A Long Short-Term Memory Network for Sparse Spatiotemporal EEG Source Imaging.

EEG inverse problem is underdetermined, which poses a long standing challenge in Neuroimaging. The combination of source-imaging and analysis of cortical directional networks enables us to noninvasively explore the underlying neural processes. However, existing EEG source imaging approaches mainly focus on performing the direct inverse operation for source estimation, which will be inevitably influenced by noise and the strategy used to find the inverse solution. Here, we develop a new source imaging technique, Deep Brain Neural Network (DeepBraiNNet), for robust sparse spatiotemporal EEG source estimation. In DeepBraiNNet, considering that Recurrent Neural Network (RNN) are usually "deep" in temporal dimension and thus suitable for time sequence modelling, the RNN with Long Short-Term Memory (LSTM) is utilized to approximate the inverse operation for the lead field matrix instead of performing the direct inverse operation, which avoids the possible effect of the direct inverse operation on the underdetermined lead field matrix prone to be influenced by noise. Simulations on various source patterns and noise conditions confirmed that the proposed approach could actually recover the spatiotemporal sources well, outperforming existing state of-the-art methods. DeepBraiNNet also estimated sparse MI related activation patterns when it was applied to a real Motor Imagery dataset, consistent with other findings based on EEG and fMRI. Based on the spatiotemporal sources estimated from DeepBraiNNet, we constructed MI related cortical neural networks, which clearly exhibited strong contralateral network patterns for the two MI tasks. Consequently, DeepBraiNNet may provide an alternative way different from the conventional approaches for spatiotemporal EEG source imaging.

Directed EEG neural network analysis by LAPPS (p≤1) Penalized sparse Granger approach.

The conventional multivariate Granger Analysis (GA) of directed interactions has been widely applied in brain network construction based on EEG recordings as well as fMRI. Nevertheless, EEG is usually inevitably contaminated by strong noise, which may cause network distortion due to the L2-norm used in GAs for directed network recovery. The Lp (p ≤1) norm has been shown to be more robust to outliers as compared to LASSO and L2-GAs. Motivated to construct the sparse brain networks under strong noise condition, we hereby introduce a new approach for GA analysis, termed LAPPS (Least Absolute LP (0

Measuring the Non-linear Directed Information Flow in Schizophrenia by Multivariate Transfer Entropy.

People living with schizophrenia (SCZ) experience severe brain network deterioration. The brain is constantly fizzling with non-linear causal activities measured by electroencephalogram (EEG) and despite the variety of effective connectivity methods, only few approaches can quantify the direct non-linear causal interactions. To circumvent this problem, we are motivated to quantitatively measure the effective connectivity by multivariate transfer entropy (MTE) which has been demonstrated to be able to capture both linear and non-linear causal relationships effectively. In this work, we propose to construct the EEG effective network by MTE and further compare its performance with the Granger causal analysis (GCA) and Bivariate transfer entropy (BVTE). The simulation results quantitatively show that MTE outperformed GCA and BVTE under varied signal-to-noise conditions, edges recovered, sensitivity, and specificity. Moreover, its applications to the P300 task EEG of healthy controls (HC) and SCZ patients further clearly show the deteriorated network interactions of SCZ, compared to that of the HC. The MTE provides a novel tool to potentially deepen our knowledge of the brain network deterioration of the SCZ.

Sparse EEG Source Localization Using LAPPS: Least Absolute l-P (0 < p < 1) Penalized Solution.

OBJECTIVE: The electroencephalographic (EEG) inverse problem is ill-posed owing to the electromagnetism Helmholtz theorem and since there are fewer observations than the unknown variables. Apart from the strong background activities (ongoing EEG), evoked EEG is also inevitably contaminated by strong outliers caused by head movements or ocular movements during recordings. METHODS: Considering the sparse activations during high cognitive processing, we propose a novel robust EEG source imaging algorithm, LAPPS (Least Absolute -P (0 < p < 1) Penalized Solution), which employs the -loss for the residual error to alleviate the effect of outliers and another -penalty norm (p=0.5) to obtain sparse sources while suppressing Gaussian noise in EEG recordings. The resulting optimization problem is solved using a modified ADMM algorithm. RESULTS: Simulation study was performed to recover sparse signals of randomly selected sources using LAPPS and various methods commonly used for EEG source imaging including WMNE, -norm, sLORETA and FOCUSS solution. The simulation comparison quantitatively demonstrates that LAPPS obtained the best performances in all the conducted simulations for various dipoles configurations under various SNRs on a realistic head model. Moreover, in the localization of brain neural generators in a real visual oddball experiment, LAPPS obtained sparse activations consistent with previous findings revealed by EEG and fMRI. CONCLUSION: This study demonstrates a potentially useful sparse method for EEG source imaging, creating a platform for investigating the brain neural generators. SIGNIFICANCE: This method alleviates the effect of noise and recovers sparse sources while maintaining a low computational complexity due to the cheap matrix-vector multiplication.