Project of the Scientific Grant Agency VEGA 2/7087/27

Duration of the project: 01/2007 - 12/2009

Project Summary

The design of the project is focused on application and advancement of modern methods of nonlinear dynamical systems, artificial neural networks and mathematical statistics to analyze electroencephalogram signals (EEG).  Its objective lies in investigation of the dynamical states of EEG and the design of original algorithms which are capable to characterize, eventually to predict specific brain states (sleep stages, relaxation, attention decrease). The results may be applicable in neuro-diagnostics, therapy as well as in design of effective strategies of attention control.Individual methods can contribute to analysis and prediction of complex time series from different experimental areas.

Results

Research in the field of chaos theory and fractals has brought new ways of looking at complex systems through the fractal dimension. In the case of many seemingly complicated real processes, it was found that the dimension is low and could be modeled by small number of nonlinear differential equations with chaotic dynamics. But further research showed that low dimensions may also be a manifestation of a special class of stochastic systems, which generate scale-invariant, fractal-like structures. The signs which help diverging the two types of behavior include the speed of the decline in the power spectrum of high frequencies. While the exponential decrease is typical for a chaotic signal, power reduction (the so-called fractal exponent) is characteristic for stochastic systems with 1/f noise.

Also in brain electrical activity, represented by EEG, the estimates of fractal dimension have led to surprisingly low values. Our research showed that the EEG signals are characterized by a power decline of the spectrum with fractal exponent around 2.8. We found a strong correlation between the dimension and the fractal exponent. This shows that the low estimates of the dimensions of EEG should be credited to presence of scale-invariant, fractal-like structures in the data, not the deterministic chaos, but the stochastic system with 1/f noise (Krakovská, Štolc, 2008).

In the case of EEG, it appears that the hypothesis of deterministic chaos cannot be confirmed, however, the presence scale-invariant structures in the dynamics of the human brain remains an important discovery. The fact that this is a key feature of brain activity begins to be evident from the success of fractal exponent to detect specific brain activity states (phase of sleep, relaxation, loss of attention). This has been confirmed by our tests of a  large number of traditional and modern measures and indicators to compare the ability to classify sleep stages (Šušmáková, Krakovská, 2008).

Publications