Detrended Fluctuation Analysis of EEG Signals

Abstract

Scaling properties are one of the most important quantifiers of complexity in many events, as time series (TS). To try to have a glimpse how brain is working, we need new methods of analysis. The structural characteristics of biomedical signals are often visually apparent, but not captured by conventional measures (average amplitude, Fourier analysis based methods, up to second order statistics). Biomedical signals (as LFP, ECoG, EEG) could possess a scale invariant structure. Scale invariance means that the structure repeats itself on subintervals of the signal. We know that the time series x(t) are scale invariant when: x[c·n]=cH·x[n]. The Hurst Exponent (H) is a dimensionless estimator for the self-similarity of a time series. Presence of scaling exponents can point to an inner fractal structure of the series. The constant c represent a scaling coefficient (c > 1 - contraction, c < dilation). The power law exponent H, is the Hurst exponent and represent a particular kind of scale invariant structure in biomedical signals. Fractal analysis or moving average estimates this power law exponent H, characteristic for time series. To compare two time series is a difficult task. For biomedical signals, usually, H is time dependent. The Hurst exponent can be used to compare time series. But a best way to describe the scale invariant structure of biosignals is the use of multifractal characterization. This kind of study for the non-stationary biological signals is based on the detrended fluctuation analysis (DFA) method. Multiple scales can be characterized through various techniques with Multifractal Spectrum (MS). Mutlifractal spectrum is a generalization of the H exponent. This paper is presenting the results of the use of detrended fluctuation analysis of multichannel EEG recordings. The main goal is the comparison of recording's fractal structure and their behavior at low and high frequency ranges. The method is proper to be used in the analysis of nonlinear and non-stationary signals.