- Open Access
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.
- Andrzejak RG, Lehnertz K, Mormann F, Rieke C, David P, Christian EE: Indications of nonlinear deterministic and finite dimensional structures in time series of brain electrical activity: dependence on recording region and brain state. Phys Rev E. 2001, 64: 061907-10.1103/PhysRevE.64.061907.View ArticleADSGoogle Scholar
- Diambra L, Malta CP: BRCA1 protein products: functional motifs. Phys Rev E. 1999, 59: 929-10.1103/PhysRevE.59.929.View ArticleADSGoogle Scholar
- Rombouts SARB, Keunen RWM, Stam CJ: Investigation of nonlinear structure in multichannel EEG. Phys Letts A. 1995, 202: 352-10.1016/0375-9601(95)00335-Z.View ArticleADSGoogle Scholar
- Dafilis MP, David TJL, Cadusch PJ: Robust chaos in a model of the electroencephalogram: Implications for brain dynamics. Chaos. 2001, 11: 474-10.1063/1.1394193.View ArticleADSMATHGoogle Scholar
- Robinson PA, Rennie CJ, Rowe DL: Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E. 2002, 65: 041924-10.1103/PhysRevE.65.041924.View ArticleADSGoogle Scholar
- Stam CJ: Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field. Clinical Neurophysiology. 2005, 116: 2266-2301. 10.1016/j.clinph.2005.06.011.View ArticleGoogle Scholar
- Pradhan N, Sadasivan PK: Relevence of surrogate-data testing in electroencephalograms. Phys Rev E. 1996, 53: 2684-10.1103/PhysRevE.53.2684.View ArticleADSGoogle Scholar
- Krakovská A, Štolc SJ: Spectral decay vs. correlation dimension of EEG. Neurocomputing. 2008, 71: 2978-10.1016/j.neucom.2007.06.007.View ArticleGoogle Scholar
- Pereda E, Gamundi A, Rial R, Gonzalez J: Non-linear behaviour of human EEG: fractal exponent versus correlation dimension in awake and sleep stages. Neurosci Lett. 1998, 250: 91-10.1016/S0304-3940(98)00435-2.View ArticleGoogle Scholar
- Pereda E, Gamundi A, Nicolau MC, Rial R, Gonzalez J: Interhemispheric differences in awake and sleep human EEG: a comparison between nonlinear and spectral measures. Neurosci Lett. 1999, 263: 37-10.1016/S0304-3940(99)00104-4.View ArticleGoogle Scholar
- Hughes JR: Progress in predicting seizure episodes with nonlinear methods. Epilepsy & Behavior. 2008, 12: 128-10.1016/j.yebeh.2007.08.004.View ArticleGoogle Scholar
- Mormann F, Kreuz T, Rieke C, Andrzejak RG, Kraskov A, David P, Christian Elger E, Lehnertza K: On the predictability of epileptic seizures. Clin Neurophysiol. 2005, 116: 569-10.1016/j.clinph.2004.08.025.View ArticleGoogle Scholar
- Jerger KK, Theoden NI, Joseph TF, Timothy S, Pecora L, Steven WL, Steven SJ: Early seizure detection. J Clin Neurophysiol. 2001, 18: 259-10.1097/00004691-200105000-00005.View ArticleGoogle Scholar
- Lopes da Silva FH, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN: Dynamical diseases of brain systems: different routes to epileptic seizures. IEEE Trans Biomed Eng. 2003, 50: 540-10.1109/TBME.2003.810703.View ArticleGoogle Scholar
- Slutzky MW, Cvitanovic P, Mogul DJ: Deterministic chaos and noise in three in vitro hippocampal models of epilepsy. Ann Biomed Eng. 2001, 29: 607-10.1114/1.1380419.View ArticleGoogle Scholar
- Savit R, Li D, Zhou W, I D: Understanding dynamic state changes in temporal lobe epilepsy. J Clin Neurophysiol. 2001, 18: 246-10.1097/00004691-200105000-00004.View ArticleGoogle Scholar
- Gautama T, Mandic DP, Hulle MMV: Indications of nonlinear structures in brain electrical activity. Phys Rev E. 2003, 67: 046204-10.1103/PhysRevE.67.046204.View ArticleADSGoogle Scholar
- Harikrishnan K, Misra R, Ambika G, Kembhavi A: A non-subjective approach to the GP algorithm for analysing noisy time series. Physica D. 2006, 215: 137-10.1016/j.physd.2006.01.027.View ArticleADSMathSciNetMATHGoogle Scholar
- EEG time series download page. [http://www.meb.uni-bonn.de/epileptologie/cms/front_content.php?idcat=193]
- Pijn JP, Velis DN, Heyden van der MJ, DeGoede J, van Veelen CW, Lopes da Silva FH: Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings. Brain Topogr. 1997, 9: 249-10.1007/BF01464480.View ArticleGoogle Scholar
- Shen Y, Olbricha E, Achermann P, Meier P: Dimensional complexity and spectral properties of the human sleep EEG. Clinical Neurophysiology. 2003, 114: 199-10.1016/S1388-2457(02)00338-3.View ArticleGoogle Scholar
- Lee JS, Yang BH, Lee JH, Choi JH, Choi IG, Kim SB: Detrended fluctuation analysis of resting EEG in depressed outpatients and healthy controls. Clinical Neurophysiology. 2007, 118: 2489-10.1016/j.clinph.2007.08.001.View ArticleGoogle Scholar
- Kannathal N, Acharya UR, Lim C, Sadasivan PK: Characterization of EEG-A comparative study. Computer Methods and Programs in Biomedicine. 2005, 80: 17-10.1016/j.cmpb.2005.06.005.View ArticleGoogle Scholar
- Freeman WJ, Holmes MD, Burke BC, Vanhatalo S: Spatial spectra of scalp EEG and EMG from awake humans. Clinical Neurophysiology. 2003, 114: 1053-10.1016/S1388-2457(03)00045-2.View ArticleGoogle Scholar
- Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL: Prediction of electroencephalographic spectra from neurophysiology. Phys Rev E. 2001, 63: 021903-10.1103/PhysRevE.63.021903.View ArticleADSGoogle Scholar
- Nikolic D, Moca VV, Singera W, Muresan RC: Properties of multivariate data investigated by fractal dimensionality. Journal of Neuroscience Methods. 2008, 172: 27-10.1016/j.jneumeth.2008.04.007.View ArticleGoogle Scholar
- Natarajan K, Acharya R, Alias F, Tiboleng T, Puthusserypady SK: Nonlinear analysis of EEG signals at different mental states. BioMedical Engineering OnLine. 2004, 3: 7-10.1186/1475-925X-3-7.View ArticleGoogle Scholar
- Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer D: Testing for nonlinearity in time series: the method of surrogate data. Physica D. 1992, 58: 77-10.1016/0167-2789(92)90102-S.View ArticleADSMATHGoogle Scholar
- Nakamura T, Small M: Applying the method of Small-Shuffle surrogate data: Testing for dynamics in fluctuating data with trends. International Journal of Bifurcations and Chaos. 2006, 16: 3581-10.1142/S0218127406016999.View ArticleMATHGoogle Scholar
- Small M, Tse CK: Detecting determinism in time series: The method of surrogate data. IEEE Transactions on circuits and systems-I. 2003, 50: 663-10.1109/TCSI.2003.811020.View ArticleMathSciNetGoogle Scholar
- van Milligen BP, Pedrosa MA, Balbín R, Hidalgo C, Newman DE, Sánchez E, Frances M, García-Cortés I, Bleuel J, Endler M, Riccardi C, Davies S, Matthews GF, Latten A, Klinger T: Self-similarity of the plasma edge fluctuations. Phys Plasmas. 1998, 5: 3632-10.1063/1.873081.View ArticleADSGoogle Scholar
- Dori G, Fishman S, Ben-Haim SA: The correlation dimension of rat hearts in an experimentally controlled environment. Chaos. 2000, 10: 257-10.1063/1.166471.View ArticleADSGoogle Scholar
- Harrison MAF, Osorio I, Frei MG, Asuri S, Lai YC: Correlation dimension and integral do not predict epileptic seizures. Chaos. 2005, 15: 033106-10.1063/1.1935138.View ArticleADSGoogle Scholar
- Nurujjaman M, Iyengar ANS: Realization of SOC behavior in a dc glow discharge plasma. Phys Letts A. 2007, 360: 717-10.1016/j.physleta.2006.09.005.View ArticleADSGoogle Scholar
- Cajueiro DO, Tabak BM: The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient. Physica A. 2004, 336: 521-10.1016/j.physa.2003.12.031.View ArticleADSMathSciNetGoogle Scholar
- Schwartzkroin PA: Progress in Epilepsy Research: Origins of the Epileptic State 38 (8): 853–858 (1997). Epilepsia. 1997, 38: 853-10.1111/j.1528-1157.1997.tb01250.x.View ArticleGoogle Scholar
- Bromfield EB: Epileptiform Discharges. [http://emedicine.medscape.com/article/1138880-overview]
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.