Rank-based multi-scale entropy analysis of biological signals

The method of Multi-Scale Entropy (MSE) is an invaluable tool to quantify and compare the complexity of physiological time series at di erent time scales. MSE works by constructing coarse-grained versions of the original time series and computing the entropy measure corresponding to each scale factor. Although MSE traditionally employs sample entropy to measure the unpredictability of each coarsegrained series, the same framework can be applied to other metrics. Here I investigate the use of a new entropy de nition, the Rank-based entropy, within the MSE framework, on biological signals. 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. Its ability in assess the complexity of signals is compared with that of MSE based on sample entropy. Analysis of simulated time series with known properties highlight the ability of this entropy measure of extracting a speci c type of information and to best distinguish signals with di erent characteristics. Applied to short noisy real world data, Rank-based Multi-scale Entropy has shown its robustness and it has proved that it can be used with great results within a multi-scale framework. On arterial blood pressure data in patients with Atrial Fibrillation it has outperformed the traditional Multi-Scale Entropy in nding statistically signi cant di erences between rest and tilt phases. Also on postural sway signals, in patients with Parkinson's Disease, it has proved to have good performance in the analysis of the medio-lateral direction of CoP. These encouraging results obtained in this work suggest the possibility of using this measure to perform an assessment of complexity in short biological signals over multiple time scales.