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The inverse problem arising from EEG and MEG is largely underdetermined. One strategy to alleviate this problem is the restriction to a limited number of point-like sources, the focal source model. Although the singular value decomposition of the spatio-temporal data gives an estimate of the minimal number of dipoles contributing to the measurement...
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... calculations were carried out in CAUCHY and visualization of reference sources, generated noisy potential distributions (rereferenced to common aver- age) and inverse source reconstructions was done in CURRY. In the following simulations, reference sources were placed on surface mesh nodes inside the sulcus ( figure 3) and of the inner sphere and the potential distri- bution at the electrode locations was calculated. As a measure for the global field strength, we used the euclid- ean norm of the calculated electrode potentials (zero potential at Cz) ...
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... We use no regularization for the EEG and combined EEG/MEG dipole scan. We used the truncated singular value decomposition (tSVD) as regularization method [27,76] for the MEG dipole scan. Thereby, the MEG leadfield was reduced to the two quasi-tangential directions by an SVD. ...
MEG and EEG source analysis is frequently used for the presurgical evaluation of pharmacoresistant epilepsy patients. The source localization of the epileptogenic zone depends, among other aspects, on the selected inverse and forward approaches and their respective parameter choices. In this validation study, we compare the standard dipole scanning method with two beamformer approaches for the inverse problem, and we investigate the influence of the covariance estimation method and the strength of regularization on the localization performance for EEG, MEG, and combined EEG and MEG. For forward modelling, we investigate the difference between calibrated six-compartment and standard three-compartment head modelling. In a retrospective study, two patients with focal epilepsy due to focal cortical dysplasia type IIb and seizure freedom following lesionectomy or radiofrequency-guided thermocoagulation (RFTC) used the distance of the localization of interictal epileptic spikes to the resection cavity resp. RFTC lesion as reference for good localization. We found that beamformer localization can be sensitive to the choice of the regularization parameter, which has to be individually optimized. Estimation of the covariance matrix with averaged spike data yielded more robust results across the modalities. MEG was the dominant modality and provided a good localization in one case, while it was EEG for the other. When combining the modalities, the good results of the dominant modality were mostly not spoiled by the weaker modality. For appropriate regularization parameter choices, the beamformer localized better than the standard dipole scan. Compared to the importance of an appropriate regularization, the sensitivity of the localization to the head modelling was smaller, due to similar skull conductivity modelling and the fixed source space without orientation constraint.
... For the EEG and combined EEG/MEG dipole scan we use no regularization. For the MEG dipole scan, we used the truncated singular value decomposition (tSVD) as regularization method [27,76]. Therefore, the MEG leadfield was reduced to the two quasitangential directions by an SVD. ...
MEG and EEG source analysis is frequently used for the presurgical evaluation of pharmacoresistant epilepsy patients.
The source localization of the epileptogenic zone depends, among other aspects, on the selected inverse and forward approaches
and their respective parameter choices.
In this validation study, we compare for the inverse problem the standard dipole scanning method with two beamformer approaches and
we investigate the influence of the covariance estimation method and the strength of regularization on the localization performance for EEG, MEG and combined EEG and MEG.
For forward modeling, we investigate the difference between calibrated six-compartment and standard three-compartment head modeling. In a retrospective study of two patients with focal epilepsy due to focal cortical dysplasia type IIb and seizure-freedom following lesionectomy or radiofrequency-guided thermocoagulation, we used the distance of the localization of interictal epileptic spikes to the resection cavity resp. rediofrequency lesion as reference for good localization. We found that beamformer localization can be sensitive to the choice of the regularization parameter, which has to be individually optimized. Estimation of the covariance matrix with averaged spike data yielded more robust results across the modalities. MEG was the dominant modality and provided a good localization in one case, while it was EEG for the other. When combining the modalities, the good results of the dominant modality were mostly not spoiled by the weaker modality. For appropriate regularization parameter choices, the beamformer localized better than the standard dipole scan. Compared to the importance of an appropriate regularization, the sensitivity of the localization to the head modeling was smaller, due to similar skull conductivity modeling and the fixed source space without orientation constraint.
... In most of our validation tests, realistic noise is added to the simulated data, as described in section 2.3. Additionally, functions l EEG : (Wolters et al 1999). These functions l EEG and l MEG compute the EEG and MEG leadfields L EEG,x,σ skull and L MEG,x , respectively, i.e. the simulated sensor signals for a dipolar source at location x with moments oriented in the three Cartesian directions. ...
... Therefore, similar to Antonakakis et al (2020), Fuchs et al (1998), Huang et al (2007), Wolters et al (2010), Aydin et al (2014) and Haueisen et al (1997), the MEG is used to fix the location of the P20/N20 source. In step 1, an MEG equivalent current dipole scan is used to find the best fitting source location x MEG within the source space S. From here on, j denotes the dipole moment and [·] + the Moore-Penrose pseudo-inverse of a matrix, which in case of the MEG leadfield relies on a truncated singular value decomposition (Wolters et al 1999). In step 2, a derivative free minimization method, the so called Brent method (Brent 1972), is used within the Matlab routine fminbnd to iteratively perform the steps described below for different skull conductivities σ i skull in the predefined continuous range. ...
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. Accurate skull conductivity calibration will improve individualized head modeling for EEG and combined EEG/MEG source analysis as well as for optimized TES.
... This is due to the close-to-singularity of the covariance matrix of the two regressors . Similar issues exist in dipole source localization when different dipole sources have a high spatial correlation, in which case the source temporal activity will have complementary patterns resembling amplification of noise (Wolters et al. 1999). A solution to this issue that is both practically and theoretically sound has yet to be found. ...
The brain displays dynamical system behaviors at various levels that are functionally and cognitively relevant. Ample researches have examined how the dynamical properties of brain activity reflect the neural cognitive working mechanisms. A prevalent approach in this field is to extract the trial-averaged brain electrophysiological signals as a representation of the dynamical response of the complex neural system to external stimuli. However, the responses are intrinsically variable in latency from trial to trial. The variability compromises the accuracy of the detected dynamical response pattern based on trial-averaged approach, which may mislead subsequent modelling works. More accurate characterization of the brain’s dynamical response incorporating single trial variability information is of profound significance in deepening our understanding of neural cognitive dynamics and brain’s working principles. Various methods have been attempted to address the trial-to-trial asynchrony issue in order to achieve an improved representation of the dynamical response. We review the latest development of methodology in this area and the contribution of latency variability-based decomposition and reconstruction of dynamical response to neural cognitive researches.
... The main goal of the dipole scan is the determination of the source for which the residual variance (RV) between the measured and the simulated SEF data at 20 ms post-stimulus is minimal. Furthermore, the dipole scan is regularized accordingly to suppress the amplification of high-frequency spatial noise into erroneously high radial dipole orientation components within the inversion procedure ( Fuchs et al., 1998 ;Wolters, Beckmann, Rienäcker, & Buchner, 1999 ). This source location is then fixed as the outcome of step 1 and will no longer be modified by the next two steps of our calibration procedure. ...
Skull conductivity has a substantial influence on EEG and combined EEG and MEG source analysis as well as on optimized transcranial electric stimulation. To overcome the use of standard literature values, we propose a non-invasive two-level calibration procedure to estimate skull conductivity individually in a group study with twenty healthy adults. Our procedure requires only an additional run of combined somatosensory evoked potential and field data, which can be easily integrated in EEG/MEG experiments. The calibration procedure uses the P20/N20 topographies and subject-specific realistic head models from MRI. We investigate the inter-subject variability of skull conductivity and relate it to skull thickness, age and gender of the subjects, to the individual scalp P20/N20 surface distance between the P20 potential peak and the N20 potential trough as well as to the individual source depth of the P20/N20 source. We found a considerable inter-subject variability for (calibrated) skull conductivity (8.44 ± 4.84 mS/m) and skull thickness (5.97 ± 1.19 mm) with a statistically significant correlation between them (rho = 0.52). Age showed a statistically significant negative correlation with skull conductivity (rho =-0.5). Furthermore, P20/N20 surface distance and source depth showed large inter-subject variability of 12.08 ± 3.21 cm and 15.45 ± 4.54 mm, respectively, but there was no significant correlation between them. We also found no significant differences among gender subgroups for the investigated measures. It is thus important to take the inter-subject variability of skull conductivity and thickness into account by means of using subject-specific calibrated realistic head modeling.
... conductor model for solving the inverse problem Huang et al., 2007;Brette and 114 Destexhe, 2012; Lucka et al., 2012;Wolters et al., 1999), which relies on the realistic simulation of EEG 115 ...
... Overall, per subject, the whole skull conductivity 355 calibration process and the leadfield calculations for EEG and MEG for 6CA head modeling needed 15h 356 and 15min on average across all subjects using a standard laptop (Dell, XPS15, 2016), i.e., an overnight 357 computation job per subject. 3582.6 EEG and MEG inverse solutionsBased on the assumption that the generator is focal and single-dipolar (Allison et al., 1991; Hari et al., 360 1993; Kakigi, 1994; Nakamura et al., 1998; Fuchs et al., 1998; Aydin et al., 2014), we used single dipole 361scans (also known as deviation-, goal function-or residual variance-scans) to estimate the P20/N20 362 sources(Knösche, 1997;Fuchs et al., 1998;Wolters et al., 1999) for each measurement modality (EEG, 363 MEG, EMEG). We expected them being located in the primary somatosensory cortex in Brodmann area 364 3b. ...
Modeling and experimental parameters influence the Electro- (EEG) and Magnetoencephalography (MEG) source analysis of the somatosensory P20/N20 component. In a sensitivity group study, we compare P20/N20 source analysis due to different stimulation type (Electric-Wrist (EW), Braille-Tactile (BT) or Pneumato-Tactile (PT)), measurement modality (combined EEG/MEG – EMEG, EEG or MEG) and head model (standard or individually-skull-conductivity calibrated including brain anisotropic conductivity). Considerable differences between pairs of stimulation types occurred (EW-BT: 8.7±3.3 mm / 27.1o±16.4o, BT-PT: 9±5 mm / 29.9o±17.3o and EW-PT: 9.8±7.4 mm / 15.9o±16.5o and 75 % strength reduction of BT or PT when compared to EW) regardless of the head model used. EMEG has nearly no localization differences to MEG, but large ones to EEG (16.1±4.9 mm), while source orientation differences are non-negligible to both EEG (14o±3.7o) and MEG (12.5o±10.9o). Our calibration results show a considerable inter-subject variability (3.1 – 14 mS/m) for skull conductivity. The comparison due to different head model show localization differences smaller for EMEG (EW: 3.4±2.4 mm, BT: 3.7±3.4 mm, PT: 5.9±6.8 mm) than for EEG (EW: 8.6±8.3 mm, BT: 11.8±6.2 mm, PT: 10.5±5.3 mm), while source orientation differences for EMEG (EW: 15.4o±6.3o, BT: 25.7o±15.2o and PT: 14o±11.5o) and EEG (EW: 14.6o±9.5o, BT: 16.3o±11.1o and PT: 12.9o±8.9o) are in the same range. Our results show that stimulation type, modality and head modeling all have a non-negligible influence on the source reconstruction of the P20/N20 component. The complementary information of both modalities in EMEG can be exploited on the basis of detailed and individualized head models.
... For the reconstruction of single, focal sources, the principal results found in this study remain valid for any inverse method that is suited for the accurate reconstruction of such dipole sources, such as dipole fits (Wolters et al., 1999;Güllmar et al., 2010) and beamformer methods (Sekihara and Nagarajan, 2008;Neugebauer et al., 2017). We further assume that the observed effects also translate to hierarchical Bayesian methods (HBM) that are suited for the localization of focal sources (Calvetti et al., 2009;Lucka et al., 2012). ...
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.
... where pinv is the pseudoinverse (Björck, 1996) of the matrix LW −1 L T with tolerance βµ, i.e. setting all singular values of the matrix LW −1 L T less than the tolerance to zero. This resembles the truncated singular value decomposition introduced to source analysis in Wolters et al. (1999). ...
Low resolution electromagnetic tomography (LORETA) is a well-known method for the solution of the l2-based minimization problem for EEG/MEG source reconstruction. LORETA with a volume-based source space is widely used and much effort has been invested in the theory and the application of the method in an experimental context. However, it is especially interesting to use anatomical prior knowledge and constrain the LORETA's solution to the cortical surface. This strongly reduces the number of unknowns in the inverse approach. Unlike the Laplace operator in the volume case with a rectangular and regular grid, the mesh is triangulated and highly irregular in the surface case. Thus, it is not trivial to choose or construct a Laplace operator (termed Laplace-Beltrami operator when applied to surfaces) that has the desired properties and takes into account the geometry of the mesh. In this paper, the basic methodology behind cortical LORETA is discussed and the method is applied for source reconstruction of simulated data using different Laplace-Beltrami operators in the smoothing term. The results achieved with the different operators are compared with respect to their accuracy using various measures. Conclusions about the choice of an appropriate operator are deduced from the results.
... This study concentrates on finite element method (FEM) based electroencephalography (EEG) forward simulation in which the electric potential field evoked by neural activity is to be approximated given the geometry, conductivity distribution and a primary source current field of the target domain [1], [2], [3], [4], [5]. With respect to the current standard in EEG forward simulation, that is, the boundary element method (BEM) coupled with a compartment-wise isotropic and homogeneous volume conductor model [5], [6], [7], [8], [9], 3D approaches such as the FEM or the finite difference method (FDM) constitute a substantial improvement, as they enable modeling of the strongly folded outer brain surface [10], [11], detailed structures of skull compacta and spongiosa [12], [11], and the distinctly anisotropic conductivity of the white matter [13], [14], [11]. ...
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.
... 100000 Buchner et al., 1997/Wolters et al., 1999Wolters et al., 2002Rullmann et al., 2009Waberski et al., 1998Wolters et al., 2004 Computation 6.17. On the left a typical BEM mesh is shown. ...
