Univariate and Multivariate Generalized Multiscale Entropy to Characterise EEG Signals in Alzheimer's Disease

Alzheimer's disease (AD) is a degenerative brain disorder leading to memory loss and changes in other cognitive abilities. The complexity of electroencephalogram (EEG) signals may help to characterise AD. To this end, we propose an extension of multiscale entropy based on variance (MSE sigma 2) to multichannel signals, termed multivariate MSE sigma 2 (mvMSE(sigma 2)), to take into account both the spatial and time domains of time series. Then, we investigate the mvMSE(sigma 2) of EEGs at different frequency bands, including the broadband signals filtered between 1 and 40 Hz, theta, alpha, and beta bands, and compare it with the previously-proposed multiscale entropy based on mean (MSE mu), multivariate MSE mu (mvMSE(mu)), and MSE sigma 2, to distinguish different kinds of dynamical properties of the spread and the mean in the signals. Results from 11 AD patients and 11 age-matched controls suggest that the presence of broadband activity of EEGs is required for a proper evaluation of complexity. MSE sigma 2 and mvMSE(sigma 2) results, showing a loss of complexity in AD signals, led to smaller p-values in comparison with MSE mu and mvMSE(mu) ones, suggesting that the variance-based MSE and mvMSE can characterise changes in EEGs as a result of AD in a more detailed way. The p-values for the slope values of the mvMSE curves were smaller than for MSE at large scale factors, also showing the possible usefulness of multivariate techniques.