Devising a new filtration method and proof of self-similarity of electromyograms

Authors

DOI:

https://doi.org/10.15587/1729-4061.2021.239165

Keywords:

electromyograms, Poincaré plot, scaling law, fractal dimensionality, variability, Haar wavelets

Abstract

The main attention is paid to the analysis of electromyogram (EMG) signals using Poincaré plots (PP). It was established that the shapes of the plots are related to the diagnoses of patients. To study the fractal dimensionality of the PP, the method of counting the coverage figures was used. The PP filtration was carried out with the help of Haar wavelets. The self-similarity of Poincaré plots for the studied electromyograms was established, and the law of scaling was used in a fairly wide range of coverage figures. Thus, the entire Poincaré plot is statistically similar to its own parts. The fractal dimensionalities of the PP of the studied electromyograms belong to the range from 1.36 to 1.48. This, as well as the values of indicators of Hurst exponent of Poincaré plots for electromyograms that exceed the critical value of 0.5, indicate the relative stability of sequences.

The algorithm of the filtration method proposed in this research involves only two simple stages:

  1. Conversion of the input data matrix for the PP using the Jacobi rotation.
  2. Decimation of both columns of the resulting matrix (the so-called "lazy wavelet-transformation", or double downsampling).

The algorithm is simple to program and requires less machine time than existing filters for the PP.

Filtered Poincaré plots have several advantages over unfiltered ones. They do not contain extra points, allow direct visualization of short-term and long-term variability of a signal. In addition, filtered PPs retain both the shape of their prototypes and their fractal dimensionality and variability descriptors. The detected features of electromyograms of healthy patients with characteristic low-frequency signal fluctuations can be used to make clinical decisions.

Author Biographies

Gennady Chuiko, Petro Mohyla Black Sea National University

Doctor of Physical and Mathematical Sciences, Professor

Department of Computer Engineering

Olga Dvornik, Petro Mohyla Black Sea National University

PhD, Associated Professor

Department of Computer Engineering

Yevhen Darnapuk, Petro Mohyla Black Sea National University

Postgraduate Student

Department of Computer Engineering

Yevgen Baganov, Kherson National Technical University

PhD, Associated Professor

Department of Energy, Electrical Engineering and Physics

References

  1. Goldberger, A. L., Amaral, L. A. N., Glass, L., Hausdorff, J. M., Ivanov, P. C., Mark, R. G. et. al. (2000). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation, 101 (23), e215–e220. doi: http://doi.org/10.1161/01.cir.101.23.e215
  2. Reaz, M. B. I., Hussain, M. S., Mohd-Yasin, F. (2006). Techniques of EMG signal analysis: detection, processing, classification and applications. Biological Procedures Online, 8 (1), 11–35. doi: http://doi.org/10.1251/bpo115
  3. Chuiko, G. P., Shyian, I. A. (2015). Processing and analysis of electroneuromyograms with Maple tools. Biomedical Engineering and Electronics, 10. Available at: http://biofbe.esrae.ru/pdf/2015/3/1006.pdf Last accessed: 06.02.2020
  4. Kantz, H., Schreiber, T. (2010). Nonlinear Time Series Analysis. Cambridge: Cambridge University Press. doi: http://doi.org/10.1017/cbo9780511755798
  5. Burykin, A., Costa, M. D., Citi, L., Goldberger, A. L. (2014). Dynamical density delay maps: simple, new method for visualising the behaviour of complex systems. BMC Medical Informatics and Decision Making, 14 (1). doi: http://doi.org/10.1186/1472-6947-14-6
  6. Karmakar, C. K., Khandoker, A. H., Gubbi, J., Palaniswami, M. (2009). Complex Correlation Measure: a novel descriptor for Poincaré plot. BioMedical Engineering OnLine, 8 (1). doi: http://doi.org/10.1186/1475-925x-8-17
  7. Golińska, A. K. (2013). Poincaré Plots in Analysis of Selected Biomedical Signals. Studies in Logic, Grammar and Rhetoric, 35 (1), 117–127. doi: http://doi.org/10.2478/slgr-2013-0031
  8. Tulppo, M. P., Makikallio, T. H., Takala, T. E., Seppanen, T., Huikuri, H. V. (1996). Quantitative beat-to-beat analysis of heart rate dynamics during exercise. American Journal of Physiology-Heart and Circulatory Physiology, 271 (1), H244–H252. doi: http://doi.org/10.1152/ajpheart.1996.271.1.h244
  9. Piskorski, J., Guzik, P. (2005). Filtering Poincaré plots. Computational Methods in Science and Technology, 11 (1), 39–48. doi: http://doi.org/10.12921/cmst.2005.11.01.39-48
  10. Hansen, P. C., Jensen, S. H. (1998). FIR filter representations of reduced-rank noise reduction. IEEE Transactions on Signal Processing, 46 (6), 1737–1741. doi: http://doi.org/10.1109/78.678511
  11. Figueiredo, N., Georgieva, P., Lang, E. W., Santos, I. M., Teixeira, A. R., Tomé, A. M. (2010). SSA of biomedical signals: A linear invariant systems approach. Statistics and Its Interface, 3 (3), 345–355. doi: http://doi.org/10.4310/sii.2010.v3.n3.a8
  12. Harris, T. J., Yuan, H. (2010). Filtering and frequency interpretations of Singular Spectrum Analysis. Physica D: Nonlinear Phenomena, 239 (20-22), 1958–1967. doi: http://doi.org/10.1016/j.physd.2010.07.005
  13. Review of New Features in Maple 18. Available at: https://www.wolfram.com/mathematica/compare-mathematica/files/ReviewOfMaple18.pdf Last accessed: 06.02.2020
  14. Chuiko, G. P., Shyian, I. O., Galyak, D. A. (2015). Interface elements of scientific web-resource physionet and import data to computer mathematics system Maple 17. Medical Informatics and Engineering, (3), 84–88. doi: http://doi.org/10.11603/mie.1996-1960.2015.3.5008
  15. Gorban, A. N., Zinovyev, A. Y. (2008). Principal Graphs and Manifolds. Handbook of Research on Machine Learning Applications and Trends, 28–59. doi: http://doi.org/10.4018/978-1-60566-766-9.ch002
  16. Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, 1256.
  17. Haar, A. (1910). Zur Theorie der orthogonalen Funktionensysteme. Mathematische Annalen, 69 (3), 331–371. doi: http://doi.org/10.1007/bf01456326
  18. Dastourian, B., Dastourian, E., Dastourian, S., Mahnaie, O. (2014). Discrete Wavelet Transforms Of Haar’s Wavelet. International Journal of Scientific & Technology Research, 3 (9), 247–251. Available at: http://www.ijstr.org/final-print/sep2014/Discrete-Wavelet-Transforms-Of-Haars-Wavelet-.pdf Last accessed: 06.02.2020
  19. Mandelbrot, B. (1967). How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, 156 (3775), 636–638. doi: http://doi.org/10.1126/science.156.3775.636
  20. Bourke, P. (2014). Box counting fractal dimension of volumetric data. Available at: http://paulbourke.net/fractals/cubecount/ Last accessed: 06.02.2020
  21. Gneiting, T., Schlather, M. (2004). Stochastic Models That Separate Fractal Dimension and the Hurst Effect. SIAM Review, 46 (2), 269–282. doi: http://doi.org/10.1137/s0036144501394387
  22. Mäkikallio, T. (1998). Analysis of heart rate dynamics by methods derived from nonlinear mathematics. Clinical applicability and prognostic significance. Oulu: University of Oulu. Available at: http://jultika.oulu.fi/files/isbn9514250133.pdf Last accessed: 06.02.2020
  23. Huikuri, H. V., Mäkikallio, T. H., Peng, C.-K., Goldberger, A. L., Hintze, U., Møller, M. (2000). Fractal Correlation Properties of R-R Interval Dynamics and Mortality in Patients With Depressed Left Ventricular Function After an Acute Myocardial Infarction. Circulation, 101 (1), 47–53. doi: http://doi.org/10.1161/01.cir.101.1.47
  24. Voss, A., Schulz, S., Schroeder, R., Baumert, M., Caminal, P. (2008). Methods derived from nonlinear dynamics for analysing heart rate variability. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 367 (1887), 277–296. doi: http://doi.org/10.1098/rsta.2008.0232
  25. Carvalho, T. D., Pastre, C. M., Moacir Fernandes de Godoy, Pitta, F. O., de Abreu, L. C., Ercy Mara Cipulo Ramos et. al. (2011). Fractal correlation property of heart rate variability in chronic obstructive pulmonary disease. International Journal of Chronic Obstructive Pulmonary Disease, 6, 23–28. doi: http://doi.org/10.2147/copd.s15099
  26. Gomes, R. L., Vanderlei, L. C. M., Garner, D. M., Vanderlei, F. M., Valenti, V. E. (2017). Higuchi Fractal Analysis of Heart Rate Variability is Sensitive during Recovery from Exercise in Physically Active Men. Medical Express, 4 (2). doi: http://doi.org/10.5935/medicalexpress.2017.02.03
  27. Antônio, A. M. S., Cardoso, M. A., Carlos de Abreu, L., Raimundo, R. D., Fontes, A. M. G. G., Garcia da Silva A. et. al. (2014). Fractal Dynamics of Heart Rate Variability: A Study in Healthy Subjects. Journal of Cardiovascular Development and Disease, 2 (3), 2330–460.
  28. Chuiko, G. P., Dvornik, O. V., Darnapuk, Y. S. (2018). Shape Evolutions of Poincaré Plots for Electromyograms in Data Acquisition Dynamics. 2018 IEEE Second International Conference on Data Stream Mining & Processing (DSMP), 119–122. doi: http://doi.org/10.1109/dsmp.2018.8478516

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Published

2021-08-31

How to Cite

Chuiko, G., Dvornik, O., Darnapuk, Y., & Baganov, Y. (2021). Devising a new filtration method and proof of self-similarity of electromyograms. Eastern-European Journal of Enterprise Technologies, 4(9(112), 15–22. https://doi.org/10.15587/1729-4061.2021.239165

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Section

Information and controlling system