Measures of coupling between neural populations based on Granger causality principle

This paper shortly reviews the measures used to estimate neural synchronization in experimental settings. Our focus is on multivariate measures of dependence based on the Granger causality (G-causality) principle, their applications and performance in respect of robustness to noise, volume conduction, common driving, and presence of a weak node. Application of G-causality measures to EEG, intracranial signals and fMRI time series is addressed. G-causality based measures defined in the frequency domain allow the synchronization between neural populations and the directed propagation of their electrical activity to be determined. The time-varying G-causality based measure Short-time Directed Transfer Function (SDTF) supplies information on the dynamics of synchronization and the organization of neural networks. Inspection of effective connectivity patterns indicates a modular structure of neural networks, with a stronger coupling within modules than between them. The hypothetical plausible mechanism of information processing, suggested by the identified synchronization patterns, is communication between tightly coupled modules intermitted by sparser interactions providing synchronization of distant structures

Parameters of SSVEP structures provided by both dictionaries in P4 channel.

<p>(E-enriched dictionary, G-Gabor dictionary)</p><p>Parameters of SSVEP structures provided by both dictionaries in P4 channel.</p

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Parameters of TOAE structures provided by standard Gabor dictionary.

<p>Parameters of TOAE structures provided by standard Gabor dictionary.</p

Time-frequency distributions obtained by: A—windowed Fourier transform (spectrogram), B—Rihaczek transform, C—Morlet wavelets, D—Wigner de Ville transform, E—MP with the enriched dictionary, F—MP with the Gabor dictionary.

<p>Components of simulated signal consisting of asymmetric waveform of frequency 15 Hz and two spindles of frequencies 12 Hz and 10 Hz are shown at the very top of the picture. On the horizontal axis time, on the vertical axis frequency in Hz. The colors represent: for four upper panels energy and for two lowest panels amplitude (red the strongest, dark blue the weakest).</p

Parameters of SSVEP structures provided by both dictionaries in O2 channel.

<p>(E-enriched dictionary, G-Gabor dictionary)</p><p>Parameters of SSVEP structures provided by both dictionaries in O2 channel.</p

Examples of functions with different asymmetry used in the enriched dictionary.

<p>Examples of functions with different asymmetry used in the enriched dictionary.</p

Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization - Fig 5

<p>The decomposition of the TOAE signal shown at the very top; obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below the time-frequency-amplitude maps, at the bottom the first five (strongest) atoms of the decomposition. The maxima of amplitudes of the first five atoms are marked by crosses.</p

Parameters of TOAE structures provided by enriched dictionary.

<p>Parameters of TOAE structures provided by enriched dictionary.</p