The Effect of Head Model Simplification on Beamformer Source Localization

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.

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.

Localized estimation of electromagnetic sources underlying event-related fields using recurrent neural networks

Objective. To use a recurrent neural network (RNN) to reconstruct neural activity responsible for generating noninvasively measured electromagnetic signals.Approach. Output weights of an RNN were fixed as the lead field matrix from volumetric source space computed using the boundary element method with co-registered structural magnetic resonance images and magnetoencephalography (MEG). Initially, the network was trained to minimise mean-squared-error loss between its outputs and MEG signals, causing activations in the penultimate layer to converge towards putative neural source activations. Subsequently, L1 regularisation was applied to the final hidden layer, and the model was fine-tuned, causing it to favour more focused activations. Estimated source signals were then obtained from the outputs of the last hidden layer. We developed and validated this approach with simulations before applying it to real MEG data, comparing performance with beamformers, minimum-norm estimate, and mixed-norm estimate source reconstruction methods.Main results. The proposed RNN method had higher output signal-to-noise ratios and comparable correlation and error between estimated and simulated sources. Reconstructed MEG signals were also equal or superior to the other methods regarding their similarity to ground-truth. When applied to MEG data recorded during an auditory roving oddball experiment, source signals estimated with the RNN were generally biophysically plausible and consistent with expectations from the literature.Significance. This work builds on recent developments of RNNs for modelling event-related neural responses by incorporating biophysical constraints from the forward model, thus taking a significant step towards greater biological realism and introducing the possibility of exploring how input manipulations may influence localised neural activity.

In silicostudy of the effects of cerebral circulation on source localization using a dynamical anatomical atlas of the human head

Objective.This study focuses on the effects of dynamical vascular modeling on source localization errors in electroencephalography (EEG). Our aim of thisin silicostudy is to (a) find out the effects of cerebral circulation on the accuracy of EEG source localization estimates, and (b) evaluate its relevance with respect to measurement noise and interpatient variation.Approach.We employ a four-dimensional (3D + T) statistical atlas of the electrical properties of the human head with a cerebral circulation model to generate virtual patients with different cerebral circulatory conditions for EEG source localization analysis. As source reconstruction techniques, we use the linearly constraint minimum variance (LCMV) beamformer, standardized low-resolution brain electromagnetic tomography (sLORETA), and the dipole scan (DS).Main results.Results indicate that arterial blood flow affects source localization at different depths and with varying significance. The average flow rate plays an important role in source localization performance, while the pulsatility effects are very small. In cases where a personalized model of the head is available, blood circulation mismodeling causes localization errors, especially in the deep structures of the brain where the main cerebral arteries are located. When interpatient variations are considered, the results show differences up to 15 mm for sLORETA and LCMV beamformer and 10 mm for DS in the brainstem and entorhinal cortices regions. In regions far from the main arteries vessels, the discrepancies are smaller than 3 mm. When measurement noise is added and interpatient differences are considered in a deep dipolar source, the results indicate that the effects of conductivity mismatch are detectable even for moderate measurement noise. The signal-to-noise ratio limit for sLORETA and LCMV beamformer is 15 dB, while the limit is under 30 dB for DS.Significance.Localization of the brain activity via EEG constitutes an ill-posed inverse problem, where any modeling uncertainty, e.g. a slight amount of noise in the data or material parameter discrepancies, can lead to a significant deviation of the estimated activity, especially in the deep structures of the brain. Proper modeling of the conductivity distribution is necessary in order to obtain an appropriate source localization. In this study, we show that the conductivity of the deep brain structures is particularly impacted by blood flow-induced changes in conductivity because large arteries and veins access the brain through that region.

Parietofrontal oscillations show hand-specific interactions with top-down movement plans

To generate a hand-specific reach plan, the brain must integrate hand-specific signals with the desired movement strategy. Although various neurophysiology/imaging studies have investigated hand-target interactions in simple reach-to-target tasks, the whole brain timing and distribution of this process remain unclear, especially for more complex, instruction-dependent motor strategies. Previously, we showed that a pro/anti pointing instruction influences magnetoencephalographic (MEG) signals in frontal cortex that then propagate recurrently through parietal cortex (Blohm G, Alikhanian H, Gaetz W, Goltz HC, DeSouza JF, Cheyne DO, Crawford JD. NeuroImage 197: 306-319, 2019). Here, we contrasted left versus right hand pointing in the same task to investigate 1) which cortical regions of interest show hand specificity and 2) which of those areas interact with the instructed motor plan. Eight bilateral areas, the parietooccipital junction (POJ), superior parietooccipital cortex (SPOC), supramarginal gyrus (SMG), medial/anterior interparietal sulcus (mIPS/aIPS), primary somatosensory/motor cortex (S1/M1), and dorsal premotor cortex (PMd), showed hand-specific changes in beta band power, with four of these (M1, S1, SMG, aIPS) showing robust activation before movement onset. M1, SMG, SPOC, and aIPS showed significant interactions between contralateral hand specificity and the instructed motor plan but not with bottom-up target signals. Separate hand/motor signals emerged relatively early and lasted through execution, whereas hand-motor interactions only occurred close to movement onset. Taken together with our previous results, these findings show that instruction-dependent motor plans emerge in frontal cortex and interact recurrently with hand-specific parietofrontal signals before movement onset to produce hand-specific motor behaviors.NEW & NOTEWORTHY The brain must generate different motor signals depending on which hand is used. The distribution and timing of hand use/instructed motor plan integration are not understood at the whole brain level. Using MEG we show that different action planning subnetworks code for hand usage and integrating hand use into a hand-specific motor plan. The timing indicates that frontal cortex first creates a general motor plan and then integrates hand specificity to produce a hand-specific motor plan.

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.

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.

A unified view on beamformers for M/EEG source reconstruction

Beamforming is a popular method for functional source reconstruction using magnetoencephalography (MEG) and electroencephalography (EEG) data. Beamformers, which were first proposed for MEG more than two decades ago, have since been applied in hundreds of studies, demonstrating that they are a versatile and robust tool for neuroscience. However, certain characteristics of beamformers remain somewhat elusive and there currently does not exist a unified documentation of the mathematical underpinnings and computational subtleties of beamformers as implemented in the most widely used academic open source software packages for MEG analysis (Brainstorm, FieldTrip, MNE, and SPM). Here, we provide such documentation that aims at providing the mathematical background of beamforming and unifying the terminology. Beamformer implementations are compared across toolboxes and pitfalls of beamforming analyses are discussed. Specifically, we provide details on handling rank deficient covariance matrices, prewhitening, the rank reduction of forward fields, and on the combination of heterogeneous sensor types, such as magnetometers and gradiometers. The overall aim of this paper is to contribute to contemporary efforts towards higher levels of computational transparency in functional neuroimaging.

The Influence of the Head Model Conductor on the Source Localization of Auditory Evoked Potentials

The accuracy of EEG source analysis reconstruction improves when a realistic head volume conductor is modeled. In this study we investigated how the progressively more complex head representations influence the spatial localization of auditory-evoked potentials (AEPs). Fourteen young-adult participants with normal hearing performed the AEP task. Individualized head models were obtained from structural MRI and diffusion-weighted imaging scans collected in a separate session. AEPs were elicited by 1 k Hz and 4 k Hz tone bursts during a passive-listening tetanizing paradigm. We compared the amplitude of the N1 and P2 components before and after 4 min of tetanic-stimulation with 1 k Hz sounds. Current density reconstruction values of both components were investigated in the primary auditory cortex and adjacent areas. Furthermore, we compared the signal topography and magnitude obtained with 10 different head models on the EEG forward solution. Starting from the simplest model (scalp, skull, brain), we investigated the influence of modeling the CSF, distinguishing between GM and WM conductors, and including anisotropic WM values. We localized the activity of AEPs within the primary auditory cortex, but not in adjacent areas. The inclusion of the CSF compartment had the strongest influence on the source reconstruction, whereas white matter anisotropy led to a smaller improvement. We conclude that individualized realistic head models provide the best solution for the forward solution when modeling the CSF conductor.

High-Resolution EEG Source Localization in Segmentation-Free Head Models Based on Finite-Difference Method and Matching Pursuit Algorithm

Electroencephalogram (EEG) is a method to monitor electrophysiological activity on the scalp, which represents the macroscopic activity of the brain. However, it is challenging to identify EEG source regions inside the brain based on data measured by a scalp-attached network of electrodes. The accuracy of EEG source localization significantly depends on the type of head modeling and inverse problem solver. In this study, we adopted different models with a resolution of 0.5 mm to account for thin tissues/fluids, such as the cerebrospinal fluid (CSF) and dura. In particular, a spatially dependent conductivity (segmentation-free) model created using deep learning was developed and used for more realist representation of electrical conductivity. We then adopted a multi-grid-based finite-difference method (FDM) for forward problem analysis and a sparse-based algorithm to solve the inverse problem. This enabled us to perform efficient source localization using high-resolution model with a reasonable computational cost. Results indicated that the abrupt spatial change in conductivity, inherent in conventional segmentation-based head models, may trigger source localization error accumulation. The accurate modeling of the CSF, whose conductivity is the highest in the head, was an important factor affecting localization accuracy. Moreover, computational experiments with different noise levels and electrode setups demonstrate the robustness of the proposed method with segmentation-free head model.

Data-driven beamforming technique to attenuate ballistocardiogram artefacts in electroencephalography-functional magnetic resonance imaging without detecting cardiac pulses in electrocardiography recordings

Simultaneous recording of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) is a very promising non‐invasive neuroimaging technique. However, EEG data obtained from the simultaneous EEG–fMRI are strongly influenced by MRI‐related artefacts, namely gradient artefacts (GA) and ballistocardiogram (BCG) artefacts. When compared to the GA correction, the BCG correction is more challenging to remove due to its inherent variabilities and dynamic changes over time. The standard BCG correction (i.e., average artefact subtraction [AAS]), require detecting cardiac pulses from simultaneous electrocardiography (ECG) recording. However, ECG signals are also distorted and will become problematic for detecting reliable cardiac peaks. In this study, we focused on a beamforming spatial filtering technique to attenuate all unwanted source activities outside of the brain. Specifically, we applied the beamforming technique to attenuate the BCG artefact in EEG–fMRI, and also to recover meaningful task‐based neural signals during an attentional network task (ANT) which required participants to identify visual cues and respond accurately. We analysed EEG–fMRI data in 20 healthy participants during the ANT, and compared four different BCG corrections (non‐BCG corrected, AAS BCG corrected, beamforming + AAS BCG corrected, beamforming BCG corrected). We demonstrated that the beamforming approach did not only significantly reduce the BCG artefacts, but also significantly recovered the expected task‐based brain activity when compared to the standard AAS correction. This data‐driven beamforming technique appears promising especially for longer data acquisition of sleep and resting EEG–fMRI. Our findings extend previous work regarding the recovery of meaningful EEG signals by an optimized suppression of MRI‐related artefacts.

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.

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.

The impact of improved MEG-MRI co-registration on MEG connectivity analysis

Co-registration between structural head images and functional MEG data is needed for anatomically-informed MEG data analysis. Despite the efforts to minimize the co-registration error, conventional landmark- and surface-based strategies for co-registering head and MEG device coordinates achieve an accuracy of typically 5-10 mm. Recent advances in instrumentation and technical solutions, such as the development of hybrid ultra-low-field (ULF) MRI-MEG devices or the use of 3D-printed individualized foam head-casts, promise unprecedented co-registration accuracy, i.e., 2 mm or better. In the present study, we assess through simulations the impact of such an improved co-registration on MEG connectivity analysis. We generated synthetic MEG recordings for pairs of connected cortical sources with variable locations. We then assessed the capability to reconstruct source-level connectivity from these recordings for 0-15-mm co-registration error, three levels of head modeling detail (one-, three- and four-compartment models), two source estimation techniques (linearly constrained minimum-variance beamforming and minimum-norm estimation MNE) and five separate connectivity metrics (imaginary coherency, phase-locking value, amplitude-envelope correlation, phase-slope index and frequency-domain Granger causality). We found that beamforming can better take advantage of an accurate co-registration than MNE. Specifically, when the co-registration error was smaller than 3 mm, the relative error in connectivity estimates was down to one-third of that observed with typical co-registration errors. MNE provided stable results for a wide range of co-registration errors, while the performance of beamforming rapidly degraded as the co-registration error increased. Furthermore, we found that even moderate co-registration errors (>6 mm, on average) essentially decrease the difference of four- and three- or one-compartment models. Hence, a precise co-registration is important if one wants to take full advantage of highly accurate head models for connectivity analysis. We conclude that an improved co-registration will be beneficial for reliable connectivity analysis and effective use of highly accurate head models in future MEG connectivity studies.

Partial Least Square Aided Beamforming Algorithm in Magnetoencephalography Source Imaging

Beamforming techniques have played a prominent role in source imaging in neuroimaging and in locating epileptogenic zones. However, existing vector-beamformers are sensitive to noise on localization of epileptogenic zones. In this study, partial least square (PLS) was used to aid the minimum variance beamforming approach for source imaging with magnetoencephalography (MEG) arrays, and verified its effectiveness in simulated data and epilepsy data. First, PLS was employed to extract the components of the MEG arrays by maximizing the covariance between a linear combination of the predictors and the class variable. Noise was then removed by reconstructing the MEG arrays based on those components. The minimum variance beamforming method was used to estimate a source model. Simulations with a realistic head model and varying noise levels indicated that the proposed approach can provide higher spatial accuracy than other well-known beamforming methods. For real MEG recordings in 10 patients with temporal lobe epilepsy, the ratios of the number of spikes localized in the surgical excised region to the total number of spikes using the proposed method were higher than that of the dipole fitting method. These localization results using the proposed method are more consistent with the clinical evaluation. The proposed method may provide a new imaging marker for localization of epileptogenic zones.

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.