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FRACTAL ANALYSIS OF MULTI-CHANNEL EEG-DATA IN PATIENTS WITH SEASONAL AFFECTIVE DISORDER

Fractal analysis of multi-channel EEG-data enables data reduction without loosing important information and is very resistant to noise. It may be used as EEG-signal quantifier to assess impact of photo-therapy in patients with SAD. Introduction Brain activity shows non-linear chaotic-like phenomena, which in turn are reflected in EEG data. Diminishing chaos in the brain may lead to serious pathology, such as epileptic seizures [1] it is healthy to be chaotic. Therefore it is not surprised that in analysis of multi-channel EEG data one may use methods of non-linear dynamics and deterministic chaos theory to assess state of the brain, possible pathological changes, and the influence of applied therapy. Therapy of some pathological states may be based on techniques which control chaos in the brain, using either chemicals (drugs) or physical fields (electro-shocks, magnetotherapy, phototherapy). So called Bright Light Therapy (BLT), which involves exposure of eyes to intense level of light under controlled conditions, is applied in patients with Seasonal Affective Disorder (SAD) [2]. Also called Seasonal Depressions it can be so severe. that those sufferring feel unable to function normally; about five times as many people suffer from a sub-clinical level of SAD. Therapeutic mechanism of BLT is still unclear. Methods For data collection we used EEG Digitrack system (ELMIKO) with 16 channels. Sampling frequency was 128 Hz.. Files for analysis were extracted from standard EEG-records, for each subject the first recording done before BLT and the second 2 weeks after BLT treatment. Previously, while searching for quantitative descriptors of multi-channel EEG data [3] which could be relatively easily and quickly calculated so to help doctors in assessing the applied therapy, we computed KL-transforms of the signals and several standard chaotic quantifiers for each of 16 channels (time delay, needed for attractor reconstruction using Taken’s method, by the first zero crossing of autocorrelation function; embedding dimension by saturation of correlation dimension; pointwise correlation dimension; the largest Lyapunov exponent). However, the results obtained show no consistent pattern of changes when EEG-signals before and after therapy are compared. Moreover, calculation of some of these quantifiers requires long stationary EEG-signal epochs and needs relatively long time. We think that quantifiers which do not require attractor reconstruction but are calculated directly from the EEG-signal may be more appropriate for medical application. Fractal dimension of EEG-signal, Df , calculated using Higuchi’s algorithm [4,5] seems to be the most promissing of such quantifiers. Df measures complexity of the curve for a simple curve Df is equal 1, for a curve which nearly fills out the plane Df is close to 2. Since the time series of EEGsignal amplitude registered on a selected channel may be considered a representation of a plane curve (for many years EEG was registered in a form of curves on a band of paper) Df may be used to characterize EEG-signal. Results About 100 points is enough to calculate fractal dimension, Df , using Higuchi’s algorithm. If Df is calculated for subsequent 1 sec. intervals with 10% overlap on both ends, one gets about 100-times data-reduction (with 128 Hz sampling). Df is independent of signal scaling, very resistant to noise, and shows characteristical changes with changing of brain state, e.g. with eyes opening or closing. Df calculated from EEG-data is usually between 1.2 and 1.8; for random data Df is close to 2 while for Gaussian noise it is about 1.3 (Fig. 1). For surrogate data obtained from the given epoch of EEGdata characteristical changes in Df completely disappear (Fig. 2). It brought us an idea to use changes in Df during eyes-opening and eyes-closing as a quantitative descriptors of multi-channel EEG data.