Normal heartbeat series are nonchaotic, nonlinear, and multifractal: New evidence from semiparametric and parametric tests

Abstract

We present new evidence that normal heartbeat series are nonchaotic, nonlinear, and multifractal. In addition to considering the largest Lyapunov exponent and the correlation dimension, the results of the parametric and semiparametric estimation of the long memory parameter (long-range dependence) unambiguously reveal that the underlying process is nonstationary, multifractal, and has strong nonlinearity.

Beyond long memory in heart rate variability: An approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

“…Similar numbers are observed for the congestive heart failure patients: 95.9% and 85.8%, respectively, see Table III. These results are in concordance with Baillie et al 16 and Leite et al 14,37,38 Moreover, patients suffering from congestive heart failure present increased values ford; during night and day periods, while patients undergoing atrial fibrillation present lower values ford; compared with normal subjects. In fact, only 54.2% of the segments in atrial fibrillation patients present statistically significance values for d as tested with surrogate data, Table III.…”

“…The authors Leite et al 14 use segmentation of 24-h recordings of HRV to find that the long memory parameter (or scaling exponent) changes with time. These findings were corroborated later by Baillie et al 16 In this work, this characteristic is designated by time-varying fractal in the sense that the memory parameter changes over time and between regimes (day and night).…”

“…(1) is covariance stationary but the autocorrelation decays at a slow hyperbolic rate compared with exponential rate of decay of the stationary and invertible ARMA process. In the range À0:5 < d < 0:5, the long memory parameter is related to the Hurst coefficient, 16 H, to the fractal dimension, 13 D, and to the slope of the (generalized) spectral density in the low frequency range, 15 a, by d ¼ H À 0.5, H ¼ 2 À D and a ¼ 2d, respectively. Moreover, for 0:5 d < 1, the process is non-stationary and mean reverting.…”

Characterizing Nonlinear Heartbeat Dynamics Within a Point Process Framework

“…Our test result confirms that the heartbeat dynamics from healthy subjects are more nonlinear to some degree. The fact that a lower degree of nonlinearity was found in the CHF patients suggests that pathological conditions might reduce the nonlinearity in the heartbeat interval series, which is also consistent with previous finding that a healthy heartbeat presents more pronounced nonlinear dynamics [5], [26], [27], [46], [62]. …”

“…The nonlinearity test provides a quantitative measure of the regularity of a tested time series [5], [9], [56]. In the study of the autonomic blockade protocol, it was found that the level of nonlinearity varies from different postures and pharmacological conditions, which essentially influence the sympathetic/parasympathetic balance in the autonomic nervous system.…”