Time-Dependent Entropy Estimation of EEG Rhythm Changes Following Brain Ischemia A. BEZERIANOS, 1,2 S. T ONG, 1,3 and N. THAKOR 1 1 Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, MD; 2 Department of Medical Physics, School of Medicine, University of Patras, Patras, Greece; and 3 Department of Biomedical Engineering, Shanghai Jiaotong University, Shanghai, China (Received 31 May 2001; accepted 15 November 2002) Abstract—Our approach is motivated by the need to generate a rigorous measure of the degree of disorder or complexity of the EEG signal in brain injury. Entropy is a method to quantify the order/disorder of a time series. It is the first time that a time-dependent entropy TDE is used in the quantification of brain injury level. The TDE was sensitive enough to monitor the significant changes in the subject’s brain rhythms during recovery from global ischemic brain injury. Among the differ- ent entropy measures, we used Tsallis entropy. This entropy is parametrized and is able to match with the particular properties of EEG, like long-range rhythms, spikes, and bursts. The method was tested in a signal composed of segments of syn- thetic signals Gaussian and uniform distributions and seg- ments of real signals. The real signal segments were extracted from normal EEG, EEG recordings from early recovery, and normal EEG corrupted by simulated spikes and bursts. Adult Wistar rats were subjected to asphyxia-cardiac arrest for 3 and 5 min. The TDE detected the pattern of ischemia-induced EEG alterations and was able to discriminate the different injury levels. Two parameters seem to be good descriptors of the recovery process; the mean entropy and the variance of the estimate followed opposite trends, with the mean entropy de- creasing and its variance increasing with injury. © 2003 Bio- medical Engineering Society. DOI: 10.1114/1.1541013 Keywords—Nonextensive, Electroencephalogram, Asphyxia, Rat. INTRODUCTION EEG is a sensitive but nonspecific measure of brain function and its use in cerebrovascular diseases is limited. 33 Nevertheless, it holds promise as a quantitative and real-time tool for diagnostic monitoring of brain injury. EEG has previously been used to prognosticate outcome after resuscitation from cardiac arrest CA with some success. 6,36 Our group has successfully utilized quantitative EEG measures to characterize the time and degree of electrophysiological response to CA. 14,32,40 The conventional approach to analyzing EEG rhythm is to obtain power spectra and delineate power in different spectral bands. 28,49 Alternatively, an algorithm that iden- tifies dominant frequencies in EEG was shown to be more responsive to recovery patterns of brain rhythm following ischemic injury. 16 Clinically, it may be useful to obtain a single measure of such a recovery response as a diagnostic monitoring tool. Distance metrics, spectral and cepstral distance, have been proposed to determine the differences in the spectra of normal and injured brain. 15,25 However, such distance measures require com- parison with base line, and in clinical situations, particu- larly unanticipated cardiac arrest, such base-line data are usually not available. Moreover, the distance metrics are not sensitive to the rapidly changing signal statistics nonstationarities of the recovering EEG. The approach taken here is motivated by the need to develop a rigorous measure of the degree of disorder or complexity of the EEG signal in brain injury. The EEG signal complexity has been studied by means of the cor- relation dimension D 2 . 10,27,41 A basic requirement for applying the tools of nonlinear dynamics chaos theory to experimental data is the stationary of the time series. This suggests that the time series is representative of a unique and stable attractor and is statistically invariant over different time intervals. Also, for the evaluation chaotic measures like D 2 , long-time recordings are re- quired. Generally, these measures are noise sensitive and their usefulness decreases especially in the case of addi- tive noise. 4,5 Unfortunately, the EEG data are noisy and the stationarity requirement is not fulfilled; therefore, other methods have to be explored. We postulate that entropy analysis will provide a quantitative measure of the degree of disorder in the brain rhythm at various times in brain injury and recov- ery. Approaches involving direct use of entropy for sig- nal analysis have been reported. 7,26,31 Another method to measure complexity is to use the spectral entropy as defined from the Fourier power spectrum. 20,35 However, application of this method to short lasting and nonsta- tionary data segments such as EEG during recovery has Address correspondence to Nitish V. Thakor, Department of Bio- medical Engineering, Johns Hopkins University, 720 Rutland Avenue, Baltimore, MD 21205-2195. Electronic mail: nthakor@bme.jhu.edu Annals of Biomedical Engineering, Vol. 31, pp. 221–232, 2003 0090-6964/2003/312/221/12/$20.00 Printed in the USA. All rights reserved. Copyright © 2003 Biomedical Engineering Society 221