Abstract
We describe a method for analyzing the stochasticity in non-stationary data for the beat-to-beat fluctuations in the heart rates of healthy subjects, as well as those with congestive heart failure. The method analyzes the return time series of the data as a Markov process, and computes the Markov time scale, i.e., the time scale over which the data are a Markov process. We also construct an effective stochastic continuum equation for the return series. We show that the drift and diffusion coefficients, as well as the amplitude of the return time series for healthy subjects are distinct from those with CHF. Thus, the method may potentially provide a diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, as it can distinguish small differences between the data for the two classes of subjects in terms of well-defined and physically-motivated quantities.
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Peng, C.-K., Mietus, J., Hausdorff, J.M., Havlin, S., Stanley, H.E., and Goldberger, A.L.: Phys. Rev. Lett. 70 (1993), 1343.
Bunde, A., Havlin, S., Kantelhardt, J.W., Penzel, T., Peter, J.-H., and Voigt, K.: Phys. Rev. Lett. 85 (2000), 3736.
Bernaola-Galvan, P., Ivanov, P. Ch., Amaral, L.N., and Stanley, H.E.: Phys. Rev. Lett. 87 (2001), 168105.
Schulte-Frohlinde, V., Ashkenanzy, Y., Ivanov, P. Ch., Glass, L., Goldberger, A.L., and Stanley, H.E.: Phys. Rev. Lett. 87 (2001), 068104.
Ashkenazy, Y., Ivanov, P. Ch., Havlin, S., Peng, C-K., Goldberger, A.L., and Stanley, H.E.: Phys. Rev. Lett. 86, (2001) 1900.
Kuusela, T.: Phys. Rev. E 69 (2004), 031916.
Torquato, S., Random Heterogeneous Materials, Microstructure and Macroscopic Properties (Springer, New York, 2002); C.L.Y. Yeong and S. Torquato: Phys. Rev. E 57, 495 (1998); ibid. 58, 224, (1998).
Sahimi, M.: Heterogeneous Materials, Volume II (Springer, New York, 2003).
Jafari, G.R., Fazlei, S.M., Ghasemi, F., Vaez Allaei, S.M., Reza Rahimi Tabar, M., Iraji Zad, A., and Kavei, G.: Phys. Rev. Lett. 91 (2003), 226101.
Reza Rahimi Tabar, M., Ghasemi, F., Peinke, J., Friedrich, R., Kaviani, K., Taghavi, F., Sadeghi, S., Bijani, G., and Sahimi, M.: Computing In Science and Engeering 86 (2006).
Ghasemi, F., Peinke, J., Sahimi, M., and Rahimi Tabar, M.R.: Europhys. J.B 47(29) (2005), 411415.
Ghasemi, F., Peinke, J., Reza Rahimi Tabar M., and Sahimi, M., to be published in Intl J. Modern Physics C, (2005).
Friedrich, R., and Peinke, J.: Phys. Rev. Lett. 78 (1997), 863.
Davoudi, J., and Reza Rahimi Tabar, M.: Phys. Rev. Lett. 82 (1999), 1680.
Friedrich, R., Peinke, J., and Renner, C.: Phys. Rev. Lett. 84 (2000), 5224.
Friedrich, R., Galla, Th., Naert, A., Peinke J., and Schimmel, Th., In: Parisi, J., Muller, S.C., and Zimmerman, W. (eds.), A Perspective Look at Nonlinear Media, Lecture Notes in Physics, 503 (Springer, Berlin, 1997), p. 313; R. Friedrich, S. Siegert, J. Peinke, et al.: Phys. Lett. A 271 (2000), 217.
Siefert, M., Kittel, A., Friedrich, R., and Peinke, J.: Europhys. Lett. 61, (2003) 466; S. Kriso, et al., Phys. Lett. A 299, (2002) 287; S. Siegert, R. Friedrich, and J. Peinke, Phys. Lett. A 243 (1998), 275.
Risken, H.: The Fokker-Planck Equation (Springer, Berlin, 1984).
Wolf, M.M., Varigos, G.A., Hunt, D., and Sloman, J.G.: Med. J. Aust. 2 (1978), 52.
Ivanov, P. Ch., Bunde, A., Amaral, L.A.N., Havlin, S., Fritsch-Yelle, J., Baevsky, R.M., Stanley, H.E., and Goldberger, A.L.: Europhys. Lett. 48 (1999), 594.
Ivanov, P. Ch., Amaral, L.A.N., Goldberger, A.L., Havlin, S., Rosenblum, M.G., Struzik, Z., and Stanley, H.E.: Nature (London) 399 (1999), 461.
Peng, C.-K., Havlin, S., Stanley, H.E., and Goldberger, A.L.: Chaos 5 (1995), 82.
Peng, C.-K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., and Goldberger, A.L.: Phys. Rev. E 49 (1994), 1685.
Ivanov, P. Ch., Amaral, L.A.N., Goldberger, A.L., and Stanley, H.E.: Europhys. Lett. 43 (1998), 363.
Turcott, R.G., and Teich, M.C.: Fractal Character of the Electrocardiogram: Distinguishing Heart-failure and Normal Patients Ann. Biomed. Eng. 24 (1996), 269.
Lipsitz, L.A., Mietus, J., Moody, G.B., and Goldberger, A.L.: Circulation 81 (1990), 1803.
Kaplan, D.T., et al.: Biophys. J. 59 (1991), 945.
Iyengar, N., et al.: Am. J. Physiol. 271 (1996), R1078.
Peng, C.-K., Hausdorff, J.M., and Goldberger, A.L.: In: Walleczek, J. (ed.) Nonlinear Dynamics, Self-Organization, and Biomedicine, Cambridge University Press, Cambridge (1999).
Lin, D.C.: Discrete Scale Invariance in the Cascade Heart Rate Variability of Healthy Humans, Int. J. Mod. Phys. C 16 (2005), 465.
Novikov, E.A.: Dokl. Akad. Nauk USSR 168 (1966), 1279.
Sornette, D.: Phys. Rep. 297 (1998), 239.
Johansen, A., Sornette, D., and Ledoit, O.: J. Risk 1, (1999), 5.
Zhou, W.-X., and Sornette, D.: Physica D 165 (2002), 94.
Sornette D., and Sammis, C.G.: J. Phys. I France 5 (1995), 607.
Stauffer D., and Sornette, D.: Physica A 252 (1998), 21.
Saadatfar M., and Sahimi, M.: Phys. Rev. E. 65 (2002), 036116.
Sahimi M., and Arbabi, S.: Phys. Rev. Lett. 77 (1996), 3689.
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PACS: 05.10.Gg 05.40.-a, 05.45.Tp, 87.19.Hh
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Ghasemi, F., Sahimi, M., Peinke, J. et al. Analysis of Non-stationary Data for Heart-rate Fluctuations in Terms of Drift and Diffusion Coefficients. J Biol Phys 32, 117–128 (2006). https://doi.org/10.1007/s10867-006-9006-z
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DOI: https://doi.org/10.1007/s10867-006-9006-z