Errors in the Estimation of Approximate Entropy and Other Recurrence-Plot-Derived Indices Due to the Finite Resolution of RR Time Series

An analysis of the errors due to the finite resolution of RR time series in the estimation of the approximate entropy (ApEn) is described. The quantification errors in the discrete RR time series produce considerable errors in the ApEn estimation (bias and variance) when the signal variability or the sampling frequency is low. Similar errors can be found in indices related to the quantification of recurrence plots. An easy way to calculate a figure of merit [the signal to resolution of the neighborhood ratio (SRN)] is proposed in order to predict when the bias in the indices could be high. When SRN is close to an integer value n, the bias is higher than when near n-1/2 or n+1/2. Moreover, if SRN is close to an integer value, the lower this value, the greater the bias is.

[1]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[2]  J. Zbilut,et al.  Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals. , 2002, Medical engineering & physics.

[3]  Frank Beckers,et al.  Aging and nonlinear heart rate control in a healthy population. , 2006, American journal of physiology. Heart and circulatory physiology.

[4]  Wuon-Shik Kim,et al.  Nonlinear characteristics of heart rate time series: influence of three recumbent positions in patients with mild or severe coronary artery disease , 2005, Physiological measurement.

[5]  J. Kurths,et al.  Estimation of dynamical invariants without embedding by recurrence plots. , 2004, Chaos.

[6]  F. Estafanous,et al.  Entropy measures of heart rate variation in conscious dogs. , 1998, American journal of physiology. Heart and circulatory physiology.

[7]  Hsiao-Lung Chan,et al.  Nonlinear characteristics of heart rate variability during unsupervised and steady physical activities. , 2007, Physiological measurement.

[8]  M. Merri,et al.  Sampling frequency of the electrocardiogram for spectral analysis of the heart rate variability , 1988, Proceedings. Computers in Cardiology 1988.

[9]  Wojciech Zareba,et al.  Heart Rate Variability in Patients with Congenital Long QT Syndrome , 2001, Annals of noninvasive electrocardiology : the official journal of the International Society for Holter and Noninvasive Electrocardiology, Inc.

[10]  Philippe Faure,et al.  A new method to estimate the Kolmogorov entropy from recurrence plots: its application to neuronal signals , 1998 .

[11]  Junichiro Hayano,et al.  Prognostic value of nonlinear heart rate dynamics in hemodialysis patients with coronary artery disease. , 2003, Kidney international.

[12]  G. Breithardt,et al.  Heart rate variability: standards of measurement, physiological interpretation and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. , 1996 .

[13]  A. Giuliani,et al.  Recurrence quantification analysis of the logistic equation with transients , 1996 .

[14]  Jeffrey M. Hausdorff,et al.  Physionet: Components of a New Research Resource for Complex Physiologic Signals". Circu-lation Vol , 2000 .

[15]  A. Malliani,et al.  Heart rate variability. Standards of measurement, physiological interpretation, and clinical use , 1996 .

[16]  Willis J. Tompkins,et al.  Quantitative Investigation of QRS Detection Rules Using the MIT/BIH Arrhythmia Database , 1986, IEEE Transactions on Biomedical Engineering.

[17]  Vern Paxson,et al.  Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traffic , 1997, CCRV.

[18]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[19]  J. Kurths,et al.  Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Davor Milicic,et al.  The 〈〈Chaos Theory〉〉 and Nonlinear Dynamics in Heart Rate Variability Analysis: Does it Work in Short‐Time Series in Patients with Coronary Heart Disease? , 2007, Annals of noninvasive electrocardiology : the official journal of the International Society for Holter and Noninvasive Electrocardiology, Inc.

[21]  T. Seppänen,et al.  Quantitative beat-to-beat analysis of heart rate dynamics during exercise. , 1996, The American journal of physiology.

[22]  Yutaka Kubo,et al.  Toward chronocardiologic and chronomic insights: dynamics of heart rate associated with head-up tilting. , 2003, Biomedicine & pharmacotherapy = Biomedecine & pharmacotherapie.

[23]  Dirk Ramaekers,et al.  Approximate Entropy of Heart Rate Variability: Validation of Methods and Application in Heart Failure , 2001 .

[24]  C. Peng,et al.  Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory. , 1999, Circulation.

[25]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[26]  Jürgen Kurths,et al.  Influence of observational noise on the recurrence quantification analysis , 2002 .