Tracking EEG signal dynamics during mental tasks. A combined linear/nonlinear approach

The authors propose a combined approach using both linear and nonlinear methods to track the dynamics of short-term segments of EEG activity. This method was applied to EEG data collected during performance of voluntary movements under a condition of free choice of the instant of task performance for: (a) fine goal-directed movements to reach a chosen target, and (b) reproducing a temporal interval by twice pressing a button. In such an experimental set-up, the EEG activity is expected to change its characteristics in the short time periods passing from idle to active stage, the latter probably consisting of several successive phases. The hypothesis was that the dynamic state of EEG activity should change, and thus the EEG signal should be processed in segments with the use of different methods. Two linear methods were used: (a) singular spectrum analysis (SSA) to detect the temporal dynamic changes in decomposed segments of significant frequency bands, and (b) time-frequency analysis based on auto-regressive (AR) model coefficients, where abrupt short transients of their values were exhibited. To test whether linear techniques capture all of the information in the time series, four nonlinear methods were applied, as a function of time: point-wise dimension, Kolmogorov entropy, largest Lyapunov exponent, and nonlinear prediction. The results suggest that even in short periods, the EEG signal changes its dynamic structure, and thus different methods for dynamic analysis should be used.