Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series
by
Madalena D. Costa 1,* and Ary L. Goldberger 1,2
Madalena D. Costa 1,* and Ary L. Goldberger 1,2
1
Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA 02215, USA
2
Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA 02215, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Niels Wessel
Entropy 2015, 17(3), 1197-1203; https://doi.org/10.3390/e17031197
Received: 26 January 2015 / Revised: 5 March 2015 / Accepted: 6 March 2015 / Published: 12 March 2015
(This article belongs to the Special Issue Entropy and Cardiac Physics)
We introduce a generalization of multiscale entropy (MSE) analysis. The method is termed MSEn, where the subscript denotes the moment used to coarse-grain a time series. MSEμ, described previously, uses the mean value (first moment). Here, we focus on MSEσ2 , which uses the second moment, i.e., the variance. MSEσ2 quantifies the dynamics of the volatility (variance) of a signal over multiple time scales. We use the method to analyze the structure of heartbeat time series. We find that the dynamics of the volatility of heartbeat time series obtained from healthy young subjects is highly complex. Furthermore, we find that the multiscale complexity of the volatility, not only the multiscale complexity of the mean heart rate, degrades with aging and pathology. The “bursty” behavior of the dynamics may be related to intermittency in energy and information flows, as part of multiscale cycles of activation and recovery. Generalized MSE may also be useful in quantifying the dynamical properties of other physiologic and of non-physiologic time series.
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Keywords:
aging; complexity; entropy; fractal; heart rate; multiscale entropy; nonlinear dynamics
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MDPI and ACS Style
Costa, M.D.; Goldberger, A.L. Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series. Entropy 2015, 17, 1197-1203.
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