Abstract
The paper mainly introduces a method combining detrended fluctuation analysis (DFA) with moving fitting window to analyze the heartbeat time series in different pathologic states. Compared to traditional approaches, the estimation of the local scale exponent method shows more details of scale properties and provides a reliable analysis. We also quantify the effects of outliers, subseries length and gender on scale spectrum α(s). Comparing the results of the healthy subjects, patients with congestive heart failure (CHF), and patients with atrial fibrillation (AF) indicate clearly that at small scales, the exponents show great volatility and they all have their own scale pattern. In addition, the length of the series should be relatively longer to avoid properties losing. For the effect of gender, contrary to healthy results, the scale exponents of CHF male subjects are continuously greater than female. The spectrum of DFA scale exponents provides a new way to measure the heartbeat series and distinguishes healthy and pathologic groups.
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Ho, K.K.L., Moody, G.B., Peng, C.K., Mietus, J.E., Larson, M.G., Levy, D., Goldberger, A.L.: Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics. Circulation 96, 842–848 (1997)
Ivanov, P.C., Amaral, L.A.N., Goldberger, A.L., Havlin, S., Rosenblum, M.G., Struzik, Z.R., Stanley, H.E.: Multifractality in human heartbeat dynamics. Nature 399, 461–465 (1999)
Amaral, L.A.N., Ivanov, P.C., Aoyagi, N., Hidaka, I., Tomono, S., Goldberger, A.L., Stanley, H.E., Yamamoto, Y.: Behavioral-independent features of complex heartbeat dynamics. Phys. Rev. Lett. 86, 6026–6029 (2001)
Rajendra, A.U., Paul, J.K., Kannathal, N., Lim, C.M., Suri, J.S.: Heart rate variability: a review. Med. Biol. Eng. Comput. 44, 1031–1051 (2006)
Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.K., Stanley, H.E.: Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals. Circulation 101, E215–E220 (2000)
Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Goldberger, A.L.: Mosaic organization of DNA sequences. Phys. Rev. E 49, 1685–1689 (1994)
Peng, C.K., Mietus, J.E., Hausdorff, J.M., Havlin, S., Stanley, H.E., Goldberger, A.L.: Long-range anti-correlations and non-Gaussian behavior of the heartbeat. Phys. Rev. Lett. 70, 1343–1346 (1993)
Hu, K., Ivanov, P.C., Zhi, C., Carpena, P., Stanley, H.E.: Effects of trends on detrended fluctuation analysis. Phys. Rev. E 64, 011114 (2001)
Wang, J., Shang, P.J., Ge, W.J.: Multifractal cross-correlation analysis based on statistical moments. Fractals 20, 271–279 (2012)
Lin, A.J., Shang, P.J., Zhao, X.J.: The cross-correlations of stock markets based on DCCA and time-delay DCCA. Nonlinear Dyn. 67, 425–435 (2012)
Zhao, X.J., Shang, P.J., Lin, A.J., Chen, G.: Multifractal Fourier detrended cross-correlation analysis of traffic signals. Physica A 390, 3670–3678 (2011)
Xu, N., Shang, P.J., Kamae, S.: Modeling traffic flow correlation using DFA and DCCA. Nonlinear Dyn. 61, 207–216 (2010)
Peng, C.K., Havlin, S., Stanley, H.E., Goldberger, A.L.: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5, 82–87 (1995)
Viswanathan, G.M., Peng, C.K., Stanley, H.E., Goldberger, A.L.: Deviations from uniform power law scaling in nonstationary time series. Phys. Rev. E 55, 845–849 (1997)
Echeverria, J.C., Woolfson, M.S., Crowe, J.A., Hayes-Gill, B.R., Croaker, G.D., Vyas, H.: Interpretation of heart rate variability via detrended fluctuation analysis and alphabeta filter. Chaos 13, 467–475 (2003)
Castiglioni, P., Parati, G., Civijian, A., Quintin, L., Rienzo, M.D.: Local scale exponents of blood pressure and heart rate variability by detrended fluctuation analysis: effects of posture, exercise, and aging. IEEE Trans. Biomed. Eng. 56, 675–684 (2009)
Castiglioni, P., Parati, G., Lombardi, C., Quintin, L., Rienzo, M.D.: Assessing the fractal structure of heart rate by the temporal spectrum of scale exponents: a new approach for detrended fluctuation analysis of heart rate variability. Biomed. Tech. 56, 175–183 (2011)
Castiglioni, P., Parati, G., Rienzo, M.D., Carabalona, R., Cividjian, A., Quintin, L.: Scale exponents of blood pressure and heart rate during autonomic blockade as assessed by detrended fluctuation analysis. J. Physiol. 589, 355–369 (2011)
Gieraltowski, J., Zebrowski, J.J., Baranowski, R.: Multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia. Phys. Rev. E 85, 021915 (2012)
MIT-BIH Normal Sinus Rhythm Database, BIDMC Congestive Heart Failure Database and Long-Term Atrial Fibrillation Database. Available at http://physionet.org/physiobank/database
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The financial supports from the funds of the China National Science (61071142, 61371130), the Beijing National Science (4122059), and the National High Technology Research Development Program of China (863 Program) (2011AA110306) are gratefully acknowledged.
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Xia, J., Shang, P. & Wang, J. Estimation of local scale exponents for heartbeat time series based on DFA. Nonlinear Dyn 74, 1183–1190 (2013). https://doi.org/10.1007/s11071-013-1033-2
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DOI: https://doi.org/10.1007/s11071-013-1033-2