Multiscale entropy (MSE) was proposed to characterize complexity as a function of the time-scale factor tau. Despite its broad use, this technique suffers from two limitations: (1) the artificial MSE reduction due to the coarse graining procedure and (2) the introduction of spurious MSE oscillations due to the suboptimal procedure for the elimination of the fast temporal scales. We propose a refined MSE (RMSE), and we apply it to simulations and to 24-h Holter recordings of heart rate variability (HRV) obtained from healthy and aortic stenosis (AS) groups. The study showed that the refinement relevant to the elimination of the fast temporal scales was more helpful at short scales (spanning the range of short-term HRV oscillations), while that relevant to the procedure of coarse graining was more useful at large scales. In healthy subjects, during daytime, RMSE was smaller at short scales (i.e., tau =1-2) and larger at longer scales (i.e., tau =4-20) than during nighttime. In AS population, RMSE was smaller during daytime both at short and long time scales (i.e., tau = 1 -11) than during nighttime. RMSE was larger in healthy group than in AS population during both daytime (i.e., tau = 2 -9) and nighttime (i.e., tau = 2). RMSE overcomes two limitations of MSE and confirms the complementary information that can be derived by observing complexity as a function of the temporal scale.
['José F. Valencia', 'Alberto Porta', 'Montserrat Vallverdú', 'Francesc Claria', 'Rafal Baranowski', 'Ewa Orłowska-Baranowska', 'Pere Caminal']
Refined Multiscale Entropy: Application to 24-h Holter Recordings of Heart Period Variability in Healthy and Aortic Stenosis Subjects