A novel method for calibrating head models to account for variability in conductivity and its evaluation in a sphere model.

The accuracy in electroencephalography (EEG) and combined EEG and magnetoencephalography (MEG) source reconstructions as well as in optimized transcranial electric stimulation (TES) depends on the conductive properties assigned to the head model, and most importantly on individual skull conductivity. In this study, we present an automatic pipeline to calibrate head models with respect to skull conductivity based on the reconstruction of the P20/N20 response using somatosensory evoked potentials and fields. In order to validate in a well-controlled setup without interplay with numerical errors, we evaluate the accuracy of this algorithm in a 4-layer spherical head model using realistic noise levels as well as dipole sources at different eccentricities with strengths and orientations related to somatosensory experiments. Our results show that the reference skull conductivity can be reliably reconstructed for sources resembling the generator of the P20/N20 response. In case of erroneous assumptions on scalp conductivity, the resulting skull conductivity parameter counterbalances this effect, so that EEG source reconstructions using the fitted skull conductivity parameter result in lower errors than when using the standard value. We propose an automatized procedure to calibrate head models which only relies on non-invasive modalities that are available in a standard MEG laboratory, measures under in vivo conditions and in the low frequency range of interest. Calibrated head modeling can improve EEG and combined EEG/MEG source analysis as well as optimized TES.

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.

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.

Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem.

To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively.

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.

Specificity and sensitivity of visual evoked potentials in the diagnosis of schizophrenia: rethinking VEPs.

Alterations of the visual evoked potential (VEP) component P1 at the occipital region represent the most extended functional references of early visual dysfunctions in schizophrenia (SZ). However, P1 deficits are not reliable enough to be accepted as standard susceptibility markers for use in clinical psychiatry. We have previously reported a novel approach combining a standard checkerboard pattern-reversal stimulus, spectral resolution VEP, source detection techniques and statistical procedures which allowed the correct classification of all patients as SZ compared to controls. Here, we applied the same statistical approach but to a single surface VEP - in contrast to the complex EEG source analyses in our previous report. P1 and N1 amplitude differences among spectral resolution VEPs from a POz-F3 bipolar montage were computed for each component. The resulting F-values were then Z-transformed. Individual comparisons of each component of P1 and N1 showed that in 72% of patients, their individual Z-score deviated from the normal distribution of controls for at least one of the two components. Crossvalidation against the distribution in the SZ-group improved the detection rate to 93%. In all, six patients were misclassified. Clinical validation yielded striking positive (78.13%) and negative (92.69%) predictive values. The here presented procedure offers a potential clinical screening method for increased susceptibility to SZ which should then be followed by high density electrode array and source detection analyses. The most important aspect of this work is represented by the fact that this diagnostic technique is low-cost and involves equipment that is feasible to use in typical community clinics.

Investigation of tDCS volume conduction effects in a highly realistic head model.

OBJECTIVE: We investigate volume conduction effects in transcranial direct current stimulation (tDCS) and present a guideline for efficient and yet accurate volume conductor modeling in tDCS using our newly-developed finite element (FE) approach. APPROACH: We developed a new, accurate and fast isoparametric FE approach for high-resolution geometry-adapted hexahedral meshes and tissue anisotropy. To attain a deeper insight into tDCS, we performed computer simulations, starting with a homogenized three-compartment head model and extending this step by step to a six-compartment anisotropic model. MAIN RESULTS: We are able to demonstrate important tDCS effects. First, we find channeling effects of the skin, the skull spongiosa and the cerebrospinal fluid compartments. Second, current vectors tend to be oriented towards the closest higher conducting region. Third, anisotropic WM conductivity causes current flow in directions more parallel to the WM fiber tracts. Fourth, the highest cortical current magnitudes are not only found close to the stimulation sites. Fifth, the median brain current density decreases with increasing distance from the electrodes. SIGNIFICANCE: Our results allow us to formulate a guideline for volume conductor modeling in tDCS. We recommend to accurately model the major tissues between the stimulating electrodes and the target areas, while for efficient yet accurate modeling, an exact representation of other tissues is less important. Because for the low-frequency regime in electrophysiology the quasi-static approach is justified, our results should also be valid for at least low-frequency (e.g., below 100 Hz) transcranial alternating current stimulation.

The influence of sulcus width on simulated electric fields induced by transcranial magnetic stimulation.

Volume conduction models can help in acquiring knowledge about the distribution of the electric field induced by transcranial magnetic stimulation. One aspect of a detailed model is an accurate description of the cortical surface geometry. Since its estimation is difficult, it is important to know how accurate the geometry has to be represented. Previous studies only looked at the differences caused by neglecting the complete boundary between cerebrospinal fluid (CSF) and grey matter (Thielscher et al 2011 NeuroImage 54 234-43, Bijsterbosch et al 2012 Med. Biol. Eng. Comput. 50 671-81), or by resizing the whole brain (Wagner et al 2008 Exp. Brain Res. 186 539-50). However, due to the high conductive properties of the CSF, it can be expected that alterations in sulcus width can already have a significant effect on the distribution of the electric field. To answer this question, the sulcus width of a highly realistic head model, based on T1-, T2- and diffusion-weighted magnetic resonance images, was altered systematically. This study shows that alterations in the sulcus width do not cause large differences in the majority of the electric field values. However, considerable overestimation of sulcus width produces an overestimation of the calculated field strength, also at locations distant from the target location.

Diffeomorphic susceptibility artifact correction of diffusion-weighted magnetic resonance images.

Diffusion-weighted magnetic resonance imaging is a key investigation technique in modern neuroscience. In clinical settings, diffusion-weighted imaging and its extension to diffusion tensor imaging (DTI) are usually performed applying the technique of echo-planar imaging (EPI). EPI is the commonly available ultrafast acquisition technique for single-shot acquisition with spatial encoding in a Cartesian system. A drawback of these sequences is their high sensitivity against small perturbations of the magnetic field, caused, e.g., by differences in magnetic susceptibility of soft tissue, bone and air. The resulting magnetic field inhomogeneities thus cause geometrical distortions and intensity modulations in diffusion-weighted images. This complicates the fusion with anatomical T1- or T2-weighted MR images obtained with conventional spin- or gradient-echo images and negligible distortion. In order to limit the degradation of diffusion-weighted MR data, we present here a variational approach based on a reference scan pair with reversed polarity of the phase- and frequency-encoding gradients and hence reversed distortion. The key novelty is a tailored nonlinear regularization functional to obtain smooth and diffeomorphic transformations. We incorporate the physical distortion model into a variational image registration framework and derive an accurate and fast correction algorithm. We evaluate the applicability of our approach to distorted DTI brain scans of six healthy volunteers. For all datasets, the automatic correction algorithm considerably reduced the image degradation. We show that, after correction, fusion with T1- or T2-weighted images can be obtained by a simple rigid registration. Furthermore, we demonstrate the improvement due to the novel regularization scheme. Most importantly, we show that it provides meaningful, i.e. diffeomorphic, geometric transformations, independent of the actual choice of the regularization parameters.

Good vibrations: oscillatory phase shapes perception.

In the current study, we provide compelling evidence to answer the long-standing question whether perception is continuous or periodic. Spontaneous brain oscillations are assumed to be the underlying mechanism of periodic perception. Depending on the phase angle of the oscillations, an identical stimulus results in different perceptual outcomes. Past results, however, can only account for a correlation of perception with the phase of the ongoing brain oscillations. Therefore, it is desirable to demonstrate a causal relation between phase and perception. One way to address this question is to entrain spontaneous brain oscillations by applying an external oscillation and then demonstrate behavioral consequences of this oscillation. We conducted an auditory detection experiment with humans, recorded the electroencephalogram (EEG) concurrently and simultaneously applied oscillating transcranial direct current stimulation at 10Hz (α-tDCS). Our approach revealed that detection thresholds were dependent on the phase of the oscillation that was entrained by α-tDCS. This behavioral effect was accompanied by an electrophysiological effect: α-power was enhanced after α-tDCS as compared to a pre-stimulation period. By showing a causal relation between phase and perception, our results extend findings of previous studies that were only able to demonstrate a correlation. We found that manipulation of the phase resulted in different detection thresholds, which supports the notion that perception can be periodically modulated by oscillatory processes. This demonstrates that tDCS can serve as a tool in neuroscience to extend the knowledge of the functional significance of brain oscillations.

Influences of skull segmentation inaccuracies on EEG source analysis.

The low-conducting human skull is known to have an especially large influence on electroencephalography (EEG) source analysis. Because of difficulties segmenting the complex skull geometry out of magnetic resonance images, volume conductor models for EEG source analysis might contain inaccuracies and simplifications regarding the geometry of the skull. The computer simulation study presented here investigated the influences of a variety of skull geometry deficiencies on EEG forward simulations and source reconstruction from EEG data. Reference EEG data was simulated in a detailed and anatomically plausible reference model. Test models were derived from the reference model representing a variety of skull geometry inaccuracies and simplifications. These included erroneous skull holes, local errors in skull thickness, modeling cavities as bone, downward extension of the model and simplifying the inferior skull or the inferior skull and scalp as layers of constant thickness. The reference EEG data was compared to forward simulations in the test models, and source reconstruction in the test models was performed on the simulated reference data. The finite element method with high-resolution meshes was employed for all forward simulations. It was found that large skull geometry inaccuracies close to the source space, for example, when cutting the model directly below the skull, led to errors of 20mm and more for extended source space regions. Local defects, for example, erroneous skull holes, caused non-negligible errors only in the vicinity of the defect. The study design allowed a comparison of influence size, and guidelines for modeling the skull geometry were concluded.

Complete electrode model in EEG: relationship and differences to the point electrode model.

In electroencephalography (EEG) source analysis, a primary current density generated by the neural activity of the brain is reconstructed from external electrode voltage measurements. This paper focuses on accurate and effective simulations of EEG through the complete electrode model (CEM). The CEM allows for the incorporation of the electrode size, shape and effective contact impedance into the forward simulation. Both neural currents in the brain and shunting currents between the electrodes and the skin can affect the measured voltages in the CEM. The goal of this study was to investigate the CEM by comparing it with the point electrode model (PEM), which is the current standard electrode model for EEG. We used a three-dimensional, realistic and high-resolution finite element head model as the reference computational domain in the comparison. The PEM could be formulated as a limit of the CEM, in which the effective impedance of each electrode goes to infinity and the size tends to zero. Numerical results concerning the forward and inverse errors and electrode voltage strengths with different impedances and electrode sizes are presented. Based on the results obtained, limits for extremely high and low impedance values of the shunting currents are suggested.

A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation.

A mathematical dipole is widely used as a model for the primary current source in electroencephalography (EEG) source analysis. In the governing Poisson-type differential equation, the dipole leads to a singularity on the right-hand side, which has to be treated specifically. In this paper, we will present a full subtraction approach where the total potential is divided into a singularity and a correction potential. The singularity potential is due to a dipole in an infinite region of homogeneous conductivity. The correction potential is computed using the finite element (FE) method. Special care is taken in order to evaluate the right-hand side integral appropriately with the objective of achieving highest possible convergence order for linear basis functions. Our new approach allows the construction of transfer matrices for fast computation of the inverse problem for anisotropic volume conductors. A constrained Delaunay tetrahedralisation (CDT) approach is used for the generation of high-quality FE meshes. We validate the new approach in a four-layer sphere model with a highly conductive cerebrospinal fluid (CSF) and an anisotropic skull compartment. For radial and tangential sources with eccentricities up to 1 mm below the CSF compartment, we achieve a maximal relative error of 0.71% in a CDT-FE model with 360 k nodes which is not locally refined around the source singularity and therefore useful for arbitrary dipole locations. The combination of the full subtraction approach with the high quality CDT meshes leads to accuracies that, to the best of the author's knowledge, have not yet been presented before.

Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis.

Accuracy and run-time play an important role in medical diagnostics and research as well as in the field of neuroscience. In Electroencephalography (EEG) source reconstruction, a current distribution in the human brain is reconstructed noninvasively from measured potentials at the head surface (the EEG inverse problem). Numerical modeling techniques are used to simulate head surface potentials for dipolar current sources in the human cortex, the so-called EEG forward problem.In this paper, the efficiency of algebraic multigrid (AMG), incomplete Cholesky (IC) and Jacobi preconditioners for the conjugate gradient (CG) method are compared for iteratively solving the finite element (FE) method based EEG forward problem. The interplay of the three solvers with a full subtraction approach and two direct potential approaches, the Venant and the partial integration method for the treatment of the dipole singularity is examined. The examination is performed in a four-compartment sphere model with anisotropic skull layer, where quasi-analytical solutions allow for an exact quantification of computational speed versus numerical error. Specifically-tuned constrained Delaunay tetrahedralization (CDT) FE meshes lead to high accuracies for both the full subtraction and the direct potential approaches. Best accuracies are achieved by the full subtraction approach if the homogeneity condition is fulfilled. It is shown that the AMG-CG achieves an order of magnitude higher computational speed than the CG with the standard preconditioners with an increasing gain factor when decreasing mesh size. Our results should broaden the application of accurate and fast high-resolution FE volume conductor modeling in source analysis routine.