Rank-based multi-scale entropy analysis of heart rate variability

The method of MultiScale Entropy (MSE) is an invaluable tool to quantify and compare the complexity of physiological time series at different time scales. Although MSE traditionally employs sample entropy to measure the unpredictability of each coarse-grained series, the same framework can be applied to other metrics. Here we investigate the use of a rank-based entropy measure within the MSE framework. Like in the traditional method, the series are studied in an embedding space of dimension m. The novel entropy assesses the unpredictability of the series quantifying the "amount of shuffling" that the ranks of the mutual distances between pairs of m-long vectors undergo when considering the next observation. The algorithm was tested on recordings from the Fantasia database in a time-varying fashion using non-overlapping 300-samples windows. The method was able to find statistically significant differences between young and healthy elderly subjects at 7 scales/time-windows after accounting for multiple comparisons using the Holm-Bonferroni correction. These promising results suggest the possibility of using this measure to perform a time-varying assessment of complexity with increased accuracy and temporal resolution.