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The directed transfer function (DTF) and the partial directed coherence (PDC) are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods is based on the multivariate autoregressive modelling (MVAR) of time series, which requires the stationarity of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR) and to apply it to a set of real high resolution EEG data. This approach will allow the observation of rapidly changing influences between the cortical areas during the execution of a task. The simulation results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of signal-to-noise ratio (SNR) ad number of trials. An SNR of five and a number of trials of at least 20 provide a good accuracy in the estimation. After testing the method by the simulation study, we provide an application to the cortical estimations obtained from high resolution EEG data recorded from a group of healthy subject during a combined foot-lips movement and present the time-varying connectivity patterns resulting from the application of both DTF and PDC. Two different cortical networks were detected with the proposed methods, one constant across the task and the other evolving during the preparation of the joint movement.

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The present work intends to evaluate the dynamics of the cerebral networks during the preparation and the execution of the foot movement. In order to achieve this objective, we have used mathematical tools capable of estimating the cortical activity via high-resolution EEG techniques. Afterwards we estimated, the instantaneous relationships occurring among the time-series of sixteen regions of interest (ROIs) in the Alpha (7-12 Hz) and Beta (13-29 Hz) band through the adaptive multivariate autoregressive models. Eventually, we evaluated the weighted-topology of the cerebral networks by calculating some theoretical graph indexes. The results show that the main structural changes are encoded in the highest spectral contents (Beta band). In particular, during the execution of the foot movement the cingulate motor areas (CM) work as network "hubs" presenting a large amount of outgoing links to the other ROIs. Moreover, the connectivity pattern changes its structure according to the different temporal stages of the task. In particular, the communication between the ROIs reaches its highest level of efficiency during the preparation of the foot movement, as revealed by the "small-world" property of the network, which is characterized by the presence of abundant clustering connections combined with short average distances between the cortical areas.

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Several imaging techniques have identified different brain areas involved in the processing of noxious stimulation and thus in the constitution of pain. However, only little is known how these brain areas communicate with one another after activation by stimulus processing and which areas directionally affect or modulate the activity of succeeding areas. One measure for the analysis of such interactions is represented by the Granger Causality Index (GCI). In applying time-varying bivariate and partial variants of this concept (tvGCI), the aim of the present study was to investigate the interaction of neural activities between a set of scalp electrodes that best represent the brain electrical neural activity of major cortical areas involved in the processing of noxious laser-heat stimuli and their variation in time. Bivariate and partial tvGCIs were calculated within four different intervals of laser-evoked event-related potentials (LEPs) including a baseline period prior to stimulus application and three intervals immediately following stimulus application, i.e., between 170 and 200 ms (at the N2 component), between 260 and 320 ms (P2 component), and between 320 and 400 ms (P3 component of LEPs). Results show some similarities, but also some striking differences between bivariate and partial tvGCIs. These differences might be explained by the nature of bivariate and partial tvGCIs. However, both tvGCI approaches revealed a directed interaction between medial and lateral electrodes of the centroparietal region. This result was interpreted as a directed interaction between the anterior cingulate cortex and the secondary somatosensory cortex and the insula, structures that are significantly involved in the constitution of pain.

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Several analysis techniques have been developed for time series to detect interactions in multidimensional dynamic systems. When analyzing biosignals generated by unknown dynamic systems, awareness of the different concepts upon which these analysis techniques are based, as well as the particular aspects the methods focus on, is a basic requirement for drawing reliable conclusions. For this purpose, we compare four different techniques for linear time series analysis. In general, these techniques detect the presence of interactions, as well as the directions of information flow, in a multidimensional system. We review the different conceptual properties of partial coherence, a Granger causality index, directed transfer function, and partial directed coherence. The performance of these tools is demonstrated by application to linear dynamic systems.