A Mixed Finite Element Method to Solve the EEG Forward Problem

Three-Dimensional Electrode Model for EEG Forward Problem

OBJECTIVE

This study aims to address inaccuracies in model description and boundary representation due to dimension-ality loss in the commonly-used point electrode model (PEM) and complete electrode model (CEM) for EEG forward problem (FP).

METHODS

To overcome these limitations, this paper proposes a three-dimensional electrode model (TEM). Firstly, we devise an extension-constraint framework to generate an electrode mesh based on the structural priors and seamlessly integrate it into the MRI-based head mesh through two modules: (1) an extension module designed to extend a cuboid mesh containing both head and electrode meshes to avoid the challenges in fusing two irregular stepped surface mesh, and (2) loosely coupled constraints formulated in the constraint module to describe the electrode structure and enhance the flexibility and extensibility. Secondly, an accurate boundary representation is achieved by setting a local equipotential on the metal surface of the electrodes.

RESULTS

Experimental results indicate that, compared with PEM and CEM, TEM exhibits significant differences in FP and inverse problem. Further explorations reveal that alterations in electrode height, structure, and contact area exert a more profound impact than conductivity, whereas the impact of air bubbles, hair, and gel bridges is structure-dependent.

CONCLUSION

The proposed TEM has the potential to enhance the solution accuracy of FP and inverse problem.

SIGNIFICANCE

This paper introduces an ingenious method for incorporating the 3D structure of electrodes into FP solution to improve the accuracy and explore the effect of electrode structure.

Flexible-Center Hat Complete Electrode Model for EEG Forward Problem

OBJECTIVE

This study aims to develop a more realistic electrode model by incorporating the non-uniform distribution of electrode contact conductance (ECC) and the shunting effects, to accurately solve EEG forward problem (FP).

METHODS

Firstly, a hat function is introduced to construct a more realistic hat-shaped distribution (HD) for ECC. Secondly, this hat function is modified by applying two parameters - offset ratio and offset direction - to account for the variability in ECC's center and to develop the flexible-center HD (FCHD). Finally, by integrating this FCHD into the complete electrode model (CEM) with the shunting effects, a novel flexible-center hat complete electrode model (FCH-CEM) is proposed and used to solve FP.

RESULTS

Simulation experiments using a realistic head model demonstrate the necessity of FCH-CEM and its potential to improve the accuracy of the FP solution compared to current models, i.e., the point electrode model (PEM) and CEM. And compared to PEM, it has better performance under coarse mesh conditions (2 mm). Further experiments indicate the significance of considering shunting effects, as ignoring them results in larger errors than coarse mesh when the average contact conductance is large (101S/m2).

CONCLUSION

The proposed FCH-CEM has better accuracy and performance than PEM and complements CEM in finer meshes, making it necessary for coarse meshes.

SIGNIFICANCE

This study proposes a novel model that enhances electrode modeling and FP accuracy, and provides new ideas and methods for future research.

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling

This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

A novel method for dynamically altering the surface area of intracranial EEG electrodes

Objective.Intracranial electroencephalogram (iEEG) plays a critical role in the treatment of neurological diseases, such as epilepsy and Parkinson's disease, as well as the development of neural prostheses and brain computer interfaces. While electrode geometries vary widely across these applications, the impact of electrode size on iEEG features and morphology is not well understood. Some insight has been gained from computer simulations, as well as experiments in which signals are recorded using electrodes of different sizes concurrently in different brain regions. Here, we introduce a novel method to record from electrodes of different sizes in the exact same location by changing the size of iEEG electrodes after implantation in the brain.Approach.We first present a theoretical model and anin vitrovalidation of the method. We then report the results of anin vivoimplementation in three human subjects with refractory epilepsy. We recorded iEEG data from three different electrode sizes and compared the amplitudes, power spectra, inter-channel correlations, and signal-to-noise ratio (SNR) of interictal epileptiform discharges, i.e. epileptic spikes.Main Results.We found that iEEG amplitude and power decreased as electrode size increased, while inter-channel correlation did not change significantly with electrode size. The SNR of epileptic spikes was generally highest in the smallest electrodes, but 39% of spikes had maximal SNR in larger electrodes. This likely depends on the precise location and spatial spread of each spike.Significance.Overall, this new method enables multi-scale measurements of electrical activity in the human brain that can facilitate our understanding of neurophysiology, treatment of neurological disease, and development of novel technologies.

Patient-specific solution of the electrocorticography forward problem in deforming brain

Invasive intracranial electroencephalography (iEEG), or electrocorticography (ECoG), measures electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery. Combined with numerical modeling it can further improve accuracy of epilepsy surgery planning. Accurate solution of the iEEG forward problem, which is a crucial prerequisite for solving the iEEG inverse problemin epilepsy seizure onset zone localization, requires accurate representation of the patient's brain geometry and tissue electrical conductivity after implantation of electrodes. However, implantation of subdural grid electrodes causes the brain to deform, which invalidates preoperatively acquired image data. Moreover, postoperative magnetic resonance imaging (MRI) is incompatible with implanted electrodes and computed tomography (CT) has insufficient range of soft tissue contrast, which precludes both MRI and CT from being used to obtain the deformed postoperative geometry. In this paper, we present a biomechanics-based image warping procedure using preoperative MRI for tissue classification and postoperative CT for locating implanted electrodes to perform non-rigid registration of the preoperative image data to the postoperative configuration. We solve the iEEG forward problem on the predicted postoperative geometry using the finite element method (FEM) which accounts for patient-specific inhomogeneity and anisotropy of tissue conductivity. Results for the simulation of a current source in the brain show large differences in electric potential predicted by the models based on the original images and the deformed images corresponding to the brain geometry deformed by placement of invasive electrodes. Computation of the lead field matrix (useful for solution of the iEEG inverse problem) also showed significant differences between the different models. The results suggest that rapid and accurate solution of the forward problem in a deformed brain for a given patient is achievable.

Detection of Brain Network Communities During Natural Speech Comprehension From Functionally Aligned EEG Sources

In recent years, electroencephalograph (EEG) studies on speech comprehension have been extended from a controlled paradigm to a natural paradigm. Under the hypothesis that the brain can be approximated as a linear time-invariant system, the neural response to natural speech has been investigated extensively using temporal response functions (TRFs). However, most studies have modeled TRFs in the electrode space, which is a mixture of brain sources and thus cannot fully reveal the functional mechanism underlying speech comprehension. In this paper, we propose methods for investigating the brain networks of natural speech comprehension using TRFs on the basis of EEG source reconstruction. We first propose a functional hyper-alignment method with an additive average method to reduce EEG noise. Then, we reconstruct neural sources within the brain based on the EEG signals to estimate TRFs from speech stimuli to source areas, and then investigate the brain networks in the neural source space on the basis of the community detection method. To evaluate TRF-based brain networks, EEG data were recorded in story listening tasks with normal speech and time-reversed speech. To obtain reliable structures of brain networks, we detected TRF-based communities from multiple scales. As a result, the proposed functional hyper-alignment method could effectively reduce the noise caused by individual settings in an EEG experiment and thus improve the accuracy of source reconstruction. The detected brain networks for normal speech comprehension were clearly distinctive from those for non-semantically driven (time-reversed speech) audio processing. Our result indicates that the proposed source TRFs can reflect the cognitive processing of spoken language and that the multi-scale community detection method is powerful for investigating brain networks.

Cortical Source Analysis of Event-Related Potentials: A Developmental Approach

Cortical source analysis of electroencephalographic (EEG) signals has become an important tool in the analysis of brain activity. The aim of source analysis is to reconstruct the cortical generators (sources) of the EEG signal recorded on the scalp. The quality of the source reconstruction relies on the accuracy of the forward problem, and consequently the inverse problem. An accurate forward solution is obtained when an appropriate imaging modality (i.e., structural magnetic resonance imaging - MRI) is used to describe the head geometry, precise electrode locations are identified with 3D maps of the sensor positions on the scalp, and realistic conductivity values are determined for each tissue type of the head model. Together these parameters contribute to the definition of realistic head models. Here, we describe the steps necessary to reconstruct the cortical generators of the EEG signal recorded on the scalp. We provide an example of source reconstruction of event-related potentials (ERPs) during a face-processing task performed by a 6-month-old infant. We discuss the adjustments necessary to perform source analysis with measures different from the ERPs. The proposed pipeline can be applied to the investigation of different cognitive tasks in both younger and older participants.

Conservative Finite Element Modeling of EEG and MEG on Unstructured Grids

For interpretation of electroencephalography (EEG) and magnetoencephalography (MEG) data, multiple solutions of the respective forward problems are needed. In this paper, we assess performance of the mixed-hybrid finite element method (MHFEM) applied to EEG and MEG modeling. The method provides an approximate potential and induced currents and results in a system with a positive semi-definite matrix. The system thus can be solved with a variety of standard methods (e.g. the preconditioned conjugate gradient method). The induced currents satisfy discrete charge conservation law making the method conservative. We studied its performance on unstructured tetrahedral grids for a layered spherical head model as well as a realistic head model. We also compared its accuracy versus the conventional nodal finite element method ( P₁ FEM). To avoid modeling singular sources, we completed our computations with a subtraction approach; the derived expression for the MEG response different from earlier published and involves integration of finite quantities only. We conclude that although the MHFEM is more computationally demanding than the P₁ FEM, its use is justified for EEG and MEG modeling on low-resolution head models where P₁ FEM loses accuracy.

Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes

Objective. To formulate, validate, and apply an alternative to the finite element method (FEM) high-resolution modeling technique for electrical brain stimulation-the boundary element fast multipole method (BEM-FMM). To include practical electrode models for both surface and embedded electrodes.Approach. Integral equations of the boundary element method in terms of surface charge density are combined with a general-purpose fast multipole method and are expanded for voltage, shunt, current, and floating electrodes. The solution of coupled and properly weighted/preconditioned integral equations is accompanied by enforcing global conservation laws: charge conservation law and Kirchhoff's current law.Main results.A sub-percent accuracy is reported as compared to the analytical solutions and simple validation geometries. Comparison to FEM considering realistic head models resulted in relative differences of the electric field magnitude in the range of 3%-6% or less. Quantities that contain higher order spatial derivatives, such as the activating function, are determined with a higher accuracy and a faster speed as compared to the FEM. The method can be easily combined with existing head modeling pipelines such as headreco or mri2mesh.Significance.The BEM-FMM does not rely on a volumetric mesh and is therefore particularly suitable for modeling some mesoscale problems with submillimeter (and possibly finer) resolution with high accuracy at moderate computational cost. Utilizing Helmholtz reciprocity principle makes it possible to expand the method to a solution of EEG forward problems with a very large number of cortical dipoles.

Advances in Electrical Source Imaging: A Review of the Current Approaches, Applications and Challenges

Brain source localization has been consistently implemented over the recent years to elucidate complex brain operations, pairing the high temporal resolution of the EEG with the high spatial estimation of the estimated sources. This review paper aims to present the basic principles of Electrical source imaging (ESI) in the context of the recent progress for solving the forward and the inverse problems, and highlight the advantages and limitations of the different approaches. As such, a synthesis of the current state-of-the-art methodological aspects is provided, offering a complete overview of the present advances with regard to the ESI solutions. Moreover, the new dimensions for the analysis of the brain processes are indicated in terms of clinical and cognitive ESI applications, while the prevailing challenges and limitations are thoroughly discussed, providing insights for future approaches that could help to alleviate methodological and technical shortcomings.

DUNEuro-A software toolbox for forward modeling in bioelectromagnetism

Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free and open-source C++ software toolbox for the numerical computation of forward solutions in bioelectromagnetism. Building upon the DUNE framework, it provides implementations of modern fitted and unfitted finite element methods to efficiently solve the forward problems of electro- and magnetoencephalography. The user can choose between a variety of different source models that are implemented. The software's aim is to provide interfaces that are extendable and easy-to-use. In order to enable a closer integration into existing analysis pipelines, interfaces to Python and MATLAB are provided. The practical use is demonstrated by a source analysis example of somatosensory evoked potentials using a realistic six-compartment head model. Detailed installation instructions and example scripts using spherical and realistic head models are appended.

Electroencephalographic Source Reconstruction by the Finite-Element Approximation of the Elliptic Cauchy Problem

OBJECTIVE

This paper develops a novel approach for fast and reliable reconstruction of EEG sources in MRI-based head models.

METHODS

The inverse EEG problem is reduced to the Cauchy problem for an elliptic partial-derivative equation. The problem is transformed into a regularized minimax problem, which is directly approximated in a finite-element space. The resulting numerical method is efficient and easy to program. It eliminates the need to solve forward problems, which can be a tedious task. The method applies to complex anatomical head models, possibly containing holes in surfaces, anisotropic conductivity, and conductivity variations inside each tissue. The method has been verified on a spherical shell model and an MRI-based head.

RESULTS

Numerical experiments indicate high accuracy of localization of brain activations (both cortical potential and current) and rapid execution time.

CONCLUSION

This study demonstrates that the proposed approach is feasible for EEG source analysis and can serve as a rapid and reliable tool for EEG source analysis.

SIGNIFICANCE

The significance of this study is that it develops a fast, accurate, and simple numerical method of EEG source analysis, applicable to almost arbitrary complex head models.

Multimodal alterations of directed connectivity profiles in patients with attention-deficit/hyperactivity disorders

Functional and effective connectivity measures for tracking brain region interactions that have been investigated using both electroencephalography (EEG) and magnetoencephalography (MEG) bringing up new insights into clinical research. However, the differences between these connectivity methods, especially at the source level, have not yet been systematically studied. The dynamic characterization of coherent sources and temporal partial directed coherence, as measures of functional and effective connectivity, were applied to multimodal resting EEG and MEG data obtained from 11 young patients (mean age 13.2 ± 1.5 years) with attention-deficit/hyperactivity disorder (ADHD) and age-matched healthy subjects. Additionally, machine-learning algorithms were applied to the extracted connectivity features to identify biomarkers differentiating the two groups. An altered thalamo-cortical connectivity profile was attested in patients with ADHD who showed solely information outflow from cortical regions in comparison to healthy controls who exhibited bidirectional interregional connectivity in alpha, beta, and gamma frequency bands. We achieved an accuracy of 98% by combining features from all five studied frequency bands. Our findings suggest that both types of connectivity as extracted from EEG or MEG are sensitive methods to investigate neuronal network features in neuropsychiatric disorders. The connectivity features investigated here can be further tested as biomarkers of ADHD.

A retrospective evaluation of automated optimization of deep brain stimulation parameters

OBJECTIVE

We performed a retrospective analysis of an optimization algorithm for the computation of patient-specific multipolar stimulation configurations employing multiple independent current/voltage sources. We evaluated whether the obtained stimulation configurations align with clinical data and whether the optimized stimulation configurations have the potential to lead to an equal or better stimulation of the target region as manual programming, while reducing the time required for programming sessions.

APPROACH

For three patients (five electrodes) diagnosed with essential tremor, we derived optimized multipolar stimulation configurations using an approach that is suitable for the application in clinical practice. To evaluate the automatically derived stimulation settings, we compared them to the results of the monopolar review.

MAIN RESULTS

We observe a good agreement between the findings of the monopolar review and the optimized stimulation configurations, with the algorithm assigning the maximal voltage in the optimized multipolar pattern to the contact that was found to lead to the best therapeutic effect in the clinical monopolar review in all cases. Additionally, our simulation results predict that the optimized stimulation settings lead to the activation of an equal or larger volume fraction of the target compared to the manually determined settings in all cases.

SIGNIFICANCE

Our results demonstrate the feasibility of an automatic determination of optimal DBS configurations and motivate a further evaluation of the applied optimization algorithm.

Modeling Trans-Spinal Direct Current Stimulation in the Presence of Spinal Implants

Trans-spinal direct current stimulation (tsDCS) is a technique considered for the treatment of corticospinal damage or dysfunction. TsDCS aims to induce functional modulation in the corticospinal circuitry via a direct current (DC) generated an electric field (EF). To ensure subject safety, subjects with metallic implants are generally excluded from receiving neural dc stimulation. However, spinal injuries often require spinal implants for stabilization. Our goal was to investigate implant imposed changes to EF and current density (CD) magnitude during tsDCS. We simulated the EF and CD, generated by tsDCS in the presence of spinal rods for two electrode configurations and four implant locations along the spinal cord. For each scenario, a no-implant condition was computed for comparison. We assessed changes in EF and CD at the implant location and the EF inside the spinal cord. Our results show that implant presence was able to influence peak CD, compared to the no-implant condition. Nonetheless, the highest calculated CD levels were a factor six lower than those thought to lead to hazardous tissue-damaging effects. Additionally, implant presence did not considerably affect the average EF inside the spinal cord. Our findings do therefore not indicate potentially unsafe CD levels, or significant alterations to stimulation intensity inside the spinal cord, caused by a spinal implant during tsDCS. Our results are relevant to the safety of transcutaneous spinal stimulation applied in the presence of metallic spinal implants.

Benchmarking transcranial electrical stimulation finite element models: a comparison study

OBJECTIVE

To compare field measure differences in simulations of transcranial electrical stimulation (tES) generated by variations in finite element (FE) models due to boundary condition specification, use of tissue compartment smoothing filters, and use of free or structured tetrahedral meshes based on magnetic resonance imaging (MRI) data.

APPROACH

A structural MRI head volume was acquired at 1 mm³ resolution and segmented into ten tissue compartments. Predicted current densities and electric fields were computed in segmented models using modeling pipelines involving either an in-house (block) or a commercial platform commonly used in previous FE tES studies involving smoothed compartments and free meshing procedures (smooth). The same boundary conditions were used for both block and smooth pipelines. Differences caused by varying boundary conditions were examined using a simple geometry. Percentage differences of median current density values in five cortical structures were compared between the two pipelines for three electrode montages (F3-right supraorbital, T7-T8 and Cz-Oz).

MAIN RESULTS

Use of boundary conditions commonly used in previous tES FE studies produced asymmetric current density profiles in the simple geometry. In head models, median current density differences produced by the two pipelines, using the same boundary conditions, were up to 6% (isotropic) and 18% (anisotropic) in structures targeted by each montage. Tangential electric field measures calculated via either pipeline were within the range of values reported in the literature, when averaged over cortical surface patches.

SIGNIFICANCE

Apparently equivalent boundary settings may affect predicted current density outcomes and care must be taken in their specification. Smoothing FE model compartments may not be necessary, and directly translated, voxellated tissue boundaries at 1 mm³ resolution may be sufficient for use in tES FE studies, greatly reducing processing times. The findings here may be used to inform future current density modeling studies.

A Finite-Difference Solution for the EEG Forward Problem in Inhomogeneous Anisotropic Media

Accurate source localization of electroencephalographic (EEG) signals requires detailed information about the geometry and physical properties of head tissues. Indeed, these strongly influence the propagation of neural activity from the brain to the sensors. Finite difference methods (FDMs) are head modelling approaches relying on volumetric data information, which can be directly obtained using magnetic resonance (MR) imaging. The specific goal of this study is to develop a computationally efficient FDM solution that can flexibly integrate voxel-wise conductivity and anisotropy information. Given the high computational complexity of FDMs, we pay particular attention to attain a very low numerical error, as evaluated using exact analytical solutions for spherical volume conductor models. We then demonstrate the computational efficiency of our FDM numerical solver, by comparing it with alternative solutions. Finally, we apply the developed head modelling tool to high-resolution MR images from a real experimental subject, to demonstrate the potential added value of incorporating detailed voxel-wise conductivity and anisotropy information. Our results clearly show that the developed FDM can contribute to a more precise head modelling, and therefore to a more reliable use of EEG as a brain imaging tool.

Solving 3-D PDEs by Tensor B-Spline Methodology: A High Performance Approach Applied to Optical Diffusion Tomography

Solutions of 3-D elliptic PDEs form the basis of many mathematical models in medicine and engineering. Solving elliptic PDEs numerically in 3-D with fine discretization and high precision is challenging for several reasons, including the cost of 3-D meshing, the massive increase in operation count, and memory consumption when a high-order basis is used, and the need to overcome the "curse of dimensionality." This paper describes how these challenges can be either overcome or relaxed by a Tensor B-spline methodology with the following key properties: 1) the tensor structure of the variational formulation leads to regularity, separability, and sparsity, 2) a method for integration over the complex domain boundaries eliminates meshing, and 3) the formulation induces high-performance and memory-efficient computational algorithms. The methodology was evaluated by application to the forward problem of Optical Diffusion Tomography (ODT), comparing it with the solver from a state-of-the-art Finite-Element Method (FEM)-based ODT reconstruction framework. We found that the Tensor B-spline methodology allows one to solve the 3-D elliptic PDEs accurately and efficiently. It does not require 3-D meshing even on complex and non-convex boundary geometries. The Tensor B-spline approach outperforms and is more accurate than the FEM when the order of the basis function is > 1, requiring fewer operations and lower memory consumption. Thus, the Tensor B-spline methodology is feasible and attractive for solving large elliptic 3-D PDEs encountered in real-world problems.

A realistic, accurate and fast source modeling approach for the EEG forward problem

The aim of this paper is to advance electroencephalography (EEG) source analysis using finite element method (FEM) head volume conductor models that go beyond the standard three compartment (skin, skull, brain) approach and take brain tissue inhomogeneity (gray and white matter and cerebrospinal fluid) into account. The new approach should enable accurate EEG forward modeling in the thin human cortical structures and, more specifically, in the especially thin cortices in children brain research or in pathological applications. The source model should thus be focal enough to be usable in the thin cortices, but should on the other side be more realistic than the current standard mathematical point dipole. Furthermore, it should be numerically accurate and computationally fast. We propose to achieve the best balance between these demands with a current preserving (divergence conforming) dipolar source model. We develop and investigate a varying number of current preserving source basis elements n (n=1,…,n=5). For validation, we conducted numerical experiments within a multi-layered spherical domain, where an analytical solution exists. We show that the accuracy increases along with the number of basis elements, while focality decreases. The results suggest that the best balance between accuracy and focality in thin cortices is achieved with n=4 (or in extreme cases even n=3) basis functions, while in thicker cortices n=5 is recommended to obtain the highest accuracy. We also compare the current preserving approach to two further FEM source modeling techniques, namely partial integration and St. Venant, and show that the best current preserving source model outperforms the competing methods with regard to overall balance. For all tested approaches, FEM transfer matrices enable high computational speed. We implemented the new EEG forward modeling approaches into the open source duneuro library for forward modeling in bioelectromagnetism to enable its broader use by the brain research community. This library is build upon the DUNE framework for parallel finite elements simulations and integrates with high-level toolboxes like FieldTrip. Additionally, an inversion test has been implemented using the realistic head model to demonstrate and compare the differences between the aforementioned source models.

New Strategy for Finite Element Mesh Generation for Accurate Solutions of Electroencephalography Forward Problems

The finite element method (FEM) is a numerical method that is often used for solving electroencephalography (EEG) forward problems involving realistic head models. In this study, FEM solutions obtained using three different mesh structures, namely coarse, densely refined, and adaptively refined meshes, are compared. The simulation results showed that the accuracy of FEM solutions could be significantly enhanced by adding a small number of elements around regions with large estimated errors. Moreover, it was demonstrated that the adaptively refined regions were always near the current dipole sources, suggesting that selectively generating additional elements around the cortical surface might be a new promising strategy for more efficient FEM-based EEG forward analysis.

Reducing the Computational Complexity of EEG Source Localization With Cortical Patch Decomposition and Optimal Electrode Selection

OBJECTIVE

Real-time implementation of EEG source localization can be employed in a broad area of applications such as clinical diagnosis of neurologic diseases and brain-computer interface. However, a power-efficient, low-complexity, and real-time implementation of EEG source localization is still challenging due to extensive iterations in the solutions. In this study, two techniques are introduced to reduce the computational burden of the subspace-based MUltiple SIgnal Classification (MUSIC) algorithm.

METHODS

To shrink the exhaustive search inherent in MUSIC, the cortex is parsed into cortical regions. A novel nomination procedure involving a dictionary learning step will pick a number of regions to be searched for the active sources. In addition, a new electrode selection algorithm based on the Cramer-Rao bound of the errors is introduced to pick the best set of an arbitrary number of electrodes out of the total.

RESULTS

The performance of the proposed techniques were evaluated using simulated EEG signal under variation of different parameters such as the number of nominated regions, the signal to noise ratio, and the number of electrodes. The proposed techniques can reduce the computational complexity by up to $90\%$. Furthermore, the proposed techniques were tested on EEG data from an auditory oddball experiment.

CONCLUSION

A good concordance was observed in the comparison of the topographies and the localization errors derived from the proposed technique and regular MUSIC.

SIGNIFICANCE

Such reduction can be exploited in the real-time, long-run, and mobile monitoring of cortical activity for clinical diagnosis and research purposes.

The FieldTrip-SimBio pipeline for EEG forward solutions

Background

Accurately solving the electroencephalography (EEG) forward problem is crucial for precise EEG source analysis. Previous studies have shown that the use of multicompartment head models in combination with the finite element method (FEM) can yield high accuracies both numerically and with regard to the geometrical approximation of the human head. However, the workload for the generation of multicompartment head models has often been too high and the use of publicly available FEM implementations too complicated for a wider application of FEM in research studies. In this paper, we present a MATLAB-based pipeline that aims to resolve this lack of easy-to-use integrated software solutions. The presented pipeline allows for the easy application of five-compartment head models with the FEM within the FieldTrip toolbox for EEG source analysis.

Methods

The FEM from the SimBio toolbox, more specifically the St. Venant approach, was integrated into the FieldTrip toolbox. We give a short sketch of the implementation and its application, and we perform a source localization of somatosensory evoked potentials (SEPs) using this pipeline. We then evaluate the accuracy that can be achieved using the automatically generated five-compartment hexahedral head model [skin, skull, cerebrospinal fluid (CSF), gray matter, white matter] in comparison to a highly accurate tetrahedral head model that was generated on the basis of a semiautomatic segmentation with very careful and time-consuming manual corrections.

Results

The source analysis of the SEP data correctly localizes the P20 component and achieves a high goodness of fit. The subsequent comparison to the highly detailed tetrahedral head model shows that the automatically generated five-compartment head model performs about as well as a highly detailed four-compartment head model (skin, skull, CSF, brain). This is a significant improvement in comparison to a three-compartment head model, which is frequently used in praxis, since the importance of modeling the CSF compartment has been shown in a variety of studies.

Conclusion

The presented pipeline facilitates the use of five-compartment head models with the FEM for EEG source analysis. The accuracy with which the EEG forward problem can thereby be solved is increased compared to the commonly used three-compartment head models, and more reliable EEG source reconstruction results can be obtained.

Electronic supplementary material

The online version of this article (10.1186/s12938-018-0463-y) contains supplementary material, which is available to authorized users.