Generally, for healthy adults, the entropy of electroencephalogram (EEG) signals gradually decreases from wake to sleep stages N1, N2, to N3, and increases during REM. However, some researchers found that multiscale entropy curves of sleep and wakefulness intercept, a cross-over phenomenon whose origin remains unexplored. The objective of the present work is to trace the origin of the cross-over phenomenon and to propose a workaround strategy. We simulated EEG by generating 1/f broadband signal and chirp signals with continuously varying frequencies. We then retrieved the rhythmic component from simulated EEG and real-world EEG and conducted MSE analysis of the instantaneous frequency variation (IFV) of the rhythmic component. The simulation revealed that this interception was ubiquitous in the MSE analysis of simulated EEG with rhythmic components of different frequencies. The cross-over point moved toward larger scale factors with the increasing sampling rate. We found that the MSE curve of IFV from real-world EEG for the wakefulness group was higher than that for sleep, showing no interception. These results suggest that (1) for a rhythmic signal like EEG, MSE analysis of the raw signal is highly affected by the rhythmic component, presenting artificial cross-over curves in sleep EEG study, (2) frequency variation of rhythmic components are complex signal which differs between wakefulness and sleep, in accordance with the complexity loss theory.INDEX TERMS Multiscale entropy analysis, complexity, sleep, brain wave.

No abstract

Mental fatigue (MF) jeopardizes performance and safety through a variety of cognitive impairments and according to the complexity loss theory, should represent “complexity loss” in electroencephalogram (EEG). However, the studies are few and inconsistent concerning the relationship between MF and loss of complexity, probably because of the susceptibility of brain waves to noise. In this study, MF was induced in thirteen male college students by a simulated flight task. Before and at the end of the task, spontaneous EEG and auditory steady-state response (ASSR) were recorded and instantaneous frequency variation (IFV) in alpha rhythm was extracted and analyzed by multiscale entropy (MSE) analysis. The results show that there were significant differences in IFV in alpha rhythm either from spontaneous EEG or from ASSR for all subjects. Therefore, the proposed method can be effective in revealing the complexity loss caused by MF in spontaneous EEG and ASSR, which may serve as a promising analyzing method to mark mild mental impairments.

Multiscale entropy (MSE) has attracted many applications in revealing the complexity of bio-signals since its introduction in early 2000. To better understand the MSE method, a lot of researchers have been working on its analytical solution. The existing analytical solutions are limited either to bulky double integrals, or to a proportional relation. This study intends to solve the double integrals and further approximate the analytical formula of MSE. Combining Costa's method with Briggs' integral and Taylor series expansion, we approximated the analytical formula of MSE for uncorrelated (white) noise. With the additional help of the eigenvalue of a fractal Brownian motion process, we approximated the analytical formula of MSE for correlated noise (1/f noise). The analytical formulae were verified on simulated power noise with known scaling exponent. The proposed analytical solution may shed some light on the understanding of MSE in analyzing biological time series.