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Fast EEG/MEG BEM-based forward problem solution for high-resolution head models
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Electroencephalographic (EEG) source localization is a fundamental tool for clinical diagnoses and brain-computer interfaces. We investigate the impact of model complexity on reconstruction accuracy by comparing the widely used three-layer boundary element method (BEM) as an inverse method against a five-layer BEM accelerated by the fast multipole method (BEM-FMM) and coupled with adaptive mesh refinement (AMR) as forward solver. Modern BEM-FMM with AMR can solve high-resolution multi-tissue models efficiently and accurately. We generated noiseless 256-channel EEG data from 15 subjects in the Connectome Young Adult dataset, using four anatomically relevant dipole positions, three conductivity sets, and two head segmentations; we mapped localization errors across the entire grey matter from 4,000 dipole positions. The average location error among our four selected dipoles is ∼5mm (±2mm) with an orientation error of ∼12∘ (±7∘). The average source localization error across the entire grey matter is ∼9mm (±4mm), with a tendency for smaller errors on the occipital lobe. Our findings indicate that while three-layer models are robust under noiseless conditions, substantial localization errors (10–20mm) are common. Therefore, models of five or more layers may be needed for accurate source reconstruction in critical applications involving noisy EEG data.
Objective
In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.
Approach
We propose, describe, and systematically investigate an AMR method using the Boundary Element Method with Fast Multipole Acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy.
The implemented AMR method’s accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a “silver-standard” solution found by subsequent 4:1 global refinement of the adaptively-refined model.
Main Results
Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.
Significance
This error has especially important implications for TES dosing prediction – where the stimulation strength plays a central role – and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.
When modeling transcranial magnetic stimulation (TMS) in the brain, a fast and accurate electric field solver can support interactive neuronavigation tasks as well as comprehensive biophysical modeling. We formulate, test, and disseminate a direct (i.e., non-iterative) TMS solver that can accurately determine global TMS fields for any coil type everywhere in a high-resolution MRI-based surface model with ~ 200,000 or more arbitrarily selected observation points within approximately 5 s, with the solution time itself of 3 s. The solver is based on the boundary element fast multipole method (BEM-FMM), which incorporates the latest mathematical advancement in the theory of fast multipole methods—an FMM-based LU decomposition. This decomposition is specific to the head model and needs to be computed only once per subject. Moreover, the solver offers unlimited spatial numerical resolution. Despite the fast execution times, the present direct solution is numerically accurate for the default model resolution. In contrast, the widely used brain modeling software SimNIBS employs a first-order finite element method that necessitates additional mesh refinement, resulting in increased computational cost. However, excellent agreement between the two methods is observed for various practical test cases following mesh refinement, including a biophysical modeling task. The method can be readily applied to a wide range of TMS analyses involving multiple coil positions and orientations, including image-guided neuronavigation. It can even accommodate continuous variations in coil geometry, such as flexible H-type TMS coils. The FMM-LU direct solver is freely available to academic users.
Background
When modeling transcranial electrical stimulation (TES) and transcranial magnetic stimulation (TMS) in the brain, the meninges – dura, arachnoid, and pia mater – are often neglected due to high computational costs.
Objective
We investigate the impact of the meningeal layers on the cortical electric field in TES and TMS while considering the headreco segmentation as the base model.
Method
We use T1/T2 MRI data from 16 subjects and apply the boundary element fast multipole method with adaptive mesh refinement, which enables us to accurately solve this problem and establish method convergence at reasonable computational cost. We compare electric fields in the presence and absence of various meninges for two brain areas (M1HAND and DLPFC) and for several distinct TES and TMS setups.
Results
Maximum electric fields in the cortex for focal TES consistently increase by approximately 30% on average when the meninges are present in the CSF volume. Their effect on the maximum field can be emulated by reducing the CSF conductivity from 1.65 S/m to approximately 0.85 S/m. In stark contrast to that, the TMS electric fields in the cortex are only weakly affected by the meningeal layers and slightly (∼6%) decrease on average when the meninges are included.
Conclusion
Our results quantify the influence of the meninges on the cortical TES and TMS electric fields. Both focal TES and TMS results are very consistent. The focal TES results are also in a good agreement with a prior relevant study. The solver and the mesh generator for the meningeal layers (compatible with SimNIBS) are available online.
Background:
The first dorsal interosseous muscle (FDI) is usually innervated by the deep branch of the ulnar nerve. However, as was first noted by Sunderland in 1946, some individuals have variable innervation of the FDI. This study investigated the incidence of variable innervation of the FDI by using electrophysiological examination and further evaluated the relevance of this variation in patients with cubital tunnel syndrome (CuTS).
Methods:
This study included 211 patients who underwent peripheral nerve surgery in Huashan hospital, Fudan University, between October, 2012 and February, 2014. The patients were divided into three groups: the carpal tunnel syndrome (CTS) group, the CuTS group and the control group. During surgery, electromyography was used to determine FDI variation, and a hand function instrument was employed to estimate the pinch strength between the thumb and index finger in both hands of the CuTS patients.
Results:
The electromyogram test showed that 22 of the patients enrolled had variable innervation of the FDI. Compared with the CTS group and the control group, the incidence of variable innervation of the FDI was much higher in the CuTS group (P<0.05). Patients under the age of 60 years old in the CuTS group were more likely to have the variation (P=0.043). A higher pinch strength ratio was significantly associated with variable innervation of the FDI in the CuTS patients (P=0.030).
Conclusions:
Using electromyography, our study demonstrated that the variable innervation of the FDI could be innervated by the median nerve. In the CuTS patients, the higher incidence of FDI variation was possibly related to age. This variation might lead to a better prognosis for CuTS patients.
Transcranial brain stimulation (TBS) has been established as a method for modulating and mapping the function of the human brain, and as a potential treatment tool in several brain disorders. Typically, the stimulation is applied using a one-size-fits-all approach with predetermined locations for the electrodes, in electric stimulation (TES), or the coil, in magnetic stimulation (TMS), which disregards anatomical variability between individuals. However, the induced electric field distribution in the head largely depends on anatomical features implying the need for individually tailored stimulation protocols for focal dosing. This requires detailed models of the individual head anatomy, combined with electric field simulations, to find an optimal stimulation protocol for a given cortical target. Considering the anatomical and functional complexity of different brain disorders and pathologies, it is crucial to account for the anatomical variability in order to translate TBS from a research tool into a viable option for treatment.
In this article we present a new method, called CHARM, for automated segmentation of fifteen different head tissues from magnetic resonance (MR) scans. The new method compares favorably to two freely available software tools on a five-tissue segmentation task, while obtaining reasonable segmentation accuracy over all fifteen tissues. The method automatically adapts to variability in the input scans and can thus be directly applied to clinical or research scans acquired with different scanners, sequences or settings. We show that an increase in automated segmentation accuracy results in a lower relative error in electric field simulations when compared to anatomical head models constructed from reference segmentations. However, also the improved segmentations and, by implication, the electric field simulations are affected by systematic artifacts in the input MR scans. As long as the artifacts are unaccounted for, this can lead to local simulation differences up to 30% of the peak field strength on reference simulations. Finally, we exemplarily demonstrate the effect of including all fifteen tissue classes in the field simulations against the standard approach of using only five tissue classes and show that for specific stimulation configurations the local differences can reach 10% of the peak field strength.
Modeling and experimental parameters influence the Electro- (EEG) and Magnetoencephalography (MEG) source analysis of the somatosensory P20/N20 component. In a sensitivity group study, we compare P20/N20 source analysis due to different stimulation type (Electric-Wrist (EW), Braille-Tactile (BT) or Pneumato-Tactile (PT)), measurement modality (combined EEG/MEG – EMEG, EEG or MEG) and head model (standard or individually-skull-conductivity calibrated including brain anisotropic conductivity). Considerable differences between pairs of stimulation types occurred (EW-BT: 8.7±3.3 mm / 27.1o±16.4o, BT-PT: 9±5 mm / 29.9o±17.3o and EW-PT: 9.8±7.4 mm / 15.9o±16.5o and 75 % strength reduction of BT or PT when compared to EW) regardless of the head model used. EMEG has nearly no localization differences to MEG, but large ones to EEG (16.1±4.9 mm), while source orientation differences are non-negligible to both EEG (14o±3.7o) and MEG (12.5o±10.9o). Our calibration results show a considerable inter-subject variability (3.1 – 14 mS/m) for skull conductivity. The comparison due to different head model show localization differences smaller for EMEG (EW: 3.4±2.4 mm, BT: 3.7±3.4 mm, PT: 5.9±6.8 mm) than for EEG (EW: 8.6±8.3 mm, BT: 11.8±6.2 mm, PT: 10.5±5.3 mm), while source orientation differences for EMEG (EW: 15.4o±6.3o, BT: 25.7o±15.2o and PT: 14o±11.5o) and EEG (EW: 14.6o±9.5o, BT: 16.3o±11.1o and PT: 12.9o±8.9o) are in the same range. Our results show that stimulation type, modality and head modeling all have a non-negligible influence on the source reconstruction of the P20/N20 component. The complementary information of both modalities in EMEG can be exploited on the basis of detailed and individualized head models.
Numerical simulation of the electric fields induced by Non-Invasive Brain Stimulation (NIBS), using realistic anatomical head models has gained interest in recent years for understanding the NIBS effects in individual subjects. Although automated tools for generating the head models and performing the electric field simulations have become available, individualized modelling is still not standard practice in NIBS studies. This is likely partly explained by the lack of robustness and usability of the previously available software tools, and partly by the still developing understanding of the link between physiological effects and electric field distributions in the brain. To facilitate individualized modelling in NIBS, we have introduced the SimNIBS (Simulation of NIBS) software package, providing easy-to-use automated tools for electric field modelling. In this article, we give an overview of the modelling pipeline in SimNIBS 2.1, with step-by-step examples of how to run a simulation. Furthermore, we demonstrate a set of scripts for extracting average electric fields for a group of subjects, and finally demonstrate the accuracy of automated placement of standard electrode montages on the head model. SimNIBS 2.1 is freely available at www.simnibs.org.
BACKGROUND AND PURPOSE
Automated cortical thickness (CT) measurements are often used to assess gray matter changes in the healthy and diseased human brain. The FreeSurfer software is frequently applied for this type of analysis. The computational anatomy toolbox (CAT12) for SPM, which offers a fast and easy‐to‐use alternative approach, was recently made available.
METHODS
In this study, we compared region of interest (ROI)‐wise CT estimations of the surface‐based FreeSurfer 6 (FS6) software and the volume‐based CAT12 toolbox for SPM using 44 elderly healthy female control subjects (HC). In addition, these 44 HCs from the cross‐sectional analysis and 34 age‐ and sex‐matched patients with Alzheimer's disease (AD) were used to assess the potential of detecting group differences for each method. Finally, a test‐retest analysis was conducted using 19 HC subjects. All data were taken from the OASIS database and MRI scans were recorded at 1.5 Tesla.
RESULTS
A strong correlation was observed between both methods in terms of ROI mean CT estimates (R² = .83). However, CAT12 delivered significantly higher CT estimations in 32 of the 34 ROIs, indicating a systematic difference between both approaches. Furthermore, both methods were able to reliably detect atrophic brain areas in AD subjects, with the highest decreases in temporal areas. Finally, FS6 as well as CAT12 showed excellent test‐retest variability scores.
CONCLUSION
Although CT estimations were systematically higher for CAT12, this study provides evidence that this new toolbox delivers accurate and robust CT estimates and can be considered a fast and reliable alternative to FreeSurfer.
In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM) EEG forward approach has been proposed as an alternative to CG-FEM (Engwer et al., 2017). It was shown that DG-FEM preserves the property of conservation of charge and that it can, in certain situations such as the so-called skull leakages, be superior to the standard CG-FEM approach. In this paper, we developed, implemented, and evaluated two DG-FEM approaches for the MEG forward problem, namely a conservative and a non-conservative one. The subtraction approach was used as source model. The validation and evaluation work was done in statistical investigations in multi-layer homogeneous sphere models, where an analytic solution exists, and in a six-compartment realistically shaped head volume conductor model. In agreement with the theory, the conservative DG-FEM approach was found to be superior to the non-conservative DG-FEM implementation. This approach also showed convergence with increasing resolution of the hexahedral meshes. While in the EEG case, in presence of skull leakages, DG-FEM outperformed CG-FEM, in MEG, DG-FEM achieved similar numerical errors as the CG-FEM approach, i.e., skull leakages do not play a role for the MEG modality. In particular, for the finest mesh resolution of 1 mm sources with a distance of 1.59 mm from the brain-CSF surface, DG-FEM yielded mean topographical errors (relative difference measure, RDM%) of 1.5% and mean magnitude errors (MAG%) of 0.1% for the magnetic field. However, if the goal is a combined source analysis of EEG and MEG data, then it is highly desirable to employ the same forward model for both EEG and MEG data. Based on these results, we conclude that the newly presented conservative DG-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches in EEG or combined MEG/EEG source analysis scenarios, which motivates a further evaluation of DG-FEM for applications in bioelectromagnetism.
The heart is located in the chest between the lungs behind the sternum and above the diaphragm. It is surrounded by the pericardium. Its size is about that of a fist, and its weight is about 250-300 g. Its center is located about 1.5 cm to the left of the midsagittal plane. Located above the heart are the great vessels: the superior and inferior vena cava, the pulmonary artery and vein, as well as the aorta. The aortic arch lies behind the heart. The esophagus and the spine lie further behind the heart. An overall view is given in Figure 6.1 (Williams and Warwick, 1989).
The walls of the heart are composed of cardiac muscle, called myocardium. It also has striations similar to skeletal muscle. It consists of four compartments: the right and left atria and ventricles. The heart is oriented so that the anterior aspect is the right ventricle while the posterior aspect shows the left atrium (see Figure 6.2). The atria form one unit and the ventricles another. This has special importance to the electric function of the heart, which will be discussed later. The left ventricular free wall and the septum are much thicker than the right ventricular wall. This is logical since the left ventricle pumps blood to the systemic circulation, where the pressure is considerably higher than for the pulmonary circulation, which arises from right ventricular outflow.
The cardiac muscle fibers are oriented spirally (see Figure 6.3) and are divided into four groups: Two groups of fibers wind around the outside of both ventricles. Beneath these fibers a third group winds around both ventricles. Beneath these fibers a fourth group winds only around the left ventricle. The fact that cardiac muscle cells are oriented more tangentially than radially, and that the resistivity of the muscle is lower in the direction of the fiber has importance in electrocardiography and magnetocardiography.
The heart has four valves. Between the right atrium and ventricle lies the tricuspid valve, and between the left atrium and ventricle is the mitral valve. The pulmonary valve lies between the right ventricle and the pulmonary artery, while the aortic valve lies in the outflow tract of the left ventricle (controlling flow to the aorta).
The blood returns from the systemic circulation to the right atrium and from there goes through the tricuspid valve to the right ventricle. It is ejected from the right ventricle through the pulmonary valve to the lungs. Oxygenated blood returns from the lungs to the left atrium, and from there through the mitral valve to the left ventricle. Finally blood is pumped through the aortic valve to the aorta and the systemic circulation.
The present invention smooths piece-wise linear shapes by defining neighborhoods of vertices around vertices of the shape. One or more vectors is defined between the vertex and each of its neighbors. Vector sums are alternately multiplied by one of two scale factors. The scale factors are opposite in sign with the negative scale factor of larger magnitude. The vertices of the shape are displaced by the multiplied vector sums to attain new positions. The process is repeated with the vertices moving back and forth approximately through their final position until the shape is smoothed without shrinkage.
FreeSurfer software package automatically estimates the cerebral cortical thickness. Its use is widely accepted, albeit this tool was validated against histologic measurements in only two post-mortem isolated brain MR scans. Indeed, a comparison between histologic measurements and FreeSurfer estimation from in vivo data was never performed. At the "Claudio Munari" Center for Epilepsy and Parkinson Surgery we have included FreeSurfer in our presurgical workflow since 2008, mainly because the automatic reconstruction of the brain surface is useful for carefully planning the surgical resection. We therefore compared cortical thickness values obtained by the automatic software pipeline with manual histologic measurements performed on 27 histologic specimens resected from the corresponding brain regions of the same epileptic subjects. This method-comparison study, including Passing-Bablok regression and Bland-Altman plot analysis, showed a good agreement between FreeSurfer estimation and histologic measurements of cortical thickness. The mean cortical thickness values (±Standard Deviation) obtained with FreeSurfer and histologic measurements were 3.65 mm ± 0.44 and 3.72 mm ± 0.36, respectively (P value = 0.32). Our findings strengthen previous reports on cortical thickness changes as biomarkers of different neurological conditions.
Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and simple MATLAB code, described in more detail than usual, so the reader can experiment (and add to the code) knowing the underlying principles. We find the node locations by solving for equilibrium in a truss structure (using piecewise linear force-displacement relations) and we reset the topology by the Delaunay algorithm. The geometry is described implicitly by its distance function. In addition to being much shorter and simpler than other meshing techniques, our algorithm typically produces meshes of very high quality. We discuss ways to improve the robustness and the performance, but our aim here is simplicity. Readers can download (and edit) the codes from http://math.mit.edu/~persson/mesh.
Brainstorm is a collaborative open-source application dedicated to magnetoencephalography (MEG) and electroencephalography (EEG) data visualization and processing, with an emphasis on cortical source estimation techniques and their integration with anatomical magnetic resonance imaging (MRI) data. The primary objective of the software is to connect MEG/EEG neuroscience investigators with both the best-established and cutting-edge methods through a simple and intuitive graphical user interface (GUI).
This paper describes FieldTrip, an open source software package that we developed for the analysis of MEG, EEG, and other electrophysiological data. The software is implemented as a MATLAB toolbox and includes a complete set of consistent and user-friendly high-level functions that allow experimental neuroscientists to analyze experimental data. It includes algorithms for simple and advanced analysis, such as time-frequency analysis using multitapers, source reconstruction using dipoles, distributed sources and beamformers, connectivity analysis, and nonparametric statistical permutation tests at the channel and source level. The implementation as toolbox allows the user to perform elaborate and structured analyses of large data sets using the MATLAB command line and batch scripting. Furthermore, users and developers can easily extend the functionality and implement new algorithms. The modular design facilitates the reuse in other software packages.
A solution of the forward problem is an important component of any method for computing the spatio-temporal activity of the neural sources of magnetoencephalography (MEG) and electroencephalography (EEG) data. The forward problem involves computing the scalp potentials or external magnetic field at a finite set of sensor locations for a putative source configuration. We present a unified treatment of analytical and numerical solutions of the forward problem in a form suitable for use in inverse methods. This formulation is achieved through factorization of the lead field into the product of the moment of the elemental current dipole source with a "kernel matrix" that depends on the head geometry and source and sensor locations, and a "sensor matrix" that models sensor orientation and gradiometer effects in MEG and differential measurements in EEG. Using this formulation and a recently developed approximation formula for EEG, based on the "Berg parameters," we present novel reformulations of the basic EEG and MEG kernels that dispel the myth that EEG is inherently more complicated to calculate than MEG. We also present novel investigations of different boundary element methods (BEM's) and present evidence that improvements over currently published BEM methods can be realized using alternative error-weighting methods. Explicit expressions for the matrix kernels for MEG and EEG for spherical and realistic head geometries are included.
Representations of the active cell populations on the cortical surface via electric and magnetic measurements are known as electromagnetic source images (EMSIs) of the human brain. Numerical solution of the potential and magnetic fields for a given electrical source distribution in the human brain is an essential part of electromagnetic source imaging. In this study, the performance of the boundary element method (BEM) is explored with different surface element types. A new BEM formulation is derived that makes use of isoparametric linear, quadratic or cubic elements. The surface integration is performed with Gauss quadrature. The potential fields are solved assuming a concentric three-shell model of the human head for a tangential dipole at different locations. In order to achieve 2% accuracy in potential solutions, the number of quadratic elements is of the order of hundreds. However, with linear elements, this number is of the order of ten thousand. The relative difference measures (RDMs) are obtained for the numerical models that use different element types. The numerical models that employ quadratic and cubic element types provide superior performance over linear elements in terms of accuracy in solutions. Assuming a homogeneous sphere model of the head, the RDMs are also obtained for the three components (radial and tangential) of the magnetic fields. The RDMs obtained for the tangential fields are, in general, much higher than those obtained for the radial fields. Both quadratic and cubic elements provide superior performance compared with linear elements for a wide range of dipole locations.
For a number of computational purposes, including visualization of scientific data and registration of multimodal medical data, smooth curves must be approximated by polygonal curves, and surfaces by polyhedral surfaces. An inherent problem of these approximation algorithms is that the resulting curves and surfaces appear faceted. Boundary-following and iso-surface construction algorithms are typical examples. To reduce the apparent faceting, smoothing methods are used. In this paper, we introduce a new method for smoothing piecewise linear shapes of arbitrary dimension and topology. This new method is in fact a linear low-pass filter that removes high-curvature variations, and does not produce shrinkage. Its computational complexity is linear in the number of edges or faces of the shape, and the required storage is linear in the number of vertices
Objective:
A new numerical modeling approach is proposed which provides forward-problem solutions for both noninvasive recordings (EEG/MEG) and higher-resolution intracranial recordings (iEEG).
Methods:
The algorithm is our recently developed boundary element fast multipole method or BEM-FMM. It is based on the integration of the boundary element formulation in terms of surface charge density and the fast multipole method originating from its inventors. The algorithm still possesses the major advantage of the conventional BEM - high speed - but is simultaneously capable of processing a very large number of surface-based unknowns. As a result, an unprecedented spatial resolution could be achieved, which enables multiscale modeling.
Results:
For non-invasive EEG/MEG, we are able to accurately solve the forward problem with approximately 1 mm anatomical resolution in the cortex within 1-2 min given several thousand cortical dipoles. Targeting high-resolution iEEG, we are able to compute, for the first time, an integrated electromagnetic response for an ensemble (2,450) of tightly packed realistic pyramidal neocortical neurons in a full-head model with 0.6 mm anatomical cortical resolution. The neuronal arbor is comprised of 5.9 M elementary 1.2 μm long dipoles. On a standard server, the computations require about 5 min.
Conclusion:
Our results indicate that the BEM-FMM approach may be well suited to support numerical multiscale modeling pertinent to modern high-resolution and submillimeter iEEG.
Significance:
Based on the speed and ease of implementation, this new algorithm represents a method that will greatly facilitate simulations at multi-scale across a variety of applications.
Objective:
We develop a new accurate version of the boundary element fast multipole method for TMS-related problems. This method is based on the surface-charge formulation and is using the highly efficient fast multipole accelerator along with analytical computations of neighbor surface integrals.
Results:
The method accuracy is demonstrated by comparison with the proven commercial FEM software ANSYS Maxwell 18.2 2017 operating on unstructured grids and with adaptive mesh refinement. Five realistic high-definition head models from the Population Head Repository (IT-IS Foundation, Switzerland) have been acquired and augmented with a commercial TMS coil model (MRi-B91, MagVenture, Denmark). For each head model, simulations with our method and simulations with the FEM software ANSYS Maxwell 18.2 2017 have been performed. These simulations have been compared with each other and an excellent agreement was established in every case.
Significance:
At the same time, our new method runs approximately 500 times faster than the ANSYS FEM, finishes in about 200 sec on a standard server, and naturally provides a sub-millimeter field resolution, which is justified using mesh refinement.
Conclusions:
Our method can be applied to modeling of brain stimulation and recording technologies such as transcranial magnetic stimulation (TMS) and magnetoencephalography (MEG), and has the potential to become a real-time high-resolution simulation tool.
In order to perform electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, which is the so-called EEG forward problem. To solve it accurately, it is necessary to apply numerical methods that are able to take the individual geometry and conductivity distribution of the subject's head into account. In this context, the finite element (FE) method (FEM) has shown high numerical accuracy with the possibility to model complex geometries and conductive features, e.g., white matter conductivity anisotropy. In this article, we introduce and analyze the application of a discontinuous Galerkin (DG) method, an FEM that includes features of the finite volume framework, to the EEG forward problem. The DG-FEM approach fulfills the conservation property of electric charge also in the discrete case, making it attractive for a variety of applications. Furthermore, as we show, this approach can alleviate modeling inaccuracies that might occur in head geometries when using classical FE methods, e.g., socalled "skull leakage effects," which may occur in areas where the thickness of the skull is in the range of the mesh resolution. Therefore, we derive a DG formulation of the FEM subtraction approach for the EEG forward problem and present numerical results that highlight the advantageous features and the potential benefits of the proposed approach.
Experimental MEG source imaging studies have typically been carried out with either a spherically symmetric head model or a single-shell boundary-element (BEM) model that is shaped according to the inner skull surface. The concepts and comparisons behind these simplified models have led to misunderstandings regarding the role of skull and scalp in MEG. In this work, we assess the forward-model errors due to different skull/scalp approximations and due to differences and errors in model geometries.
The Human Connectome Project (HCP) is an ambitious 5-year effort to characterize brain connectivity and function and their variability in healthy adults. This review summarizes the data acquisition plans being implemented by a consortium of HCP investigators who will study a population of 1200 subjects (twins and their non-twin siblings) using multiple imaging modalities along with extensive behavioral and genetic data. The imaging modalities will include diffusion imaging (dMRI), resting-state fMRI (R-fMRI), task-evoked fMRI (T-fMRI), T1- and T2-weighted MRI for structural and myelin mapping, plus combined magnetoencephalography and electroencephalography (MEG/EEG). Given the importance of obtaining the best possible data quality, we discuss the efforts underway during the first two years of the grant (Phase I) to refine and optimize many aspects of HCP data acquisition, including a new 7T scanner, a customized 3T scanner, and improved MR pulse sequences.
FreeSurfer is a suite of tools for the analysis of neuroimaging data that provides an array of algorithms to quantify the functional, connectional and structural properties of the human brain. It has evolved from a package primarily aimed at generating surface representations of the cerebral cortex into one that automatically creates models of most macroscopically visible structures in the human brain given any reasonable T1-weighted input image. It is freely available, runs on a wide variety of hardware and software platforms, and is open source.
1. To clarify the generators of human short-latency somatosensory evoked potentials (SEPs) thought to arise in sensorimotor cortex, we studied the effects on SEPs of surgical excision of somatosensory or motor cortex in humans and monkeys. 2. Normal median nerve SEPs (P20-N30, N20-P30, and P25-N35) were recorded from the cortical surface of a patient (G13) undergoing a cortical excision for relief of focal seizures. All SEPs were abolished both acutely and chronically after excision of the hand area of somatosensory cortex. Similarly, excision of the hand area of somatosensory cortex abolished corresponding SEPs (P10-N20, N10-P20, and P12-N25) in monkeys. Excision of the crown of monkey somatosensory cortex abolished P12-N25 while leaving P10-N20 and N10-P20 relatively unaffected. 3. After excision of the hand area of motor cortex, all SEPs were present when recorded from the cortical surface of a patient (W1) undergoing a cortical excision for relief of focal seizures. Similarly, all SEPs were present in monkeys after excision of the hand area of motor cortex. 4. Although all SEPs were present after excision of motor cortex in monkeys, variable changes were observed in SEPs after the excisions. However, these changes were not larger than the changes observed after excision of parietal cortex posterior to somatosensory cortex. We concluded that the changes were not specific to motor cortex excision. 5. These results support two major conclusions. 1) Median nerve SEPs recorded from sensorimotor cortex are produced by generators in two adjacent regions of somatosensory cortex: a tangentially oriented generator in area 3b, which produces P20-N30 (human) and P10-N20 (monkey) [recorded anterior to the central sulcus (CS)] and N20-P30 (human) and N10-P20 (monkey) posterior to the CS; and a radially oriented generator in area 1, which produces P25-N35 (human) and P12-N25 (monkey) recorded from the postcentral gyrus near the CS. 2) Motor cortex makes little or no contribution to these potentials.
In this paper basic mathematical and physical concepts of the biomagnetic inverse problem are reviewed with some new approaches. The forward problem is discussed for both homogeneous and inhomogeneous media. Geselowitz' formulae and a surface integral equation are presented to handle a piecewise homogeneous conductor. The special cases of a spherically symmetric conductor and a horizontally layered medium are discussed in detail. The non-uniqueness of the solution of the magnetic inverse problem is discussed and the difficulty caused by the contribution of the electric potential to the magnetic field outside the conductor is studied. As practical methods of solving the inverse problem, a weighted least-squares search with confidence limits and the method of minimum norm estimate are discussed.
Institute of Physics and Engineering in Medicine IPEM's aim is to promote the advancement of physics and engineering applied to medicine and biology for the public benefit. Its members are professionals working in healthcare, education, industry and research. IPEM publishes scientific journals and books and organises conferences to disseminate knowledge and support members in their development. It sets and advises on standards for the practice, education and training of scientists and engineers working in healthcare to secure an effective and appropriate workforce.
A comprehensive review of factors affecting the accuracy of the boundary element method (BEM) for calculating surface potentials is presented. A relative-error statistic is developed which is only sensitive to calculation errors that could affect the inverse solution for source position, and insensitive to errors that only affect the solution for source strength. The factors considered in this paper are: numerical approximations intrinsic to the BEM, such as constant-potential versus linear-potential basis functions and sharp-edged versus smooth-surfaced volumes; aspects of the volume conductor including the volume shape, density of surface elements, and element shape; source position and orientation; and effects of "refinements" in the numerical methods. The effects of these factors are considered in both smooth-shaped (spheres and spheroids) and sharp-edged (cubes) volume conductors. This represents the first attempt to assess the effects of many of these factors pertaining to the numerical methods commonly used in fields such as electrocardiography (ECG) and electroencephalography (EEG). Strategies for obtaining the most accurate solutions are presented.
In serial sensory processing, information flows from the thalamus via primary sensory cortices to higher-order association areas. However, association cortices also receive, albeit weak, direct thalamocortical sensory inputs of unknown function. For example, while information proceeds from primary (SI) to secondary (SII) somatosensory cortex in a serial fashion, both areas are known to receive direct thalamocortical sensory input. The present study examines the potential roles of such parallel input arrangements. The subjects were presented with median nerve somatosensory stimuli with the instruction to respond with the contralateral hand. The locations and time courses of the activated brain areas were first identified with magnetoencephalography (MEG). In a subsequent session, these brain areas were modulated with single-pulse transcranial magnetic stimulation (TMS) at 15-210 ms after the somatosensory stimulus while electroencephalography (EEG) was recorded. TMS pulses at 15-40 ms post-stimulus significantly speeded up reaction times and somatosensory-evoked responses, with largest facilitatory effects when the TMS pulse was given to contralateral SII at about 20 ms. To explain the results, we propose that the early somatosensory-evoked physiological SII activation exerts an SII-->SI influence that facilitates the reciprocal SI-->SII pathway - with TMS to SII we apparently amplified this mechanism. The results suggest that the human brain may utilize parallel inputs to facilitate long-distance cortico-cortical connections, resulting in accelerated processing and speeded reaction times. This arrangement could also allow very early top-down modulation of the bottom-up stream of sensory information.
BEM-FMM with B-Refinement for EEG
- Wartman