Multifractal detrended fluctuation analysis of human EEG: preliminary investigation and comparison with the wavelet transform modulus maxima technique.

Todd Zorick,Mark A Mandelkern,Christof Markus Aegerter

doi:10.1371/journal.pone.0068360

Abstract

Recently, many lines of investigation in neuroscience and statistical physics have converged to raise the hypothesis that the underlying pattern of neuronal activation which results in electroencephalography (EEG) signals is nonlinear, with self-affine dynamics, while scalp-recorded EEG signals themselves are nonstationary. Therefore, traditional methods of EEG analysis may miss many properties inherent in such signals. Similarly, fractal analysis of EEG signals has shown scaling behaviors that may not be consistent with pure monofractal processes. In this study, we hypothesized that scalp-recorded human EEG signals may be better modeled as an underlying multifractal process. We utilized the Physionet online database, a publicly available database of human EEG signals as a standardized reference database for this study. Herein, we report the use of multifractal detrended fluctuation analysis on human EEG signals derived from waking and different sleep stages, and show evidence that supports the use of multifractal methods. Next, we compare multifractal detrended fluctuation analysis to a previously published multifractal technique, wavelet transform modulus maxima, using EEG signals from waking and sleep, and demonstrate that multifractal detrended fluctuation analysis has lower indices of variability. Finally, we report a preliminary investigation into the use of multifractal detrended fluctuation analysis as a pattern classification technique on human EEG signals from waking and different sleep stages, and demonstrate its potential utility for automatic classification of different states of consciousness. Therefore, multifractal detrended fluctuation analysis may be a useful pattern classification technique to distinguish among different states of brain function.

Highlights

While human electroencephalography (EEG) recordings have been utilized for clinical and research purposes since the 1920s, still much is unknown about the underlying neuronal dynamics responsible for scalp-recorded electric potential changes as a function of time [1,2]
Human EEG is Well-modeled as a Multifractal Process using MF-detrended fluctuation analysis (DFA)
Given that finite-size effects result in a level of uncertainty in the calculation of multifractal DFA (MF-DFA) spectra, care must be taken to ensure that MFDFA results are consistent with true multifractality [24,33,46]

Summary

Introduction

While human electroencephalography (EEG) recordings have been utilized for clinical and research purposes since the 1920s, still much is unknown about the underlying neuronal dynamics responsible for scalp-recorded electric potential changes as a function of time [1,2]. Many lines of investigation into the neuronal dynamics which underlie scalp-recorded EEG have opened up the possibility that other techniques, derived from statistical mechanics, may be useful for the analysis of EEG signals [6,7,8]. Evidence of scale-free network activation has been demonstrated utilizing functional magnetic resonance imaging, magnetoencephalography, and electrocorticography [7,8,15,16] This experimental evidence collected on neuronal dynamics is matched by theoretical observations demonstrating that information networks operating at a ‘‘critical’’ state (exhibiting scale-free or self-affine dynamics) tend to maximize information transmission [12,17]. Traditional statistical methods of EEG analysis (e.g., spectral analysis via Fourier transform) may lose essential information about the neuronal dynamics underlying EEG signals, since these techniques would miss many properties inherent in nonstationary signals with self-affine dynamics

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Conclusion