Examination of scale-invariant characteristics of epileptic electroencephalograms using wavelet-based analysis

https://doi.org/10.1016/j.compeleceng.2014.04.005Get rights and content

Highlights

  • A wavelet-based approach is applied to examine scale-invariant characteristics of epileptic EEGs.

  • The spectral exponents of epileptic EEGs corresponding to various states are different.

  • The wavelet bases used have an effect on the estimated spectral exponents.

  • The spectral exponent is shown to be related to the Hurst exponent.

Abstract

There is evidence that biological and physiological systems including the brain exhibit can exhibit fractal characteristics that can be used to identify the state of the system. In this study, wavelet-based fractal analysis is used to examine self-similar or scale-invariant characteristics of intracranial EEG data in terms of the spectral exponent. The intracranial EEG data were recorded from subjects with epilepsy during non-seizure period and during epileptic seizure activity. From the computational results, it is observed that the self-similar or scale-invariant characteristics of the intracranial EEG data obtained during these two periods are significantly different. The actual value of the estimated spectral exponent depends on the wavelet bases used for the computations.

Introduction

Physiological signals and systems have been shown to exhibit an extraordinary range of patterns and behaviors [1]. The introduction of the concept of fractals and corresponding quantitative measures has provided additional avenues of investigation and applications in biology and medicine including neuroscience [2], [3]. The mathematical concept of a fractal is commonly associated with irregular objects that exhibit a geometric property called scale-invariance or self-similarity [1], [4]. Fractal forms are composed of subunits resembling the structure of the macroscopic object [1] which in nature can emerge from statistical scaling behavior in the underlying physical phenomena [5].

The existence of fractal behaviors in the brain has been widely accepted at various levels including anatomic, functional, pathological, molecular, and epigenetic [2]. Although such characteristics and behaviors may be visually apparent, they can be difficult to capture using conventional computational analyses and measures [6]. Conventional methods such as Fourier analysis are simple and quick but may lead to erroneous interpretations [7]. Computational analyses and measures for quantifying and characterizing fractal behaviors and complexity such as the Hurst exponent, the scaling exponent, fractal dimension and various forms of entropy [8], [9], [10] have been applied in epilepsy research to characterize brain behaviors and for epileptic seizure detection. Recent studies (e.g., [11], [12]) documented fractal organization of the brain and nervous system.

An important class of statistical scale-invariant or self-similar random processes is the 1/f processes [5]. A traditional mathematical model and the empirical properties of 1/f processes have largely been inspired by the fractional Brownian motion framework [5], [13], [14]. In general, models of 1/f processes are represented using a frequency domain characterization and exhibit power law behavior [15] that can be characterized in the frequency domain by X(ω)1/|ω|γ. The wavelet transform is a natural tool for characterizing self-similar or scale-invariant signals and plays a significant role in the study of self-similar signals and systems [5], in particular 1/f processes [5], [13]. The spectral exponent γ that specifies the distribution of power in 1/f processes from low to high frequencies can be characterized in terms of the slope of the log-variance of the wavelet coefficients versus scale graph.

The Hurst exponent H is the most common quantitative measure that is used to characterize the long-range correlation or self-similarity of signals. There are a number of methods for estimating the Hurst exponent H. The most commonly used method is the rescaled range (R/S) analysis [16]. Another method is detrended fluctuation analysis (DFA), originally introduced in [17], is a robust method for estimating the Hurst exponent H. The Hurst exponent is in the range 0<H<1. When 0<H<0.5, the process is considered to have short-range correlation [21], indicating that an increase in the process is more probably followed by a decrease and vice versa (anti-persistence). The process is considered to have long-range correlation when 0.5<H<1 (persistence), indicating that an increase in the process is more probably followed by an increase and vice versa [18]. A value of H=0.5 indicates that the signal is uncorrelated.

In this study, we apply the wavelet-based representation for 1/f processes and use the spectral exponent γ to examine the scale-invariant or self-similar characteristics of the dynamics of the brain of subjects with epilepsy. A number of different wavelet bases are used to investigate their effects on the estimation of the spectral exponent. Furthermore, the scale-invariant or self-similar characteristics of intracranial EEG data obtained during different pathological states of the brain (ictal and interictal states) assessed from the spectral exponent γ are compared to the Hurst exponent H.

The remainder of this paper is organized as follows. Section 2 presents background information and methods. Data and the experimental setup are discussed in Section 3. Section 4 details and discusses the computational results. Finally, Section 5 summarizes the results and provides concluding remarks.

Section snippets

1/f Processes

In general, models of 1/f processes are represented using a frequency domain characterization. The dynamics of 1/f processes exhibit power-law behavior [15] and can be characterized in the form of [13]X(ω)σx2ωγover several decades of frequency ω, where X(ω) and σx2 are, respectively, the Fourier transform and the variance of the signal x(t), and γ denotes the spectral exponent. The spectral exponent γ specifies the distribution of spectral content from low to high frequencies, and an

Experimental data

The data used in this study consists of two sets of intracranial EEG data of epilepsy patients obtained from the Department of Epileptology, University of Bonn (available online at http://epileptologie-bonn.de/cms/front_content.php?idcat=193), that originated from the study presented in [24]. The intracranial EEG data sets, referred to as F and S, were recorded using intracranial electrodes from five epilepsy patients whom had achieved complete seizure control after resection of one of the

Spectral exponents of the intracranial EEG signals

The mean and the standard deviation of the log2-var of the wavelet coefficients of the intracranial EEG signals of data sets F and S obtained using Db1, Db2, Db6, and Db25 are summarized in Table 1. It is observed that the log2-var of the wavelet coefficients of the intracranial EEG signals of both data sets tends to increase from a lower level to a higher level. At any level, the log2-var of the wavelet coefficients of the intracranial EEG signals of data set S tends to be higher than that of

Conclusions

The computational results suggest that the intracranial EEG signals obtained during seizure activity tend to be less scale-invariant or self-similar than that during non-seizure periods. This structural characteristics of the intracranial EEG signals can be clearly observed as the intracranial EEG signals obtained during epileptic seizure activity tend to have dominant scales or frequencies. These scale-invariant or self-similar characteristics of the intracranial EEG data observed from the

Acknowledgments

This work is supported by a TRF-CHE Research Grant for New Scholar, jointly funded by the Thailand Research Fund (TRF) and the Commission on Higher Education (CHE), the Ministry of Education, Thailand, under Contract No. MRG5280189.

Suparerk Janjarasjitt received his M.S. degree in 2002 and Ph.D. degree in 2006 in systems and control engineering from Case Western Reserve University, Cleveland, Ohio, USA. He is currently an Assistant Professor at the Department of Electrical and Electronic Engineering, Ubon Ratchathani University, Ubon Ratchathani, Thailand.

References (25)

  • W. Klonowski

    Everything you wanted to ask about EEG but were afraid to get the right answer

    Nonlinear Biomed Phys

    (2009)
  • U.R. Acharya et al.

    Application of non-linear and wavelet based features for the automated identification of epileptic EEG signals

    Int J Neural Syst

    (2012)
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    Suparerk Janjarasjitt received his M.S. degree in 2002 and Ph.D. degree in 2006 in systems and control engineering from Case Western Reserve University, Cleveland, Ohio, USA. He is currently an Assistant Professor at the Department of Electrical and Electronic Engineering, Ubon Ratchathani University, Ubon Ratchathani, Thailand.

    Kenneth A. Loparo received his Ph.D. degree in systems and control engineering from Case Western Reserve University, Cleveland, Ohio, USA in 1977. He is the Nord Professor of Engineering and currently serves as the Chair of Department of Electrical Engineering and Computer Science, Case Western Reserve University.

    Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek.

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