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Register a new userEvaluating the Performance of BSBL Methodology for EEG Source Localization On a Realistic Head Model
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Source localization in EEG represents a high dimensional inverse problem, which is severely ill-posed by nature. Fortunately, sparsity constraints have come into rescue as it helps solving the ill-posed problems when the signal is sparse. When the signal has a structure such as block structure, consideration of block sparsity produces better results. Knowing sparse Bayesian learning is an important member in the family of sparse recovery, and a superior choice when the projection matrix is highly coherent (which is typical the case for EEG), in this work we evaluate the performance of block sparse Bayesian learning (BSBL) method for EEG source localization. It is already accepted by the EEG community that a group of dipoles rather than a single dipole are activated during brain activities; thus, block structure is a reasonable choice for EEG. In this work we use two definitions of blocks: Brodmann areas and automated anatomical labelling (AAL), and analyze the reconstruction performance of BSBL methodology for them. A realistic head model is used for the experiment, which was obtained from segmentation of MRI images. When the number of simultaneously active blocks is 2, the BSBL produces overall localization accuracy of less than 5 mm without the presence of noise. The presence of more than 3 simultaneously active blocks and noise significantly affect the localization performance. Consideration of AAL based blocks results more accurate source localization in comparison to Brodmann area based blocks.
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Advances in imaging methods such as electron microscopy, tomography and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for biophysical and mathematical modeling once these data can be represented as a geometric mesh, which, when carefully conditioned, enables the discretization and solution of partial differential equations. In this study, we outline the steps for a naive user to approach GAMer 2, a mesh generation code written in C++ designed to convert structural datasets to realistic geometric meshes, while preserving the underlying shapes. We present two example cases, 1) mesh generation at the subcellular scale as informed by electron tomography, and 2) meshing a protein with structure from x-ray crystallography. We further demonstrate that the meshes generated by GAMer are suitable for use with numerical methods. Together, this collection of libraries and tools simplifies the process of constructing realistic geometric meshes from structural biology data.
Purpose: Localizing the sources of electrical activity from electroencephalographic (EEG) data has gained considerable attention over the last few years. In this paper, we propose an innovative source localization method for EEG, based on Sparse Bayesian Learning (SBL). Methods: To better specify the sparsity profile and to ensure efficient source localization, the proposed approach considers grouping of the electrical current dipoles inside human brain. SBL is used to solve the localization problem in addition with imposed constraint that the electric current dipoles associated with the brain activity are isotropic. Results: Numerical experiments are conducted on a realistic head model that is obtained by segmentation of MRI images of the head and includes four major components, namely the scalp, the skull, the cerebrospinal fluid (CSF) and the brain, with appropriate relative conductivity values. The results demonstrate that the isotropy constraint significantly improves the performance of SBL. In a noiseless environment, the proposed method was 1 found to accurately (with accuracy of >75%) locate up to 6 simultaneously active sources, whereas for SBL without the isotropy constraint, the accuracy of finding just 3 simultaneously active sources was <75%. Conclusions: Compared to the state-of-the-art algorithms, the proposed method is potentially more consistent in specifying the sparsity profile of human brain activity and is able to produce better source localization for EEG.
Localizing the sources of electrical activity in the brain from Electroencephalographic (EEG) data is an important tool for non-invasive study of brain dynamics. Generally, the source localization process involves a high-dimensional inverse problem that has an infinite number of solutions and thus requires additional constraints to be considered to have a unique solution. In the context of EEG source localization, we propose a novel approach that is based on dividing the cerebral cortex of the brain into a finite number of Functional Zones which correspond to unitary functional areas in the brain. In this paper we investigate the use of Brodmanns areas as the Functional Zones. This approach allows us to apply a sparsity constraint to find a unique solution for the inverse EEG problem. Compared to previously published algorithms which use different sparsity constraints to solve this problem, the proposed method is potentially more consistent with the known sparsity profile of the human brain activity and thus may be able to ensure better localization. Numerical experiments are conducted on a realistic head model obtained from segmentation of MRI images of the head and includes four major compartments namely scalp, skull, cerebrospinal fluid (CSF) and brain with relative conductivity values. Three different electrode setups are tested in the numerical experiments.
It has been conjectured that in head-on collisions of neutron stars (NSs), the merged object would not collapse promptly even if the total mass is higher than the maximum stable mass of a cold NS. In this paper, we show that the reverse is true: even if the total mass is {it less} than the maximum stable mass, the merged object can collapse promptly. We demonstrate this for the case of NSs with a realistic equation of state (the Lattimer-Swesty EOS) in head-on {it and} near head-on collisions. We propose a ``Prompt Collapse Conjecture for a generic NS EOS for head on and near head-on collisions.
EEG source localization is an important technical issue in EEG analysis. Despite many numerical methods existed for EEG source localization, they all rely on strong priors and the deep sources are intractable. Here we propose a deep learning framework using spatial basis function decomposition for EEG source localization. This framework combines the edge sparsity prior and Gaussian source basis, called Edge Sparse Basis Network (ESBN). The performance of ESBN is validated by both synthetic data and real EEG data during motor tasks. The results suggest that the supervised ESBN outperforms the traditional numerical methods in synthetic data and the unsupervised fine-tuning provides more focal and accurate localizations in real data. Our proposed deep learning framework can be extended to account for other source priors, and the real-time property of ESBN can facilitate the applications of EEG in brain-computer interfaces and clinics.
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