Time-delayed mutual information of the phase as a measure of functional connectivity

We propose a time-delayed mutual information of the phase for detecting nonlinear synchronization in electrophysiological data such as MEG. Palus already introduced the mutual information as a measure of synchronization. To obtain estimates on small data-sets as reliably as possible, we adopt the numerical implementation as proposed by Kraskov and colleagues. An embedding with a parametric time-delay allows a reconstruction of arbitrary nonstationary connective structures--so-called connectivity patterns--in a wide class of systems such as coupled oscillatory or even purely stochastic driven processes. By using this method we do not need to make any assumptions about coupling directions, delay times, temporal dynamics, nonlinearities or underlying mechanisms. For verifying and refining the methods we generate synthetic data-sets by a mutual amplitude coupled network of Rössler oscillators with an a-priori known connective structure. This network is modified in such a way, that the power-spectrum forms a 1/f power law, which is also observed in electrophysiological recordings. The functional connectivity measure is tested on robustness to additive uncorrelated noise and in discrimination of linear mixed input data. For the latter issue a suitable de-correlation technique is applied. Furthermore, the compatibility to inverse methods for a source reconstruction in MEG such as beamforming techniques is controlled by dedicated dipole simulations. Finally, the method is applied on an experimental MEG recording.