Application of fractal theory in analysis of human electroencephalographic signals

Authors:
P. Paramanathan;R. Uthayakumar
Affiliations:
Department of Mathematics, Gandhigram Rural University, Gandhigram 624 302, Tamil Nadu, India;Department of Mathematics, Gandhigram Rural University, Gandhigram 624 302, Tamil Nadu, India
Venue:
Computers in Biology and Medicine
Year:
2008

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Abstract

In medical discipline, complexity measure is focused on the analysis of nonlinear patterns in processing waveform signals. The complexity measure of such waveform signals is well performed by fractal dimension technique, which is an index for measuring the complexity of an object. Its applications are found in diverse fields like medical, image and signal processing. Several algorithms have been suggested to compute the fractal dimension of waveforms. We have evaluated the performance of the two famous algorithms namely Higuchi and Katz. They contain some problems of determining the initial and final length of scaling factors and their performance with electroencephalogram (EEG) signals did not give better results. In this paper, fractal dimension is proposed as an effective tool for analyzing and measuring the complexity of nonlinear human EEG signals. We have developed an algorithm based on size measure relationship (SMR) method. The SMR algorithm can be used to detect the brain disorders and it locates the affected brain portions by analyzing the behavior of signals. The efficiency of the algorithm to locate the critical brain sites (recurrent seizure portion) is compared to other fractal dimension algorithms. The K-means clustering algorithm is used for grouping of electrode positions.