The Dynamics of EEG Entropy

M. Ignaccolo1, M. Latka2, W. Jernajczyk3, P. Grigolini4 and B.J. West,1'5

1) Physics Department, Duke University, Durham, NC

2) Institute of Biomedical Engineering, Wroclaw University of Technology, Wroclaw, Poland

3) Department of Clinical Neurophysiology, Institute of Psychiatry and Neurology, Warsaw, Poland

4) Center for Nonlinear Science, University of North Texas, Denton, TX

5) Mathematics and Information Science Directorate, Army Research Office

(Dated: March 5, 2009)

EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy

manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation.

These properties are faithfully modeled by a phenomenological Langevin equation interpreted within

a neural network context.

PACS numbers:

I. INTRODUCTION

In the nearly one hundred years since the electroencephalogram (EEG) was introduced into neuroscience there

have been a variety of methods used in attempts to establish a taxonomy of EEG patterns in order to delineate

the correspondence between brain wave patterns and brain activity. Over that time the single channel EEG time

series has been interpreted as consisting of relatively slow regular variations called signal and the relatively rapid

erratic fluctuations called noise. This separation implies that the signal contains information about the EEG channels

in the brain, whereas the erratic fluctuations are a property of a channel's environment and does not contain any

useful information. Recent studies have refined this engineering model and extracted information from the random

fluctuations by concentrating on what is believed to be the scaling behavior of the time series. Analysis of the second

moment of the single channel time series shows an algebraic scaling in time, i.e., (X(t)2 c t2H. The brackets denote

a suitably defined averaging procedure and detrended fluctuation analysis (DFA) [1], which measures the standard

deviation of the detrended fluctuations, has been the method of choice for the recent analysis of EEG data [2]. Buiatti

et al. [3] use DFA to show that specific task-demands can modify the temporal scale-free dynamics of the ongoing

brain activity as measured by the scaling index.

The 'signal' parts of the EEG time series are called waves or rhythms. The nature and scope of these waves have

been widely investigated, see Basar [4] for a review. The alpha rhythm (7-12 Hz) has been shown to be typical of

awake individuals under no stimulation. Basar, along with colleagues, have developed an integrative theory of alpha

oscillations in brain functioning [5]. They hypothesize that there is not one, but several alpha generators distributed

within the brain and note that the alpha rhythm may act as a nonlinear clock in the manner suggested by Wiener [6]

to serve as a gating function to facilitate the association mechanisms in the brain.

As a measure of order/disorder, entropy has been used to characterize EEG signals. Schlogl et al. [8] measured the

entropy of 16 bits EEG polysomnograhic records and found it in the range of 8-11 bits. Inouye et al. [9] employed

spectral entropy, as defined by the Fourier power spectrum, but the fact that EEG time series are not stationary, in

the sense that the autocorrelation function is not simply a function of the two-time difference, obviates the use of

Fourier transforms. Subsequently, wavelet entropy was used by Rosso et al. [10] to study the order/disorder dynamics

in short duration EEG signals including evoked response potentials. Patel et al. [7], using a combination of MRI and

entropy maximization, demonstrated that the generators of alpha rhythm are mainly concentrated over the posterior

regions of the cortex.

The diffusion entropy (DE) method [11] has been successfully used to discriminate between the contributions of

the low frequency waves (signal) and the high frequency fluctuations (noise), e.g., the influence of the seasons on the

daily number of teen births in Texas [12] and the effect of solar cycles on the statistics of solar flares [13]. In this

Letter we use the DE method to provide insight on the low/high frequency dynamics of EEG time series.

II. EEG ANALYSIS

Each single channel recording of the EEG time series consists of a sequence of N + 1 data points, and the difference

between successive data points is denoted by ( for j = 1, 2, .., N. For the DE analysis a set of stochastic variables

Ignaccolo, Massimiliano; Latka, Miroslaw; Jernajczyk, Wojciech; Grigolini, Paolo & West, Bruce J.
*The Dynamics of EEG Entropy*.
[Berlin, Heidelberg].
UNT Digital Library.
http://digital.library.unt.edu/ark:/67531/metadc132967/. Accessed January 29, 2015.