Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros–cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks.

We propose a model for surface electromyography (EMG) signal generation with cylindrical description of the volume conductor. The model is more general and complete with respect to previous approaches. The volume conductor is described as a multilayered cylinder in which the source can be located either along the longitudinal or the angular direction, in any of the layers. The source is represented as a spatio-temporal function which describes the generation, propagation, and extinction of the intracellular action potential at the end-plate, along the fiber, and at the tendons, respectively. The layers are anisotropic. The volume conductor effect is described as a two-dimensional spatial filtering. Electrodes of any shape or dimension are simulated, forming structures which are described as spatial filters. The analytical derivation which leads to the signal in the temporal domain is performed in the spatial and temporal frequency domains. Numerical issues related to the frequency-based approach are discussed. The descriptions of the volume conductor and of the source are applied to the cases of signal generation from a limb and a sphincter muscle. Representative simulations of both cases are provided. The resultant model is based on analytical derivations and constitutes a step forward in surface EMG signal modeling, including features not described in any other analytical approach.