Multiscale Entropy Analysis of Instantaneous Frequency Variation to Overcome the Cross-Over Artifact in Rhythmic EEG

Abstract

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.

Mental fatigue decreases complexity: Evidence from multiscale entropy analysis of instantaneous frequency variation in alpha rhythm

“…Alpha peak frequency varies constantly, and the variation does not represent random fluctuations but instead constitutes the basis of an adaptive mechanism mirroring the activation level of neural populations (Mierau et al, 2017 ). Previously, we have shown that the EEG alpha rhythm changes its peak frequency constantly and the MSE analysis of the instantaneous frequency variation (IVF) can be used to show the complexity loss of the brain in sleep comparing to in wakefulness (Li et al, 2021 ).…”

“…In Li et al ( 2021 )'s work, the reason for using MSE analysis on IFV in spontaneous alpha rhythm or delta wave instead of on the brain wave itself is that the MSE algorithm suffers from the artifact of the carrying frequency of the brain waves. In this study, we have also shown the IFV in alpha rhythm either from spontaneous EEG or from ASSR has much higher separation power.…”

“…Alpha rhythm time series extracted from SPON and ASSR were named SPON-α and ASSR-α. Instantaneous frequencies were computed from alpha rhythm by Hilbert transform and then detrended to obtain the IFV (Li et al, 2021 ), resulting in time series SPON-α-IFV and ASSR-α-IFV, with data length 10,000 points.…”

“…Since MF impairs a variety of cognitive functions, it should present “complexity loss” in physiological signals, e.g., electroencephalogram (EEG), heart rate variation, according to complexity loss theory, which was initially proposed to define aging as a progressive loss of complexity in the dynamics of all physiologic systems (Lipsitz and Goldberger, 1992 ). Since it was proposed, complexity loss theory has been applied to various diseases, e.g., epilepsy (Lehnertz and Elger, 1995 ), heart failure (Costa et al, 2003 ), Alzheimer's disease (Dauwels et al, 2011 ), diabetes (Churruca et al, 2008 ), patients with vegetative state (Goldberger et al, 2002 ; Sarà and Pistoia, 2010 ), as well as in sleep studies (Shi et al, 2017 ; Li et al, 2021 ).…”

“…In the previous study, we have found that alpha frequency fluctuates constantly in a nonlinear fashion by analyzing the complexity of instantaneous frequency variation (IFV) of alpha rhythms (Li et al, 2021 ). And it turns out that this complexity of IFV well-differentiates underlying cognitive states showing low complexity in sleep EEG than in wakeful EEG, which is in accordance with the complexity loss theory (Li et al, 2021 ).…”