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Despite the well-established use of partial directed coherence (PDC) to estimate interactions between brain signals, the assessment of its statistical significance still remains controversial. Commonly used approaches are based on the generation of empirical distributions of the null case, implying a considerable computational time, which may become a serious limitation in practical applications. Recently, rigorous asymptotic distributions for PDC were proposed. The aim of this work is to compare the performances of the asymptotic statistics with those of an empirical approach, in terms of both accuracy and computational time., Methods: Indices of performance were derived for the two approaches by a simulation study implementing different ground-truth networks under different levels of signal-to-noise ratio and amount of data available for the estimate. The two approaches were then applied to the resting-state EEG data acquired in a group of minimally conscious state and vegetative state/unresponsive wakefulness syndrome patients., Results: The performances of the asymptotic statistics in simulations matched those obtained by the empirical approach, with a considerable reduction of the computational time. Results of the application to real data showed that the asymptotic statistics led to the extraction of connectivity-based indices able to discriminate patients in different disorders of consciousness conditions and to correlate significantly with clinical scales. Such results were similar to those obtained by the empirical assessment, but with a considerable time economy., Significance: Asymptotic statistics provide an approach to the assessment of PDC significance with comparable performances with respect to the previously used empirical approaches but with a substantial advantage in terms of computational time.

Hyperscanning consists in the simultaneous recording of hemodynamic or neuroelectrical signals from two or more subjects acting in a social context. Well-established methodologies for connectivity estimation have already been adapted to hyperscanning purposes. The extension of graph theory approach to multi-subjects case is still a challenging issue. In the present work we aim to test the ability of the currently used graph theory global indices in describing the properties of a network given by two interacting subjects. The testing was conducted first on surrogate brain-to-brain networks reproducing typical social scenarios and then on real EEG hyperscanning data recorded during a Joint Action task. The results of the simulation study highlighted the ability of all the investigated indexes in modulating their values according to the level of interaction between subjects. However, only global efficiency and path length indexes demonstrated to be sensitive to an asymmetry in the communication between the two subjects. Such results were, then, confirmed by the application on real EEG data. Global efficiency modulated, in fact, their values according to the inter-brain density, assuming higher values in the social condition with respect to the non-social condition.

Partial Directed Coherence (PDC) is a powerful estimator of effective connectivity. In neuroscience it is used in different applications with the aim to investigate the communication between brain regions during the execution of different motor or cognitive tasks. When multiple trials are available, PDC can be computed over multiple realizations, provided that the assumption of stationarity across trials is verified. This allows to improve the amount of data, which is an important constraint for the estimation accuracy. However, the stationarity of the data across trials is not always guaranteed, especially when dealing with patients. In this study we investigated how the inter-trials variability of an EEG dataset affects the PDC accuracy. Effects of density variations and of changes of connectivity values across trials were first investigated with a simulation study and then tested on real EEG data collected from two post-stroke patients during a motor imagery task and characterized by different inter-trials variability. Results showed the effect of different factors on the PDC accuracy and the robustness of such estimator in a range of conditions met in practical applications.

For the past decade, the detection and quantification of interactions within and between physiological networks has become a priority-in-common between the fields of biomedicine and computer science. Prominent examples are the interaction analysis of brain networks and of the cardiovascular-respiratory system. The aim of the study is to show how and to what extent results from time-variant partial directed coherence analysis are influenced by some basic estimator and data parameters. The impacts of the Kalman filter settings, the order of the autoregressive (AR) model, signal-to-noise ratios, filter procedures and volume conduction were investigated. These systematic investigations are based on data derived from simulated connectivity networks and were performed using a Kalman filter approach for the estimation of the time-variant multivariate AR model. Additionally, the influence of electrooculogram artefact rejection on the significance and dynamics of interactions in 29 channel electroencephalography recordings, derived from a photic driving experiment, is demonstrated. For artefact rejection, independent component analysis was used. The study provides rules to correctly apply particular methods that will aid users to achieve more reliable interpretations of the results.

The evaluation of the topological properties of brain networks is an emergent research topic, since the estimated cerebral connectivity patterns often have relatively large size and complex structure. Since a graph is a mathematical representation of a network, the use of a theoretical graph approach would describe concisely the topological features of the functional brain connectivity network estimated using neuroimaging techniques. In the present study, we analyze the changes in brain synchronization networks using high-resolution EEG signals obtained during performance of a complex goal-directed visuomotor task. Our results show that the cortical network is more stable when subjects reach the goal than when they fail by hitting an obstacle. These findings suggest the presence of a possible cerebral "marker" for motor actions that result in successful reaching of a target.

In this paper, different linear and nonlinear methodologies for the estimation of cortical connectivity from neuroelectric and hemodynamic measurements are reviewed and applied on common data set in order to highlight similarities and differences in the results. Different effective and functional connectivity methods were applied to motor and cognitive data sets, including structural equation modeling (SEM), directed transfer function (DTF), partial directed coherence (PDC), and direct directed transfer function (dDTF). Comparisons were made between the results in order to understand if, for a same dataset, effective and functional connectivity estimators can return the same cortical connectivity patterns. An application of a nonlinear method [phase synchronization index (PSI)] to similar executed and imagined movements was also reviewed. Connectivity patterns estimated with the use of the neuroelectric information and of the information from the multimodal integration of neuroelectric and hemodynamic data were also compared. Results suggests that the estimation of the cortical connectivity patterns performed with the linear methods (SEM, DTF, PDC, dDTF) or with the nonlinear method (PSI) on movement related potentials returned similar cortical networks. Differences in cortical connectivity were noted between the patterns estimated with the use of multimodal integration and those estimated by using only the neuroelectric data.

In the present work, a neural mass model consisting of four interconnected neural groups (pyramidal neurons, excitatory interneurons, inhibitory interneurons with slow synaptic kinetics, and inhibitory interneurons with fast synaptic kinetics) is used to investigate the mechanisms which cause the appearance of multiple rhythms in EEG spectra, and to assess how these rhythms can be affected by connectivity among different populations. In particular, we analyze a circuit, composed of three interconnected populations, each with a different synaptic kinetics (hence, with a different intrinsic rhythm). Results demonstrate that a single population can exhibit many different simultaneous rhythms, provided that some of these come from external sources (for instance, from remote regions). Analysis of coherence, and of the position of peaks in power spectral density, reveals important information on the possible connections among populations, especially useful to follow temporal changes in connectivity. Subsequently, the model is validated by comparing the power spectral density simulated in one population with that computed in the controlateral cingulated cortex (a region involved in motion preparation) during a right foot movement task in four normal subjects. The model is able to simulate real spectra quite well with only moderate parameter changes within the subject. In perspective, the results may be of value for a deeper comprehension of mechanism causing EEGs rhythms, for the study of brain connectivity and for the test of neurophysiological hypotheses.

Assessment of brain connectivity among different brain areas during cognitive or motor tasks is a crucial problem in neuroscience today. Aim of this work is to use a neural mass model to assess the effect of various connectivity patterns in cortical electroencephalogram (EEG) power spectral density, and investigate the possibility to derive connectivity circuits from EEG data. To this end, a model of an individual region of interest (ROI) has been built as the parallel arrangement of three populations, each described as in Wendling et al. (Eur J Neurosci 15:1499-1508, 2002). Connectivity among ROIs includes three parameters, which specify the strength of connection in the different frequency bands. The following main steps have been followed: (1) we analyzed how the power spectral density (PSD) is significantly modified by the kind of coupling hypothesized among the ROIs; (2) with the model, and using an automatic fitting procedure, we looked for a simple connectivity circuit able to reproduce PSD of cortical EEG in three ROIs during a finger-movement task. The estimated parameters represent the strength of connections among the ROIs in the different frequency bands. Cortical EEGs were computed with an inverse propagation algorithm, starting from measurement performed with 96 electrodes on the scalp. The present study suggests that the model can be used as a simulation tool, able to mimic the effect of connectivity on EEG. Moreover, it can be used to look for simple connectivity circuits, able to explain the main features of observed cortical PSD. These results may open new prospectives in the use of neurophysiological models, instead of empirical models, to assess effective connectivity from neuroimaging information.

Static hemodynamic or neuroelectric images of brain regions activated during particular tasks do not convey the information of how these regions communicate to each other. Cortical connectivity estimation aims at describing these interactions as connectivity patterns which hold the direction and strength of the information flow between cortical areas. In this study, we attempted to estimate the causality between distributed cortical systems during a movement volition task in preparation for execution of simple movements by a group of normal healthy subjects and by a group of Spinal Cord Injured (SCI) patients. To estimate the causality between the spatial distributed patterns of cortical activity in the frequency domain, we applied a series of processing steps on the recorded EEG data. From the high-resolution EEG recordings we estimated the cortical waveforms for the regions of interest (ROIs), each representing a selected sensor group population. The solutions of the linear inverse problem returned a series of cortical waveforms for each ROI considered and for each trial analyzed. For each subject, the cortical waveforms were then subjected to Independent Component Analysis (ICA) pre-processing. The independent components obtained by the application of the ThinICA algorithm were further processed by a Partial Directed Coherence algorithm, in order to extract the causality between spatial cortical patterns of the estimated data. The source-target cortical dependencies found in the group of normal subjects were relatively similar in all frequency bands analyzed. For the normal subjects we observed a common source pattern in an ensemble of cortical areas including the right parietal and right lip primary motor areas and bilaterally the primary foot and posterior SMA areas. The target of this cortical network, in the Granger-sense of causality, was shown to be a smaller network composed mostly by the primary foot motor areas and the posterior SMA bilaterally. In the case of the SCI population, both the source and the target cortical patterns had larger sizes than in the normal population. The source cortical areas included always the primary foot and lip motor areas, often bilaterally. In addition, the right parietal area and the bilateral premotor area 6 were also involved. Again, the patterns remained substantially stable across the different frequency bands analyzed. The target cortical patterns observed in the SCI population had larger extensions when compared to the normal ones, since in most cases they involved the bilateral activation of the primary foot movement areas as well as the SMA, the primary lip areas and the parietal cortical areas.

Over the last 20 years, a body of techniques known as high resolution EEG has allowed precise estimation of cortical activity from non-invasive EEG measurements. The availability of cortical waveforms from non-invasive EEG recordings allows to have not only the level of activation within a single region of interest (ROI) during a particular task, but also to estimate the causal relationships among activities of several cortical regions. However, interpreting resulting connectivity patterns is still an open issue, due to the difficulty to provide an objective measure of their properties across different subjects or groups. A novel approach addressed to solve this difficulty consists in manipulating these functional brain networks as graph objects for which a large body of indexes and tools are available in literature and already tested for complex networks at different levels of scale (Social, WorldWide-Web and Proteomics). In the present work, we would like to show the suitability of such approach, showing results obtained comparing separately two groups of subjects during the same motor task and two different motor tasks performed by the same group. In the first experiment two groups of subjects (healthy and spinal cord injured patients) were compared when they moved and attempted to move simultaneously their right foot and lips, respectively. The contrast between the foot-lips movement and the simple foot movement was addressed in the second experiment for the population of the healthy subjects. For both the experiments, the main question is whether the "architecture" of the functional connectivity networks obtained could show properties that are different in the two groups or in the two tasks. All the functional connectivity networks gathered in the two experiments showed ordered properties and significant differences from "random" networks having the same characteristic sizes. The proposed approach, based on the use of indexes derived from graph theory, can apply to cerebral connectivity patterns estimated not only from the EEG signals but also from different brain imaging methods.

The aim of this work is to characterize quantitatively the performance of a body of techniques in the frequency domain for the estimation of cortical connectivity from high-resolution EEG recordings in different operative conditions commonly encountered in practice. Connectivity pattern estimators investigated are the Directed Transfer Function (DTF), its modification known as direct DTF (dDTF) and the Partial Directed Coherence (PDC). Predefined patterns of cortical connectivity were simulated and then retrieved by the application of the DTF, dDTF, and PDC methods. Signal-to-noise ratio (SNR) and length (LENGTH) of EEG epochs were studied as factors affecting the reconstruction of the imposed connectivity patterns. Reconstruction quality and error rate in estimated connectivity patterns were evaluated by means of some indexes of quality for the reconstructed connectivity pattern. The error functions were statistically analyzed with analysis of variance (ANOVA). The whole methodology was then applied to high-resolution EEG data recorded during the well-known Stroop paradigm. Simulations indicated that all three methods correctly estimated the simulated connectivity patterns under reasonable conditions. However, performance of the methods differed somewhat as a function of SNR and LENGTH factors. The methods were generally equivalent when applied to the Stroop data. In general, the amount of available EEG affected the accuracy of connectivity pattern estimations. Analysis of 27 s of nonconsecutive recordings with an SNR of 3 or more ensured that the connectivity pattern could be accurately recovered with an error below 7% for the PDC and 5% for the DTF. In conclusion, functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in most EEG recordings by combining high-resolution EEG techniques, linear inverse estimation of the cortical activity, and frequency domain multivariate methods such as PDC, DTF, and dDTF.

Neural mass models have been used for many years to study the macroscopic dynamics of neural populations in a simple and computationally inexpensive way. In this paper, we modified a model proposed by Wendling et al. [Wendling F, Bartolomei F, Bellanger JJ, Chauvel P. Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur J Neurosci 2002;15:1499-508] to simulate EEG power spectral density (PSD) in some regions of interest (ROIs) during simple tasks (finger movement or working memory tests). The work consists of two subsequent stages: (1) in the first we evaluated the role of some model parameters (i.e., average gain of synapses and their time constants) in affecting power spectral density. This analysis confirmed the possibility to simulate various EEG rhythms (in the alpha, beta and gamma frequency ranges) by modifying just the time constants of the synapses. The position of the individual rhythms (i.e., the corresponding peaks in the PSD) can be finely tuned acting on the average gain of fast inhibitory synapses. This analysis suggested that a single neural mass model produces a unimodal spectrum, which can be finely adjusted, but cannot mimic the overall complexity of EEG in an entire cortical area. (2) Hence, in the second stage we built a model of a ROI by combining three neural mass models arranged in parallel. With this model, and using an automatic fitting procedure, we carefully reproduced the PSD of cortical EEG in several ROIs during finger movement, and their temporal changes during a working memory task, by estimating nine parameters. The estimated parameters represent the excitation of each population (mean value and variance of exogenous input noise) and the average gain of fast inhibitory synapses. Cortical EEGs were computed with an inverse propagation algorithm, starting from measurement performed with a high number of electrodes on the scalp (46-96). Results show that the proposed model is able to mimic PSD of cortical activity acting on a few parameters, which represent external activation and short-time synaptic changes. This information may be exploited to reach a quantitative summary of electrical activity in ROIs during a task, and to derive information on connectivity, starting from non-invasive EEG measurements.

The aim of this paper is to test a technique called partial directed coherence (PDC) and its modification (squared PDC; sPDC) for the estimation of human cortical connectivity by means of simulation study, in which both PDC and sPDC were studied by analysis of variance. The statistical analysis performed returned that both PDC and sPDC are able to estimate correctly the imposed connectivity patterns when data exhibit a signal-to-noise ratio of at least 3 and a length of at least 27 s of nonconsecutive recordings at 250 Hz of sampling rate, equivalent, more generally, to 6750 data samples.

In the last decade, the possibility to noninvasively estimate cortical activity has been highlighted by the application of the techniques known as high resolution EEG. These techniques include a subject's multi-compartment head model (scalp, skull, dura mater, cortex) constructed from individual magnetic resonance images, multi-dipole source model, and regularized linear inverse source estimates of cortical current density. The aim of this paper is to demonstrate that the use of cortical activity estimated from noninvasive EEG recordings of motor imagery is useful in the context of a brain computer interface as compared with others scalp spatial filters usually used on-line.

Eye movements and blinks may produce unusual voltage changes that propagates from the eyeball through the head as volume conductor up to the scalp electrodes, generating severe electroencephalographic artifacts. Several methods are now available to correct the distortion induced by these events on the EEG, having different advantages and drawbacks. The main focus of this work is to quantify the performance of the removal of EOG artifact due to the application of the independent component analysis (ICA) methodology. The precise quantification of the effects of artifact removal by ICA is possible by using a simulation setup, with a realistic head model, that it is able to mimic the occurrence of an eye blink. The electrical activity generated by the simulated eyeblink were propagated through the realistic head model and superimposed to a clean segment of EEG. Then, artifact removal was performed by using the ICA approach. Ocular artifact removal was evaluated in different operative conditions, characterized by different signal to noise ratio and number of electrodes. The error measures used were the relative error and the correlation coefficient between the clear, original EEG segment and those obtained after the application of the ICA procedure.

Assessment of brain connectivity among different brain areas during cognitive or motor tasks is a crucial problem in neuroscience today. Aim of this work is to use a neural mass model to assess the effect of various connectivity patterns in the power spectral density (PSD) of cortical EEG, and investigate the possibility to derive connectivity circuits from real EEG data. To this end, a model of an individual region of interest (ROI) has been built as the parallel arrangement of three populations. The present study suggests that the model can be used as a simulation tool, able to produce reliable intracortical EEG signals. Moreover, it can be used to look for simple connectivity circuits, able to explain the main features of observed cortical PSD. These results may open new prospective in the use of neurophysiological models, instead of empirical models, to assess effective connectivity from neuroimaging information.

Today, the concept of brain connectivity plays a central role in the neuroscience. While functional connectivity is defined as the temporal coherence between the activities of different brain areas, the effective connectivity is defined as the simplest brain circuit that would produce the same temporal relationship as observed experimentally between cortical sites. The most used method to estimate effective connectivity in neuroscience is the structural equation modeling (SEM), typically used on data related to the brain hemodynamic behavior. However, the use of hemodynamic measures limits the temporal resolution on which the brain process can be followed. The present research proposes the use of the SEM approach on the cortical waveforms estimated from the high-resolution EEG data, which exhibits a good spatial resolution and a higher temporal resolution than hemodynamic measures. We performed a simulation study, in which different main factors were systematically manipulated in the generation of test signals, and the errors in the estimated connectivity were evaluated by the analysis of variance (ANOVA). Such factors were the signal-to-noise ratio and the duration of the simulated cortical activity. Since SEM technique is based on the use of a model formulated on the basis of anatomical and physiological constraints, different experimental conditions were analyzed, in order to evaluate the effect of errors made in the a priori model formulation on its performances. The feasibility of the proposed approach has been shown in a human study using high-resolution EEG recordings related to finger tapping movements.

Different brain imaging devices are presently available to provide images of the human functional cortical activity, based on hemodynamic, metabolic or electromagnetic measurements. However, static images of brain regions activated during particular tasks do not convey the information of how these regions are interconnected. The concept of brain connectivity plays a central role in the neuroscience, and different definitions of connectivity, functional and effective, have been adopted in literature. While the functional connectivity is defined as the temporal coherence among the activities of different brain areas, the effective connectivity is defined as the simplest brain circuit that would produce the same temporal relationship as observed experimentally among cortical sites. The structural equation modeling (SEM) is the most used method to estimate effective connectivity in neuroscience, and its typical application is on data related to brain hemodynamic behavior tested by functional magnetic resonance imaging (fMRI), whereas the directed transfer function (DTF) method is a frequency-domain approach based on both a multivariate autoregressive (MVAR) modeling of time series and on the concept of Granger causality. This study presents advanced methods for the estimation of cortical connectivity by applying SEM and DTF on the cortical signals estimated from high-resolution electroencephalography (EEG) recordings, since these signals exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. To estimate correctly the cortical signals, we used a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from individual MRI, a distributed source model and a regularized linear inverse source estimates of cortical current density. Before the application of SEM and DTF methodology to the cortical waveforms estimated from high-resolution EEG data, we performed a simulation study, in which different main factors (signal-to-noise ratio, SNR, and simulated cortical activity duration, LENGTH) were systematically manipulated in the generation of test signals, and the errors in the estimated connectivity were evaluated by the analysis of variance (ANOVA). The statistical analysis returned that during simulations, both SEM and DTF estimators were able to correctly estimate the imposed connectivity patterns under reasonable operative conditions, that is, when data exhibit an SNR of at least 3 and a LENGTH of at least 75 s of nonconsecutive EEG recordings at 64 Hz of sampling rate. Hence, effective and functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high-resolution EEG techniques and linear inverse estimation with SEM or DTF methods. We conclude that the estimation of cortical connectivity can be performed not only with hemodynamic measurements, but also with EEG signals treated with advanced computational techniques.

Many recent neuroimaging studies of episodic memory have indicated an asymmetry in prefrontal involvement, with the left prefrontal cortex more involved than the right in encoding, the right more than the left in retrieval (hemispheric encoding and retrieval asymmetry, or HERA model). In this electroencephalographic (EEG) high-resolution study, we studied brain rhythmicity during a visual episodic memory (recognition) task. The theta (4-6 Hz), alpha (6-12 Hz) and gamma (28-48 Hz) oscillations were investigated during a visuospatial long-term episodic memory task including an encoding (ENC) and retrieval (RET) phases. During the ENC phase, 25 figures representing interiors of buildings ("indoor") were randomly intermingled with 25 figures representing landscapes ("landscapes"). Subject's response was given at left ("indoor") or right ("landscapes") mouse button. During the RET phase (1 h later), 25 figures representing previously presented "indoor" pictures ("tests") were randomly intermingled with 25 figures representing novel "indoor" ("distractors"). Again, a mouse response was required. Theta and alpha EEG results showed no change of frontal rhythmicity. In contrast, the HERA prediction of asymmetry was fitted only by EEG gamma responses, but only in the posterior parietal areas. The ENC phase was associated with gamma EEG oscillations over left parietal cortex. Afterward, the RET phase was associated with gamma EEG oscillations predominantly over right parietal cortex. The predicted HERA asymmetry was thus observed in an unexpected location. This discrepancy may be due to the differential sensitivity of neuroimaging methods to selected components of cognitive processing. The strict relation between gamma response and perception suggests that retrieval processes of long-term memory deeply impinged upon sensory representation of the stored material.

In this chapter, advanced methods for the modeling of human cortical activity from combined high-resolution electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data are reviewed. These methods include a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from magnetic resonance images, multidipole source model, and regularized linear inverse source estimates. Determination of the priors in the resolution of the linear inverse problem was performed with the use of information from the hemodynamic responses of the cortical areas as revealed by block-designed (strength of activated voxels) and event-related (coupling of activated voxels) fMRI. As an example, these methods were applied to EEG (128 electrodes) and fMRI data, which were recorded in separate sessions while normal subjects executed voluntary right one-digit movements.

Previous simulation studies have stressed the importance of the use of fMRI priors in the estimation of cortical current density. However, no systematic variations of signal-to-noise ratio (SNR) and number of electrodes were explicitly taken into account in the estimation process. In this simulation study we considered the utility of including information as estimated from fMRI. This was done by using as the dependent variable both the correlation coefficient and the relative error between the imposed and the estimated waveforms at the level of cortical region of interests (ROI). A realistic head and cortical surface model was used. Factors used in the simulations were the different values of SNR of the scalp-generated data, the different inverse operators used to estimated the cortical source activity, the strengths of the fMRI priors in the fMRI-based inverse operators, and the number of scalp electrodes used in the analysis. Analysis of variance results suggested that all the considered factors significantly afflict the correlation and the relative error between the estimated and the simulated cortical activity. For the ROIs analyzed with simulated fMRI hot spots, it was observed that the best estimation of cortical source currents was performed with the inverse operators that used fMRI information. When the ROIs analyzed do not present fMRI hot spots, both standard (i.e., minimum norm) and fMRI-based inverse operators returned statistically equivalent correlation and relative error values.

EEG-based Brain Computer Interfaces (BCIs) require on-line detection of mental states from spontaneous EEG signals. In this framework, it was suggested that EEG patterns can be better detected with EEG data transformed with Surface Laplacian computation (SL) than with the unprocessed raw potentials. However, accurate SL estimates require the use of many EEG electrodes, when local estimation methods are used. Since BCI devices have to use a limited number of electrodes for practical reasons, we investigated the performances of spline methods for SL estimates using a limited number of electrodes (low resolution SL). Recognition of mental activity was attempted on both raw and SL-transformed EEG data from five healthy people performing two mental tasks, namely imagined right and left hand movements. Linear classifiers were used including Signal Space Projection (SSP) and Fisher's linear discriminant. Results showed an acceptable average correlation between the waveforms obtained with the low resolution SL and these obtained with the SL computed from 26 electrodes (full resolution SL). More importantly, satisfactorily recognition scores for mental EEG-patterns were obtained with the low-resolution surface Laplacian transformation of the recorded potentials when compared with those obtained by using full resolution SL (82%). These results demonstrated also the utility of linear classifiers for the detection of mental patterns in the BCI field.

This paper presents a new model-dependent method for the spatial deblurring of scalp-recorded EEG potentials based on boundary-element and cortical imaging techniques. This model-dependent spatial deblurring (MDSD) method used MR images for the reconstruction of the subject's head model, and a layer of 364 radially-oriented equivalent current dipoles as a source model. The validation of the MDSD method was performed on simulated potential distributions generated from equivalent dipoles oriented radially, obliquely, and tangentially to the head surface. Furthermore, this method was used to localize neocortical sources of human movement-related and somatosensory-evoked potentials. It was shown that the new MDSD method improved markedly the spatial resolution of the simulated surface potentials and scalp-recorded event-related potentials. The spatial information content of the scalp-recorded EEG potentials increased progressively by increasing the spatial sampling from 28 to 128 channels. These results indicate that the new method could be satisfactorily used for high resolution EEG studies.

This paper presents a realistic Laplacian (RL) estimator based on a tensorial formulation of the surface Laplacian (SL) that uses the 2-D thin plate spline function to obtain a mathematical description of a realistic scalp surface. Because of this tensorial formulation, the RL does not need an orthogonal reference frame placed on the realistic scalp surface. In simulation experiments the RL was estimated with an increasing number of "electrodes" (up to 256) on a mathematical scalp model, the analytic Laplacian being used as a reference. Second and third order spherical spline Laplacian estimates were examined for comparison. Noise of increasing magnitude and spatial frequency was added to the simulated potential distributions. Movement-related potentials and somatosensory evoked potentials sampled with 128 electrodes were used to estimate the RL on a realistically shaped, MR-constructed model of the subject's scalp surface. The RL was also estimated on a mathematical spherical scalp model computed from the real scalp surface. Simulation experiments showed that the performances of the RL estimator were similar to those of the second and third order spherical spline Laplacians. Furthermore, the information content of scalp-recorded potentials was clearly better when the RL estimator computed the SL of the potential on an MR-constructed scalp surface model.

A technique of stochastic parametric identification and filtering is applied to the analysis of single-sweep event-related potentials. This procedure, called AutoRegressive with n eXogenous inputs (ARXn), models the recorded signal as the sum of n+1 signals: the background EEG activity, modeled as an autoregressive process driven by white noise, and n signals, one of which represents a filtered version of a reference signal carrying the average information contained in each sweep. The other (n-1) signals could represent various sources of noise (i.e., artifacts, EOG, etc.). An evaluation of the effects of both artifact suppression and accurate selection of the average signal on mono- or multi-channel scalp recordings is presented.