CutFEM forward modeling for EEG source analysis

IntroductionSource analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction effects in the human head, represented by a partial differential equation which can be solved using the finite element method (FEM). FEM offers flexibility when modeling anisotropic tissue conductivities but requires a volumetric discretization, a mesh, of the head domain. Structured hexahedral meshes are easy to create in an automatic fashion, while tetrahedral meshes are better suited to model curved geometries. Tetrahedral meshes, thus, offer better accuracy but are more difficult to create.MethodsWe introduce CutFEM for EEG forward simulations to integrate the strengths of hexahedra and tetrahedra. It belongs to the family of unfitted finite element methods, decoupling mesh and geometry representation. Following a description of the method, we will employ CutFEM in both controlled spherical scenarios and the reconstruction of somatosensory-evoked potentials.ResultsCutFEM outperforms competing FEM approaches with regard to numerical accuracy, memory consumption, and computational speed while being able to mesh arbitrarily touching compartments.DiscussionCutFEM balances numerical accuracy, computational efficiency, and a smooth approximation of complex geometries that has previously not been available in FEM-based EEG forward modeling

CutFEM forward modeling for EEG source analysis

Introduction: Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction effects in the human head, represented by a partial differential equation which can be solved using the finite element method (FEM). FEM offers flexibility when modeling anisotropic tissue conductivities but requires a volumetric discretization, a mesh, of the head domain. Structured hexahedral meshes are easy to create in an automatic fashion, while tetrahedral meshes are better suited to model curved geometries. Tetrahedral meshes, thus, offer better accuracy but are more difficult to create. Methods: We introduce CutFEM for EEG forward simulations to integrate the strengths of hexahedra and tetrahedra. It belongs to the family of unfitted finite element methods, decoupling mesh and geometry representation. Following a description of the method, we will employ CutFEM in both controlled spherical scenarios and the reconstruction of somatosensory-evoked potentials. Results: CutFEM outperforms competing FEM approaches with regard to numerical accuracy, memory consumption, and computational speed while being able to mesh arbitrarily touching compartments. Discussion: CutFEM balances numerical accuracy, computational efficiency, and a smooth approximation of complex geometries that has previously not been available in FEM-based EEG forward modeling.Peer reviewe

Data and Code for Reproducibility of Results in Paper "Comparing the Performance of Beamformer Algorithms in Estimating Orientations of Neural Sources"

<h1>Evaluation of beamformer algorithms for estimating orientations of neural sources</h1> <p>This repository contains the scripts and data to reproduce the results presented in our forthcoming paper on the performance of beamformer algorithms in estimating orientations of neural sources based on EEG and MEG data (preprint available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4523138 ).</p> <p>We will quickly go over the scripts.</p> <ol> <li>random_orientations_evaluation.py: In this script, random orientations are generated, which are then estimated using different beamformer algorithms. The differences between the true orientations and the reconstructed orientations are then evaluated.</li> <li>influence_of_noise_levels_evaluation.py: In this script, the MEG noise level is kept fixed, while the EEG noise level varies. Then, for each value of the EEG noise level, random orientations are generated and then estimated using different beamformer algorithms. For each EEG noise level, the mean error between the true and the reconstruction orientations is then evaluated.</li> <li>fixed_orientations_evaluation.py: In this script, the set of possible orientations is scanned with a certain resolution. Each of the orientations is then estimated multiple times and the mean estimation error is evaluated.</li> </ol> <p>For a detailed description of these evaluation methods and the reasoning for choosing them, we refer to the preprint cited above.</p> <p>Furthermore, the following scripts in this repository are used in the above evaluations.</p> <ol> <li>orientation_reconstruction_utilities.py: This file implements the actual beamformer algorithms used in the reconstruction.</li> <li> random_orientation_utilities.py: This file implements functions that generate random orientations on the unit sphere. </li> <li>visualization_utilities.py: This file implements various functions used for the visualization of the results.</li> </ol> <p>Furthermore, the folder 'data' contains the data used in the simulations.</p> <ul> <li>V5_eeg_lf.npy and FEF_eeg_lf.npy :      53 x 3 matrices containing the EEG lead fields</li> <li>V5_meg_lf.npy and FEF_meg_lf.npy :   272 x 3 matrices containing the MEG lead fields</li> </ul> <p>We again refer to the preprint above for details on how these lead fields were computed.</p> <p>Finally, the folder 'output' is supposed to contain the results of the evaluation scripts.</p> <h1>Acknowledgements</h1> <p>This work was supported by the Deutsche Forschungsgemeinschaft (DFG), projects WO1425/10-1, GR2024/8-1 & LE1122/7-1 and by the Bundesministerium für Gesundheit (BMG) as project ZMI1-2521FSB006, under the frame of ERA PerMed as project ERAPERMED2020-227.</p&gt

Comparing the performance of beamformer algorithms in estimating orientations of neural sources

Summary: The efficacy of transcranial electric stimulation (tES) to effectively modulate neuronal activity depends critically on the spatial orientation of the targeted neuronal population. Therefore, precise estimation of target orientation is of utmost importance. Different beamforming algorithms provide orientation estimates; however, a systematic analysis of their performance is still lacking. For fixed brain locations, EEG and MEG data from sources with randomized orientations were simulated. The orientation was then estimated (1) with an EEG and (2) with a combined EEG-MEG approach. Three commonly used beamformer algorithms were evaluated with respect to their abilities to estimate the correct orientation: Unit-Gain (UG), Unit-Noise-Gain (UNG), and Array-Gain (AG) beamformer. Performance depends on the signal-to-noise ratios for the modalities and on the chosen beamformer. Overall, the UNG and AG beamformers appear as the most reliable. With increasing noise, the UG estimate converges to a vector determined by the leadfield, thus leading to insufficient orientation estimates