Mathematical Biosciences and Engineering (MBE)

Heart rate variability as determinism with jump stochastic parameters
Pages: 1253 - 1264, Issue 4, August 2013

doi:10.3934/mbe.2013.10.1253      Abstract        References        Full text (833.5K)           Related Articles

Jiongxuan Zheng - 8 Clarkson AVE. P.O.5817, Potsdam, NY 13676, United States (email)
Joseph D. Skufca - 8 Clarkson AVE. P.O.5817, Potsdam, NY 13676, United States (email)
Erik M. Bollt - 8 Clarkson AVE. P.O.5817, Potsdam, NY 13676, United States (email)

1 Katrin Suder, Friedhelm R. Drepper, Michael Schiek and Hans-Henning Abel, One-dimensional, nonlinear determinism characterizes heart rate pattern during paced respiration, Am. J. Phiciol Heart Circ. Physiol, 275 (1998), 1092-1102.
2 N. B. Janson, A. G. Balanov, V. S. Anishchenko and P. V. E. McClintock, Modelling the dynamics of angles of human R-R intervals, Physiol. Meas., 22 (2001), 565-579.
3 Yuo-Hsien Shiau, Shu-Shya Hseu and Huey-Wen Yien, One-dimensional deterministic process extracted from noisy R-R intervals under spontaneous breathing conditions, Journal of Medical and Biological Engineering, 26 (2001), 121-124.
4 T. Schreiber, Extremely simple nonlinear noise-reduction method, Phys. Rev. E, 47 (1993), 2401-2404.
5 Claudia Lerma, Trine Krogh-Madsen, Micheal Guevara and Leon Glass, Stochastic aspects of cardiac arrhymias, Journal Statistical Physics, 128 (2007), 347-374.       
6 Tom Kuusela, Tony Shepherd and Jarmo Hietarinta, Stochastic model for heart-rate fluctuations, Phys. Rev. E, 67 (2003), 061904.
7 Task Force of the European Socirty of Cariology and the North American Scirty of Pacing and Electrophysiology, Heart rate variability: Standards of measurement, physiological interpretation and clinical use, European Heart Journal, 17 (1996), 354-381.
8 M. Pomeranz, R. J. B. Macaulay and M. A. Caudill, Assessment of autonomic function in humans by heart rate spectral analysis, Am. J. Physiol, 248 (1985), H151-3.
9 M. Pagani, F. Lombardi and S. Guzzetti, et al., Power spetral analysis of heart rate and arterial pressure variablities as a marker of sympatho-vagal interaction in man and conscious dog, Circ. Res., 59 (1986), 178-193.
10 C-K. Peng, J. E. Mietus, Y. Liu, G. Khalsa, P. S. Douglas, H. Benson and A. L. Goldberger, Exaggerated heart rate oscillations during two meditation techniques, International Journal of Cardiology, 70 (1999), 101-107.
11 Leon Glass, Cardiac arrhythmias and circles maps-A classical problem, Chaos: An Interdisciplinary Journal of Nonlinear Science, 1 (1991), 13-19.       
12 Edward Ott, "Chaos in Dynamical Systems," First ed., Cambridge University Press., 1993.       
13 Steven H. Strogatz, "Nonlinear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry and Engineering," First ed., Westview Press., 1995.
14 Otakar Fojt and Jiri Holcik, Applying nonlinear dynamics to ECG signal processing, IEEE Engineering in Medicine and Biology., (1998).
15 Joseph D. Skufca and Erik M. Bollt, A concept of homeomorphic defect for defining mostly conjugate dynamical systems, Chaos., 18 (2008), 013008.       
16 T. Schreiber and A. Schmitz, Improved surrogate data for nonlinearity tests, Phys. Rev. Lett., 77 (1996), 635-638.
17 Holger Kantz and Thomas Schreiber, "Nonlinear Time Series Analysis," Second ed., Cambridge Press., 2004.       

Go to top