Melissa Zavaglia

Comparison of different cortical connectivity estimators for high-resolution EEG recordings

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. Hum. Brain Mapp, 2007.

Tracking the Time-Varying Cortical Connectivity Patterns by Adaptive Multivariate Estimators

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 Ave 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.

Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data

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

A neural mass model for the simulation of cortical activity estimated from high resolution EEG during cognitive or motor tasks.

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.

A neural mass model of interconnected regions simulates rhythm propagation observed via TMS-EEG

Knowledge of cortical rhythms represents an important aspect of modern neuroscience, to understand how the brain realizes its functions. Recent data suggest that different regions in the brain may exhibit distinct electroencephalogram (EEG) rhythms when perturbed by Transcranial Magnetic Stimulation (TMS) and that these rhythms can change due to the connectivity among regions. In this context, in silico simulations may help the validation of these hypotheses that would be difficult to be verified in vivo. Neural mass models can be very useful to simulate specific aspects of electrical brain activity and, above all, to analyze and identify the overall frequency content of EEG in a cortical region of interest (ROI). In this work we implemented a model of connectivity among cortical regions to fit the impulse responses in three ROIs recorded during a series of TMS/EEG experiments performed in five subjects and using three different impulse intensities. In particular we investigated Brodmann Area (BA) 19 (occipital lobe), BA 7 (parietal lobe) and BA 6 (frontal lobe). Results show that the model can reproduce the natural rhythms of the three regions quite well, acting on a few internal parameters. Moreover, the model can explain most rhythm changes induced by stimulation of another region, and inter-subject variability, by estimating just a few long-range connectivity parameters among ROIs.

The Effect of Connectivity on EEG Rhythms, Power Spectral Density and Coherence Among Coupled Neural Populations: Analysis With a Neural Mass Model

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.

Visuotactile representation of peripersonal space: A neural network study

Neurophysiological and behavioral studies suggest that the peripersonal space is represented in a multisensory fashion by integrating stimuli of different modalities. We developed a neural network to simulate the visual-tactile representation of the peripersonal space around the right and left hands. The model is composed of two networks (one per hemisphere), each with three areas of neurons: two are unimodal (visual and tactile) and communicate by synaptic connections with a third downstream multimodal (visual-tactile) area. The hemispheres are interconnected by inhibitory synapses. We applied a combination of analytic and computer simulation techniques. The analytic approach requires some simplifying assumptions and approximations (linearization and a reduced number of neurons) and is used to investigate network stability as a function of parameter values, providing some emergent properties. These are then tested and extended by computer simulations of a more complex nonlinear network that does not rely on the previous simplifications. With basal parameter values, the extended network reproduces several in vivo phenomena: multisensory coding of peripersonal space, reinforcement of unisensory perception by multimodal stimulation, and coexistence of simultaneous right- and left-hand representations in bilateral stimulation. By reducing the strength of the synapses from the right tactile neurons, the network is able to mimic the responses characteristic of right-brain-damaged patients with left tactile extinction: perception of unilateral left tactile stimulation, cross-modal extinction and cross-modal facilitation in bilateral stimulation. Finally, a variety of sensitivity analyses on some key parameters was performed to shed light on the contribution of single-model components in network behaviour. The model may help us understand the neural circuitry underlying peripersonal space representation and identify its alterations explaining neurological deficits. In perspective, it could help in interpreting results of psychophysical and behavioral trials and clarifying the neural correlates of multisensory-based rehabilitation procedures.

Changes in EEG power spectral density and cortical connectivity in healthy and tetraplegic patients during amotor imagery task

Knowledge of brain connectivity is an important aspect of modern neuroscience, to understand how the brain realizes its functions. In this work, neural mass models including four groups of excitatory and inhibitory neurons are used to estimate the connectivity among three cortical regions of interests (ROIs) during a foot-movement task. Real data were obtained via high-resolution scalp EEGs on two populations: healthy volunteers and tetraplegic patients. A 3-shell Boundary Element Model of the head was used to estimate the cortical current density and to derive cortical EEGs in the three ROIs. The model assumes that each ROI can generate an intrinsic rhythm in the beta range, and receives rhythms in the alpha and gamma ranges from other two regions. Connectivity strengths among the ROIs were estimated by means of an original genetic algorithm that tries to minimize several cost functions of the difference between real and model power spectral densities. Results show that the stronger connections are those from the cingulate cortex to the primary and supplementary motor areas, thus emphasizing the pivotal role played by the CMA_L during the task. Tetraplegic patients exhibit higher connectivity strength on average, with significant statistical differences in some connections. The results are commented and virtues and limitations of the proposed method discussed.

Comparison of different multivariate methods for the estimation of cortical connectivity: simulations and applications to EEG data

The problem of the definition and evaluation of brain connectivity has become a central one in neuroscience during the latest years, as a way to understand the organization and interaction of cortical areas during the execution of cognitive or motor tasks. Among various methods established during the years, the directed transfer function (DTF), the partial directed coherence (PDC) and the direct DTF (dDTF) are frequency-domain approaches to this problem, all based on a multivariate autoregressive modeling of time series and on the concept of Granger causality. In this paper we propose the use of these methods on cortical signals estimated from high resolution EEG recordings, a non invasive method which exhibits a higher spatial resolution than conventional cerebral electromagnetic measures. The principle contribution of this work are the results of a simulation study, testing the capability of the three estimators to reconstruct a connectivity model imposed, with a particular eye on the capability to distinguish between direct and indirect causality. An application to high resolution EEG recordings during a foot movement is also presented

Estimation of the cortical connectivity patterns during the intention of limb movements

The problem of the definition and evaluation of brain connectivity has become a central one in neuroscience during recent years as a way to understand the organization and interaction of cortical areas during the execution of cognitive or motor tasks. In this article, we propose the use of the directed transfer function (DTF) method on cortical signals estimated from high-resolution electroencephalography (EEG) recordings. An application of the proposed technique to the estimation of the cortical connectivity pattern in normal subjects and in one spinal-cord-injured patient is also provided