Document Type : Original Article
Authors
Physics Department, Persian Gulf University, Bushehr, Iran
Abstract
The Jump-Diffusion equation is a generalization of the Langevin equation; it has been usually applied to reconstruct discontinuous stochastic processes. In this article, by using this equation, we investigate the electrocardiogram of the electric activity of the heart beat, for three groups of subjects with normal, atrial fibrillation and ventricular arrhythmia. At first, we demonstrate that the time series of electrocardiogram is a discontinuous process that can be modeled by the jump-diffusion equation. Then, by calculating the Kramers-Moyal coefficients related to this equation, we show that there is a significant difference between the heart dynamics of the normal subjects and the ones with heart failure exists. Finally, we introduce a measure that may be used for the diagnosis of heart failures.
Keywords
- A Einstein, Ann. phys. 322 (1905) 549.
- P Langevin, C. R. Acad. Sci. Paris 146 (1908) 530.
- M Anvari, et al., Sci. Rep. 6 (2016) 35435.
- A Aliakbari, P Manshour, and M J Salehi, Chaos 27 (2017) 033116.
- P Manshour, et al., Sci. Rep. 6 (2016) 27452.
- W Coffey and Y P Kalmykov, “The Langevin equation: with applications to stochastic problems in physics, chemistry and electrical engineering”, World Scientific, Singapore (2012).
- H Risken, “The Fokker- Planck Equation”, Springer Series in Synergetics Springer, Berlin (1996).
- S Stenholm, “Foundations of Laser Spectroscopy”, Wiley, New York (1984).
- H Haken, “Laser Theory”, Springer, Berlin (1984).
10. K S Schmitz, “An Introduction to Dynamic Light Scattering by Macromolecules”, Academic Press, San Diego (1990).
11. O G Bakunin, Phys.- Uspekhi 46 (2003) 309.
12. P Brüesch, et al. Phys. Rev. B 15 (1977) 4631.
13. M Fujiwara, et al., Sci. Rep. 8 (2018) 14773.
14. W T Coffey, J. Phys. D 11 (1978) 1377.
15. M Perc, Eur. J. Phys. 26 (2005) 757.
16. J Wang, et al., Phys. Rev. E 71 (2005) 062902.
17. H Yang, S T Bukkapatnam, and R Komanduri, Phys. Rev. E 76 (2007) 026214.
18. A N Beni, B Mirza, F Shahbazi and A Kazempour, Iranian J. Phys. Res. 6 (2006) 137.
- ا ن بنی، ب میرزا، ف شهبازی و ع کاظمپور، مجله پژوهش فیزیک ایران 6، 2 (1385) ۱۴۴.
19. F Atiyabi, M Akbari Livari and K Kaviani, Iranian J. Phys. Res. 7 (2007) 53.
- ف اطیابی، م اکبری لیواری و ک کاویانی، مجله پژوهش فیزیک ایران 7، 1 (1386) ۵۹.
20. M Boorboor, F shahbazi and B Mirza, Iranian J. Phys. Res. 7 (2007) 113.
- م بوربور، ف شهبازی و ب میرزا، مجله پژوهش فیزیک ایران 7، 2 (1386) ۱۱۳.
21. R Friedrich, J Peinke, M Sahimi, and M R Rahimi Tabar, Phys. Rep. 506 (2011) 87.
22. K Lehnertz, L Zabawa, and M R Rahimi Tabar, New J. Phys. 20 (2018) 113043.
23. R F Pawula, Phys. Rev. 162 (1967) 186.
24. R J P Keijsers, O I Shklyarevskii, and H van Kempen, Phys. Rev. Lett. 77 (1996) 3411.
25. A L Efros and M Rosen, Phys. Rev. Lett. 78 (1997) 1110.
26. E Shung, et al., Phys. Rev. B 56 (1997) R11431.
27. L Gammaitoni, P Hänggi, P Jung and F Marchesoni, Rev. Mod. Phys. 70 (1998) 223.
28. M Anvari, et al., New J. Phys. 18 (2016) 063027.
29. S S Lee and P A Mykland, Rev. Financial Stud. 21 (2008) 2535.
30. B Goswami, et al., Nat. Commun. 9 (2018) 48.
31. S Martinez- Conde, S L Macknik, and D H Hubel, Nat. Rev. Neurosci. 5 (2004) 229.
32. H F Credidio, et al., Sci. Rep. 2 (2012) 920.
33. G B Moody and R G Mark, Comput. Cardiol. 10 (1983) 227.
34. G B Moody and R G Mark, IEEE Eng. in Med. and Biol. 20 (2001) 45.
35. A L Goldberger, et al., Circulation 101 (2000) e215.
36. H J Bierens, “The Nadaraya- Watson Kernel Regression Function Estimator”, In: Topics in Advanced Econometrics, Cambridge University Press, New York )1994).