Entropy changes in brain function Osvaldo A. Rosso Chaos and Biology Group, Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires, Argentina Received 20 May 2006; received in revised form 24 June 2006; accepted 13 July 2006 Available online 17 January 2007 Abstract The traditional way of analyzing brain electrical activity, on the basis of electroencephalography (EEG) records, relies mainly on visual inspection and years of training. Although it is quite useful, of course, one has to acknowledge its subjective nature that hardly allows for a systematic protocol. In the present work quantifiers based on information theory and wavelet transform are reviewed. The “relative wavelet energy” provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The “normalized total wavelet entropy” carries information about the degree of order–disorder associated with a multi- frequency signal response. Their application in the analysis and quantification of short duration EEG signals (event-related potentials) and epileptic EEG records are summarized. © 2007 Published by Elsevier B.V. Keywords: EEG; ERP; Epilepsy; Wavelet analysis; Signal entropy 1. Introduction Synchronous neuronal discharges create rhythmic potential fluctuations, which can be recorded from the scalp through electroencephalography. The electroencephalogram (EEG) can be roughly defined as the mean brain electrical activity mea- sured at different sites of the head. The EEG reflects not only characteristics of the brain activity itself but also yields clues concerning the underlying associated neural dynamics. The processing of information by the brain results in dynamical changes of its electrical activity in three variables, namely, time, frequency, and space. Therefore, the concomitant studies require methods capable of describing the qualitative and quantitative variation of the signal in both time and frequency. The appropriate mathematical tool to such an end is the so- called “wavelet analysis”, of which more below. In recent years oscillatory EEG activity has been discussed in relation with functional neuronal mechanisms (Başar, 1980, 1998, 1999, 2004). In this regard, it is of major interest to investigate how brain electric oscillations get synchronized in pathological or physiological brain states (e.g., epileptic seizures, sleep–wake stages, etc.), or by external and internal stimulation (event-related potentials (ERP) or evoked potentials (EP)). This issue can be addressed by applying methods of system analysis to the EEG signals, because changes in EEG activity occur in temporal relation to triggering events, and could be thought of as transitions from disordered to ordered states (or vice versa). The EEG can be regarded as reflecting the activity of ensembles of generators producing oscillations in several fre- quency ranges, which are active in a very complex manner (Başar, 1980, 1998, 1999, 2004). According to this hypothesis, the EEG reflects the activity of such generators that produce oscillations in several frequency ranges. Upon stimulation, a resonance phenomenon occurs, and the generators begin to act together in a coherent way. This transition from a disordered to an ordered state gives rise to superimposed event-related oscil- lations in several frequency ranges. A natural approach to quantify the degree of order in a signal is to consider its spectral entropy, as defined from the Fourier power spectrum (Powell and Percival, 1979). For the analysis of EEG order/disorder the spectral entropy has been used by Inouye and co-workers (Inouye et al., 1991, 1993). The Fourier spectral entropy measures the extent to which the Fourier power spectrum of the signal is concentrated (or not) into a given (narrow) frequency range (Powell and Percival, 1979). The International Journal of Psychophysiology 64 (2007) 75 – 80 www.elsevier.com/locate/ijpsycho E-mail address: oarosso@fibetel.com.ar . 0167-8760/$ - see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.ijpsycho.2006.07.010