Comparative study of nonlinear properties of EEG signals of normal persons and epileptic patients
© Nurujjaman et al; licensee BioMed Central Ltd. 2009
Received: 04 December 2008
Accepted: 20 July 2009
Published: 20 July 2009
Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent.
Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak et al. [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases.
In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation.
The brain is a highly complex and vital organ of a human body whose neurons interact with the local as well as the remote ones in a very complicated way [1–4]. These interactions evolve as the spatio-temporal electro magnetic field of the brain, and are recorded as Electroencephalogram (EEG) [1, 4–6]. Though the detail link between EEGs and the underlying physiology is not well understood, the former is widely used for detection and prediction of epilepsy, localization of epileptic zone and characterization of the pre and post-ictal [1, 6, 7] using linear and nonlinear analysis techniques [1, 6–11]. Though mainly nonlinear methods have been applied to predict the onset of epileptic seizure and localizing epileptic regions, limited progress has been achieved so far . Even some negative results have also been reported like linear measures are better than nonlinear measures [12, 13], seizure is not a low dimensional process , it lacks determinism [8, 15, 16], etc. Hence finding proper analysis techniques is also one of the main issues and experts try out different analysis tools for characterizing the normal and diseased brain states, especially the epileptic brain.
In 2001, Ralph G. Andrzejak, et al. and later some other authors [17, 18] have analyzed five sets of EEG signals  each set containing 100 epochs to study the determinism in the brain dynamics for five different physiological and pathological conditions. Sets A and B are for normal persons with eyes open and closed respectively and recorded extracranially. Sets C and D were recorded intracranially from the hippocampal formation which was nonepiletogenic of the opposite hemisphere of the brain and from within the epileptogenic zone of an epileptic patient during seizure free intervals respectively. Set E was recorded intracranially from the epileptic zone during seizure. The details of the experiments and the conditions have been described in Ref . R.G. Andrzejak, et al.  had shown that the normal healthy subject with eyes closed and open shows stochastic behavior using amplitude adjusted Fourier transform surrogate analysis where discriminating statistics were the effective correlation dimension and nonlinear prediction error whereas, using delay vector variance discriminating statistics, significant nonlinear determinism was shown in the same subject . So two conflicting results were obtained for the same subject using nonlinear methods. In the case of epileptic patients during seizure and seizure free intervals, determinism was shown using two different methods [1, 17] though other studies show lack of determinism for different epileptic patients during seizure [12, 15, 16, 20].
On the other hand, characterization of EEGs by scaling properties of the signal is also a major area of research interest [8–10, 21–27]. Power spectral exponent has been used to characterize the different subjects with different physiological conditions [8, 9, 24, 25] and the same exponent has also been used to estimate the correlation dimension (D corr ) . Fractal dimension and hurst exponent have also been used to characterize the EEGs [26, 27]. Hence a number of experts prefer scaling properties to characterize EEG for different physiological and pathological conditions .
In this paper, we have reinvestigated the EEG data studied in Refs. [1, 17, 18] by random shuffled surrogate analysis using D corr as discriminating statistics in order to find determinism in the signal [28–30] and the results have been compared with earlier analyses [1, 17]. Probability distribution function shows a difference between normal and epileptic brain states and this has been discussed in latter Section. Finally, we have quantified the five different physiological brain states by Hurst exponent (H) which has been estimated using R/S analysis .
Results and discussion
Probability distribution functions
In this paper we have reinvestigated the EEG data of normal and epileptic subjects to get an insight into the brain dynamics at different imposed and diseased conditions using RS surrogate analysis, PDF and H exponents. From these analysis we have found that RS and PDF may be useful to find a broad difference between normal and epileptic subjects but not helpful for constrained and seizure free intervals. Whereas, using H exponent, we have obtained differences in characteristics for normal subjects with eyes open and closed, and epileptic subjects during seizure and seizure free interval. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brains show long range anticorrelation.
We gratefully acknowledge the use of TISEAN package for the estimation of the correlation dimension.
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