Accuracy of dipole source reconstruction in the 3-layer BEM model against the 5-layer BEM-FMM model.

Objective: To compare cortical dipole fitting spatial accuracy between the widely used yet highly simplified 3-layer and modern more realistic 5-layer BEM-FMM models with and without adaptive mesh refinement (AMR) methods. Methods: We generate simulated noiseless 256-channel EEG data from 5-layer (7-compartment) meshes of 15 subjects from the Connectome Young Adult dataset. For each subject, we test four dipole positions, three sets of conductivity values, and two types of head segmentation. We use the boundary element method (BEM) with fast multipole method (FMM) acceleration, with or without (AMR), for forward modeling. Dipole fitting is carried out with the FieldTrip MATLAB toolbox. Results: The average position error (across all tested dipoles, subjects, and models) is ~4 mm, with a standard deviation of ~2 mm. The orientation error is ~20° on average, with a standard deviation of ~15°. Without AMR, the numerical inaccuracies produce a larger disagreement between the 3- and 5-layer models, with an average position error of ~8 mm (6 mm standard deviation), and an orientation error of 28° (28° standard deviation). Conclusions: The low-resolution 3-layer models provide excellent accuracy in dipole localization. On the other hand, dipole orientation is retrieved less accurately. Therefore, certain applications may require more realistic models for practical source reconstruction. AMR is a critical component for improving the accuracy of forward EEG computations using a high-resolution 5-layer volume conduction model. Significance: Improving EEG source reconstruction accuracy is important for several clinical applications, including epilepsy and other seizure-inducing conditions.

Fast and Accurate EEG/MEG BEM-Based Forward Problem Solution for High-Resolution Head Models.

A BEM (boundary element method) based approach is developed to accurately solve an EEG/MEG forward problem for a modern high-resolution head model in approximately 60 seconds using a common workstation. The method utilizes a charge-based BEM with fast multipole acceleration (BEM-FMM) and a "smart" mesh pre-refinement (called b-refinement) close to the singular source(s). No costly matrix-filling or direct solution steps typical for the standard BEM are required; the method generates on-skin voltages as well as MEG magnetic fields for high-resolution head models in approximately 60 seconds after initial model assembly. The method is verified both theoretically and experimentally.

Enabling Electric Field Modeling of Microscopically Realistic Brain.

Across all domains of brain stimulation (neuromodulation), conventional analysis of neuron activation involves two discrete steps: i) prediction of macroscopic electric field, ignoring presence of cells and; ii) prediction of cell activation from tissue electric fields. The first step assumes that current flow is not distorted by the dense tortuous network of cell structures. The deficiencies of this assumption have long been recognized, but - except for trivial geometries - ignored, because it presented intractable computation hurdles. This study introduces a novel approach for analyzing electric fields within a microscopically realistic brain volume. Our pipeline overcomes the technical intractability that prevented such analysis while also showing significant implications for brain stimulation. Contrary to the standard finite element method (FEM), we suggest using a nested iterative boundary element method (BEM) coupled with the fast multipole method (FMM). This approach allows for solving problems with multiple length scales more efficiently. A target application is a subvolume of the L2/3 P36 mouse primary visual cortex containing approximately 400 detailed densely packed neuronal cells at a resolution of 100 nm, which is obtained from scanning electron microscopy data. Our immediate result is a reduction of the stimulation field strength necessary for neuron activation by a factor of 0.85-0.55 (by 15%-45%) as compared to macroscopic predictions. This is in line with modern experimental data stating that existing macroscopic theories substantially overestimate electric field levels necessary for brain stimulation.