklichnyi vypadkovyi protses yak matematychna model kolyvnykh syhnaliv ta protsesiv iz podviinoiu stokhastychnistiu. Polihrafiia i vydavnycha sprava. Printing and Publishing. No. 1 (71). 2016. 2016. Р. 147–159.
26. Chouhan V. S., Mehta S. S., Lingayat N. S. Delineation of QRS-complex, P and T-wave in 12-lead ECG. IJCSNS International Journal of Computer Science and Network Security. 2008. Vol. 8. P. 185–190.
27. Laguna P., Jane R., Caminal P. Automatic detection of wave boundaries in multilead ECG signals. Computers and Biomedical Research. 1994. Vol. 27. P. 45–60.
28. Sahambi J. S., Tandon S. B. Using wavelet transform for ECG characterization. IEEE Engineering in Medicine and Biology. 2000. Vol. 9. P. 1532–1546.
29. Talmon J. L., Van Bemmel J. H. Template wave-form recognition revisited. Results of CSE database. Proc. of Comput. Cardiol. 10-th Annu. meet. Aechen., Okt., 1983. Los Angeles. Calif., 1983. P. 246–252.
30. Vitec M. A. Hrubes J., Kozumplik J. Wavelet-based ECG delineation in Multilead ECG signals: Evaluation on the CSE Database. IFMBE Proceedings. 2009. Vol. 25. P. 177–180.
31. Sandeep Raj, Kailash Chandra Ray. Sparse representation of ECG signals for automated recognition of cardiac arrhythmias. Expert Systems with Applications. Vol. 105. 2018. P. 49–64. URL: https://doi.org/ 10.1016/j.eswa.2018.03.038.
32. Schurmann J. Pattern Classification – A unified view of statistical and neural approaches. New York: Wiley. 1996.
33. Xunde Dong, Cong Wang, Wenjie Si. ECG beat classification via deterministic learning, Neurocomputing. Vol. 240. 2017. P. 1–12. URL: https://doi.org/10.1016/j.neucom.2017.02.056.
34. Lytvynenko I. V. The method of segmentation of stochastic cyclic signals for the problems of their processing and modeling. Journal of Hydrocarbon Power Engineering, Oil and Gas Measurement and Testing. 2017. Vol. 4. No. 2. Р. 93–103.
35. Lytvynenko I., Horkunenko A., Kuchvara O., Palaniza Y. Methods of processing cyclic signals in automated cardiodiagnostic complexes. Proceedings of the 1st International Workshop on Information-Communication Technologies & Embedded Systems. (ICT&ES-2019). Mykolaiv: 2019. P. 116–127.

1. Brandão G. S. et al., “Analysis of heart rate variability in the measurement of the activity of the autonomic nervous system: technical note”. Manual Therapy, Posturology & Rehabilitation Journal. 2014. 12. Р. 243–251.
2. Kotel’nikov S. A. et al. “Cardiac rhythm variability: approaches to mechanisms”. Human Physiology. 2002. 28. Р. 114–127.
3. Carvalho J. L., Rocha A. F., Oliveira F. A. Nascimento Development of a Matlab Software for Analysis of Heart Rate Variability: 6th International Conf. Signal Processing, ICSP’02: proc. conf. Beijing, China, 2002. Vol. 2. Р. 1488–1491.
4. Lupenko S., Lutsyk N., Yasniy O. and Sobaszek Ł. “Statistical analysis of human heart with increased informativeness”. Аcta mechanica et automatic. Vol. 12. 2018. Р. 311–315.
5. Lupenko S., Lutsyk N., Yasniy O., Zozulia A. The Modeling and Diagnostic Features in the Computer Systems of the Heart Rhythm Analysis with the Increased Informativeness: 9th International Conference on Advanced Computer Information Technologies (ACIT). IEEE, 2019. Р. 121–124.
6. Christov I. I. Real time electrocardiogram QRS detection using combined adaptive threshold. BioMed. 2004. Vol. 3. No. 28. 9 p. URL: http://www.biomedical-engineering-online.com/content/3/1/28.
7. Pan J., Tomhins W. J. A real-time QRS detection algorithm. IEEE Trans. Biomed. Eng. 1985. V. 32. P. 230–236.
8. Hamilton P. S., Tompkins W. J. Quantitative investigation of QRS detection rules using the MIT/BIH Arryhthmia database. IEEE Transactions on Biomed. Eng. 1986. Vol. 33. Р. 1157–1165.
9. De Chazazl P., Celler B. Automatic measurement of the QRS onset and offset in individual ECG leads. IEEE Engineering in Medicine and Biology Society. 1996. Vol. 4. P. 1399–1403.
10. Khaled Daqrouq, Ibrahim N. AbuIsbeih, Abdel-Rahman Al-Qawasmi QRS Complex Detection Based on Symmlets Wavelet Function: 5th International MultiConference on Systems, Signals and Devices. 2008.
11. Santanu Sahoo, Prativa Biswal, Tejaswini Das, Sukanta Sabut. De-noising of ECG Signal and QRS Detection Using Hilbert Transform and Adaptive Thresholding. Procedia Technology. Vol. 25. 2016.
    P. 68–75. URL: https://doi.org/10.1016/j.protcy.2016.08.082.
12. Semchyshyn O. V., Leshchyshyn Yu. Z., Zabytivskyi V. P. Alhorytm vydilennia RR-intervaliv kardiosyhnalu dlia zadachi analizu variabelnosti sertsevoho rytmu v systemi realnoho chasu. Visnyk Khmelnytskoho natsionalnoho universytetu. 2007. T. 1. № 6. Р. 130–136.
13. Darrington J. Towards real time QRS detection: A fast method using minimal pre-processing. Biomedical Signal Processing and Control. Elsevier inc. 2006. Vol. 1. Р. 169–176.
14. Friesen G. M., Jannett T. C., Jadallah M. A. et al A comparison of the noise sensitivity of nine QRS detection algorithms. IEEE Transactions on BME. January 1990: proc. conf. 1990. Vol. 37. No. 1. Р. 85–98.
15. Christov I. I. Real time electrocardiogram QRS detection using combined adaptive threshold. BioMed. 2004. Vol. 3. No. 28. 9 p. URL: http://www.biomedical-engineering-online.com/content/3/1/28.
16. Ferdi Y., Herbeuval J. P., Charef A., Boucheham B. R wave detection using fractional digital differentiation. ITBM-RBM. Elsevier Inc. 2003. Vol. 24. Р. 273–280.
17. Chen S.-W., Chen H.-C., Chan H.-L. H.-L. A real-time QRS detection method based on moving-averaging incorporating with wavelet denoising. Computer Methods and Programs in Biomedicine. Elsevier Inc. 2006. Vol. 82. Р. 187–195.
18. Xue Q., Hu Y. H., Tompkins W. J. Neural-network- based adaptive matched filtering for QRS detection. IEEE Trans. Biomed. Eng. 1992. Vol. 39 (4). Р. 317–329.
19. Li C., Zheng C., Tai C. Detection of ECG characteristic points using the wavelet transform. IEEE Trans. Biomed. Eng. 1995. Vol. 42. Р. 21–28.
20. Hamilton P. S., Tompkins W. J. Quantitative investigation of QRS detection rules using the MIT/BIH Arryhthmia database. IEEE Transactions on Biomed. Eng. 1986. Vol. 33. Р. 1157–1165.
21. Pan J., Tompkins W. J. A real-time QRS detection algorithm. IEEE Trans. Biomed. Eng. 1985. Vol. 32.
    No. 3. Р. 230–236.
22. Lupenko S., Lutsyk N., Lapusta Y. Cyclic Linear Random Process As A Mathematical Model Of Cyclic Signals. Acta mechanica et automatic. 2015. № 9 (4). Р. 219–224.
23. Lupenko S., Orobchuk O., Stadnik N., Zozulya A. Modeling and signals processing using cyclic random functions: 13th IEEE International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT) (Lviv, September 11–14. 2018.). Lviv, 2018. T. 1. Р. 360–363. ISBN 978-1-5386-6463-6. IEEE Catalog Number: CFP18D36-PRT.
24. Lupenko S., Zozulia A., Sverstiuk A., Stadnyk N. Matematychne modeliuvannia ta metody opratsiuvannia syhnaliv sertsia na bazi tsyklichnykh vypadkovykh protsesiv ta vektoriv. Sciences and Education a New Dimension. Natural and Technical Sciences. VI (20). ISSUE 172. Budapest, 2018. P. 47–54.
25. Lupenko S., Sverstiuk A., Lutsyk N., Stadnyk N., Zozulia A. Umovnyi tsyklichnyi vypadkovyi protses yak matematychna model kolyvnykh syhnaliv ta protsesiv iz podviinoiu stokhastychnistiu. Polihrafiia i vydavnycha sprava. Printing and Publishing. No. 1 (71). 2016. 2016. Р. 147–159.
26. Chouhan V. S., Mehta S. S., Lingayat N. S. Delineation of QRS-complex, P and T-wave in 12-lead ECG. IJCSNS International Journal of Computer Science and Network Security. 2008. Vol. 8. P. 185–190.
27. Laguna P., Jane R., Caminal P. Automatic detection of wave boundaries in multilead ECG signals. Computers and Biomedical Research. 1994. Vol. 27. P. 45–60.
28. Sahambi J. S., Tandon S. B. Using wavelet transform for ECG characterization. IEEE Engineering in Medicine and Biology. 2000. Vol. 9. P. 1532–1546.
29. Talmon J. L., Van Bemmel J. H. Template wave-form recognition revisited. Results of CSE database. Proc. of Comput. Cardiol. 10-th Annu. meet. Aechen., Okt., 1983. Los Angeles. Calif., 1983. P. 246–252.
30. Vitec M. A. Hrubes J., Kozumplik J. Wavelet-based ECG delineation in Multilead ECG signals: Evaluation on the CSE Database. IFMBE Proceedings. 2009. Vol. 25. P. 177–180.
31. Sandeep Raj, Kailash Chandra Ray. Sparse representation of ECG signals for automated recognition of cardiac arrhythmias. Expert Systems with Applications. Vol. 105. 2018. P. 49–64. URL: https://doi.org/ 10.1016/j.eswa.2018.03.038.
32. Schurmann J. Pattern Classification – A unified view of statistical and neural approaches. New York: Wiley. 1996.
33. Xunde Dong, Cong Wang, Wenjie Si. ECG beat classification via deterministic learning, Neurocomputing. Vol. 240. 2017. P. 1–12. URL: https://doi.org/10.1016/j.neucom.2017.02.056.
34. Lytvynenko I. V. The method of segmentation of stochastic cyclic signals for the problems of their processing and modeling. Journal of Hydrocarbon Power Engineering, Oil and Gas Measurement and Testing. 2017. Vol. 4. No. 2. Р. 93–103.
35. Lytvynenko I., Horkunenko A., Kuchvara O., Palaniza Y. Methods of processing cyclic signals in automated cardiodiagnostic complexes. Proceedings of the 1st International Workshop on Information-Communication Technologies & Embedded Systems. (ICT&ES-2019). Mykolaiv: 2019. P. 116–127.