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.

Comparing the performance of beamformer algorithms in estimating orientations of neural sources.

The efficacy of transcranial electric stimulation (tES) to effectively modulate neuronal activity depends critically on the spatial orientation of the targeted neuronal population. Therefore, precise estimation of target orientation is of utmost importance. Different beamforming algorithms provide orientation estimates; however, a systematic analysis of their performance is still lacking. For fixed brain locations, EEG and MEG data from sources with randomized orientations were simulated. The orientation was then estimated (1) with an EEG and (2) with a combined EEG-MEG approach. Three commonly used beamformer algorithms were evaluated with respect to their abilities to estimate the correct orientation: Unit-Gain (UG), Unit-Noise-Gain (UNG), and Array-Gain (AG) beamformer. Performance depends on the signal-to-noise ratios for the modalities and on the chosen beamformer. Overall, the UNG and AG beamformers appear as the most reliable. With increasing noise, the UG estimate converges to a vector determined by the leadfield, thus leading to insufficient orientation estimates.

Standardized hierarchical adaptive Lp regression for noise robust focal epilepsy source reconstructions.

OBJECTIVE: To investigate the ability of standardization to reduce source localization errors and measurement noise uncertainties for hierarchical Bayesian algorithms with L1- and L2-norms as priors in electroencephalography and magnetoencephalography of focal epilepsy. METHODS: Description of the standardization methodology relying on the Hierarchical Bayesian framework, referred to as the Standardized Hierarchical Adaptive Lp-norm Regularization (SHALpR). The performance was tested using real data from two focal epilepsy patients. Simulated data that resembled the available real data was constructed for further localization and noise robustness investigation. RESULTS: The proposed algorithms were compared to their non-standardized counterparts, Standardized low-resolution brain electromagnetic tomography, Standardized Shrinking LORETA-FOCUSS, and Dynamic statistical parametric maps. Based on the simulations, the standardized Hierarchical adaptive algorithm using L2-norm was noise robust for 10 dB signal-to-noise ratio (SNR), whereas the L1-norm prior worked robustly also with 5 dB SNR. The accuracy of the standardized L1-normed methodology to localize focal activity was under 1 cm for both patients. CONCLUSIONS: Numerical results of the proposed methodology display improved localization and noise robustness. The proposed methodology also outperformed the compared methods when dealing with real data. SIGNIFICANCE: The proposed standardized methodology, especially when employing the L1-norm, could serve as a valuable assessment tool in surgical decision-making.

Normative tDCS over V5 and FEF reveals practice-induced modulation of extraretinal smooth pursuit mechanisms, but no specific stimulation effect.

The neural networks subserving smooth pursuit eye movements (SPEM) provide an ideal model for investigating the interaction of sensory processing and motor control during ongoing movements. To better understand core plasticity aspects of sensorimotor processing for SPEM, normative sham, anodal or cathodal transcranial direct current stimulation (tDCS) was applied over visual area V5 and frontal eye fields (FEF) in sixty healthy participants. The identical within-subject paradigm was used to assess SPEM modulations by practice. While no specific tDCS effects were revealed, within- and between-session practice effects indicate plasticity of top-down extraretinal mechanisms that mainly affect SPEM in the absence of visual input and during SPEM initiation. To explore the potential of tDCS effects, individual electric field simulations were computed based on calibrated finite element head models and individual functional localization of V5 and FEF location (using functional MRI) and orientation (using combined EEG/MEG) was conducted. Simulations revealed only limited electric field target intensities induced by the applied normative tDCS montages but indicate the potential efficacy of personalized tDCS for the modulation of SPEM. In sum, results indicate the potential susceptibility of extraretinal SPEM control to targeted external neuromodulation (e.g., personalized tDCS) and intrinsic learning protocols.

EEG Source Analysis with a Convolutional Neural Network and Finite Element Analysis.

To reconstruct the electrophysiological activity of brain responses, source analysis is performed through the solution of the forward and inverse problems. The former contains a unique solution while the latter is ill-posed. In this regard, many algorithms have been suggested relying on different prior information for solving the inverse problem. Recently, neural networks have been used to deal with source analysis. However, their underlying training for inverse solutions is based on suboptimal forward modeling. In this work, we propose a CNN that is able to reconstruct EEG brain activity. To train our proposed CNN, a skull-conductivity calibrated and white matter anisotropic head model. Based on this model, we generate simulated EEG data and used them to train our CNN. We first evaluate the performance of our CNN using the simulated EEG data while a realistic application with somatosensory evoked potentials follows. From the results, we observed that the CCN correctly localized the P20/N20 component at the subject-specific Brodmann area 3b and it can potentially localize deeper sources. A comparison is also presented with well-known inverse solutions (single dipole scans and sLORETA) showing similar localization performance. Through these results, an emerging potential for real applications appears on the basis of realistic head modeling.

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.

Personalized alpha-tACS targeting left posterior parietal cortex modulates visuo-spatial attention and posterior evoked EEG activity.

BACKGROUND: Covert visuo-spatial attention is marked by the anticipatory lateralization of neuronal alpha activity in the posterior parietal cortex. Previous applications of transcranial alternating current stimulation (tACS) at the alpha frequency, however, were inconclusive regarding the causal contribution of oscillatory activity during visuo-spatial attention. OBJECTIVE: Attentional shifts of behavior and electroencephalography (EEG) after-effects were assessed in a cued visuo-spatial attention paradigm. We hypothesized that parietal alpha-tACS shifts attention relative to the ipsilateral visual hemifield. Furthermore, we assumed that modulations of behavior and neurophysiology are related to individual electric field simulations. METHODS: We applied personalized tACS at alpha and gamma frequencies to elucidate the role of oscillatory neuronal activity for visuo-spatial attention. Personalized tACS montages were algorithmically optimized to target individual left and right parietal regions that were defined by an EEG localizer. RESULTS: Behavioral performance in the left hemifield was specifically increased by alpha-tACS compared to gamma-tACS targeting the left parietal cortex. This hemisphere-specific effect was observed despite the symmetry of simulated electric fields. In addition, visual event-related potential (ERP) amplitudes showed a reduced lateralization over posterior sites induced by left alpha-tACS. Neuronal sources of this effect were localized in the left premotor cortex. Interestingly, accuracy modulations induced by left parietal alpha-tACS were directly related to electric field magnitudes in the left premotor cortex. CONCLUSION: Overall, results corroborate the notion that alpha lateralization plays a causal role in covert visuo-spatial attention and indicate an increased susceptibility of parietal and premotor brain regions of the left dorsal attention network to subtle tACS-neuromodulation.

Validating EEG source imaging using intracranial electrical stimulation.

Electrical source imaging is used in presurgical epilepsy evaluation and in cognitive neurosciences to localize neuronal sources of brain potentials recorded on EEG. This study evaluates the spatial accuracy of electrical source imaging for known sources, using electrical stimulation potentials recorded on simultaneous stereo-EEG and 37-electrode scalp EEG, and identifies factors determining the localization error. In 11 patients undergoing simultaneous stereo-EEG and 37-electrode scalp EEG recordings, sequential series of 99-110 biphasic pulses (2 ms pulse width) were applied by bipolar electrical stimulation on adjacent contacts of implanted stereo-EEG electrodes. The scalp EEG correlates of stimulation potentials were recorded with a sampling rate of 30 kHz. Electrical source imaging of averaged stimulation potentials was calculated utilizing a dipole source model of peak stimulation potentials based on individual four-compartment finite element method head models with various skull conductivities (range from 0.0413 to 0.001 S/m). Fitted dipoles with a goodness of fit of ≥80% were included in the analysis. The localization error was calculated using the Euclidean distance between the estimated dipoles and the centre point of adjacent stimulating contacts. A total of 3619 stimulation locations, respectively, dipole localizations, were included in the evaluation. Mean localization errors ranged from 10.3 to 26 mm, depending on source depth and selected skull conductivity. The mean localization error increased with an increase in source depth (r(3617) = [0.19], P = 0.000) and decreased with an increase in skull conductivity (r(3617) = [-0.26], P = 0.000). High skull conductivities (0.0413-0.0118 S/m) yielded significantly lower localization errors for all source depths. For superficial sources (<20 mm from the inner skull), all skull conductivities yielded insignificantly different localization errors. However, for deeper sources, in particular >40 mm, high skull conductivities of 0.0413 and 0.0206 S/m yielded significantly lower localization errors. In relation to stimulation locations, the majority of estimated dipoles moved outward-forward-downward to inward-forward-downward with a decrease in source depth and an increase in skull conductivity. Multivariate analysis revealed that an increase in source depth, number of skull holes and white matter volume, while a decrease in skull conductivity independently led to higher localization error. This evaluation of electrical source imaging accuracy using artificial patterns with a high signal-to-noise ratio supports its application in presurgical epilepsy evaluation and cognitive neurosciences. In our artificial potential model, optimizing the selected skull conductivity minimized the localization error. Future studies should examine if this accounts for true neural signals.

Brainstorm-DUNEuro: An integrated and user-friendly Finite Element Method for modeling electromagnetic brain activity.

Human brain activity generates scalp potentials (electroencephalography - EEG), intracranial potentials (iEEG), and external magnetic fields (magnetoencephalography - MEG). These electrophysiology (e-phys) signals can often be measured simultaneously for research and clinical applications. The forward problem involves modeling these signals at their sensors for a given equivalent current dipole configuration within the brain. While earlier researchers modeled the head as a simple set of isotropic spheres, today's magnetic resonance imaging (MRI) data allow for a detailed anatomic description of brain structures and anisotropic characterization of tissue conductivities. We present a complete pipeline, integrated into the Brainstorm software, that allows users to automatically generate an individual and accurate head model based on the subject's MRI and calculate the electromagnetic forward solution using the finite element method (FEM). The head model generation is performed by integrating the latest tools for MRI segmentation and FEM mesh generation. The final head model comprises the five main compartments: white-matter, gray-matter, CSF, skull, and scalp. The anisotropic brain conductivity model is based on the effective medium approach (EMA), which estimates anisotropic conductivity tensors from diffusion-weighted imaging (DWI) data. The FEM electromagnetic forward solution is obtained through the DUNEuro library, integrated into Brainstorm, and accessible with either a user-friendly graphical interface or scripting. With tutorials and example data sets available in an open-source format on the Brainstorm website, this integrated pipeline provides access to advanced FEM tools for electromagnetic modeling to a broader neuroscience community.

Bioelectromagnetism in Human Brain Research: New Applications, New Questions.

Bioelectromagnetism has contributed some of the most commonly used techniques to human neuroscience such as magnetoencephalography (MEG), electroencephalography (EEG), transcranial magnetic stimulation (TMS), and transcranial electric stimulation (TES). The considerable differences in their technical design and practical use give rise to the impression that these are quite different techniques altogether. Here, we review, discuss and illustrate the fundamental principle of Helmholtz reciprocity that provides a common ground for all four techniques. We show that, more than 150 years after its discovery by Helmholtz in 1853, reciprocity is important to appreciate the strengths and limitations of these four classical tools in neuroscience. We build this case by explaining the concept of Helmholtz reciprocity, presenting a methodological account of this principle for all four methods and, finally, by illustrating its application in practical clinical studies.

Can individually targeted and optimized multi-channel tDCS outperform standard bipolar tDCS in stimulating the primary somatosensory cortex?

BACKGROUND: Transcranial direct current stimulation (tDCS) has emerged as a non-invasive neuro-modulation technique. Most studies show that anodal tDCS increases cortical excitability, however, with variable outcomes. Previously, we have shown in computer simulations that our multi-channel tDCS (mc-tDCS) approach, the distributed constrained maximum intensity (D-CMI) method can potentially lead to better controlled tDCS results due to the improved directionality of the injected current at the target side for individually optimized D-CMI montages. OBJECTIVE: In this study, we test the application of the D-CMI approach in an experimental study to stimulate the somatosensory P20/N20 target source in Brodmann area 3b and compare it with standard bipolar tDCS and sham conditions. METHODS: We applied anodal D-CMI, the standard bipolar and D-CMI based Sham tDCS for 10 min to target the 20 ms post-stimulus somatosensory P20/N20 target brain source in Brodmann area 3b reconstructed using combined magnetoencephalography (MEG) and electroencephalography (EEG) source analysis in realistic head models with calibrated skull conductivity in a group-study with 13 subjects. Finger-stimulated somatosensory evoked fields (SEF) were recorded and the component at 20 ms post-stimulus (M20) was analyzed before and after the application of the three tDCS conditions in order to read out the stimulation effect on Brodmann area 3b. RESULTS: Analysis of the finger stimulated SEF M20 peak before (baseline) and after tDCS shows a significant increase in source amplitude in Brodmann area 3b for D-CMI (6-16 min after tDCS), while no significant effects are found for standard bipolar (6-16 min after tDCS) and sham (6-16 min after tDCS) stimulation conditions. For the later time courses (16-26 and 27-37 min post-stimulation), we found a significant decrease in M20 peak source amplitude for standard bipolar and sham tDCS, while there was no effect for D-CMI. CONCLUSION: Our results indicate that targeted and optimized, and thereby highly individualized, mc-tDCS can outperform standard bipolar stimulation and lead to better control over stimulation outcomes with, however, a considerable amount of additional work compared to standard bipolar tDCS.

Directionality of the injected current targeting the P20/N20 source determines the efficacy of 140 Hz transcranial alternating current stimulation (tACS)-induced aftereffects in the somatosensory cortex.

Interindividual anatomical differences in the human cortex can lead to suboptimal current directions and may result in response variability of transcranial electrical stimulation methods. These differences in brain anatomy require individualized electrode stimulation montages to induce an optimal current density in the targeted area of each individual subject. We aimed to explore the possible modulatory effects of 140 Hz transcranial alternating current stimulation (tACS) on the somatosensory cortex using personalized multi-electrode stimulation montages. In two randomized experiments using either tactile finger or median nerve stimulation, we measured by evoked potentials the plasticity aftereffects and oscillatory power changes after 140 Hz tACS at 1.0 mA as compared to sham stimulation (n = 17, male = 9). We found a decrease in the power of oscillatory mu-rhythms during and immediately after tactile discrimination tasks, indicating an engagement of the somatosensory system during stimulus encoding. On a group level both the oscillatory power and the evoked potential amplitudes were not modulated by tACS neither after tactile finger stimulation nor after median nerve stimulation as compared to sham stimulation. On an individual level we could however demonstrate that lower angular difference (i.e., differences between the injected current vector in the target region and the source orientation vector) is associated with significantly higher changes in both P20/N20 and N30/P30 source activities. Our findings suggest that the higher the directionality of the injected current correlates to the dipole orientation the greater the tACS-induced aftereffects are.

Validating EEG, MEG and Combined MEG and EEG Beamforming for an Estimation of the Epileptogenic Zone in Focal Cortical Dysplasia.

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.

Testing the effect of tACS over parietal cortex in modulating endogenous alpha rhythm and temporal integration windows in visual perception.

Neural oscillations in the alpha band (8-12 Hz) have been proposed as a key mechanism for the temporal resolution of visual perception. Higher alpha frequencies have been related to improved segregation of visual events over time, whereas lower alpha frequencies have been related to improved temporal integration. Similarly, also the phase of ongoing alpha has been shown to correlate with temporal integration/segregation. To test a causal relationship between alpha oscillations and perception, we here employed multi-channel transcranial alternating current stimulation (mc-tACS) over the right parietal cortex, whereas participants performed a visual temporal integration/segregation task that used identical stimuli with different instructions. Before and after mc-tACS we recorded the resting-state electroencephalogram (EEG) to extract the individual alpha frequency (IAF) and delivered electrical stimulation at slightly slower and faster frequencies (IAF±2 Hz). We hypothesized that this would not only drive endogenous alpha rhythms, but also affect temporal integration and segregation in an opposite way. However, the mc-tACS protocol used here did not consistently increase or decrease the IAF after the stimulation and did not affect temporal integration/segregation accuracy as expected. Although we found some preliminary evidence for an influence of tACS phase on temporal integration accuracy, the ongoing phase of mc-tACS oscillations did not reliably modulate temporal integration/segregation accuracy in a sinusoidal way as would have been predicted by an effective entrainment of brain oscillations. These findings may guide future studies using different stimulation montages for investigating the role of cortical alpha oscillations for human vision.

Individually optimized multi-channel tDCS for targeting somatosensory cortex.

OBJECTIVE: Transcranial direct current stimulation (tDCS) is a non-invasive neuro-modulation technique that delivers current through the scalp by a pair of patch electrodes (2-Patch). This study proposes a new multi-channel tDCS (mc-tDCS) optimization method, the distributed constrained maximum intensity (D-CMI) approach. For targeting the P20/N20 somatosensory source at Brodmann area 3b, an integrated combined magnetoencephalography (MEG) and electroencephalography (EEG) source analysis is used with individualized skull conductivity calibrated realistic head modeling. METHODS: Simulated electric fields (EF) for our new D-CMI method and the already known maximum intensity (MI), alternating direction method of multipliers (ADMM) and 2-Patch methods were produced and compared for the individualized P20/N20 somatosensory target for 10 subjects. RESULTS: D-CMI and MI showed highest intensities parallel to the P20/N20 target compared to ADMM and 2-Patch, with ADMM achieving highest focality. D-CMI showed a slight reduction in intensity compared to MI while reducing side effects and skin level sensations by current distribution over multiple stimulation electrodes. CONCLUSION: Individualized D-CMI montages are preferred for our follow up somatosensory experiment to provide a good balance between high current intensities at the target and reduced side effects and skin sensations. SIGNIFICANCE: An integrated combined MEG and EEG source analysis with D-CMI montages for mc-tDCS stimulation potentially can improve control, reproducibility and reduce sensitivity differences between sham and real stimulations.

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.

DUNEuro-A software toolbox for forward modeling in bioelectromagnetism.

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

Source imaging of deep-brain activity using the regional spatiotemporal Kalman filter.

BACKGROUND AND OBJECTIVE: The human brain displays rich and complex patterns of interaction within and among brain networks that involve both cortical and subcortical brain regions. Due to the limited spatial resolution of surface electroencephalography (EEG), EEG source imaging is used to reconstruct brain sources and investigate their spatial and temporal dynamics. The majority of EEG source imaging methods fail to detect activity from subcortical brain structures. The reconstruction of subcortical sources is a challenging task because the signal from these sources is weakened and mixed with artifacts and other signals from cortical sources. In this proof-of-principle study we present a novel EEG source imaging method, the regional spatiotemporal Kalman filter (RSTKF), that can detect deep brain activity. METHODS: The regional spatiotemporal Kalman filter (RSTKF) is a generalization of the spatiotemporal Kalman filter (STKF), which allows for the characterization of different regional dynamics in the brain. It is based on state-space modeling with spatially heterogeneous dynamical noise variances, since models with spatial and temporal homogeneity fail to describe the dynamical complexity of brain activity. First, RSTKF is tested using simulated EEG data from sources in the frontal lobe, putamen, and thalamus. After that, it is applied to non-averaged interictal epileptic spikes from a presurgical epilepsy patient with focal epileptic activity in the amygdalo-hippocampal complex. The results of RSTKF are compared to those of low-resolution brain electromagnetic tomography (LORETA) and of standard STKF. RESULTS: Only RSTKF is successful in consistently and accurately localizing the sources in deep brain regions. Additionally, RSTKF shows improved spatial resolution compared to LORETA and STKF. CONCLUSIONS: RSTKF is a generalization of STKF that allows for accurate, focal, and consistent localization of sources, especially in the deeper brain areas. In contrast to standard source imaging methods, RSTKF may find application in the localization of the epileptogenic zone in deeper brain structures, such as mesial frontal and temporal lobe epilepsies, especially in EEG recordings for which no reliable averaged spike shape can be obtained due to lack of the necessary number of spikes required to reach a certain signal-to-noise ratio level after averaging.