Mathematical Biosciences and Engineering, 2013, 10(4): 1253-1264. doi: 10.3934/mbe.2013.10.1253.

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Heart rate variability as determinism with jump stochastic parameters

1. 8 Clarkson AVE. P.O.5817, Potsdam, NY 13676

We use measured heart rate information (RR intervals) to develop a one-dimensional nonlinear map that describes short term deterministic behavior in the data. Our study suggests that there is a stochastic parameter with persistence which causes the heart rate and rhythm system to wander about a bifurcation point. We propose a modified circle map with a jump process noise term as a model which can qualitatively capture such this behavior of low dimensional transient determinism with occasional (stochastically defined) jumps from one deterministic system to another within a one parameter family of deterministic systems.
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Keywords circle map; next angle map; electrocardiography; jump process.; Heart rate variability

Citation: Jiongxuan Zheng, Joseph D. Skufca, Erik M. Bollt. Heart rate variability as determinism with jump stochastic parameters. Mathematical Biosciences and Engineering, 2013, 10(4): 1253-1264. doi: 10.3934/mbe.2013.10.1253

References

  • 1. Am. J. Phiciol Heart Circ. Physiol, 275 (1998), 1092-1102.
  • 2. Physiol. Meas., 22 (2001), 565-579.
  • 3. Journal of Medical and Biological Engineering, 26 (2001), 121-124.
  • 4. Phys. Rev. E, 47 (1993), 2401-2404.
  • 5. Journal Statistical Physics, 128 (2007), 347-374.
  • 6. Phys. Rev. E, 67 (2003), 061904.
  • 7. European Heart Journal, 17 (1996), 354-381.
  • 8. Am. J. Physiol, 248 (1985), H151-3.
  • 9. Circ. Res., 59 (1986), 178-193.
  • 10. International Journal of Cardiology, 70 (1999), 101-107.
  • 11. Chaos: An Interdisciplinary Journal of Nonlinear Science, 1 (1991), 13-19.
  • 12. First ed., Cambridge University Press., 1993.
  • 13. First ed., Westview Press., 1995.
  • 14. IEEE Engineering in Medicine and Biology., (1998).
  • 15. Chaos., 18 (2008), 013008.
  • 16. Phys. Rev. Lett., 77 (1996), 635-638.
  • 17. Second ed., Cambridge Press., 2004.

 

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