Symbolic joint entropy reveals the coupling of various brain regions

The convergence and divergence of oscillatory behavior of different brain regions are very important for the procedure of information processing. Measurements of coupling or correlation are very useful to study the difference of brain activities. In this study, EEG signals were collected from ten subjects under two conditions, i.e. eyes closed state and idle with eyes open. We propose a nonlinear algorithm, symbolic joint entropy, to compare the coupling strength among the frontal, temporal, parietal and occipital lobes and between two different states. Instead of decomposing the EEG into different frequency bands (theta, alpha, beta, gamma etc.), the novel algorithm is to investigate the coupling from the entire spectrum of brain wave activities above 4Hz. The coupling coefficients in two states with different time delay steps are compared and the group statistics are presented as well. We find that the coupling coefficient of eyes open state with delay consistently lower than that of eyes close state across the group except for one subject, whereas the results without delay are not consistent. The differences between two brain states with non-zero delay can reveal the intrinsic inter-region coupling better. We also use the well-known Hénon map data to validate the algorithm proposed in this paper. The result shows that the method is robust and has a great potential for other physiologic time series.