It is largely recognized in Neuroscience that the concept of brain connectivity (i.e., how the cortical regions communicate one to each other) is central for the understanding of the organized behavior of cortical regions beyond the simple mapping of their activity. 

At present, this organization is thought to be based on the interaction between different and differently specialized cortical sites. Cortical connectivity estimation aims at describing interactions between cortical areas as connectivity patterns holding the direction and strength of the information flow between such areas. 

Connectivity estimators based on the use of multivariate autoregressive (MVAR) models of the original time-series in the frequency domain, like for instance Directed Transfer Function (DTF) or Partial Directed Coherence (PDC) have been proposed in literature (Kaminski et al., 2001; Baccalà and Sameshima, 2001). The advantages of MVAR modeling with respect to conventional bivariate methods, like the Ordinary Coherence, has been stressed recently (Kus et al., 2004). 

The MVAR methods have been demonstrated (Baccalà and Sameshima, 2001) to rely on the key concept of Granger causality between time series [26], according to which an observed time series x(n) causes another series y(n) if the knowledge of x(n)’s past significantly improves prediction of y(n); this relation between time series is not reciprocal, i.e., x(n) may cause y(n) without y(n) necessarily causing x(n). This lack of reciprocity allows the evaluation of the direction of information flow between structures. 

Among the frequency-based connectivity estimators available in literature, the PDC is of particular interest due to its capability to properly distinguish between direct and indirect causality flows in the estimated connectivity pattern. This property is particularly interesting for the application to the study of brain signals, where the meaning of a direct connection between cortical regions is straightforward.

The properties of different multivariate estimators and their application to High Resolution EEG data during motor and cognitive tasks were provided in (Babiloni et al., 2005; Astolfi et al., 2005, 2006).

Next figure illustrates the working principles of the Directed Transfer Function, a tool able to achieve connectivity patterns from High Resolution EEG signals.