Data-driven forward model inference for EEG brain imaging

Robust Empirical Bayesian Reconstruction of Distributed Sources for Electromagnetic Brain Imaging

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of the magnetic fields and electric potentials. An enduring challenge in this imaging modality is estimating the number, location, and time course of sources, especially for the reconstruction of distributed brain sources with complex spatial extent. Here, we introduce a novel robust empirical Bayesian algorithm that enables better reconstruction of distributed brain source activity with two key ideas: kernel smoothing and hyperparameter tiling. Since the proposed algorithm builds upon many of the performance features of the sparse source reconstruction algorithm - Champagne and we refer to this algorithm as Smooth Champagne. Smooth Champagne is robust to the effects of high levels of noise, interference, and highly correlated brain source activity. Simulations demonstrate excellent performance of Smooth Champagne when compared to benchmark algorithms in accurately determining the spatial extent of distributed source activity. Smooth Champagne also accurately reconstructs real MEG and EEG data.

Unmixing Oscillatory Brain Activity by EEG Source Localization and Empirical Mode Decomposition

Neuronal activity is composed of synchronous and asynchronous oscillatory activity at different frequencies. The neuronal oscillations occur at time scales well matched to the temporal resolution of electroencephalography (EEG); however, to derive meaning from the electrical brain activity as measured from the scalp, it is useful to decompose the EEG signal in space and time. In this study, we elaborate on the investigations into source-based signal decomposition of EEG. Using source localization, the electrical brain signal is spatially unmixed and the neuronal dynamics from a region of interest are analyzed using empirical mode decomposition (EMD), a technique aimed at detecting periodic signals. We demonstrate, first in simulations, that the EMD is more accurate when applied to the spatially unmixed signal compared to the scalp-level signal. Furthermore, on EEG data recorded simultaneously with transcranial magnetic stimulation (TMS) over the hand area of the primary motor cortex, we observe a link between the peak to peak amplitude of the motor-evoked potential (MEP) and the phase of the decomposed localized electrical activity before TMS onset. The results thus encourage combination of source localization and EMD in the pursuit of further insight into the mechanisms of the brain with respect to the phase and frequency of the electrical oscillations and their cortical origin.

Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity

Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bayesian approximation error (BAE) approach is exploited. In BAE, we first postulate a probability distribution for the skull conductivity that describes our (lack of) knowledge on its value, and model the effects of this uncertainty on EEG recordings with the help of an additive error term in the observation model. Before the Bayesian inference, the likelihood is marginalized over this error term. Thus, in the inversion we estimate only our primary unknown, the source distribution. We quantified the improvements in the source localization when the proposed Bayesian modelling was used in the presence of different skull conductivity errors and levels of measurement noise. Based on the results, BAE was able to improve the source localization accuracy, particularly when the unknown (true) skull conductivity was much lower than the expected standard conductivity value. The source locations that gained the highest improvements were shallow and originally exhibited the largest localization errors. In our case study, the benefits of BAE became negligible when the signal-to-noise ratio dropped to 20 dB.

Electromagnetic Brain Source Imaging by Means of a Robust Minimum Variance Beamformer

OBJECTIVE

Adaptive beamformer methods that have been extensively used for functional brain imaging using EEG/MEG (magnetoencephalography) signals are sensitive to model mismatches. We propose a robust minimum variance beamformer (RMVB) technique, which explicitly incorporates the uncertainty of the lead field matrix into the estimation of spatial-filter weights that are subsequently used to perform the imaging.

METHODS

The uncertainty of the lead field is modeled by ellipsoids in the RMVB method; these hyperellipsoids (ellipsoids in higher dimensions) define regions of uncertainty for a given nominal lead field vector. These ellipsoids are estimated empirically by sampling lead field vectors surrounding each point of the source space, or more generally by building several forward models for the source space. Once these uncertainty regions (ellipsoids) are estimated, they are used to perform the source-imaging task. Computer simulations are conducted to evaluate the performance of the proposed RMVB technique.

RESULTS

Our results show that robust beamformers can outperform conventional beamformers in terms of localization error, recovering source dynamics, and estimation of the underlying source extents when uncertainty in the lead field matrix is properly determined and modeled.

CONCLUSION

The RMVB can be substituted for conventional beamformers, especially in applications where source imaging is performed off-line, and computational speed and complexity are not of major concern.

SIGNIFICANCE

A high-quality source imaging can be utilized in various applications, such as determining the epileptogenic zone in medically intractable epilepsy patients or estimating the time course of activity, which is a required step for computing the functional connectivity of brain networks.

EEG source space analysis of the supervised factor analytic approach for the classification of multi-directional arm movement

OBJECTIVE

In electroencephalography (EEG)-based brain-computer interface (BCI) systems for motor control tasks the conventional practice is to decode motor intentions by using scalp EEG. However, scalp EEG only reveals certain limited information about the complex tasks of movement with a higher degree of freedom. Therefore, our objective is to investigate the effectiveness of source-space EEG in extracting relevant features that discriminate arm movement in multiple directions.

APPROACH

We have proposed a novel feature extraction algorithm based on supervised factor analysis that models the data from source-space EEG. To this end, we computed the features from the source dipoles confined to Brodmann areas of interest (BA4a, BA4p and BA6). Further, we embedded class-wise labels of multi-direction (multi-class) source-space EEG to an unsupervised factor analysis to make it into a supervised learning method.

MAIN RESULTS

Our approach provided an average decoding accuracy of 71% for the classification of hand movement in four orthogonal directions, that is significantly higher (>10%) than the classification accuracy obtained using state-of-the-art spatial pattern features in sensor space. Also, the group analysis on the spectral characteristics of source-space EEG indicates that the slow cortical potentials from a set of cortical source dipoles reveal discriminative information regarding the movement parameter, direction.

SIGNIFICANCE

This study presents evidence that low-frequency components in the source space play an important role in movement kinematics, and thus it may lead to new strategies for BCI-based neurorehabilitation.

Reconstructing anatomy from electro-physiological data

Here we show how it is possible to make estimates of brain structure based on MEG data. We do this by reconstructing functional estimates onto distorted cortical manifolds parameterised in terms of their spherical harmonics. We demonstrate that both empirical and simulated MEG data give rise to consistent and plausible anatomical estimates. Importantly, the estimation of structure from MEG data can be quantified in terms of millimetres from the true brain structure. We show, for simulated data, that the functional assumptions which are closer to the functional ground-truth give rise to anatomical estimates that are closer to the true anatomy.

A low-dimensional representation for individual head geometries

In the estimation of individual head geometries for source localization and electrical stimulation in neuroelectric investigations and application, mostly complex geometrical models are directly extracted from anatomical images. We present a novel method that uses a dimensionality reduction from thousands down to the range of tens of parameters to successfully represent an individual 4-shell Boundary Element Method (BEM) head model, which can successively be fitted to any kind of data from an individual head (e.g. headshape, impedances) and then used for individual head model creation. The results show, that around 15 - 20 components can lead to satisfactory results.

SEEG dipole source localization based on an empirical Bayesian approach taking into account forward model uncertainties

Electromagnetic brain source localization consists in the inversion of a forward model based on a limited number of potential measurements. A wide range of methods has been developed to regularize this severely ill-posed problem and to reduce the solution space, imposing spatial smoothness, anatomical constraint or sparsity of the activated source map. This last criteria, based on physiological assumptions stating that in some particular events (e.g., epileptic spikes, evoked potential) few focal area of the brain are simultaneously actives, has gained more and more interest. Bayesian approaches have the ability to provide sparse solutions under adequate parametrization, and bring a convenient framework for the introduction of priors in the form of probabilistic density functions. However the quality of the forward model is rarely questioned while this parameter has undoubtedly a great influence on the solution. Its construction suffers from numerous approximation and uncertainties, even when using realistic numerical models. In addition, it often encodes a coarse sampling of the continuous solution space due to the computational burden its inversion implies. In this work we propose an empirical Bayesian approach to take into account the uncertainties of the forward model by allowing constrained variations around a prior physical model, in the particular context of SEEG measurements. We demonstrate on simulations that the method enhance the accuracy of the source time-course estimation as well as the sparsity of the resulting source map. Results on real signals prove the applicability of the method in real contexts.

Spatio-temporal reconstruction of brain dynamics from EEG with a Markov prior

Electroencephalography (EEG) can capture brain dynamics in high temporal resolution. By projecting the scalp EEG signal back to its origin in the brain also high spatial resolution can be achieved. Source localized EEG therefore has potential to be a very powerful tool for understanding the functional dynamics of the brain. Solving the inverse problem of EEG is however highly ill-posed as there are many more potential locations of the EEG generators than EEG measurement points. Several well-known properties of brain dynamics can be exploited to alleviate this problem. More short ranging connections exist in the brain than long ranging, arguing for spatially focal sources. Additionally, recent work (Delorme et al., 2012) argues that EEG can be decomposed into components having sparse source distributions. On the temporal side both short and long term stationarity of brain activation are seen. We summarize these insights in an inverse solver, the so-called "Variational Garrote" (Kappen and Gómez, 2013). Using a Markov prior we can incorporate flexible degrees of temporal stationarity. Through spatial basis functions spatially smooth distributions are obtained. Sparsity of these are inherent to the Variational Garrote solver. We name our method the MarkoVG and demonstrate its ability to adapt to the temporal smoothness and spatial sparsity in simulated EEG data. Finally a benchmark EEG dataset is used to demonstrate MarkoVG's ability to recover non-stationary brain dynamics.