Last update:
07-Jul-2004

Approximate entropy (ApEn) is a real positive number which compares the regularity of different time-series of numbers under specific circumstances. Such time-series can be, for example, the beats of an electrocardiogram (ECG) or the daily secretion of hormones. Τhe algorithm of ApEn was invented in 1991 by the American Steve Pincus and has been used for the comparison between physiological and non-physiological conditions. This article presents concisely the most important applications of ApEn according to the international bibliography along with two relevant studies from our laboratory. The applications concern the evaluation of “suspicious” electroencephalogram and ECG recordings, the study of pulsatile hormone secretion and other scientific fields such as the movements of the muscles of respiration. From the mathematical point of view, ApEn states the possibility that the values of time-series are, and stay within, certain limits. These limits are the so-called filter of the algorithm (r). In practice the algorithm checks the differences between the values, not the values themselves, because the target of ApEn is the check of regularity (complexity) of a system. The number of differences in each value which will be compared with the filter of the algorithm comprises the so-called “window” of the method (m). The appropriate computerization of ApEn demands at least 60 values (N). Higher ApEn means wide disorder, in which case the values of time-series differ greatly between each other. Conversely, lower ApEn means regularity. Whenever we want to compare two or more values of ApEn, all ApEn calculations must use the same r, m and N, N being the total number of values of the time-series. For this reason the ApEn values are symbolized as ApEn (m, r, N). The sensitivity of the ApEn algorithm is specified by the researcher by choosing the parameters N, m and r. For N <500 (the most usual in medical papers) the “window” m=1 is used. The filter r is always equal to 0.2*SD, where SD is the standard deviation of the time-series.

Key words: ApEn, Approximate entropy, Complexity, Regularity, Time-series.