On the Standardization of Approximate Entropy: Multidimensional Approximate Entropy Index Evaluated on Short‐Term HRV Time Series

Abstract

Background. Nonlinear heart rate variability (HRV) indices have extended the description of autonomic nervous system (ANS) regulation of the heart. One of those indices is approximate entropy, ApEn, which has become a commonly used measure of the irregularity of a time series. To calculate ApEn, a priori definition of parameters like the threshold on similarity and the embedding dimension is required, which has been shown to be critical for interpretation of the results. Thus, searching for a parameter-free ApEn-based index could be advantageous for standardizing the use and interpretation of this widely applied entropy measurement. Methods. A novel entropy index called multidimensional approximate entropy, MApEnmax, is proposed based on summing the contribution of maximum approximate entropies over a wide range of embedding dimensions while selecting the similarity threshold leading to maximum ApEn value in each dimension. Synthetic RR interval time series with varying levels of stochasticity, generated by both MIX(P) processes and white/pink noise, were used to validate the properties of the proposed index. Aging and congestive heart failure (CHF) were characterized from RR interval time series of available databases. Results. In synthetic time series, MApEnmax values were proportional to the level of randomness; i.e., MApEnmax increased for higher values of P in generated MIX(P) processes and was larger for white than for pink noise. This result was a consequence of all maximum approximate entropy values being increased for higher levels of randomness in all considered embedding dimensions. This is in contrast to the results obtained for approximate entropies computed with a fixed similarity threshold, which presented inconsistent results for different embedding dimensions. Evaluation of the proposed index on available databases revealed that aging was associated with a notable reduction in MApEnmax values. On the other hand, MApEnmax evaluated during the night period was considerably larger in CHF patients than in healthy subjects. Conclusion. A novel parameter-free multidimensional approximate entropy index, MApEnmax, is proposed and tested over synthetic data to confirm its capacity to represent a range of randomness levels in HRV time series. MApEnmax values are reduced in elderly patients, which may correspond to the reported loss of ANS adaptability in this population segment. Increased MApEnmax values measured in CHF patients versus healthy subjects during the night period point to greater irregularity of heart rate dynamics caused by the disease.

Recognition of biosignals with nonlinear properties by approximate entropy parameters

“…They investigate the applicability of entropy in-dicators for the analysis of heart rate variability (HRV) [4,5], and also propose solutions to practical problems. These include detection of cardiac arrhythmias (atrial fibrillation) [6], detection of signs of chronic heart failure [6,7] recognition of meditative states [8], neonatal screening [9], identification of autonomic disorders of the cardiovascular system [10], assessment of the level of functioning of the autonomic nervous system by HRV [11]. In these publications, along with the discussion of the effectiveness of recognizing various states of an organism by biological time series, it is pointed out that the results obtained are highly dependent on the size of the analyzed data sample.…”

Influence of Ectopic Beats on Heart Rate Variability Analysis

“…There are various algorithms established for performing the entropy analysis, such as approximate entropy (ApEn) and sample entropy (SampEn). The SampEn has been proved more stable and consistent statistically than ApEn since SampEn excludes the self-matching in its calculation [ 21 , 22 ], and there are also various improvement methods based on ApEn and SampEn [ 23 , 24 ]. Ectopic beats can contaminate the entropy calculations as well [ 17 , 25 ].…”

Approximate Entropy Technique of Calculation Based on Parallel Computation with Usage of GPU

“…This entropy measure is by definition dependents on two predefined parameter values, namely: m (the embedding dimensions) and r (the tolerance threshold); these parameters has different values by an application area. Thus, the first main drawback of this parameter is the difficulty of comparing various studies, since different values of a priori parameters can lead to different physiological interpretations [16,17]. Another disadvantage is the complexity of the algorithm.…”