A comparison study on stages of sleep: Quantifying multiscale complexity using higher moments on coarse-graining

It is of great interests in identifying dynamical properties of human sleep signals using electroencephalographic (EEG) measures. Multiscale entropy (MSE) is effective in quantifying the degree of unpredictability of time series in different time scales. To understand the superior coarse-graining approach for the EEG analysis, we therefor use different moments to coarse-grain a time series, and examine their volatility as well as the effectiveness in quantifying the complexities of sleep EEG in different sleep stages. Both the simulated signals (logistic map) and the EEGs with different sleep stages are calculated and compared using three types of coarse-graining procedure: including MSEμ (mean), MSEσ2 (variance) and MSEskew (skewness). The simulated results show that the generalized MSE (including MSEσ2 and MSEskew) can identify the differences in chaotic more easily with less fluctuation of entropy values in different time scales. As for the analysis of human sleep EEG, we find: (1) at small scales (<0.04 s), the entropy is higher during wakefulness and increasing time scales. (2) At large scales (0.25 s-2 s) in contrast, entropy is higher during deep sleep and lower with increasing time scales.