Fig. 1
Snapshots from the animation showing the time-varying pattern of propagations for the representative subject. The numbers in the upper left corner correspond to the time [s] after the stimulus presentation
We have defined as local: connections between the neighboring electrodes in the (10–20) system and these along the diagonals of squares formed by the neighboring electrodes and as distant all other connections. Inspection of time courses of long range and short range connections revealed that at the moment of the premise presentation for all frequency bands long- and short- range connectivities were in phase and in the consecutive 3 s period they were mostly out of phase. The estimated ratio of short to long connections was in the range: 1.4 for theta to 1.5 for beta rhythm [7]. Frontal, central and two parietal modules were identified and the strength of intra-modular and inter-modular couplings were found.
4 Discussion
In CAT test the transmission between prefrontal and frontal areas observed during the initial phase complies with the involvement of frontal lobes and especially the PFC in information storage and working memory [8]. The observation of the burst of activity in target condition in beta and gamma band from C3 (contralateral finger motor cortex) is compatible with a well known phenomena of gamma activation and beta rebound connected with hand movement [9]. In case of non–target the long-range transmissions occurred either from the electrode F8 overlying rIFC (six subjects) or from premSMA (three subjects) to the finger primary motor cortex. Both structures are known to be connected with “go/no go” tasks [10, 11]. The observation of transmission between distant locations for no-go tasks (e.g. between F8 and C3) is concordant with the hypothesis that inhibition of motor structures originates from long-range cortico-cortical connections [12].
In a similar experiment involving semantic priming task Schinkel et al. [13] applied as a connectivity measure joined recurrence plots followed by graph theoretical analysis. For primed stimuli almost uniform pattern of connections emerged, which was interpreted as existence of one large network component. For unprimed stimuli broadly distributed left-lateralized network components were reported. These results have no support in imaging or electrophysiological evidence.
The role of short- and long-range connections in information processing was even better visible in the working memory experiment. In our study concerning the WM task the involvement of the frontal and posterior parietal regions was observed, which is in an excellent agreement with the imaging studies [6, 14]. Sauseng et al. [15] showed that fronto-parietal coherence in theta and upper alpha reflect central executive functions of working memory.
Working memory tasks were analyzed also by means of pairwise measures of connectivity and graph theoretical analysis. Connectivity in WM tasks (namely 2Back check) was studied by Micheloyanis et al. [16] in EEG experiment and by Kitzbichler et al. [17] by means of MEG. In both studies the connectivity patterns were close to random, with some traits of “small world” structure. The patterns of connections were very dense and did not indicate the brain regions involved in the information processing.
The lack of correspondence of the above works with our findings and other evidence may be explained by the methodological flaws present in the quoted publications. Namely the bivariate measures applied in them produce a lot of spurious connections which was demonstrated in [18, 19]. In fact, because of common feeding effect, spurious connections may outnumber the true ones. If the activity of a given source is recorded at N electrodes N true and N(N–1)/2 false connections may be found by bivariate measures. The common practice in graph theoretical analysis, of setting the threshold very low and giving all connections equal weight, further enhances such spurious connections. As a result a very dense, disorganized and close to random architecture of connectivity emerges.
Application of multivariate measure such as DTF allows for determination of connectivity patterns and quantitative description of their structure, including the dependence on frequency and the contribution of short- and long- range interactions. By means of the proposed formalism it was possible: to determine the modular structure of the brain networks, to found the intra- and inter-modular couplings and estimate their strength. Moreover the dynamic patterns of the interactions were identified involving intra-modular persistent coupling during the task, whereas the coupling between distant locations was less frequent. We have for the first time reported the dynamics of the interaction between the modules, showing that the exchange of information is taking place in certain specific moments.

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