Nonlinear time series analysis of human alpha rhythm

G. Nolte1, T. Sander2, A. Lueschow3, B. A. Pearlmutter1
1Dept. of Computer Science, University of New Mexico, Albuquerque NM, USA
2Physikalisch-Technische Bundesanstalt, Berlin, Germany
3Neurophysics Group, Universitätsklinikum Benjamin Franklin, Berlin, Germany

Although it might seem obvious that the human brain is a nonlinear dynamical system, the detection and classification of this nonlinearity from non-invasive measurements has proven surprisingly difficult. Evidence of nonlinearity is often claimed by showing that the data significantly deviate from phase randomized versions, i.e. surrogate data. Real data, however, generally contain non-stationarities. In particular, both artifacts and the onsets and offsets of rhythmic activity will cause false positives. Here, we propose a new test which detects dynamical nonlinearity by measuring time-asymmetry, and uses surrogate data merely to estimate the standard deviation of the process. Simulations have shown that this test is robust against strong non-stationarities and static nonlinearities.

The method is applied to multi-channel MEG measurements of ongoing alpha-band activity stimulated by a simple visual memory task involving motor activity. The signal to noise ratio was enhanced using ICA, and the analysis was performed on a single separated source. We found that, if the peak at 10 Hz is accompanied by a substantial higher harmonic, time asymmetry can be detected significantly in virtually any epoch of 3 seconds duration. Finally, we applied our recently proposed method to estimate correlation dimension for noisy data. We found very satisfactory scaling plots with dimension around 1.5. As a byproduct, we showed that the nondeterministic fraction can be explained almost completely by external noise.