An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging

Human brain imaging with high-density electroencephalography: Techniques and applications

Electroencephalography (EEG) is a technique for non-invasively measuring neuronal activity in the human brain using electrodes placed on the participant's scalp. With the advancement of digital technologies, EEG analysis has evolved over time from the qualitative analysis of amplitude and frequency modulations to a comprehensive analysis of the complex spatiotemporal characteristics of the recorded signals. EEG is now considered a powerful tool for measuring neural processes in the same time frame in which they happen (i.e. the subsecond range). However, it is commonly argued that EEG suffers from low spatial resolution, which makes it difficult to localize the generators of EEG activity accurately and reliably. Today, the availability of high-density EEG (hdEEG) systems, combined with methods for incorporating information on head anatomy and sophisticated source-localization algorithms, has transformed EEG into an important neuroimaging tool. hdEEG offers researchers and clinicians a rich and varied range of applications. It can be used not only for investigating neural correlates in motor and cognitive neuroscience experiments, but also for clinical diagnosis, particularly in the detection of epilepsy and the characterization of neural impairments in a wide range of neurological disorders. Notably, the integration of hdEEG systems with other physiological recordings, such as kinematic and/or electromyography data, might be especially beneficial to better understand the neuromuscular mechanisms associated with deconditioning in ageing and neuromotor disorders, by mapping the neurokinematic and neuromuscular connectivity patterns directly in the brain.

How to assess the accuracy of volume conduction models? A validation study with stereotactic EEG data

Introduction

Volume conduction models of the human head are used in various neuroscience fields, such as for source reconstruction in EEG and MEG, and for modeling the effects of brain stimulation. Numerous studies have quantified the accuracy and sensitivity of volume conduction models by analyzing the effects of the geometrical and electrical features of the head model, the sensor model, the source model, and the numerical method. Most studies are based on simulations as it is hard to obtain sufficiently detailed measurements to compare to models. The recording of stereotactic EEG during electric stimulation mapping provides an opportunity for such empirical validation.

Methods

In the study presented here, we used the potential distribution of volume-conducted artifacts that are due to cortical stimulation to evaluate the accuracy of finite element method (FEM) volume conduction models. We adopted a widely used strategy for numerical comparison, i.e., we fixed the geometrical description of the head model and the mathematical method to perform simulations, and we gradually altered the head models, by increasing the level of detail of the conductivity profile. We compared the simulated potentials at different levels of refinement with the measured potentials in three epilepsy patients.

Results

Our results show that increasing the level of detail of the volume conduction head model only marginally improves the accuracy of the simulated potentials when compared to in-vivo sEEG measurements. The mismatch between measured and simulated potentials is, throughout all patients and models, maximally 40 microvolts (i.e., 10% relative error) in 80% of the stimulation-recording combination pairs and it is modulated by the distance between recording and stimulating electrodes.

Discussion

Our study suggests that commonly used strategies used to validate volume conduction models based solely on simulations might give an overly optimistic idea about volume conduction model accuracy. We recommend more empirical validations to be performed to identify those factors in volume conduction models that have the highest impact on the accuracy of simulated potentials. We share the dataset to allow researchers to further investigate the mismatch between measurements and FEM models and to contribute to improving volume conduction models.

Development and validation of an fMRI-informed EEG model of reward-related ventral striatum activation

Reward processing is essential for our mental-health and well-being. In the current study, we developed and validated a scalable, fMRI-informed EEG model for monitoring reward processing related to activation in the ventral-striatum (VS), a significant node in the brain's reward system. To develop this EEG-based model of VS-related activation, we collected simultaneous EEG/fMRI data from 17 healthy individuals while listening to individually-tailored pleasurable music - a highly rewarding stimulus known to engage the VS. Using these cross-modal data, we constructed a generic regression model for predicting the concurrently acquired Blood-Oxygen-Level-Dependent (BOLD) signal from the VS using spectro-temporal features from the EEG signal (termed hereby VS-related-Electrical Finger Print; VS-EFP). The performance of the extracted model was examined using a series of tests that were applied on the original dataset and, importantly, an external validation dataset collected from a different group of 14 healthy individuals who underwent the same EEG/FMRI procedure. Our results showed that the VS-EFP model, as measured by simultaneous EEG, predicted BOLD activation in the VS and additional functionally relevant regions to a greater extent than an EFP model derived from a different anatomical region. The developed VS-EFP was also modulated by musical pleasure and predictive of the VS-BOLD during a monetary reward task, further indicating its functional relevance. These findings provide compelling evidence for the feasibility of using EEG alone to model neural activation related to the VS, paving the way for future use of this scalable neural probing approach in neural monitoring and self-guided neuromodulation.

Effects of individualized brain anatomies and EEG electrode positions on inferred activity of the primary auditory cortex

Due to its high temporal resolution and non-invasive nature, electroencephalography (EEG) is considered a method of great value for the field of auditory cognitive neuroscience. In performing source space analyses, localization accuracy poses a bottleneck, which precise forward models based on individualized attributes such as subject anatomy or electrode locations aim to overcome. Yet acquiring anatomical images or localizing EEG electrodes requires significant additional funds and processing time, making it an oftentimes inaccessible asset. Neuroscientific software offers template solutions, on which analyses can be based. For localizing the source of auditory evoked responses, we here compared the results of employing such template anatomies and electrode positions versus the subject-specific ones, as well as combinations of the two. All considered cases represented approaches commonly used in electrophysiological studies. We considered differences between two commonly used inverse solutions (dSPM, sLORETA) and targeted the primary auditory cortex; a notoriously small cortical region that is located within the lateral sulcus, thus particularly prone to errors in localization. Through systematical comparison of early evoked component metrics and spatial leakage, we assessed how the individualization steps impacted the analyses outcomes. Both electrode locations as well as subject anatomies were found to have an effect, which though varied based on the configuration considered. When comparing the inverse solutions, we moreover found that dSPM more consistently benefited from individualization of subject morphologies compared to sLORETA, suggesting it to be the better choice for auditory cortex localization.

Evaluation of skull conductivity using SCALE head tissue conductivity estimation using EEG

Inaccurate estimation of skull conductivity is the largest impediment to high-resolution EEG source imaging because of its strong influence and wide variability across individuals. Nonetheless, there is yet no widely applied method for noninvasively measuring individual skull conductivity. We presented a skull conductivity and source location estimation algorithm (SCALE) for simultaneously estimating skull conductivity and the cortical distributions of 18-20 effective sources derived from the EEG data by independent component analysis (ICA). SCALE combines a realistic Finite Element Method (FEM) head model built from a magnetic resonance (MR) head image with the effective source scalp maps to estimate brain-to-skull conductivity ratio (BSCR) and to map the effective sources on the cortical surface. To estimate the robustness of SCALE BSCR estimates, we applied SCALE to MR image and high-density EEG data from ten participants, five having data from 2-3 different tasks and sessions. As expected, across participants SCALE BSCR estimates differed widely (mean 32.8, range 18-78). Within-participant SCALE BSCR estimates were far more consistent than between participants. By incorporating SCALE-optimized distributed EEG source localization, stable functional imaging of cortical EEG effective sources can become routine, giving relatively low-cost EEG imaging a spatial resolution compatible with other brain imaging results and uniquely capable for studying brain dynamics supporting thought and action in laboratory, virtual, and natural environments.

A Graph Fourier Transform Based Bidirectional Long Short-Term Memory Neural Network for Electrophysiological Source Imaging

Electrophysiological source imaging (ESI) refers to the process of reconstructing underlying activated sources on the cortex given the brain signal measured by Electroencephalography (EEG) or Magnetoencephalography (MEG). Due to the ill-posed nature of ESI, solving ESI requires the design of neurophysiologically plausible regularization or priors to guarantee a unique solution. Recovering focally extended sources is more challenging, and traditionally uses a total variation regularization to promote spatial continuity of the activated sources. In this paper, we propose to use graph Fourier transform (GFT) based bidirectional long-short term memory (BiLSTM) neural network to solve the ESI problem. The GFT delineates the 3D source space into spatially high, medium and low frequency subspaces spanned by corresponding eigenvectors. The low frequency components can naturally serve as a spatially low-band pass filter to reconstruct extended areas of source activation. The BiLSTM is adopted to learn the mapping relationship between the projection of low-frequency graph space and the recorded EEG. Numerical results show the proposed GFT-BiLSTM outperforms other benchmark algorithms in synthetic data under varied signal-to-noise ratios (SNRs). Real data experiments also demonstrate its capability of localizing the epileptogenic zone of epilepsy patients with good accuracy.

A comparative study between state-of-the-art MRI deidentification and AnonyMI, a new method combining re-identification risk reduction and geometrical preservation

Deidentifying MRIs constitutes an imperative challenge, as it aims at precluding the possibility of re-identification of a research subject or patient, but at the same time it should preserve as much geometrical information as possible, in order to maximize data reusability and to facilitate interoperability. Although several deidentification methods exist, no comprehensive and comparative evaluation of deidentification performance has been carried out across them. Moreover, the possible ways these methods can compromise subsequent analysis has not been exhaustively tested. To tackle these issues, we developed AnonyMI, a novel MRI deidentification method, implemented as a user-friendly 3D Slicer plugin-in, which aims at providing a balance between identity protection and geometrical preservation. To test these features, we performed two series of analyses on which we compared AnonyMI to other two state-of-the-art methods, to evaluate, at the same time, how efficient they are at deidentifying MRIs and how much they affect subsequent analyses, with particular emphasis on source localization procedures. Our results show that all three methods significantly reduce the re-identification risk but AnonyMI provides the best geometrical conservation. Notably, it also offers several technical advantages such as a user-friendly interface, multiple input-output capabilities, the possibility of being tailored to specific needs, batch processing and efficient visualization for quality assurance.

A Method to Experimentally Estimate the Conductivity of Chronic Stroke Lesions: A Tool to Individualize Transcranial Electric Stimulation

The inconsistent response to transcranial electric stimulation in the stroke population is attributed to, among other factors, unknown effects of stroke lesion conductivity on stimulation strength at the targeted brain areas. Volume conduction models are promising tools to determine optimal stimulation settings. However, stroke lesion conductivity is often not considered in these models as a source of inter-subject variability. The goal of this study is to propose a method that combines MRI, EEG, and transcranial stimulation to estimate the conductivity of cortical stroke lesions experimentally. In this simulation study, lesion conductivity was estimated from scalp potentials during transcranial electric stimulation in 12 chronic stroke patients. To do so, first, we determined the stimulation configuration where scalp potentials are maximally affected by the lesion. Then, we calculated scalp potentials in a model with a fixed lesion conductivity and a model with a randomly assigned conductivity. To estimate the lesion conductivity, we minimized the error between the two models by varying the conductivity in the second model. Finally, to reflect realistic experimental conditions, we test the effect rotation of measurement electrode orientation and the effect of the number of electrodes used. We found that the algorithm converged to the correct lesion conductivity value when noise on the electrode positions was absent for all lesions. Conductivity estimation error was below 5% with realistic electrode coregistration errors of 0.1° for lesions larger than 50 ml. Higher lesion conductivities and lesion volumes were associated with smaller estimation errors. In conclusion, this method can experimentally estimate stroke lesion conductivity, improving the accuracy of volume conductor models of stroke patients and potentially leading to more effective transcranial electric stimulation configurations for this population.

A comprehensive study on electroencephalography and magnetoencephalography sensitivity to cortical and subcortical sources

Signal-to-noise ratio (SNR) maps are a good way to visualize electroencephalography (EEG) and magnetoencephalography (MEG) sensitivity. SNR maps extend the knowledge about the modulation of EEG and MEG signals by source locations and orientations and can therefore help to better understand and interpret measured signals as well as source reconstruction results thereof. Our work has two main objectives. First, we investigated the accuracy and reliability of EEG and MEG finite element method (FEM)-based sensitivity maps for three different head models, namely an isotropic three and four-compartment and an anisotropic six-compartment head model. As a result, we found that ignoring the cerebrospinal fluid leads to an overestimation of EEG SNR values. Second, we examined and compared EEG and MEG SNR mappings for both cortical and subcortical sources and their modulation by source location and orientation. Our results for cortical sources show that EEG sensitivity is higher for radial and deep sources and MEG for tangential ones, which are the majority of sources. As to the subcortical sources, we found that deep sources with sufficient tangential source orientation are recordable by the MEG. Our work, which represents the first comprehensive study where cortical and subcortical sources are considered in highly detailed FEM-based EEG and MEG SNR mappings, sheds a new light on the sensitivity of EEG and MEG and might influence the decision of brain researchers or clinicians in their choice of the best modality for their experiment or diagnostics, respectively.

Automated Head Tissue Modelling Based on Structural Magnetic Resonance Images for Electroencephalographic Source Reconstruction

In the last years, technological advancements for the analysis of electroencephalography (EEG) recordings have permitted to investigate neural activity and connectivity in the human brain with unprecedented precision and reliability. A crucial element for accurate EEG source reconstruction is the construction of a realistic head model, incorporating information on electrode positions and head tissue distribution. In this paper, we introduce MR-TIM, a toolbox for head tissue modelling from structural magnetic resonance (MR) images. The toolbox consists of three modules: 1) image pre-processing – the raw MR image is denoised and prepared for further analyses; 2) tissue probability mapping – template tissue probability maps (TPMs) in individual space are generated from the MR image; 3) tissue segmentation – information from all the TPMs is integrated such that each voxel in the MR image is assigned to a specific tissue. MR-TIM generates highly realistic 3D masks, five of which are associated with brain structures (brain and cerebellar grey matter, brain and cerebellar white matter, and brainstem) and the remaining seven with other head tissues (cerebrospinal fluid, spongy and compact bones, eyes, muscle, fat and skin). Our validation, conducted on MR images collected in healthy volunteers and patients as well as an MR template image from an open-source repository, demonstrates that MR-TIM is more accurate than alternative approaches for whole-head tissue segmentation. We hope that MR-TIM, by yielding an increased precision in head modelling, will contribute to a more widespread use of EEG as a brain imaging technique.

The influence of motor tasks and cut-off parameter selection on artifact subspace reconstruction in EEG recordings

Advances in EEG filtering algorithms enable analysis of EEG recorded during motor tasks. Although methods such as artifact subspace reconstruction (ASR) can remove transient artifacts automatically, there is virtually no knowledge about how the vigor of bodily movements affects ASRs performance and optimal cut-off parameter selection process. We compared the ratios of removed and reconstructed EEG recorded during a cognitive task, single-leg stance, and fast walking using ASR with 10 cut-off parameters versus visual inspection. Furthermore, we used the repeatability and dipolarity of independent components to assess their quality and an automatic classification tool to assess the number of brain-related independent components. The cut-off parameter equivalent to the ratio of EEG removed in manual cleaning was strictest for the walking task. The quality index of independent components, calculated using RELICA, reached a maximum plateau for cut-off parameters of 10 and higher across all tasks while dipolarity was largely unaffected. The number of independent components within each task remained constant, regardless of the cut-off parameter used. Surprisingly, ASR performed better in motor tasks compared with non-movement tasks. The quality index seemed to be more sensitive to changes induced by ASR compared to dipolarity. There was no benefit of using cut-off parameters less than 10. Graphical abstract The graphical abstract shows the three tasks performed during EEG recording, the two processing pipelines (manual and artifact subspace reconstruction), and the metrics the conclusion is based on.

Auditory cortical generators of the Frequency Following Response are modulated by intermodal attention

The efferent auditory system suggests that brainstem auditory regions could also be sensitive to top-down processes. In electrophysiology, the Frequency Following Response (FFR) to speech stimuli has been used extensively to study brainstem areas. Despite seemingly straight-forward in addressing the issue of attentional modulations of brainstem regions by means of the FFR, the existing results are inconsistent. Moreover, the notion that the FFR exclusively represents subcortical generators has been challenged. We aimed to gain a more differentiated perspective on how the generators of the FFR are modulated by either attending to the visual or auditory input while neural activity was recorded using magnetoencephalography (MEG). In a first step our results confirm the strong contribution of also cortical regions to the FFR. Interestingly, of all regions exhibiting a measurable FFR response, only the right primary auditory cortex was significantly affected by intermodal attention. By showing a clear cortical contribution to the attentional FFR effect, our work significantly extends previous reports that focus on surface level recordings only. It underlines the importance of making a greater effort to disentangle the different contributing sources of the FFR and serves as a clear precaution of simplistically interpreting the FFR as brainstem response.

Ear-EEG Forward Models: Improved Head-Models for Ear-EEG

Computational models for mapping electrical sources in the brain to potentials on the scalp have been widely explored. However, current models do not describe the external ear anatomy well, and is therefore not suitable for ear-EEG recordings. Here we present an extension to existing computational models, by incorporating an improved description of the external ear anatomy based on 3D scanned impressions of the ears. The result is a method to compute an ear-EEG forward model, which enables mapping of sources in the brain to potentials in the ear. To validate the method, individualized ear-EEG forward models were computed for four subjects, and ear-EEG and scalp EEG were recorded concurrently from the subjects in a study comprising both auditory and visual stimuli. The EEG recordings were analyzed with independent component analysis (ICA) and using the individualized ear-EEG forward models, single dipole fitting was performed for each independent component (IC). A subset of ICs were selected, based on how well they were modeled by a single dipole in the brain volume. The correlation between the topographic IC map and the topographic map predicted by the forward model, was computed for each IC. Generally, the correlation was high in the ear closest to the dipole location, showing that the ear-EEG forward models provided a good model to predict ear potentials. In addition, we demonstrated that the developed forward models can be used to explore the sensitivity to brain sources for different ear-EEG electrode configurations. We consider the proposed method to be an important step forward in the characterization and utilization of ear-EEG.

Characterizing the effects of deep brain stimulation with magnetoencephalography: A review

BACKGROUND

Deep brain stimulation (DBS) is an important form of neuromodulation that is being applied to patients with motor, mood, or cognitive circuit disorders. Despite the efficacy and widespread use of DBS, the precise mechanisms by which it works remain unknown. Over the last decade, magnetoencephalography (MEG) has become an important functional neuroimaging technique used to study DBS.

OBJECTIVE

This review summarizes the literature related to the use of MEG to characterize the effects of DBS.

METHODS

Peer reviewed literature on DBS-MEG was obtained by searching the publicly accessible literature databases available on PubMed. The abstracts of all reports were scanned and publications which combined DBS-MEG in human subjects were selected for review.

RESULTS

A total of 32 publications met the selection criteria, and included studies which applied DBS for Parkinson's disease, dystonia, chronic pain, phantom limb pain, cluster headache, and epilepsy. DBS-MEG studies provided valuable insights into network connectivity, pathological coupling, and the modulatory effects of DBS.

CONCLUSIONS

As DBS-MEG research continues to develop, we can expect to gain a better understanding of diverse pathophysiological networks and their response to DBS. This knowledge will improve treatment efficacy, reduce side-effects, reveal optimal surgical targets, and advance the development of closed-loop neuromodulation.

Integral equations and boundary-element solution for static potential in a general piece-wise homogeneous volume conductor

Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.

Simultaneous head tissue conductivity and EEG source location estimation

Accurate electroencephalographic (EEG) source localization requires an electrical head model incorporating accurate geometries and conductivity values for the major head tissues. While consistent conductivity values have been reported for scalp, brain, and cerebrospinal fluid, measured brain-to-skull conductivity ratio (BSCR) estimates have varied between 8 and 80, likely reflecting both inter-subject and measurement method differences. In simulations, mis-estimation of skull conductivity can produce source localization errors as large as 3cm. Here, we describe an iterative gradient-based approach to Simultaneous tissue Conductivity And source Location Estimation (SCALE). The scalp projection maps used by SCALE are obtained from near-dipolar effective EEG sources found by adequate independent component analysis (ICA) decomposition of sufficient high-density EEG data. We applied SCALE to simulated scalp projections of 15cm(2)-scale cortical patch sources in an MR image-based electrical head model with simulated BSCR of 30. Initialized either with a BSCR of 80 or 20, SCALE estimated BSCR as 32.6. In Adaptive Mixture ICA (AMICA) decompositions of (45-min, 128-channel) EEG data from two young adults we identified sets of 13 independent components having near-dipolar scalp maps compatible with a single cortical source patch. Again initialized with either BSCR 80 or 25, SCALE gave BSCR estimates of 34 and 54 for the two subjects respectively. The ability to accurately estimate skull conductivity non-invasively from any well-recorded EEG data in combination with a stable and non-invasively acquired MR imaging-derived electrical head model could remove a critical barrier to using EEG as a sub-cm(2)-scale accurate 3-D functional cortical imaging modality.

Influence of skull modeling approaches on EEG source localization

Electroencephalographic source localization (ESL) relies on an accurate model representing the human head for the computation of the forward solution. In this head model, the skull is of utmost importance due to its complex geometry and low conductivity compared to the other tissues inside the head. We investigated the influence of using different skull modeling approaches on ESL. These approaches, consisting in skull conductivity and geometry modeling simplifications, make use of X-ray computed tomography (CT) and magnetic resonance (MR) images to generate seven different head models. A head model with an accurately segmented skull from CT images, including spongy and compact bone compartments as well as some air-filled cavities, was used as the reference model. EEG simulations were performed for a configuration of 32 and 128 electrodes, and for both noiseless and noisy data. The results show that skull geometry simplifications have a larger effect on ESL than those of the conductivity modeling. This suggests that accurate skull modeling is important in order to achieve reliable results for ESL that are useful in a clinical environment. We recommend the following guidelines to be taken into account for skull modeling in the generation of subject-specific head models: (i) If CT images are available, i.e., if the geometry of the skull and its different tissue types can be accurately segmented, the conductivity should be modeled as isotropic heterogeneous. The spongy bone might be segmented as an erosion of the compact bone; (ii) when only MR images are available, the skull base should be represented as accurately as possible and the conductivity can be modeled as isotropic heterogeneous, segmenting the spongy bone directly from the MR image; (iii) a large number of EEG electrodes should be used to obtain high spatial sampling, which reduces the localization errors at realistic noise levels.

Electroencephalographic inverse localization of brain activity in acute traumatic brain injury as a guide to surgery, monitoring and treatment

OBJECTIVE

To inverse-localize epileptiform cortical electrical activity recorded from severe traumatic brain injury (TBI) patients using electroencephalography (EEG).

METHODS

Three acute TBI cases were imaged using computed tomography (CT) and multimodal magnetic resonance imaging (MRI). Semi-automatic segmentation was performed to partition the complete TBI head into 25 distinct tissue types, including 6 tissue types accounting for pathology. Segmentations were employed to generate a finite element method model of the head, and EEG activity generators were modeled as dipolar currents distributed over the cortical surface.

RESULTS

We demonstrate anatomically faithful localization of EEG generators responsible for epileptiform discharges in severe TBI. By accounting for injury-related tissue conductivity changes, our work offers the most realistic implementation currently available for the inverse estimation of cortical activity in TBI.

CONCLUSION

Whereas standard localization techniques are available for electrical activity mapping in uninjured brains, they are rarely applied to acute TBI. Modern models of TBI-induced pathology can inform the localization of epileptogenic foci, improve surgical efficacy, contribute to the improvement of critical care monitoring and provide guidance for patient-tailored treatment. With approaches such as this, neurosurgeons and neurologists can study brain activity in acute TBI and obtain insights regarding injury effects upon brain metabolism and clinical outcome.

Effects of forward model errors on EEG source localization

Subject-specific four-layer boundary element method (BEM) electrical forward head models for four participants, generated from magnetic resonance (MR) head images using NFT ( www.sccn.ucsd.edu/wiki/NFT ), were used to simulate electroencephalographic (EEG) scalp potentials at 256 recorded electrode positions produced by single current dipoles of a 3-D grid in brain space. Locations of these dipoles were then estimated using gradient descent within five template head models fit to the electrode positions. These were: a spherical model, three-layer and four-layer BEM head models based on the Montreal Neurological Institute (MNI) template head image, and these BEM models warped to the recorded electrode positions. Smallest localization errors (4.1-6.2 mm, medians) were obtained using the electrode-position warped four-layer BEM models, with largest localization errors (~20 mm) for most basal brain locations. When we increased the brain-to-skull conductivity ratio assumed in the template model scalp projections from the simulated value (25:1) to a higher value (80:1) used in earlier studies, the estimated dipole locations moved outwards (12.4 mm, median). We also investigated the effects of errors in co-registering the electrode positions, of reducing electrode counts, and of adding a fifth, isotropic white matter layer to one individual head model. Results show that when individual subject MR head images are not available to construct subject-specific head models, accurate EEG source localization should employ a four- or five-layer BEM template head model incorporating an accurate skull conductivity estimate and warped to 64 or more accurately 3-D measured and co-registered electrode positions.

Forward and inverse electroencephalographic modeling in health and in acute traumatic brain injury

OBJECTIVE

EEG source localization is demonstrated in three cases of acute traumatic brain injury (TBI) with progressive lesion loads using anatomically faithful models of the head which account for pathology.

METHODS

Multimodal magnetic resonance imaging (MRI) volumes were used to generate head models via the finite element method (FEM). A total of 25 tissue types-including 6 types accounting for pathology-were included. To determine the effects of TBI upon source localization accuracy, a minimum-norm operator was used to perform inverse localization and to determine the accuracy of the latter.

RESULTS

The importance of using a more comprehensive number of tissue types is confirmed in both health and in TBI. Pathology omission is found to cause substantial inaccuracies in EEG forward matrix calculations, with lead field sensitivity being underestimated by as much as ≈ 200% in (peri-) contusional regions when TBI-related changes are ignored. Failing to account for such conductivity changes is found to misestimate substantial localization error by up to 35 mm.

CONCLUSIONS

Changes in head conductivity profiles should be accounted for when performing EEG modeling in acute TBI.

SIGNIFICANCE

Given the challenges of inverse localization in TBI, this framework can benefit neurotrauma patients by providing useful insights on pathophysiology.

Source cancellation profiles of electroencephalography and magnetoencephalography

Recorded electric potentials and magnetic fields due to cortical electrical activity have spatial spread even if their underlying brain sources are focal. Consequently, as a result of source cancellation, loss in signal amplitude and reduction in the effective signal-to-noise ratio can be expected when distributed sources are active simultaneously. Here we investigate the cancellation effects of EEG and MEG through the use of an anatomically correct forward model based on structural MRI acquired from 7 healthy adults. A boundary element model (BEM) with four compartments (brain, cerebrospinal fluid, skull and scalp) and highly accurate cortical meshes (~300,000 vertices) were generated. Distributed source activations were simulated using contiguous patches of active dipoles. To investigate cancellation effects in both EEG and MEG, quantitative indices were defined (source enhancement, cortical orientation disparity) and computed for varying values of the patch radius as well as for automatically parcellated gyri and sulci. Results were calculated for each cortical location, averaged over all subjects using a probabilistic atlas, and quantitatively compared between MEG and EEG. As expected, MEG sensors were found to be maximally sensitive to signals due to sources tangential to the scalp, and minimally sensitive to radial sources. Compared to EEG, however, MEG was found to be much more sensitive to signals generated antero-medially, notably in the anterior cingulate gyrus. Given that sources of activation cancel each other according to the orientation disparity of the cortex, this study provides useful methods and results for quantifying the effect of source orientation disparity upon source cancellation.

Evaluation of multiple-sphere head models for MEG source localization

Magnetoencephalography (MEG) source analysis has largely relied on spherical conductor models of the head to simplify forward calculations of the brain's magnetic field. Multiple- (or overlapping, local) sphere models, where an optimal sphere is selected for each sensor, are considered an improvement over single-sphere models and are computationally simpler than realistic models. However, there is limited information available regarding the different methods used to generate these models and their relative accuracy. We describe a variety of single- and multiple-sphere fitting approaches, including a novel method that attempts to minimize the field error. An accurate boundary element method simulation was used to evaluate the relative field measurement error (12% on average) and dipole fit localization bias (3.5 mm) of each model over the entire brain. All spherical models can contribute in the order of 1 cm to the localization bias in regions of the head that depart significantly from a sphere (inferior frontal and temporal). These spherical approximation errors can give rise to larger localization differences when all modeling effects are taken into account and with more complex source configurations or other inverse techniques, as shown with a beamformer example. Results differed noticeably depending on the source location, making it difficult to recommend a fitting method that performs best in general. Given these limitations, it may be advisable to expand the use of realistic head models.

EEGLAB, SIFT, NFT, BCILAB, and ERICA: new tools for advanced EEG processing

We describe a set of complementary EEG data collection and processing tools recently developed at the Swartz Center for Computational Neuroscience (SCCN) that connect to and extend the EEGLAB software environment, a freely available and readily extensible processing environment running under Matlab. The new tools include (1) a new and flexible EEGLAB STUDY design facility for framing and performing statistical analyses on data from multiple subjects; (2) a neuroelectromagnetic forward head modeling toolbox (NFT) for building realistic electrical head models from available data; (3) a source information flow toolbox (SIFT) for modeling ongoing or event-related effective connectivity between cortical areas; (4) a BCILAB toolbox for building online brain-computer interface (BCI) models from available data, and (5) an experimental real-time interactive control and analysis (ERICA) environment for real-time production and coordination of interactive, multimodal experiments.

Application of kernel principal component analysis and support vector regression for reconstruction of cardiac transmembrane potentials

Non-invasively reconstructing the transmembrane potentials (TMPs) from body surface potentials (BSPs) constitutes one form of the inverse ECG problem that can be treated as a regression problem with multi-inputs and multi-outputs, and which can be solved using the support vector regression (SVR) method. In developing an effective SVR model, feature extraction is an important task for pre-processing the original input data. This paper proposes the application of principal component analysis (PCA) and kernel principal component analysis (KPCA) to the SVR method for feature extraction. Also, the genetic algorithm and simplex optimization method is invoked to determine the hyper-parameters of the SVR. Based on the realistic heart-torso model, the equivalent double-layer source method is applied to generate the data set for training and testing the SVR model. The experimental results show that the SVR method with feature extraction (PCA-SVR and KPCA-SVR) can perform better than that without the extract feature extraction (single SVR) in terms of the reconstruction of the TMPs on epi- and endocardial surfaces. Moreover, compared with the PCA-SVR, the KPCA-SVR features good approximation and generalization ability when reconstructing the TMPs.

OpenMEEG: opensource software for quasistatic bioelectromagnetics

Background

Interpreting and controlling bioelectromagnetic phenomena require realistic physiological models and accurate numerical solvers. A semi-realistic model often used in practise is the piecewise constant conductivity model, for which only the interfaces have to be meshed. This simplified model makes it possible to use Boundary Element Methods. Unfortunately, most Boundary Element solutions are confronted with accuracy issues when the conductivity ratio between neighboring tissues is high, as for instance the scalp/skull conductivity ratio in electro-encephalography. To overcome this difficulty, we proposed a new method called the symmetric BEM, which is implemented in the OpenMEEG software. The aim of this paper is to present OpenMEEG, both from the theoretical and the practical point of view, and to compare its performances with other competing software packages.

Methods

We have run a benchmark study in the field of electro- and magneto-encephalography, in order to compare the accuracy of OpenMEEG with other freely distributed forward solvers. We considered spherical models, for which analytical solutions exist, and we designed randomized meshes to assess the variability of the accuracy. Two measures were used to characterize the accuracy. the Relative Difference Measure and the Magnitude ratio. The comparisons were run, either with a constant number of mesh nodes, or a constant number of unknowns across methods. Computing times were also compared.

Results

We observed more pronounced differences in accuracy in electroencephalography than in magnetoencephalography. The methods could be classified in three categories: the linear collocation methods, that run very fast but with low accuracy, the linear collocation methods with isolated skull approach for which the accuracy is improved, and OpenMEEG that clearly outperforms the others. As far as speed is concerned, OpenMEEG is on par with the other methods for a constant number of unknowns, and is hence faster for a prescribed accuracy level.

Conclusions

This study clearly shows that OpenMEEG represents the state of the art for forward computations. Moreover, our software development strategies have made it handy to use and to integrate with other packages. The bioelectromagnetic research community should therefore be able to benefit from OpenMEEG with a limited development effort.

Neuroelectromagnetic forward head modeling toolbox

This paper introduces a Neuroelectromagnetic Forward Head Modeling Toolbox (NFT) running under MATLAB (The Mathworks, Inc.) for generating realistic head models from available data (MRI and/or electrode locations) and for computing numerical solutions for the forward problem of electromagnetic source imaging. The NFT includes tools for segmenting scalp, skull, cerebrospinal fluid (CSF) and brain tissues from T1-weighted magnetic resonance (MR) images. The Boundary Element Method (BEM) is used for the numerical solution of the forward problem. After extracting segmented tissue volumes, surface BEM meshes can be generated. When a subject MR image is not available, a template head model can be warped to measured electrode locations to obtain an individualized head model. Toolbox functions may be called either from a graphic user interface compatible with EEGLAB (http://sccn.ucsd.edu/eeglab), or from the MATLAB command line. Function help messages and a user tutorial are included. The toolbox is freely available under the GNU Public License for noncommercial use and open source development.

Patch-basis electrocortical source imaging in epilepsy

In this study, we developed numerical methods for investigating the sources of epileptic activity from intracranial EEG recordings acquired from intracranial subdural electrodes (iEEG) in patients undergoing pre-surgical evaluation at the epilepsy center of the Mayo Clinic (Rochester, MN). The data were analyzed using independent component analysis (ICA), which identifies and isolates maximally independent signal components in multi-channel recordings. A realistic individual head model was constructed for a patient undergoing pre-surgical evaluation. Structural models of gray matter, white matter, CSF, skull, and scalp were extracted from pre-surgical MR and post-surgical CT images. The electromagnetic source localization forward problem was solved using the Boundary Element Method (BEM). Source localization was performed using the Sparse Bayesian Learning (SBL) algorithm. The multiscale patch-basis source space constructed for this purpose includes a large number of dipole elements on the cortical layer oriented perpendicular to the local cortical surface. These source dipoles are combined into overlapping multi-scalepatches. Using this approach, we were able to detect seizure activity on sulcal walls and on gyrus of the cortex.

EEG/MEG source imaging: methods, challenges, and open issues

We present the four key areas of research-preprocessing, the volume conductor, the forward problem, and the inverse problem-that affect the performance of EEG and MEG source imaging. In each key area we identify prominent approaches and methodologies that have open issues warranting further investigation within the community, challenges associated with certain techniques, and algorithms necessitating clarification of their implications. More than providing definitive answers we aim to identify important open issues in the quest of source localization.

Neuroelectromagnetic forward modeling toolbox

This paper introduces a Neuroelectromagnetic Forward Modeling Toolbox running under MATLAB (The Mathworks, Inc.) for generating realistic head models from available data (MRI and/or electrode locations) and for solving the forward problem of electro-magnetic source imaging numerically. The toolbox includes tools for segmenting scalp, skull, cerebrospinal fluid (CSF) and brain tissues from T1-weighted magnetic resonance (MR) images. After extracting the segmented tissue volumes, mesh generation can be performed using deformable models. When MR images are not available, it is possible to warp a template head model to measured electrode locations to obtain a better-fitting realistic model. The Boundary Element Method (BEM) is used for the numerical solution of the forward problem. Toolbox functions can be called from either a graphic user interface or from the command line. Function help messages and a tutorial are included. The toolbox is freely available under the GNU Public License for noncommercial use and open source development.

Head modeling and cortical source localization in epilepsy

In this study, we developed numerical methods for investigating the dynamics of epilepsy from multi-scale EEG recordings acquired simultaneously from the scalp (sEEG) and intracranial subdural and/or depth electrodes (iEEG) in patients undergoing pre-surgical evaluation at the epilepsy center of the Mayo Clinic (Rochester, MN). The data are analyzed using independent component analysis (ICA), which identifies and isolates independent signal components from multi-channel recordings. A realistic individual head model was constructed for a patient undergoing pre-surgical evaluation. The forward problem of electro-magnetic source localization was solved using the Boundary Element Method (BEM). Using this approach, we investigated the relationships between noninvasive and invasive source localization of human electrical brain data sources. A difference of about 1 cm was observed between sources estimated from sEEG and iEEG measurements.

Parallel implementation of the accelerated BEM approach for EMSI of the human brain

Boundary element method (BEM) is one of the numerical methods which is commonly used to solve the forward problem (FP) of electro-magnetic source imaging with realistic head geometries. Application of BEM generates large systems of linear equations with dense matrices. Generation and solution of these matrix equations are time and memory consuming. This study presents a relatively cheap and effective solution for parallel implementation of the BEM to reduce the processing times to clinically acceptable values. This is achieved using a parallel cluster of personal computers on a local area network. We used eight workstations and implemented a parallel version of the accelerated BEM approach that distributes the computation and the BEM matrix efficiently to the processors. The performance of the solver is evaluated in terms of the CPU operations and memory usage for different number of processors. Once the transfer matrix is computed, for a 12,294 node mesh, a single FP solution takes 676 ms on a single processor and 72 ms on eight processors. It was observed that workstation clusters are cost effective tools for solving the complex BEM models in a clinically acceptable time.

Review on solving the forward problem in EEG source analysis

Background

The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.

Methods

While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.

Results

It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.

Conclusion

Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

Combination of the LSQR method and a genetic algorithm for solving the electrocardiography inverse problem

Computing epicardial potentials from body surface potentials constitutes one form of ill-posed inverse problem of electrocardiography (ECG). To solve this ECG inverse problem, the Tikhonov regularization and truncated singular-value decomposition (TSVD) methods have been commonly used to overcome the ill-posed property by imposing constraints on the magnitudes or derivatives of the computed epicardial potentials. Such direct regularization methods, however, are impractical when the transfer matrix is large. The least-squares QR (LSQR) method, one of the iterative regularization methods based on Lanczos bidiagonalization and QR factorization, has been shown to be numerically more reliable in various circumstances than the other methods considered. This LSQR method, however, to our knowledge, has not been introduced and investigated for the ECG inverse problem. In this paper, the regularization properties of the Krylov subspace iterative method of LSQR for solving the ECG inverse problem were investigated. Due to the 'semi-convergence' property of the LSQR method, the L-curve method was used to determine the stopping iteration number. The performance of the LSQR method for solving the ECG inverse problem was also evaluated based on a realistic heart-torso model simulation protocol. The results show that the inverse solutions recovered by the LSQR method were more accurate than those recovered by the Tikhonov and TSVD methods. In addition, by combing the LSQR with genetic algorithms (GA), the performance can be improved further. It suggests that their combination may provide a good scheme for solving the ECG inverse problem.

Generalized head models for MEG/EEG: boundary element method beyond nested volumes

Accurate geometrical models of the head are necessary for solving the forward and inverse problems of magneto- and electro-encephalography (MEG/EEG). Boundary element methods (BEMs) require a geometrical model describing the interfaces between different tissue types. Classically, head models with a nested volume topology have been used. In this paper, we demonstrate how this constraint can be relaxed, allowing us to model more realistic head topologies. We describe the symmetric BEM for this new model. The symmetric BEM formulation uses both potentials and currents at the interfaces as unknowns and is in general more accurate than the alternative double-layer formulation.

A Model-Based Objective Evaluation of Eye Movement Correction in EEG Recordings

We present a method to quantitatively and objectively compare algorithms for correction of eye movement artifacts in a simulated ongoing electroencephalographic signal (EEG). A realistic model of the human head is used, together with eye tracker data, to generate a data set in which potentials of ocular and cerebral origin are simulated. This approach bypasses the common problem of brain-potential contaminated electro-oculographic signals (EOGs), when monitoring or simulating eye movements. The data are simulated for five different EEG electrode configurations combined with four different EOG electrode configurations. In order to objectively compare correction performance for six algorithms, listed in Table III, we determine the signal to noise ratio of the EEG before and after artifact correction. A score indicating correction performance is derived, and for each EEG configuration the optimal correction algorithm and the optimal number of EOG electrodes are determined. In general, the second-order blind identification correction algorithm in combination with 6 EOG electrodes performs best for all EEG configurations evaluated on the simulated data.

Diffuse photon propagation in multilayered geometries

Diffuse optical tomography (DOT) is an emerging functional medical imaging modality which aims to recover the optical properties of biological tissue. The forward problem of the light propagation of DOT can be modelled in the frequency domain as a diffusion equation with Robin boundary conditions. In the case of multilayered geometries with piecewise constant parameters, the forward problem is equivalent to a set of coupled Helmholtz equations. In this paper, we present solutions for the multilayered diffuse light propagation for a three-layer concentric sphere model using a series expansion method and for a general layered geometry using the boundary element method (BEM). Results are presented comparing these solutions to an independent Monte Carlo model, and for an example three layered head model.

Use of the isolated problem approach for multi-compartment BEM models of electro-magnetic source imaging

The isolated problem approach (IPA) is a method used in the boundary element method (BEM) to overcome numerical inaccuracies caused by the high-conductivity difference in the skull and the brain tissues in the head. Hämäläinen and Sarvas (1989 IEEE Trans. Biomed. Eng. 36 165-71) described how the source terms can be updated to overcome these inaccuracies for a three-layer head model. Meijs et al (1989 IEEE Trans. Biomed. Eng. 36 1038-49) derived the integral equations for the general case where there are an arbitrary number of layers inside the skull. However, the IPA is used in the literature only for three-layer head models. Studies that use complex boundary element head models that investigate the inhomogeneities in the brain or model the cerebrospinal fluid (CSF) do not make use of the IPA. In this study, the generalized formulation of the IPA for multi-layer models is presented in terms of integral equations. The discretized version of these equations are presented in two different forms. In a previous study (Akalin-Acar and Gençer 2004 Phys. Med. Biol. 49 5011-28), we derived formulations to calculate the electroencephalography and magnetoencephalography transfer matrices assuming a single layer in the skull. In this study, the transfer matrix formulations are updated to incorporate the generalized IPA. The effects of the IPA are investigated on the accuracy of spherical and realistic models when the CSF layer and a tumour tissue are included in the model. It is observed that, in the spherical model, for a radial dipole 1 mm close to the brain surface, the relative difference measure (RDM*) drops from 1.88 to 0.03 when IPA is used. For the realistic model, the inclusion of the CSF layer does not change the field pattern significantly. However, the inclusion of an inhomogeneity changes the field pattern by 25% for a dipole oriented towards the inhomogeneity. The effect of the IPA is also investigated when there is an inhomogeneity in the brain. In addition to a considerable change in the scale of the potentials, the field pattern also changes by 15%. The computation times are presented for the multi-layer realistic head model.