Physiological time-series analysis using approximate entropy and sample entropy
01 Jun 2000-American Journal of Physiology-heart and Circulatory Physiology (American Physiological SocietyBethesda, MD)-Vol. 278, Iss: 6
TL;DR: A new and related complexity measure is developed, sample entropy (SampEn), and a comparison of ApEn and SampEn is compared by using them to analyze sets of random numbers with known probabilistic character, finding SampEn agreed with theory much more closely than ApEn over a broad range of conditions.
Abstract: Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.
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TL;DR: The various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV are discussed.
Abstract: Heart rate variability (HRV) is a reliable reflection of the many physiological factors modulating the normal rhythm of the heart. In fact, they provide a powerful means of observing the interplay between the sympathetic and parasympathetic nervous systems. It shows that the structure generating the signal is not only simply linear, but also involves nonlinear contributions. Heart rate (HR) is a nonstationary signal; its variation may contain indicators of current disease, or warnings about impending cardiac diseases. The indicators may be present at all times or may occur at random-during certain intervals of the day. It is strenuous and time consuming to study and pinpoint abnormalities in voluminous data collected over several hours. Hence, HR variation analysis (instantaneous HR against time axis) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system. Computer based analytical tools for in-depth study of data over daylong intervals can be very useful in diagnostics. Therefore, the HRV signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. In this paper, we have discussed the various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV.
2,344 citations
Additional excerpts
...Richman and Randall [103] have developed and...
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...Richman and Randall [103] have developed and characterized SampEn, a new family of statistics measuring complexity and regularity of clinical and experimental time-series data and compared it with ApEn, a similar family....
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TL;DR: Kubios HRV is an advanced and easy to use software for heart rate variability (HRV) analysis that includes an adaptive QRS detection algorithm and tools for artifact correction, trend removal and analysis sample selection.
1,841 citations
TL;DR: Results show that entropy falls before clinical signs of neonatal sepsis and that missing points are well tolerated, and proposes more informed selection of parameters and reexamination of studies where approximate entropy was interpreted solely as a regularity measure.
Abstract: Abnormal heart rate characteristics of reduced variability and transient decelerations are present early in the course of neonatal sepsis. To investigate the dynamics, we calculated sample entropy, a similar but less biased measure than the popular approximate entropy. Both calculate the probability that epochs of window length m that are similar within a tolerance r remain similar at the next point. We studied 89 consecutive admissions to a tertiary care neonatal intensive care unit, among whom there were 21 episodes of sepsis, and we performed numerical simulations. We addressed the fundamental issues of optimal selection of m and r and the impact of missing data. The major findings are that entropy falls before clinical signs of neonatal sepsis and that missing points are well tolerated. The major mechanism, surprisingly, is unrelated to the regularity of the data: entropy estimates inevitably fall in any record with spikes. We propose more informed selection of parameters and reexamination of studies where approximate entropy was interpreted solely as a regularity measure.
1,151 citations
Cites background from "Physiological time-series analysis ..."
...We developed a new related measure of time series regularity that we have called sample entropy (SampEn) (22)....
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...This is obviously inconsistent with the idea of new information, however, and is a strong source of bias toward CP 1 and ApEn 0 when there are few matches and A and B are small (16, 18, 20, 22)....
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TL;DR: A novel scheme of emotion-specific multilevel dichotomous classification (EMDC) is developed and compared with direct multiclass classification using the pLDA, with improved recognition accuracy of 95 percent and 70 percent for subject-dependent and subject-independent classification, respectively.
Abstract: Little attention has been paid so far to physiological signals for emotion recognition compared to audiovisual emotion channels such as facial expression or speech. This paper investigates the potential of physiological signals as reliable channels for emotion recognition. All essential stages of an automatic recognition system are discussed, from the recording of a physiological data set to a feature-based multiclass classification. In order to collect a physiological data set from multiple subjects over many weeks, we used a musical induction method that spontaneously leads subjects to real emotional states, without any deliberate laboratory setting. Four-channel biosensors were used to measure electromyogram, electrocardiogram, skin conductivity, and respiration changes. A wide range of physiological features from various analysis domains, including time/frequency, entropy, geometric analysis, subband spectra, multiscale entropy, etc., is proposed in order to find the best emotion-relevant features and to correlate them with emotional states. The best features extracted are specified in detail and their effectiveness is proven by classification results. Classification of four musical emotions (positive/high arousal, negative/high arousal, negative/low arousal, and positive/low arousal) is performed by using an extended linear discriminant analysis (pLDA). Furthermore, by exploiting a dichotomic property of the 2D emotion model, we develop a novel scheme of emotion-specific multilevel dichotomous classification (EMDC) and compare its performance with direct multiclass classification using the pLDA. An improved recognition accuracy of 95 percent and 70 percent for subject-dependent and subject-independent classification, respectively, is achieved by using the EMDC scheme.
953 citations
Cites methods from "Physiological time-series analysis ..."
...Based on the so-called approximate entropy and sample entropy proposed in [ 38 ], an MSE was introduced [39] and successfully applied to physiological data, especially for the analysis of short and noisy biosignals [40]....
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TL;DR: Vaillancourt and Newell as mentioned in this paper used fractal analysis and non-linear dynamics to study the effects of aging and disease on the behavior of a living organism, and found that nonlinear coupling may lead to an extraordinary range of dynamics, including different classes of abrupt changes, (such as bifurcations), deterministic chaos, nonlinear phase transitions, pacemakerentrainment and resetting, stochastic resonance, wave phe-nomena (including spiral waves, solitons, and scroll waves), and certain types of fractal
755 citations
References
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Book•
26 Feb 1988
TL;DR: The Diskette v 2.04, 3.5'' (720k) for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.
Abstract: Note: Includes bibliographical references and index.- Diskette v 2.04, 3.5'' (720k) for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08
9,345 citations
Book•
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
6,693 citations
"Physiological time-series analysis ..." refers background or methods in this paper
...0, we found that cross-ApEn(1,1,250)(cv\hr) was defined for only 19 of the 32 cases, whereas cross-ApEn(1,1,250)(hr \cv) was defined for only 12 cases....
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...Sets of uniformly distributed random numbers were generated using a minimal standard number generator with added random shuffling (30), and all sets passed a runs test for random arrangement (1)....
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TL;DR: Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes.
Abstract: Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.
5,055 citations
"Physiological time-series analysis ..." refers background or methods or result in this paper
...We verified our calculation of ApEn statistics by comparing our results with published values for Henon and logistic map data (21)....
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...The family of MIX(P) stochastic processes (21) provided a testing ground for cross-ApEn....
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...We employ the terminology and notation of Grassberger and Procaccia (10), Eckmann and Ruelle (5), and Pincus (21) in describing techniques for estimating the Kolmogorov entropy of a process represented by a time series and the related statistics ApEn and SampEn....
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...Pincus (21) saw that the calculation of Fm(r) 2 Fm11(r) for fixed parameters m, r, and N had intrinsic interest as a measure of regularity and complexity....
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...There are several models, including sets of iid random numbers, for which the theoretical values of the parameters ApEn(m, r)(21) and SampEn(m, r) can be calculated....
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TL;DR: Bernard Rosner's FUNDAMENTALS of BIOSTATISTICS is a practical introduction to the methods, techniques, and computation of statistics with human subjects that prepares students for their future courses and careers.
Abstract: Bernard Rosner's FUNDAMENTALS OF BIOSTATISTICS is a practical introduction to the methods, techniques, and computation of statistics with human subjects. It prepares students for their future courses and careers by introducing the statistical methods most often used in medical literature. Rosner minimizes the amount of mathematical formulation (algebra-based) while still giving complete explanations of all the important concepts. As in previous editions, a major strength of this book is that every new concept is developed systematically through completely worked out examples from current medical research problems.
4,624 citations