Multiscale Cumulative Residual Dispersion Entropy with Applications to Cardiovascular Signals

Heart rate variability (HRV) is used as an index reflecting the adaptability of the autonomic nervous system to external stimuli and can be used to detect various heart diseases. Since HRVs are the time series signal with nonlinear property, entropy has been an attractive analysis method. Among the various entropy methods, dispersion entropy (DE) has been preferred due to its ability to quantify the time series' underlying complexity with low computational cost. However, the order between patterns is not considered in the probability distribution of dispersion patterns for computing the DE value. Here, a multiscale cumulative residual dispersion entropy (MCRDE), which employs a cumulative residual entropy and DE estimation in multiple temporal scales, is presented. Thus, a generalized and fast estimation of complexity in temporal structures is inherited in the proposed MCRDE. To verify the performance of the proposed MCRDE, the complexity of inter-beat interval obtained from ECG signals of congestive heart failure (CHF), atrial fibrillation (AF), and the healthy group was compared. The experimental results show that MCRDE is more capable of quantifying physiological conditions than preceding multiscale entropy methods in that MCRDE achieves more statistically significant cases in terms of p-value from the Mann-Whitney test.