Bayesian brain source imaging based on combined MEG/EEG and fMRI using MCMC

Inferring Macroscale Brain Dynamics via Fusion of Simultaneous EEG-fMRI

Advances in the instrumentation and signal processing for simultaneously acquired electroencephalography and functional magnetic resonance imaging (EEG-fMRI) have enabled new ways to observe the spatiotemporal neural dynamics of the human brain. Central to the utility of EEG-fMRI neuroimaging systems are the methods for fusing the two data streams, with machine learning playing a key role. These methods can be dichotomized into those that are symmetric and asymmetric in terms of how the two modalities inform the fusion. Studies using these methods have shown that fusion yields new insights into brain function that are not possible when each modality is acquired separately. As technology improves and methods for fusion become more sophisticated, the future of EEG-fMRI for noninvasive measurement of brain dynamics includes mesoscale mapping at ultrahigh magnetic resonance fields, targeted perturbation-based neuroimaging, and using deep learning to uncover nonlinear representations that link the electrophysiological and hemodynamic measurements.

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website.

EEG-fMRI Bayesian framework for neural activity estimation: a simulation study

OBJECTIVE

Due to the complementary nature of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), and given the possibility of simultaneous acquisition, the joint data analysis can afford a better understanding of the underlying neural activity estimation. In this simulation study we want to show the benefit of the joint EEG-fMRI neural activity estimation in a Bayesian framework.

APPROACH

We built a dynamic Bayesian framework in order to perform joint EEG-fMRI neural activity time course estimation. The neural activity is originated by a given brain area and detected by means of both measurement techniques. We have chosen a resting state neural activity situation to address the worst case in terms of the signal-to-noise ratio. To infer information by EEG and fMRI concurrently we used a tool belonging to the sequential Monte Carlo (SMC) methods: the particle filter (PF).

MAIN RESULTS

First, despite a high computational cost, we showed the feasibility of such an approach. Second, we obtained an improvement in neural activity reconstruction when using both EEG and fMRI measurements.

SIGNIFICANCE

The proposed simulation shows the improvements in neural activity reconstruction with EEG-fMRI simultaneous data. The application of such an approach to real data allows a better comprehension of the neural dynamics.

Bayesian Models for fMRI Data Analysis

Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This paper provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatio-temporal models for fMRI data that detect task-related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as EEG/MEG and DTI data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics.

Localization of coherent sources by simultaneous MEG and EEG beamformer

Simultaneous magnetoencephalography (MEG) and electroencephalography (EEG) analysis is known generally to yield better localization performance than a single modality only. For simultaneous analysis, MEG and EEG data should be combined to maximize synergistic effects. Recently, beamformer for simultaneous MEG/EEG analysis was proposed to localize both radial and tangential components well, while single modality analyses could not detect them, or had relatively higher location bias. In practice, most interesting brain sources are likely to be activated coherently; however, conventional beamformer may not work properly for such coherent sources. To overcome this difficulty, a linearly constrained minimum variance (LCMV) beamformer may be used with a source suppression strategy. In this work, simultaneous MEG/EEG LCMV beamformer using source suppression was formulated firstly to investigate its capability over various suppression strategies. The localization performance of our proposed approach was examined mainly for coherent sources and compared thoroughly with the conventional simultaneous and single modality approaches, over various suppression strategies. For this purpose, we used numerous simulated data, as well as empirical auditory stimulation data. In addition, some strategic issues of simultaneous MEG/EEG analysis were discussed. Overall, we found that our simultaneous MEG/EEG LCMV beamformer using a source suppression strategy is greatly beneficial in localizing coherent sources.

Computing sources of epileptic discharges using the novel BMA approach: comparison with other distributed inverse solution methods

Electroencephalography (EEG) source localization in epileptology continues to be a challenge for neuroscientists. A number of inverse solution (IS) methodologies have been proposed to solve this problem, and their advantages and limitations have been described. In the present work, a previously developed IS approach called Bayesian model averaging (BMA) is introduced in clinical practice in order to improve the localization accuracy of epileptic discharge sources. For this study, 31 patients with the diagnosis of partial epilepsies were studied: 14 had benign childhood epilepsy with centrotemporal spikes and 17 had temporal lobe epilepsy (TLE). The underlying epileptic sources were localized using the BMA approach, and the results were compared with those expected from the clinical diagnosis. Additional comparisons with results obtained from 3 of the most commonly used distributed IS methods for these purposes (minimum norm [MN], weighted minimum norm [WMN], and low-resolution electromagnetic tomography [LORETA]) were carried out in terms of source localization accuracy and spatial resolutions. The BMA approach estimated discharge sources that were consistent with the clinical diagnosis, and this method outperformed LORETA, MN, and WMN in terms of both localization accuracy and spatial resolution. The BMA was able to localize deeper generators with high accuracy. In conclusion, the BMA methodology has a great potential for the noninvasive accurate localization of epileptic sources, even those located in deeper structures. Therefore, it could be a promising tool for clinical practice in epileptology, although additional studies in other types of epileptic syndromes are necessary.

Bayesian symmetrical EEG/fMRI fusion with spatially adaptive priors

In this paper, we propose a novel symmetrical EEG/fMRI fusion method which combines EEG and fMRI by means of a common generative model. We use a total variation (TV) prior to model the spatial distribution of the cortical current responses and hemodynamic response functions, and utilize spatially adaptive temporal priors to model their temporal shapes. The spatial adaptivity of the prior model allows for adaptation to the local characteristics of the estimated responses and leads to high estimation performance for the cortical current distribution and the hemodynamic response functions. We utilize a Bayesian formulation with a variational Bayesian framework and obtain a fully automatic fusion algorithm. Simulations with synthetic data and experiments with real data from a multimodal study on face perception demonstrate the performance of the proposed method.

MEG and fMRI Fusion for Non-Linear Estimation of Neural and BOLD Signal Changes

The combined analysis of magnetoencephalography (MEG)/electroencephalography and functional magnetic resonance imaging (fMRI) measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the blood oxygenation level dependent (BOLD) response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater signal-to-noise ratio, that confirms the expectation arising from the nature of the experiment. The highly non-linear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources.

Variable anisotropic brain electrical conductivities in epileptogenic foci

Source localization models assume brain electrical conductivities are isotropic at about 0.33 S/m. These assumptions have not been confirmed ex vivo in humans. This study determined bidirectional electrical conductivities from pediatric epilepsy surgery patients. Electrical conductivities perpendicular and parallel to the pial surface of neocortex and subcortical white matter (n = 15) were measured using the 4-electrode technique and compared with clinical variables. Mean (±SD) electrical conductivities were 0.10 ± 0.01 S/m, and varied by 243% from patient to patient. Perpendicular and parallel conductivities differed by 45%, and the larger values were perpendicular to the pial surface in 47% and parallel in 40% of patients. A perpendicular principal axis was associated with normal, while isotropy and parallel principal axes were linked with epileptogenic lesions by MRI. Electrical conductivities were decreased in patients with cortical dysplasia compared with non-dysplasia etiologies. The electrical conductivity values of freshly excised human brain tissues were approximately 30% of assumed values, varied by over 200% from patient to patient, and had erratic anisotropic and isotropic shapes if the MRI showed a lesion. Understanding brain electrical conductivity and ways to non-invasively measure them are probably necessary to enhance the ability to localize EEG sources from epilepsy surgery patients.

Multimodal functional imaging using fMRI-informed regional EEG/MEG source estimation

We propose a novel method, fMRI-Informed Regional Estimation (FIRE), which utilizes information from fMRI in E/MEG source reconstruction. FIRE takes advantage of the spatial alignment between the neural and the vascular activities, while allowing for substantial differences in their dynamics. Furthermore, with a region-based approach, FIRE estimates the model parameters for each region independently. Hence, it can be efficiently applied on a dense grid of source locations. The optimization procedure at the core of FIRE is related to the re-weighted minimum-norm algorithms. The weights in the proposed approach are computed from both the current source estimates and fMRI data, leading to robust estimates in the presence of silent sources in either fMRI or E/MEG measurements. We employ a Monte Carlo evaluation procedure to compare the proposed method to several other joint E/MEG-fMRI algorithms. Our results show that FIRE provides the best trade-off in estimation accuracy between the spatial and the temporal accuracy. Analysis using human E/MEG-fMRI data reveals that FIRE significantly reduces the ambiguities in source localization present in the minimum-norm estimates, and that it accurately captures activation timing in adjacent functional regions.