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.