A state-space formulation is introduced for estimating multivariate autoregressive (MVAR) models of cortical connectivity from noisy, scalp recorded EEG. A state equation represents the MVAR model of cortical dynamics while an observation equation describes the physics relating the cortical signals to the measured EEG and the presence of spatially correlated noise. We assume the cortical signals originate from known regions of cortex, but that the spatial distribution of activity within each region is unknown. An expectation maximization algorithm is developed to directly estimate the MVAR model parameters, the spatial activity distribution components, and the spatial covariance matrix of the noise from the measured EEG. Simulation and analysis demonstrate that this integrated approach is less sensitive to noise than two-stage approaches in which the cortical signals are first estimated from EEG measurements, and next an MVAR model is fit to the estimated cortical signals. The method is further demonstrated by estimating conditional Granger causality using EEG data collected while subjects passively watch a movie.

The role of bottom-up and top-down connections during visual perception and the forming of mental images was examined by analyzing high-density EEG recordings of brain activity using two state-of-the-art methods for assessing the directionality of cortical signal flow: state-space Granger causality and dynamic causal modeling. We quantified the directionality of signal flow in an occipito-parieto-frontal cortical network during perception of movie clips versus mental replay of the movies and free visual imagery. Both Granger causality and dynamic causal modeling analyses revealed increased top-down signal flow in parieto-occipital cortices during mental imagery as compared to visual perception. These results are the first direct demonstration of a reversal of the predominant direction of cortical signal flow during mental imagery as compared to perception.

The cingulate cortex is regarded as the backbone of structural and functional connectivity of the brain. While its functional connectivity has been intensively studied, little is known about its effective connectivity, its modulation by behavioral states, and its involvement in cognitive performance. Given their previously reported effects on cingulate functional connectivity, we investigated how eye-closure and sleep deprivation changed cingulate effective connectivity, estimated from resting-state high-density electroencephalography (EEG) using a novel method to calculate Granger Causality directly in source space. Effective connectivity along the cingulate cortex was dominant in the forward direction. Eyes-open connectivity in the forward direction was greater compared to eyes-closed, in well-rested participants. The difference between eyes-open and eyes-closed connectivity was attenuated and no longer significant after sleep deprivation. Individual variability in the forward connectivity after sleep deprivation predicted subsequent task performance, such that those subjects who showed a greater increase in forward connectivity between the eyes-open and the eyes-closed periods also performed better on a sustained attention task. Effective connectivity in the opposite, backward, direction was not affected by whether the eyes were open or closed or by sleep deprivation. These findings indicate that the effective connectivity from posterior to anterior cingulate regions is enhanced when a well-rested subject has his eyes open compared to when they are closed. Sleep deprivation impairs this directed information flow, proportional to its deleterious effect on vigilance. Therefore, sleep may play a role in the maintenance of waking effective connectivity.

A cross-validation (CV) method based on state-space framework is introduced for comparing the fidelity of different cortical interaction models to the measured scalp electroencephalogram (EEG) or magnetoencephalography (MEG) data being modeled. A state equation models the cortical interaction dynamics and an observation equation represents the scalp measurement of cortical activity and noise. The measured data are partitioned into training and test sets. The training set is used to estimate model parameters and the model quality is evaluated by computing test data innovations for the estimated model. Two CV metrics normalized mean square error and log-likelihood are estimated by averaging over different training/test partitions of the data. The effectiveness of this method of model selection is illustrated by comparing two linear modeling methods and two nonlinear modeling methods on simulated EEG data derived using both known dynamic systems and measured electrocorticography data from an epilepsy patient.

We propose using a state-space model to estimate cortical connectivity from scalp-based EEG recordings. A state equation describes the dynamics of the cortical signals and an observation equation describes the manner in which the cortical signals contribute to the scalp measurements. The state equation is based on a multivariate autoregressive (MVAR) process model for the cortical signals. The observation equation describes the physics relating the cortical signals to the scalp EEG measurements and spatially correlated observation noise. An expectation-maximization (EM) algorithm is employed to obtain maximum-likelihood estimates of the MVAR model parameters. The strength of influence between cortical regions is then derived from the MVAR model parameters. Simulation results show that this integrated approach performs significantly better than the two-step approach in which the cortical signals are first estimated from the EEG measurements by attempting to solve the EEG inverse problem and second, an MVAR model is fit to the estimated signals. The method is also applied to data from a subject watching a movie, and confirms that feedforward connections between visual and parietal cortex are generally stronger than feedback connections.

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The impact of the posterior callosal anomalies associated with spina bifida on interhemispheric cortical connectivity is studied using a method for estimating cortical multivariable autoregressive models from scalp magnetoencephalography data. Interhemispheric effective and functional connectivity, measured using conditional Granger causality and coherence, respectively, is determined for the anterior and posterior cortical regions in a population of five spina bifida and five control subjects during a resting eyes-closed state. The estimated connectivity is shown to be consistent over the randomly selected subsets of the data for each subject. The posterior interhemispheric effective and functional connectivity and cortical power are significantly lower in the spina bifida group, a result that is consistent with posterior callosal anomalies. The anterior interhemispheric effective and functional connectivity are elevated in the spina bifida group, a result that may reflect compensatory mechanisms. In contrast, the intrahemispheric effective connectivity is comparable in the two groups. The differences between the spina bifida and control groups are most significant in the h and a bands.

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