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Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 3 pp 103–157Cite as

Fractal Dimension in Epileptic EEG Signal Analysis

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Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi’s algorithm, advantages of this method include greater speed and the criterion to choose the maximum and minimum values for time intervals. Comparisons with the other waveform fractal dimension algorithms are also demonstrated. In order to discriminate the Healthy and the Epileptic EEGs, an improved method of Multifractal Measure such as Generalized Fractal Dimensions (GFD) is also proposed. Finally we conclude that there are significant differences between the Healthy and Epileptic Signals in the designed method than the GFD through graphical and statistical tools. The improved multifractal measure is very efficient technique to analyze the EEG Signals and to compute the state of illness of the Epileptic patients.

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Acknowledgements

The research work has been supported by University Grants Commission (UGC - MRP & SAP), Government of India, New Delhi, India.

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  1. Department of Mathematics, The Gandhigram Rural Institute – Deemed University, Gandhigram, 624 302, Dindigul, Tamil Nadu, India

    R. Uthayakumar

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  1. R. Uthayakumar
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  1. , Institute for Mathematical Research, University Putra Malaysia, Hak Cipta Terpelihara UPM 2007, Serdang, 43400, Malaysia

    Santo Banerjee

  2. , Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, Torino, 10129, Italy

    Lamberto Rondoni

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Uthayakumar, R. (2013). Fractal Dimension in Epileptic EEG Signal Analysis. In: Banerjee, S., Rondoni, L. (eds) Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 3. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34017-8_4

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