Nonlinear Quantifiers of Eeg-signal Complexity

Comparative complexity analysis of EEGsignals registered before and after exposure to strong white light was performed using nonlinear quantifiers fractal dimension and cumulative pattern entropy of the signal. Some subjects are strongly influenced by exposure to light whereas others are unresponsive. Introduction The main analytical paradigm for EEG analysis has been its spectral decomposition, resting on an assumption that the fundamental signal-generating process has stochastic properties. But new nonlinear analysis methods suggest that EEG-signal is generated by a fractal process, which contains long-range temporal correlations (cf. Watters [1] who used so called detrended fluctuation algorithm, DPA, developed by Peng et al. [2]). Signal complexity [3] can be analyzed either directly in time domain, or in frequency domain, or in the phase space. Analysis in the frequency domain requires Fourier or wavelet transform of the signal, while analysis in the phase space requires embedding of data in a multi-dimensional space. It is in the phase space where chaos meets fractals, since strange attractors have fractal dimension. But fractal analysis may be done directly in time domain. Fractal dimension [4], D , calculated this way characterizes complexity of the curve representing the signal on a plane, e.g. that of the line traced out on a moving paper tape by a pen of a classical signal recorder. Since the dimension of a plane of a line is equal to 1 and that of a plane is equal to 2, D always takes values between 1 and 2 – the greater is D (or, more precisely, the greater its fractional part is) the more complex is the signal under consideration. This fractal dimension should not be confused with fractal dimension of the attractor of the system in the phase space. In time domain calculation of D, using e.g. Higuchi’s algorithm [5-8], is much quicker and so easier to be done in real time. Another non-linear measure of signal complexity is pattern entropy [9-11], which may be calculated for multichannel signal recordings and characterizes spatio-temporal complexity of the signal. We carried out comparative analysis of EEGsignals, registered before and after exposure to different chemical agents (drugs, cf. [3,11]) and physical factors (e.g. magnetic fields [12]). Here we present analysis of complexity of EEG-signals registered before and after exposure to light. Comparison of nonlinear EEG-signal complexity quantifiers in preand post-exposure epochs reveals that light strongly influences some subjects whereas other subjects show very weak influence. This difference is not easily revealed by naked-eye inspection of EEG-records or by linear methods. Fractal dimension and Higuchi’s algorithm Higuchi’s algorithm [5-8], unlike many other methods, requires only short time intervals (about 100-500 data points) to calculate fractal dimension, D. This is very advantageous because EEG-signal remains stationary during short intervals and because in EEG analysis it is often necessary to consider short, transient events. The algorithm is fast and easy to implement. It enables compression of information a small graph of D vs. time contains information about complexity of EEG-signal of 5-10 min. and changes of value of D correlate with changes in the signal’s power spectrum. Higuchi’s algorithm is based on the measuring of the curve’s length, L(k) , by using a segment of k samples as a unit of measure [5-7]. The value of the fractal dimension DF is calculated using a least-squares best-fitting procedure as the angular coefficient of the regression line of log-log graph of the scaling law: L(k) = akF