Inverse localization of electric dipole current sources in finite element models of the human head

CutFEM-based MEG forward modeling improves source separability and sensitivity to quasi-radial sources: A somatosensory group study

Source analysis of magnetoencephalography (MEG) data requires the computation of the magnetic fields induced by current sources in the brain. This so-called MEG forward problem includes an accurate estimation of the volume conduction effects in the human head. Here, we introduce the Cut finite element method (CutFEM) for the MEG forward problem. CutFEM's meshing process imposes fewer restrictions on tissue anatomy than tetrahedral meshes while being able to mesh curved geometries contrary to hexahedral meshing. To evaluate the new approach, we compare CutFEM with a boundary element method (BEM) that distinguishes three tissue compartments and a 6-compartment hexahedral FEM in an n = 19 group study of somatosensory evoked fields (SEF). The neural generators of the 20 ms post-stimulus SEF components (M20) are reconstructed using both an unregularized and a regularized inversion approach. Changing the forward model resulted in reconstruction differences of about 1 centimeter in location and considerable differences in orientation. The tested 6-compartment FEM approaches significantly increase the goodness of fit to the measured data compared with the 3-compartment BEM. They also demonstrate higher quasi-radial contributions for sources below the gyral crowns. Furthermore, CutFEM improves source separability compared with both other approaches. We conclude that head models with 6 compartments rather than 3 and the new CutFEM approach are valuable additions to MEG source reconstruction, in particular for sources that are predominantly radial.

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

Objective

To compare cortical dipole fitting spatial accuracy between the widely used yet highly simplified 3-layer and modern more realistic 5-layer BEM-FMM models with and without adaptive mesh refinement (AMR) methods.

Methods

We generate simulated noiseless 256-channel EEG data from 5-layer (7-compartment) meshes of 15 subjects from the Connectome Young Adult dataset. For each subject, we test four dipole positions, three sets of conductivity values, and two types of head segmentation. We use the boundary element method (BEM) with fast multipole method (FMM) acceleration, with or without (AMR), for forward modeling. Dipole fitting is carried out with the FieldTrip MATLAB toolbox.

Results

The average position error (across all tested dipoles, subjects, and models) is ~4 mm, with a standard deviation of ~2 mm. The orientation error is ~20° on average, with a standard deviation of ~15°. Without AMR, the numerical inaccuracies produce a larger disagreement between the 3- and 5-layer models, with an average position error of ~8 mm (6 mm standard deviation), and an orientation error of 28° (28° standard deviation).

Conclusions

The low-resolution 3-layer models provide excellent accuracy in dipole localization. On the other hand, dipole orientation is retrieved less accurately. Therefore, certain applications may require more realistic models for practical source reconstruction. AMR is a critical component for improving the accuracy of forward EEG computations using a high-resolution 5-layer volume conduction model.

Significance

Improving EEG source reconstruction accuracy is important for several clinical applications, including epilepsy and other seizure-inducing conditions.

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.

Global sensitivity of EEG source analysis to tissue conductivity uncertainties

Introduction

To reliably solve the EEG inverse problem, accurate EEG forward solutions based on a detailed, individual volume conductor model of the head are essential. A crucial-but often neglected-aspect in generating a volume conductor model is the choice of the tissue conductivities, as these may vary from subject to subject. In this study, we investigate the sensitivity of EEG forward and inverse solutions to tissue conductivity uncertainties for sources distributed over the whole cortex surface.

Methods

We employ a detailed five-compartment head model distinguishing skin, skull, cerebrospinal fluid, gray matter, and white matter, where we consider uncertainties of skin, skull, gray matter, and white matter conductivities. We use the finite element method (FEM) to calculate EEG forward solutions and goal function scans (GFS) as inverse approach. To be able to generate the large number of EEG forward solutions, we employ generalized polynomial chaos (gPC) expansions.

Results

For sources up to a depth of 4 cm, we find the strongest influence on the signal topography of EEG forward solutions for the skull conductivity and a notable effect for the skin conductivity. For even deeper sources, e.g., located deep in the longitudinal fissure, we find an increasing influence of the white matter conductivity. The conductivity variations translate to varying source localizations particularly for quasi-tangential sources on sulcal walls, whereas source localizations of quasi-radial sources on the top of gyri are less affected. We find a strong correlation between skull conductivity and the variation of source localizations and especially the depth of the reconstructed source for quasi-tangential sources. We furthermore find a clear but weaker correlation between depth of the reconstructed source and the skin conductivity.

Discussion

Our results clearly show the influence of tissue conductivity uncertainties on EEG source analysis. We find a particularly strong influence of skull and skin conductivity uncertainties.

Limiting parameter range for cortical-spherical mapping improves activated domain estimation for attention modulated auditory response

BACKGROUND

Attention is one of the factors involved in selecting input information for the brain. We applied a method for estimating domains with clear boundaries using magnetoencephalography (the domain estimation method) for auditory-evoked responses (N100m) to evaluate the effects of attention in milliseconds. However, because the surface around the auditory cortex is folded in a complicated manner, it is unknown whether the activity in the auditory cortex can be estimated.

NEW METHOD

The parameter range to express current sources was set to include the auditory cortex. Their search region was expressed as a direct product of the parameter ranges used in the adaptive diagonal curves.

RESULTS

Without a limitation of the range, activity was estimated in regions other than the auditory cortex in all cases. However, with the limitation of the range, the activity was estimated in the primary or higher auditory cortex. Further analysis of the limitation of the range showed that the domains activated during attention included the regions activated during no attention for the participants whose amplitudes of N100m were higher during attention.

COMPARISON WITH EXISTING METHOD

We proposed a method for effectively limiting the search region to evaluate the extent of the activated domain in regions with complex folded structures.

CONCLUSION

To evaluate the extent of activated domains in regions with complex folded structures, it is necessary to limit the parameter search range. The area of the activated domains in the auditory cortex may increase by attention on the millisecond timescale.

CutFEM forward modeling for EEG source analysis

Introduction

Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction effects in the human head, represented by a partial differential equation which can be solved using the finite element method (FEM). FEM offers flexibility when modeling anisotropic tissue conductivities but requires a volumetric discretization, a mesh, of the head domain. Structured hexahedral meshes are easy to create in an automatic fashion, while tetrahedral meshes are better suited to model curved geometries. Tetrahedral meshes, thus, offer better accuracy but are more difficult to create.

Methods

We introduce CutFEM for EEG forward simulations to integrate the strengths of hexahedra and tetrahedra. It belongs to the family of unfitted finite element methods, decoupling mesh and geometry representation. Following a description of the method, we will employ CutFEM in both controlled spherical scenarios and the reconstruction of somatosensory-evoked potentials.

Results

CutFEM outperforms competing FEM approaches with regard to numerical accuracy, memory consumption, and computational speed while being able to mesh arbitrarily touching compartments.

Discussion

CutFEM balances numerical accuracy, computational efficiency, and a smooth approximation of complex geometries that has previously not been available in FEM-based EEG forward modeling.

Comparison of EEG Source Localization Using Simplified and Anatomically Accurate Head Models in Younger and Older Adults

Accuracy of electroencephalography (EEG) source localization relies on the volume conduction head model. A previous analysis of young adults has shown that simplified head models have larger source localization errors when compared with head models based on magnetic resonance images (MRIs). As obtaining individual MRIs may not always be feasible, researchers often use generic head models based on template MRIs. It is unclear how much error would be introduced using template MRI head models in older adults that likely have differences in brain structure compared to young adults. The primary goal of this study was to determine the error caused by using simplified head models without individual-specific MRIs in both younger and older adults. We collected high-density EEG during uneven terrain walking and motor imagery for 15 younger (22±3 years) and 21 older adults (74±5 years) and obtained [Formula: see text]-weighted MRI for each individual. We performed equivalent dipole fitting after independent component analysis to obtain brain source locations using four forward modeling pipelines with increasing complexity. These pipelines included: 1) a generic head model with template electrode positions or 2) digitized electrode positions, 3) individual-specific head models with digitized electrode positions using simplified tissue segmentation, or 4) anatomically accurate segmentation. We found that when compared to the anatomically accurate individual-specific head models, performing dipole fitting with generic head models led to similar source localization discrepancies (up to 2 cm) for younger and older adults. Co-registering digitized electrode locations to the generic head models reduced source localization discrepancies by  ∼  6 mm. Additionally, we found that source depths generally increased with skull conductivity for the representative young adult but not as much for the older adult. Our results can help inform a more accurate interpretation of brain areas in EEG studies when individual MRIs are unavailable.

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.

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.

Reconstructing subcortical and cortical somatosensory activity via the RAMUS inverse source analysis technique using median nerve SEP data

This study concerns reconstructing brain activity at various depths based on non-invasive EEG (electroencephalography) scalp measurements. We aimed at demonstrating the potential of the RAMUS (randomized multiresolution scanning) technique in localizing weakly distinguishable far-field sources in combination with coinciding cortical activity. As we have shown earlier theoretically and through simulations, RAMUS is a novel mathematical method that by employing the multigrid concept, allows marginalizing noise and depth bias effects and thus enables the recovery of both cortical and subcortical brain activity. To show this capability with experimental data, we examined the 14-30 ms post-stimulus somatosensory evoked potential (SEP) responses of human median nerve stimulation in three healthy adult subjects. We aim at reconstructing the different response components by evaluating a RAMUS-based estimate for the primary current density in the nervous tissue. We present source reconstructions obtained with RAMUS and compare them with the literature knowledge of the SEP components and the outcome of the unit-noise gain beamformer (UGNB) and standardized low-resolution brain electromagnetic tomography (sLORETA). We also analyzed the effect of the iterative alternating sequential technique, the optimization technique of RAMUS, compared to the classical minimum norm estimation (MNE) technique. Matching with our previous numerical studies, the current results suggest that RAMUS could have the potential to enhance the detection of simultaneous deep and cortical components and the distinction between the evoked sulcal and gyral activity.

Parametrizing the Conditionally Gaussian Prior Model for Source Localization with Reference to the P20/N20 Component of Median Nerve SEP/SEF

In this article, we focused on developing the conditionally Gaussian hierarchical Bayesian model (CG-HBM), which forms a superclass of several inversion methods for source localization of brain activity using somatosensory evoked potential (SEP) and field (SEF) measurements. The goal of this proof-of-concept study was to improve the applicability of the CG-HBM as a superclass by proposing a robust approach for the parametrization of focal source scenarios. We aimed at a parametrization that is invariant with respect to altering the noise level and the source space size. The posterior difference between the gamma and inverse gamma hyperprior was minimized by optimizing the shape parameter, while a suitable range for the scale parameter can be obtained via the prior-over-measurement signal-to-noise ratio, which we introduce as a new concept in this study. In the source localization experiments, the primary generator of the P20/N20 component was detected in the Brodmann area 3b using the CG-HBM approach and a parameter range derived from the existing knowledge of the Tikhonov-regularized minimum norm estimate, i.e., the classical Gaussian prior model. Moreover, it seems that the detection of deep thalamic activity simultaneously with the P20/N20 component with the gamma hyperprior can be enhanced while using a close-to-optimal shape parameter value.

Effect of structural complexities in head modeling on the accuracy of EEG source localization in neonates

OBJECTIVE

Neonatal electroencephalography (EEG) source localization is highly prone to errors due to head modeling deficiencies. In this study, we investigated the effect of head model complexities on the accuracy of EEG source localization in full term neonates using a realistic volume conductor head model.

APPROACH

We performed numerical simulations to investigate source localization errors caused by cerebrospinal fluid (CSF) and fontanel exclusion and gray matter (GM)/white matter (WM) distinction using the finite element method.

MAIN RESULTS

Our results showed that the exclusion of CSF from the head model could cause significant localization errors mostly for sources closer to the inner surface of the skull. With a less pronounced effect compared to the CSF exclusion, the discrimination between GM and WM also widely affected all sources, especially those located in deeper structures. The exclusion of the fontanels from the head model led to source localization errors for sources located in areas beneath the fontanels. Our finding clearly shows that the CSF inclusion and GM/WM distinction in EEG inverse modeling can substantially reduce EEG source localization errors. Moreover, fontanels should be included in neonatal head models, particularly in source localization applications, in which sources of interest are located beneath or in vicinity of fontanels.

SIGNIFICANCE

Our findings have practical implications for a better understanding of the impact of head model complexities on the accuracy of EEG source localization in neonates.

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.

Multi-Resolution Graph Based Volumetric Cortical Basis Functions From Local Anatomic Features

OBJECTIVE

Modern clinical MRI collects millimeter scale anatomic information, but scalp electroencephalography source localization is ill posed, and cannot resolve individual sources at that resolution. Dimensionality reduction in the space of cortical sources is needed to improve computational and storage complexity, yet volumetric methods still employ simplistic grid coarsening that eliminates fine scale anatomic structure. We present an approach to extend near-arbitrary spatial scaling to volumetric localization.

METHODS

Starting from a voxelwise brain parcellation, sub-parcels are identified from local cortical connectivity with an iterated graph cut approach. Spatial basis functions in each parcel are constructed using either a decomposition of the local leadfield matrix or spectral basis functions of local cortical connectivity graphs.

RESULTS

We present quantitative evaluation with extensive simulations and use multiple sets of real data to highlight how parameter changes impact computed reconstructions. Our results show that volumetric basis functions can improve accuracy by as much as 30%, while reducing computational complexity by over two orders of magnitude. In real data from epilepsy surgical candidates, accurate localization of seizure onset regions is demonstrated.

CONCLUSION

Spatial dimensionality reduction with volumetric basis functions improves reconstruction accuracy while reducing computational complexity.

SIGNIFICANCE

Near-arbitrary spatial dimensionality reduction will enable volumetric reconstruction with modern computationally intensive algorithms and anatomically driven multi-resolution methods.

The multipole approach for EEG forward modeling using the finite element method

For accurate EEG forward solutions, it is necessary to apply numerical methods that allow to take into account the realistic geometry of the subject's head. A commonly used method to solve this task is the finite element method (FEM). Different approaches have been developed to obtain EEG forward solutions for dipolar sources with the FEM. The St. Venant approach is frequently applied, since its high numerical accuracy and stability as well as its computational efficiency was demonstrated in multiple comparison studies. In this manuscript, we propose a variation of the St. Venant approach, the multipole approach, to improve the numerical accuracy of the St. Venant approach even further and to allow for the simulation of additional source scenarios, such as quadrupolar sources. Exploiting the multipole expansion of electric fields, we demonstrate that the newly proposed multipole approach achieves even higher numerical accuracies than the St. Venant approach in both multi-layer sphere and realistic head models. Additionally, we exemplarily show that the multipole approach allows to not only simulate dipolar but also quadrupolar sources.

The effect of stimulation type, head modeling, and combined EEG and MEG on the source reconstruction of the somatosensory P20/N20 component

Modeling and experimental parameters influence the Electro- (EEG) and Magnetoencephalography (MEG) source analysis of the somatosensory P20/N20 component. In a sensitivity group study, we compare P20/N20 source analysis due to different stimulation type (Electric-Wrist [EW], Braille-Tactile [BT], or Pneumato-Tactile [PT]), measurement modality (combined EEG/MEG - EMEG, EEG, or MEG) and head model (standard or individually skull-conductivity calibrated including brain anisotropic conductivity). Considerable differences between pairs of stimulation types occurred (EW-BT: 8.7 ± 3.3 mm/27.1° ± 16.4°, BT-PT: 9 ± 5 mm/29.9° ± 17.3°, and EW-PT: 9.8 ± 7.4 mm/15.9° ± 16.5° and 75% strength reduction of BT or PT when compared to EW) regardless of the head model used. EMEG has nearly no localization differences to MEG, but large ones to EEG (16.1 ± 4.9 mm), while source orientation differences are non-negligible to both EEG (14° ± 3.7°) and MEG (12.5° ± 10.9°). Our calibration results show a considerable inter-subject variability (3.1-14 mS/m) for skull conductivity. The comparison due to different head model show localization differences smaller for EMEG (EW: 3.4 ± 2.4 mm, BT: 3.7 ± 3.4 mm, and PT: 5.9 ± 6.8 mm) than for EEG (EW: 8.6 ± 8.3 mm, BT: 11.8 ± 6.2 mm, and PT: 10.5 ± 5.3 mm), while source orientation differences for EMEG (EW: 15.4° ± 6.3°, BT: 25.7° ± 15.2° and PT: 14° ± 11.5°) and EEG (EW: 14.6° ± 9.5°, BT: 16.3° ± 11.1° and PT: 12.9° ± 8.9°) are in the same range. Our results show that stimulation type, modality and head modeling all have a non-negligible influence on the source reconstruction of the P20/N20 component. The complementary information of both modalities in EMEG can be exploited on the basis of detailed and individualized head models.

Influence of Head Tissue Conductivity Uncertainties on EEG Dipole Reconstruction

Reliable EEG source analysis depends on sufficiently detailed and accurate head models. In this study, we investigate how uncertainties inherent to the experimentally determined conductivity values of the different conductive compartments influence the results of EEG source analysis. In a single source scenario, the superficial and focal somatosensory P20/N20 component, we analyze the influence of varying conductivities on dipole reconstructions using a generalized polynomial chaos (gPC) approach. We find that in particular the conductivity uncertainties for skin and skull have a significant influence on the EEG inverse solution, leading to variations in source localization by several centimeters. The conductivity uncertainties for gray and white matter were found to have little influence on the source localization, but a strong influence on the strength and orientation of the reconstructed source, respectively. As the CSF conductivity is most accurately determined of all conductivities in a realistic head model, CSF conductivity uncertainties had a negligible influence on the source reconstruction. This small uncertainty is a further benefit of distinguishing the CSF in realistic volume conductor models.

Working memory revived in older adults by synchronizing rhythmic brain circuits

Understanding normal brain aging and developing methods to maintain or improve cognition in older adults are major goals of fundamental and translational neuroscience. Here we show a core feature of cognitive decline-working-memory deficits-emerges from disconnected local and long-range circuits instantiated by theta-gamma phase-amplitude coupling in temporal cortex and theta phase synchronization across frontotemporal cortex. We developed a noninvasive stimulation procedure for modulating long-range theta interactions in adults aged 60-76 years. After 25 min of stimulation, frequency-tuned to individual brain network dynamics, we observed a preferential increase in neural synchronization patterns and the return of sender-receiver relationships of information flow within and between frontotemporal regions. The end result was rapid improvement in working-memory performance that outlasted a 50 min post-stimulation period. The results provide insight into the physiological foundations of age-related cognitive impairment and contribute to groundwork for future non-pharmacological interventions targeting aspects of cognitive decline.

A combined diffusion-weighted and electroencephalography study on age-related differences in connectivity in the motor network during bimanual performance

We studied the relationship between age-related differences in inter- and intra-hemispheric structural and functional connectivity in the bilateral motor network. Our focus was on the correlation between connectivity and declined motor performance in older adults. Structural and functional connectivity were estimated using diffusion weighted imaging and resting-state electro-encephalography, respectively. A total of 48 young and older healthy participants were measured. In addition, motor performances were assessed using bimanual coordination tasks. To pre-select regions-of-interest (ROIs), a neural model was adopted that accounts for intra-hemispheric functional connectivity between dorsal premotor area (PMd) and primary motor cortex (M1) and inter-hemispheric connections between left and right M1 (M1_L and M1_R ). Functional connectivity was determined via the weighted phase-lag index (wPLI) in the source-reconstructed beta activity during rest. We quantified structural connectivity using kurtosis anisotropy (KA) values of tracts derived from diffusion tensor-based fiber tractography between the aforementioned areas. In the group of older adults, wPLI values between M1_L -M1_R were negatively associated with the quality of bimanual motor performance. The additional association between wPLI values of PMd_L --M1_L and PMd_R -M1_L supports that functional connectivity with the left hemisphere mediated (bimanual) motor control in older adults. The correlational analysis between the selected structural and functional connections revealed a strong association between wPLI values in the left intra-hemispheric PMd_L -M1_L pathway and KA values in M1_L -M1_R and PMd_R -M1_L pathways in the group of older adults. This suggests that weaker structural connections in older adults correlate with stronger functional connectivity and, hence, poorer motor performance.

A Finite Element Solution of the Forward Problem in EEG for Multipolar Sources

Multipolar source models have been presented in the context of electro/magnetoencephalography (E/MEG) to compensate for the limitations of the classical equivalent current dipole to represent realistic generators of brain activity. Although there exist several reports accounting for the advantages of multipolar components over single dipoles, there is still no available numerical implementation in fully personalized scenarios. In this paper, we present, for the first time, a finite element framework for simulating EEG signals generated by multipolar current sources in individualized, heterogeneous, and anisotropic head models. This formulation is based on the subtraction approach, guaranteeing the existence and uniqueness of the solution. In particular, we analyze the cases of monopolar, dipolar, and quadrupolar source components, for which we study their performance in idealized and realistic head models. Numerical solutions are compared with analytical formulas in multi-layered spherical models. Such formulas are available in the case of monopolar and dipolar sources, and here derived for the quadrupolar components. We finally illustrate their advantages in the description of extended current generators using a realistic head model. The framework presented here enables further analysis towards the estimation of biophysically principled source parameters from standard E/MEG experiments.

Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity

Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bayesian approximation error (BAE) approach is exploited. In BAE, we first postulate a probability distribution for the skull conductivity that describes our (lack of) knowledge on its value, and model the effects of this uncertainty on EEG recordings with the help of an additive error term in the observation model. Before the Bayesian inference, the likelihood is marginalized over this error term. Thus, in the inversion we estimate only our primary unknown, the source distribution. We quantified the improvements in the source localization when the proposed Bayesian modelling was used in the presence of different skull conductivity errors and levels of measurement noise. Based on the results, BAE was able to improve the source localization accuracy, particularly when the unknown (true) skull conductivity was much lower than the expected standard conductivity value. The source locations that gained the highest improvements were shallow and originally exhibited the largest localization errors. In our case study, the benefits of BAE became negligible when the signal-to-noise ratio dropped to 20 dB.

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.

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.

Adaptive cortical parcellations for source reconstructed EEG/MEG connectomes

There is growing interest in the rich temporal and spectral properties of the functional connectome of the brain that are provided by Electro- and Magnetoencephalography (EEG/MEG). However, the problem of leakage between brain sources that arises when reconstructing brain activity from EEG/MEG recordings outside the head makes it difficult to distinguish true connections from spurious connections, even when connections are based on measures that ignore zero-lag dependencies. In particular, standard anatomical parcellations for potential cortical sources tend to over- or under-sample the real spatial resolution of EEG/MEG. By using information from cross-talk functions (CTFs) that objectively describe leakage for a given sensor configuration and distributed source reconstruction method, we introduce methods for optimising the number of parcels while simultaneously minimising the leakage between them. More specifically, we compare two image segmentation algorithms: 1) a split-and-merge (SaM) algorithm based on standard anatomical parcellations and 2) a region growing (RG) algorithm based on all the brain vertices with no prior parcellation. Interestingly, when applied to minimum-norm reconstructions for EEG/MEG configurations from real data, both algorithms yielded approximately 70 parcels despite their different starting points, suggesting that this reflects the resolution limit of this particular sensor configuration and reconstruction method. Importantly, when compared against standard anatomical parcellations, resolution matrices of adaptive parcellations showed notably higher sensitivity and distinguishability of parcels. Furthermore, extensive simulations of realistic networks revealed significant improvements in network reconstruction accuracies, particularly in reducing false leakage-induced connections. Adaptive parcellations therefore allow a more accurate reconstruction of functional EEG/MEG connectomes.

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We introduce adaptive cortical parcellation algorithms for E/MEG source estimation.

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Optimum number, size and locations of parcels are found based on cross-talk functions

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Algorithms yielded ∼70 distinguishable parcels regardless of the starting point.

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Parcel resolution matrices were notably improved compared to anatomical atlases.

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Network reconstruction accuracies of simulated connectomes improved significantly.

Zoomed MRI Guided by Combined EEG/MEG Source Analysis: A Multimodal Approach for Optimizing Presurgical Epilepsy Work-up and its Application in a Multi-focal Epilepsy Patient Case Study

In recent years, the use of source analysis based on electroencephalography (EEG) and magnetoencephalography (MEG) has gained considerable attention in presurgical epilepsy diagnosis. However, in many cases the source analysis alone is not used to tailor surgery unless the findings are confirmed by lesions, such as, e.g., cortical malformations in MRI. For many patients, the histology of tissue resected from MRI negative epilepsy shows small lesions, which indicates the need for more sensitive MR sequences. In this paper, we describe a technique to maximize the synergy between combined EEG/MEG (EMEG) source analysis and high resolution MRI. The procedure has three main steps: (1) construction of a detailed and calibrated finite element head model that considers the variation of individual skull conductivities and white matter anisotropy, (2) EMEG source analysis performed on averaged interictal epileptic discharges (IED), (3) high resolution (0.5 mm) zoomed MR imaging, limited to small areas centered at the EMEG source locations. The proposed new diagnosis procedure was then applied in a particularly challenging case of an epilepsy patient: EMEG analysis at the peak of the IED coincided with a right frontal focal cortical dysplasia (FCD), which had been detected at standard 1 mm resolution MRI. Of higher interest, zoomed MR imaging (applying parallel transmission, 'ZOOMit') guided by EMEG at the spike onset revealed a second, fairly subtle, FCD in the left fronto-central region. The evaluation revealed that this second FCD, which had not been detectable with standard 1 mm resolution, was the trigger of the seizures.

A Mixed Finite Element Method to Solve the EEG Forward Problem

Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as anisotropic conductivities. To date, most of the presented approaches rely on the same underlying formulation, the continuous Galerkin (CG)-FEM. In this article, a novel approach to solve the EEG forward problem based on a mixed finite element method (Mixed-FEM) is introduced. To obtain the Mixed-FEM formulation, the electric current is introduced as an additional unknown besides the electric potential. As a consequence of this derivation, the Mixed-FEM is, by construction, current preserving, in contrast to the CG-FEM. Consequently, a higher simulation accuracy can be achieved in certain scenarios, e.g., when the diameter of thin insulating structures, such as the skull, is in the range of the mesh resolution. A theoretical derivation of the Mixed-FEM approach for EEG forward simulations is presented, and the algorithms implemented for solving the resulting equation systems are described. Subsequently, first evaluations in both sphere and realistic head models are presented, and the results are compared to previously introduced CG-FEM approaches. Additional visualizations are shown to illustrate the current preserving property of the Mixed-FEM. Based on these results, it is concluded that the newly presented Mixed-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches, which motivates a further evaluation of the Mixed-FEM for applications in bioelectromagnetism.

Forward and inverse effects of the complete electrode model in neonatal EEG

The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary.

This paper investigates finite element method-based modeling in the context of neonatal electroencephalography (EEG). In particular, the focus lies on electrode boundary conditions. We compare the complete electrode model (CEM) with the point electrode model (PEM), which is the current standard in EEG. In the CEM, the voltage experienced by an electrode is modeled more realistically as the integral average of the potential distribution over its contact surface, whereas the PEM relies on a point value. Consequently, the CEM takes into account the subelectrode shunting currents, which are absent in the PEM. In this study, we aim to find out how the electrode voltage predicted by these two models differ, if standard size electrodes are attached to a head of a neonate. Additionally, we study voltages and voltage variation on electrode surfaces with two source locations: 1) next to the C6 electrode and 2) directly under the Fz electrode and the frontal fontanel. A realistic model of a neonatal head, including a skull with fontanels and sutures, is used. Based on the results, the forward simulation differences between CEM and PEM are in general small, but significant outliers can occur in the vicinity of the electrodes. The CEM can be considered as an integral part of the outer head model. The outcome of this study helps understanding volume conduction of neonatal EEG, since it enlightens the role of advanced skull and electrode modeling in forward and inverse computations.

NEW & NOTEWORTHY The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary.

Electroencephalography (EEG) forward modeling via H(div) finite element sources with focal interpolation

The goal of this study is to develop focal, accurate and robust finite element method (FEM) based approaches which can predict the electric potential on the surface of the computational domain given its structure and internal primary source current distribution. While conducting an EEG evaluation, the placement of source currents to the geometrically complex grey matter compartment is a challenging but necessary task to avoid forward errors attributable to tissue conductivity jumps. Here, this task is approached via a mathematically rigorous formulation, in which the current field is modeled via divergence conforming H(div) basis functions. Both linear and quadratic functions are used while the potential field is discretized via the standard linear Lagrangian (nodal) basis. The resulting model includes dipolar sources which are interpolated into a random set of positions and orientations utilizing two alternative approaches: the position based optimization (PBO) and the mean position/orientation (MPO) method. These results demonstrate that the present dipolar approach can reach or even surpass, at least in some respects, the accuracy of two classical reference methods, the partial integration (PI) and St. Venant (SV) approach which utilize monopolar loads instead of dipolar currents.

Skull Defects in Finite Element Head Models for Source Reconstruction from Magnetoencephalography Signals

Magnetoencephalography (MEG) signals are influenced by skull defects. However, there is a lack of evidence of this influence during source reconstruction. Our objectives are to characterize errors in source reconstruction from MEG signals due to ignoring skull defects and to assess the ability of an exact finite element head model to eliminate such errors. A detailed finite element model of the head of a rabbit used in a physical experiment was constructed from magnetic resonance and co-registered computer tomography imaging that differentiated nine tissue types. Sources of the MEG measurements above intact skull and above skull defects respectively were reconstructed using a finite element model with the intact skull and one incorporating the skull defects. The forward simulation of the MEG signals reproduced the experimentally observed characteristic magnitude and topography changes due to skull defects. Sources reconstructed from measured MEG signals above intact skull matched the known physical locations and orientations. Ignoring skull defects in the head model during reconstruction displaced sources under a skull defect away from that defect. Sources next to a defect were reoriented. When skull defects, with their physical conductivity, were incorporated in the head model, the location and orientation errors were mostly eliminated. The conductivity of the skull defect material non-uniformly modulated the influence on MEG signals. We propose concrete guidelines for taking into account conducting skull defects during MEG coil placement and modeling. Exact finite element head models can improve localization of brain function, specifically after surgery.

The role of blood vessels in high-resolution volume conductor head modeling of EEG

Reconstruction of the electrical sources of human EEG activity at high spatio-temporal accuracy is an important aim in neuroscience and neurological diagnostics. Over the last decades, numerous studies have demonstrated that realistic modeling of head anatomy improves the accuracy of source reconstruction of EEG signals. For example, including a cerebro-spinal fluid compartment and the anisotropy of white matter electrical conductivity were both shown to significantly reduce modeling errors. Here, we for the first time quantify the role of detailed reconstructions of the cerebral blood vessels in volume conductor head modeling for EEG. To study the role of the highly arborized cerebral blood vessels, we created a submillimeter head model based on ultra-high-field-strength (7T) structural MRI datasets. Blood vessels (arteries and emissary/intraosseous veins) were segmented using Frangi multi-scale vesselness filtering. The final head model consisted of a geometry-adapted cubic mesh with over 17×10(6) nodes. We solved the forward model using a finite-element-method (FEM) transfer matrix approach, which allowed reducing computation times substantially and quantified the importance of the blood vessel compartment by computing forward and inverse errors resulting from ignoring the blood vessels. Our results show that ignoring emissary veins piercing the skull leads to focal localization errors of approx. 5 to 15mm. Large errors (>2cm) were observed due to the carotid arteries and the dense arterial vasculature in areas such as in the insula or in the medial temporal lobe. Thus, in such predisposed areas, errors caused by neglecting blood vessels can reach similar magnitudes as those previously reported for neglecting white matter anisotropy, the CSF or the dura - structures which are generally considered important components of realistic EEG head models. Our findings thus imply that including a realistic blood vessel compartment in EEG head models will be helpful to improve the accuracy of EEG source analyses particularly when high accuracies in brain areas with dense vasculature are required.

Sparse EEG Source Localization Using Bernoulli Laplacian Priors

Source localization in electroencephalography has received an increasing amount of interest in the last decade. Solving the underlying ill-posed inverse problem usually requires choosing an appropriate regularization. The usual l2 norm has been considered and provides solutions with low computational complexity. However, in several situations, realistic brain activity is believed to be focused in a few focal areas. In these cases, the l2 norm is known to overestimate the activated spatial areas. One solution to this problem is to promote sparse solutions for instance based on the l1 norm that are easy to handle with optimization techniques. In this paper, we consider the use of an l0 + l1 norm to enforce sparse source activity (by ensuring the solution has few nonzero elements) while regularizing the nonzero amplitudes of the solution. More precisely, the l0 pseudonorm handles the position of the nonzero elements while the l1 norm constrains the values of their amplitudes. We use a Bernoulli-Laplace prior to introduce this combined l0 + l1 norm in a Bayesian framework. The proposed Bayesian model is shown to favor sparsity while jointly estimating the model hyperparameters using a Markov chain Monte Carlo sampling technique. We apply the model to both simulated and real EEG data, showing that the proposed method provides better results than the l2 and l1  norms regularizations in the presence of pointwise sources. A comparison with a recent method based on multiple sparse priors is also conducted.

Comparison Study for Whitney (Raviart-Thomas)-Type Source Models in Finite-Element-Method-Based EEG Forward Modeling

This study concentrates on finite-element-method (FEM)-based electroencephalography (EEG) forward simulation in which the electric potential evoked by neural activity in the brain is to be calculated at the surface of the head. The main advantage of the FEM is that it allows realistic modeling of tissue conductivity inhomogeneity. However, it is not straightforward to apply the classical model of a dipolar source with the FEM, due to its strong singularity and the resulting irregularity. The focus of this study is on comparing different methods to cope with this problem. In particular, we evaluate the accuracy of Whitney (Raviart-Thomas)-type dipole-like source currents compared to two reference dipole modeling methods: the St. Venant and partial integration approach. Common to all these methods is that they enable direct approximation of the potential field utilizing linear basis functions. In the present context, Whitney elements are particularly interesting, as they provide a simple means to model a divergence-conforming primary current vector field satisfying the square integrability condition. Our results show that a Whitney-type source model can provide simulation accuracy comparable to the present reference methods. It can lead to superior accuracy under optimized conditions with respect to both source location and orientation in a tetrahedral mesh. For random source orientations, the St. Venant approach turns out to be the method of choice over the interpolated version of the Whitney model. The overall moderate differences obtained suggest that practical aspects, such as the focality, should be prioritized when choosing a source model.

High-density electroencephalography developmental neurophysiological trajectories

Efforts to document early changes in the developing brain have resulted in the construction of increasingly accurate structural images based on magnetic resonance imaging (MRI) in newborn infants. Tractography diagrams obtained through diffusion tensor imaging have focused on white matter microstructure, with particular emphasis on neuronal connectivity at the level of fibre tract systems. Electroencephalography (EEG) provides a complementary approach with more direct access to brain electrical activity. Its temporal resolution is excellent, and its spatial resolution can be enhanced to physiologically relevant levels, through the combination of high-density recordings (e.g. by using 64 channels in newborn infants) and mathematical models (e.g. inverse modelling computation), to identify generators of different oscillation bands and synchrony patterns. The integration of functional and structural topography of the neonatal brain provides insights into typical brain organization, and the deviations seen in particular contexts, for example the effect of hypoxic-ischaemic insult in terms of damage, eventual reorganization, and functional changes. Endophenotypes can then be used for pathophysiological reasoning, management planning, and outcome measurements, and allow a longitudinal approach to individual developmental trajectories.

Influence of the head model on EEG and MEG source connectivity analyses

The results of brain connectivity analysis using reconstructed source time courses derived from EEG and MEG data depend on a number of algorithmic choices. While previous studies have investigated the influence of the choice of source estimation method or connectivity measure, the effects of the head modeling errors or simplifications have not been studied sufficiently. In the present simulation study, we investigated the influence of particular properties of the head model on the reconstructed source time courses as well as on source connectivity analysis in EEG and MEG. Therefore, we constructed a realistic head model and applied the finite element method to solve the EEG and MEG forward problems. We considered the distinction between white and gray matter, the distinction between compact and spongy bone, the inclusion of a cerebrospinal fluid (CSF) compartment, and the reduction to a simple 3-layer model comprising only the skin, skull, and brain. Source time courses were reconstructed using a beamforming approach and the source connectivity was estimated by the imaginary coherence (ICoh) and the generalized partial directed coherence (GPDC). Our results show that in both EEG and MEG, neglecting the white and gray matter distinction or the CSF causes considerable errors in reconstructed source time courses and connectivity analysis, while the distinction between spongy and compact bone is just of minor relevance, provided that an adequate skull conductivity value is used. Large inverse and connectivity errors are found in the same regions that show large topography errors in the forward solution. Moreover, we demonstrate that the very conservative ICoh is relatively safe from the crosstalk effects caused by imperfect head models, as opposed to the GPDC.

Epileptogenic focus localization in treatment-resistant post-traumatic epilepsy

Pharmacologically intractable post-traumatic epilepsy (PTE) is a major clinical challenge for patients with penetrating traumatic brain injury, where the risk for this condition remains very high even decades after injury. Although over 20 anti-epileptic drugs (AED) are in common use today, approximately one-third of epilepsy patients have drug-refractory seizures and even more have AED-related adverse effects which compromise life quality. Simultaneously, there have been repeated recommendations by radiologists and neuroimaging experts to incorporate localization based on electroencephalography (EEG) into the process of clinical decision making regarding PTE patients. Nevertheless, thus far, little progress has been accomplished towards the use of EEG as a reliable tool for locating epileptogenic foci prior to surgical resection. In this review, we discuss the epidemiology of pharmacologically resistant PTE, address the need for effective anti-epileptogenic treatments, and highlight recent progress in the development of noninvasive methods for the accurate localization of PTE foci for the purpose of neurosurgical intervention. These trends indicate the current emergence of promising methodologies for the noninvasive study of post-traumatic epileptogenesis and for the improved neurosurgical planning of epileptic foci resection.

A guideline for head volume conductor modeling in EEG and MEG

For accurate EEG/MEG source analysis it is necessary to model the head volume conductor as realistic as possible. This includes the distinction of the different conductive compartments in the human head. In this study, we investigated the influence of modeling/not modeling the conductive compartments skull spongiosa, skull compacta, cerebrospinal fluid (CSF), gray matter, and white matter and of the inclusion of white matter anisotropy on the EEG/MEG forward solution. Therefore, we created a highly realistic 6-compartment head model with white matter anisotropy and used a state-of-the-art finite element approach. Starting from a 3-compartment scenario (skin, skull, and brain), we subsequently refined our head model by distinguishing one further of the above-mentioned compartments. For each of the generated five head models, we measured the effect on the signal topography and signal magnitude both in relation to a highly resolved reference model and to the model generated in the previous refinement step. We evaluated the results of these simulations using a variety of visualization methods, allowing us to gain a general overview of effect strength, of the most important source parameters triggering these effects, and of the most affected brain regions. Thereby, starting from the 3-compartment approach, we identified the most important additional refinement steps in head volume conductor modeling. We were able to show that the inclusion of the highly conductive CSF compartment, whose conductivity value is well known, has the strongest influence on both signal topography and magnitude in both modalities. We found the effect of gray/white matter distinction to be nearly as big as that of the CSF inclusion, and for both of these steps we identified a clear pattern in the spatial distribution of effects. In comparison to these two steps, the introduction of white matter anisotropy led to a clearly weaker, but still strong, effect. Finally, the distinction between skull spongiosa and compacta caused the weakest effects in both modalities when using an optimized conductivity value for the homogenized compartment. We conclude that it is highly recommendable to include the CSF and distinguish between gray and white matter in head volume conductor modeling. Especially for the MEG, the modeling of skull spongiosa and compacta might be neglected due to the weak effects; the simplification of not modeling white matter anisotropy is admissible considering the complexity and current limitations of the underlying modeling approach.

Combining EEG and MEG for the reconstruction of epileptic activity using a calibrated realistic volume conductor model

To increase the reliability for the non-invasive determination of the irritative zone in presurgical epilepsy diagnosis, we introduce here a new experimental and methodological source analysis pipeline that combines the complementary information in EEG and MEG, and apply it to data from a patient, suffering from refractory focal epilepsy. Skull conductivity parameters in a six compartment finite element head model with brain anisotropy, constructed from individual MRI data, are estimated in a calibration procedure using somatosensory evoked potential (SEP) and field (SEF) data. These data are measured in a single run before acquisition of further runs of spontaneous epileptic activity. Our results show that even for single interictal spikes, volume conduction effects dominate over noise and need to be taken into account for accurate source analysis. While cerebrospinal fluid and brain anisotropy influence both modalities, only EEG is sensitive to skull conductivity and conductivity calibration significantly reduces the difference in especially depth localization of both modalities, emphasizing its importance for combining EEG and MEG source analysis. On the other hand, localization differences which are due to the distinct sensitivity profiles of EEG and MEG persist. In case of a moderate error in skull conductivity, combined source analysis results can still profit from the different sensitivity profiles of EEG and MEG to accurately determine location, orientation and strength of the underlying sources. On the other side, significant errors in skull modeling are reflected in EEG reconstruction errors and could reduce the goodness of fit to combined datasets. For combined EEG and MEG source analysis, we therefore recommend calibrating skull conductivity using additionally acquired SEP/SEF data.

Effects of sutures and fontanels on MEG and EEG source analysis in a realistic infant head model

In infants, the fontanels and sutures as well as conductivity of the skull influence the volume currents accompanying primary currents generated by active neurons and thus the associated electroencephalography (EEG) and magnetoencephalography (MEG) signals. We used a finite element method (FEM) to construct a realistic model of the head of an infant based on MRI images. Using this model, we investigated the effects of the fontanels, sutures and skull conductivity on forward and inverse EEG and MEG source analysis. Simulation results show that MEG is better suited than EEG to study early brain development because it is much less sensitive than EEG to distortions of the volume current caused by the fontanels and sutures and to inaccurate estimates of skull conductivity. Best results will be achieved when MEG and EEG are used in combination.

Cortical sources of ERP in prosaccade and antisaccade eye movements using realistic source models

The cortical sources of event-related-potentials (ERP) using realistic source models were examined in a prosaccade and antisaccade procedure. College-age participants were presented with a preparatory interval and a target that indicated the direction of the eye movement that was to be made. In some blocks a cue was given in the peripheral location where the target was to be presented and in other blocks no cue was given. In Experiment 1 the prosaccade and antisaccade trials were presented randomly within a block; in Experiment 2 procedures were compared in which either prosaccade and antisaccade trials were mixed in the same block, or trials were presented in separate blocks with only one type of eye movement. There was a central negative slow wave occurring prior to the target, a slow positive wave over the parietal scalp prior to the saccade, and a parietal spike potential immediately prior to saccade onset. Cortical source analysis of these ERP components showed a common set of sources in the ventral anterior cingulate and orbital frontal gyrus for the presaccadic positive slow wave and the spike potential. In Experiment 2 the same cued- and non-cued blocks were used, but prosaccade and antisaccade trials were presented in separate blocks. This resulted in a smaller difference in reaction time between prosaccade and antisaccade trials. Unlike the first experiment, the central negative slow wave was larger on antisaccade than on prosaccade trials, and this effect on the ERP component had its cortical source primarily in the parietal and mid-central cortical areas contralateral to the direction of the eye movement. These results suggest that blocked prosaccade and antisaccade trials results in preparatory or set effects that decreases reaction time, eliminates some cueing effects, and is based on contralateral parietal-central brain areas.

Lack of systematic topographic difference between attention and reasoning beta correlates

Based on previous evidence for individual-specific sets of cortical areas active during simple attention tasks, in this work we intended to perform within individual comparisons of task-induced beta oscillations between visual attention and a reasoning task. Since beta induced oscillations are not time-locked to task events and were first observed by Fourier transforms, in order to analyze the cortical topography of attention induced beta activity, we have previously computed corrected-latency averages based on spontaneous peaks of band-pass filtered epochs. We then used Independent Component Analysis (ICA) only to single out the significant portion of averaged data, above noise levels. In the present work ICA served as the main, exhaustive means for decomposing beta activity in both tasks, using 128-channel EEG data from 24 subjects. Given the previous observed similarity between tasks by visual inspection and by simple descriptive statistics, we now intended another approach: to quantify how much each ICA component obtained in one task could be explained by a linear combination of the topographic patterns from the other task in each individual. Our hypothesis was that the major psychological difference between tasks would not be reflected as important topographic differences within individuals. Results confirmed the high topographic similarity between attention and reasoning beta correlates in that few components in each individual were not satisfactorily explained by the complementary task, and if those could be considered "task-specific", their scalp distribution and estimated cortical sources were not common across subjects. These findings, along with those from fMRI studies preserving individual data and conventional neuropsychological and neurosurgical observations, are discussed in support of a new functional localization hypothesis: individuals use largely different sets of cortical association areas to perform a given task, but those individual sets do not change importantly across tasks that differ in major psychological processes.

Methods for high-resolution anisotropic finite element modeling of the human head: automatic MR white matter anisotropy-adaptive mesh generation

This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions towards more accurate analysis of bioelectromagnetic problems.

Minor and unsystematic cortical topographic changes of attention correlates between modalities

In this study we analyzed the topography of induced cortical oscillations in 20 healthy individuals performing simple attention tasks. We were interested in qualitatively replicating our recent findings on the localization of attention-induced beta bands during a visual task [1], and verifying whether significant topographic changes would follow the change of attention to the auditory modality. We computed corrected latency averaging of each induced frequency bands, and modeled their generators by current density reconstruction with Lp-norm minimization. We quantified topographic similarity between conditions by an analysis of correlations, whereas the inter-modality significant differences in attention correlates were illustrated in each individual case. We replicated the qualitative result of highly idiosyncratic topography of attention-related activity to individuals, manifested both in the beta bands, and previously studied slow potential distributions [2]. Visual inspection of both scalp potentials and distribution of cortical currents showed minor changes in attention-related bands with respect to modality, as compared to the theta and delta bands, known to be major contributors to the sensory-related potentials. Quantitative results agreed with visual inspection, supporting to the conclusion that attention-related activity does not change much between modalities, and whatever individual changes do occur, they are not systematic in cortical localization across subjects. We discuss our results, combined with results from other studies that present individual data, with respect to the function of cortical association areas.