Physiological time-series analysis using approximate entropy and sample entropy

• Published in: American journal of physiology. Heart and circulatory physiology 2000-06, Vol.278 (6), p.H2039-H2049
• Main Authors: Richman, Joshua S, Moorman, J. Randall
• Format: Article
• Language: English
• Subjects: Entropy; Humans; Models, Biological; Nonlinear Dynamics; Physiology - methods; Time Factors
• ISSN: 0363-6135; 1522-1539
• DOI: 10.1152/ajpheart.2000.278.6.h2039

1  Cardiovascular Division, Department of Internal Medicine, and Department of Molecular Physiology and Biological Physics, and Cardiovascular Research Center, University of Virginia Health Sciences Center, Charlottesville, Virginia 22908; and 2  Medical Automation Systems, Charlottesville, Virginia 22903 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. probability; nonlinear dynamics