Real MEG Data Research Articles

Joint Learning of Full-Structure Noise in Hierarchical Bayesian Regression Models.

We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

Fast parametric curve matching (FPCM) for automatic spike detection

Objective. Epilepsy is a widely spread neurological disease, whose treatment often requires resection of the pathological cortical tissue. Interictal spike analysis observed in the non-invasively collected EEG or MEG data offers an attractive way to localize epileptogenic cortical structures for surgery planning purposes. Interictal spike detection in lengthy multichannel data is a daunting task that is still often performed manually. This frequently limits such an analysis to a small portion of the data which renders the appropriate risks of missing the potentially epileptogenic region. While a plethora of automatic spike detection techniques have been developed each with its own assumptions and limitations, none of them is ideal and the best results are achieved when the output of several automatic spike detectors are combined. This is especially true in the low signal-to-noise ratio conditions. To this end we propose a novel biomimetic approach for automatic spike detection based on a constrained mixed spline machinery that we dub as fast parametric curve matching (FPCM). Approach. Using the peak-wave shape parametrization, the constrained parametric morphological model is constructed and convolved with the observed multichannel data to efficiently determine mixed spline parameters corresponding to each time-point in the dataset. Then the logical predicates that directly map to verbalized text-book like descriptions of the expected interictal event morphology allow us to accomplish the spike detection task. Main results. The results of simulations mimicking typical low SNR scenarios show the robustness and high receiver operating characteristic AUC values of the FPCM method as compared to the spike detection performed using more conventional approaches such as wavelet decomposition, template matching or simple amplitude thresholding. Applied to the real MEG and EEG data from the human patients and to rat ECoG data, the FPCM technique demonstrates reliable detection of the interictal events and localization of epileptogenic zones concordant with independent conclusions made by the epileptologist. Significance. Since the FPCM is computationally light, tolerant to high amplitude artifacts and flexible to accommodate verbalized descriptions of an arbitrary target morphology, it is likely to complement the existing arsenal of means for analysis of noisy interictal datasets.

Time-varying dynamic network model for dynamic resting state functional connectivity in fMRI and MEG imaging

Dynamic resting state functional connectivity (RSFC) characterizes fluctuations that occur over time in functional brain networks. Existing methods to extract dynamic RSFCs, such as sliding-window and clustering methods that are inherently non-adaptive, have various limitations such as high-dimensionality, an inability to reconstruct brain signals, insufficiency of data for reliable estimation, insensitivity to rapid changes in dynamics, and a lack of generalizability across multiply functional imaging modalities. To overcome these deficiencies, we develop a novel and unifying time-varying dynamic network (TVDN) framework for examining dynamic resting state functional connectivity. TVDN includes a generative model that describes the relation between a low-dimensional dynamic RSFC and the brain signals, and an inference algorithm that automatically and adaptively learns the low-dimensional manifold of dynamic RSFC and detects dynamic state transitions in data. TVDN is applicable to multiple modalities of functional neuroimaging such as fMRI and MEG/EEG. The estimated low-dimensional dynamic RSFCs manifold directly links to the frequency content of brain signals. Hence we can evaluate TVDN performance by examining whether learnt features can reconstruct observed brain signals. We conduct comprehensive simulations to evaluate TVDN under hypothetical settings. We then demonstrate the application of TVDN with real fMRI and MEG data, and compare the results with existing benchmarks. Results demonstrate that TVDN is able to correctly capture the dynamics of brain activity and more robustly detect brain state switching both in resting state fMRI and MEG data.

A new data covariance matrix estimation for improving minimum variance brain source localization

Data with finite samples results in accuracy and robustness reduction of data covariance matrix estimation, which in turn results in performance reduction of minimum variance beamformer (MVB) for brain source localization (BSL). General linear combination (GLC) and convex combination (CC) are methods of interest for data covariance matrix estimation and increasing its accuracy and robustness because their scalar coefficients are obtained automatically and adaptively. However, based on our best knowledge, the applicability of GLC and CC algorithms has not been investigated for BSL to inform us about their performance. In this paper, we have two goals: 1) Investigation of GLC and CC covariance matrices applications for BSL is carried out using various simulated MEG scenarios and real MEG and clinical epilepsy data; 2) Modified GLC and CC are developed for more accurate and robust estimation of data covariance matrix when data with finite samples is available. In the modified versions, the scalar coefficients are replaced by diagonal matrix form coefficients. These matrix form coefficients are computed using the Hadamard product and mean square error concept. The evaluations show that the CC and modified CC based MVBs are not robust for BSL due to very small values of coefficients. Based on the simulated, real, and clinical data results, it can be stated that the modified GLC is significantly superior to conventional GLC in terms of localization error, spatial resolution (all z < -2; all p-values < 0.001), and offering reliable results. Also, the proposed GLC offers fewer missed sources and less sensitivity to the depth biasing problem, particularly in a high signal-to-noise ratio. In conclusion, it can be said that the covariance matrix of modified GLC which is user-free and robust against the finite data samples can improve the MVB performance for BSL in terms of localization error and spatial resolution.

Comparison of undirected frequency-domain connectivity measures for cerebro-peripheral analysis

Analyses of cerebro-peripheral connectivity aim to quantify ongoing coupling between brain activity (measured by MEG/EEG) and peripheral signals such as muscle activity, continuous speech, or physiological rhythms (such as pupil dilation or respiration). Due to the distinct rhythmicity of these signals, undirected connectivity is typically assessed in the frequency domain. This leaves the investigator with two critical choices, namely a) the appropriate measure for spectral estimation (i.e., the transformation into the frequency domain) and b) the actual connectivity measure. As there is no consensus regarding best practice, a wide variety of methods has been applied. Here we systematically compare combinations of six standard spectral estimation methods (comprising fast Fourier and continuous wavelet transformation, bandpass filtering, and short-time Fourier transformation) and six connectivity measures (phase-locking value, Gaussian-Copula mutual information, Rayleigh test, weighted pairwise phase consistency, magnitude squared coherence, and entropy). We provide performance measures of each combination for simulated data (with precise control over true connectivity), a single-subject set of real MEG data, and a full group analysis of real MEG data. Our results show that, overall, WPPC and GCMI tend to outperform other connectivity measures, while entropy was the only measure sensitive to bimodal deviations from a uniform phase distribution. For group analysis, choosing the appropriate spectral estimation method appears to be more critical than the connectivity measure. We discuss practical implications (sampling rate, SNR, computation time, and data length) and aim to provide recommendations tailored to particular research questions.

Brain Functional Connectivity Through Phase Coupling of Neuronal Oscillations: A Perspective From Magnetoencephalography.

Magnetoencephalography has gained an increasing importance in systems neuroscience thanks to the possibility it offers of unraveling brain networks at time-scales relevant to behavior, i.e., frequencies in the 1–100 Hz range, with sufficient spatial resolution. In the first part of this review, we describe, in a unified mathematical framework, a large set of metrics used to estimate MEG functional connectivity at the same or at different frequencies. The different metrics are presented according to their characteristics: same-frequency or cross-frequency, univariate or multivariate, directed or undirected. We focus on phase coupling metrics given that phase coupling of neuronal oscillations is a putative mechanism for inter-areal communication, and that MEG is an ideal tool to non-invasively detect such coupling. In the second part of this review, we present examples of the use of specific phase methods on real MEG data in the context of resting state, visuospatial attention and working memory. Overall, the results of the studies provide evidence for frequency specific and/or cross-frequency brain circuits which partially overlap with brain networks as identified by hemodynamic-based imaging techniques, such as functional Magnetic Resonance (fMRI). Additionally, the relation of these functional brain circuits to anatomy and to behavior highlights the usefulness of MEG phase coupling in systems neuroscience studies. In conclusion, we believe that the field of MEG functional connectivity has made substantial steps forward in the recent years and is now ready for bringing the study of brain networks to a more mechanistic understanding.

Robust Empirical Bayesian Reconstruction of Distributed Sources for Electromagnetic Brain Imaging.

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of the magnetic fields and electric potentials. An enduring challenge in this imaging modality is estimating the number, location, and time course of sources, especially for the reconstruction of distributed brain sources with complex spatial extent. Here, we introduce a novel robust empirical Bayesian algorithm that enables better reconstruction of distributed brain source activity with two key ideas: kernel smoothing and hyperparameter tiling. Since the proposed algorithm builds upon many of the performance features of the sparse source reconstruction algorithm - Champagne and we refer to this algorithm as Smooth Champagne. Smooth Champagne is robust to the effects of high levels of noise, interference, and highly correlated brain source activity. Simulations demonstrate excellent performance of Smooth Champagne when compared to benchmark algorithms in accurately determining the spatial extent of distributed source activity. Smooth Champagne also accurately reconstructs real MEG and EEG data.

Bayesian multi-dipole modelling in the frequency domain

BackgroundMagneto- and Electro-encephalography record the electromagnetic field generated by neural currents with high temporal frequency and good spatial resolution, and are therefore well suited for source localization in the time and in the frequency domain. In particular, localization of the generators of neural oscillations is very important in the study of cognitive processes in the healthy and in the pathological brain. New methodWe introduce the use of a Bayesian multi-dipole localization method in the frequency domain. Given the Fourier Transform of the data at one or multiple frequencies and/or trials, the algorithm approximates numerically the posterior distribution with Monte Carlo techniques. ResultsWe use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios and correlated sources. We use dipole clusters to mimic the effect of extended sources. In addition, we test the algorithm on real MEG data to confirm its feasibility. Comparison with existing method(s)Throughout the whole study, DICS (Dynamic Imaging of Coherent Sources) is used systematically as a benchmark. The two methods provide similar general pictures; the posterior distributions of the Bayesian approach contain much richer information at the price of a higher computational cost. ConclusionsThe Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.

Phase Linearity Measurement: A Novel Index for Brain Functional Connectivity.

The problem of describing how different brain areas interact between each other has been granted a great deal of attention in the last years. The idea that neuronal ensembles behave as oscillators and that they communicate through synchronization is now widely accepted. To this regard, EEG and MEG provide the signals that allow the estimation of such communication in vivo. Hence, phase-based metrics are essential. However, the application of phased-based metrics for measuring brain connectivity has proved problematic so far, since they appear to be less resilient to noise as compared to amplitude-based ones. In this paper, we address the problem of designing a purely phase-based brain connectivity metric, insensitive to volume conduction and resilient to noise. The proposed metric, named phase linearity measurement (PLM), is based on the analysis of similar behaviors in the phases of the recorded signals. The PLM is tested in two simulated datasets as well as in real MEG data acquired at the Naples MEG center. Due to its intrinsic characteristics, the PLM shows considerable noise rejection properties as compared to other widely adopted connectivity metrics. We conclude that the PLM might be valuable in order to allow better estimation of phase-based brain connectivity.

Bayesian Optimisation of Large-Scale Biophysical Networks

The relationship between structure and function in the human brain is well established, but not yet well characterised. Large-scale biophysical models allow us to investigate this relationship, by leveraging structural information (e.g. derived from diffusion tractography) in order to couple dynamical models of local neuronal activity into networks of interacting regions distributed across the cortex. In practice however, these models are difficult to parametrise, and their simulation is often delicate and computationally expensive. This undermines the experimental aspect of scientific modelling, and stands in the way of comparing different parametrisations, network architectures, or models in general, with confidence. Here, we advocate the use of Bayesian optimisation for assessing the capabilities of biophysical network models, given a set of desired properties (e.g. band-specific functional connectivity); and in turn the use of this assessment as a principled basis for incremental modelling and model comparison. We adapt an optimisation method designed to cope with costly, high-dimensional, non-convex problems, and demonstrate its use and effectiveness. Using five parameters controlling key aspects of our model, we find that this method is able to converge to regions of high functional similarity with real MEG data, with very few samples given the number of parameters, without getting stuck in local extrema, and while building and exploiting a map of uncertainty defined smoothly across the parameter space. We compare the results obtained using different methods of structural connectivity estimation from diffusion tractography, and find that one method leads to better simulations.

A biophysical model of dynamic balancing of excitation and inhibition in fast oscillatory large-scale networks.

Over long timescales, neuronal dynamics can be robust to quite large perturbations, such as changes in white matter connectivity and grey matter structure through processes including learning, aging, development and certain disease processes. One possible explanation is that robust dynamics are facilitated by homeostatic mechanisms that can dynamically rebalance brain networks. In this study, we simulate a cortical brain network using the Wilson-Cowan neural mass model with conduction delays and noise, and use inhibitory synaptic plasticity (ISP) to dynamically achieve a spatially local balance between excitation and inhibition. Using MEG data from 55 subjects we find that ISP enables us to simultaneously achieve high correlation with multiple measures of functional connectivity, including amplitude envelope correlation and phase locking. Further, we find that ISP successfully achieves local E/I balance, and can consistently predict the functional connectivity computed from real MEG data, for a much wider range of model parameters than is possible with a model without ISP.

Hyperedge bundling: A practical solution to spurious interactions in MEG/EEG source connectivity analyses

Inter-areal functional connectivity (FC), neuronal synchronization in particular, is thought to constitute a key systems-level mechanism for coordination of neuronal processing and communication between brain regions. Evidence to support this hypothesis has been gained largely using invasive electrophysiological approaches. In humans, neuronal activity can be non-invasively recorded only with magneto- and electroencephalography (MEG/EEG), which have been used to assess FC networks with high temporal resolution and whole-scalp coverage. However, even in source-reconstructed MEG/EEG data, signal mixing, or “source leakage”, is a significant confounder for FC analyses and network localization.Signal mixing leads to two distinct kinds of false-positive observations: artificial interactions (AI) caused directly by mixing and spurious interactions (SI) arising indirectly from the spread of signals from true interacting sources to nearby false loci. To date, several interaction metrics have been developed to solve the AI problem, but the SI problem has remained largely intractable in MEG/EEG all-to-all source connectivity studies. Here, we advance a novel approach for correcting SIs in FC analyses using source-reconstructed MEG/EEG data.Our approach is to bundle observed FC connections into hyperedges by their adjacency in signal mixing. Using realistic simulations, we show here that bundling yields hyperedges with good separability of true positives and little loss in the true positive rate. Hyperedge bundling thus significantly decreases graph noise by minimizing the false-positive to true-positive ratio. Finally, we demonstrate the advantage of edge bundling in the visualization of large-scale cortical networks with real MEG data. We propose that hypergraphs yielded by bundling represent well the set of true cortical interactions that are detectable and dissociable in MEG/EEG connectivity analysis.

A multivariate method for estimating cross-frequency neuronal interactions and correcting linear mixing in MEG data, using canonical correlations

BackgroundCross-frequency interactions between distinct brain areas have been observed in connection with a variety of cognitive tasks. With electro- and magnetoencephalography (EEG/MEG) data, typical connectivity measures between two brain regions analyze a single quantity from each region within a specific frequency band; given the wideband nature of EEG/MEG signals, many statistical tests may be required to identify true coupling. Furthermore, because of the poor spatial resolution of activity reconstructed from EEG/MEG, some interactions may actually be due to the linear mixing of brain sources. New methodIn the present work, a method for the detection of cross-frequency functional connectivity in MEG data using canonical correlation analysis (CCA) is described. We demonstrate that CCA identifies correlated signals and also the frequencies that cause the correlation. We also implement a procedure to deal with linear mixing based on symmetry properties of cross-covariance matrices. ResultsOur tests with both simulated and real MEG data demonstrate that CCA is able to detect interacting locations and the frequencies that cause them, while accurately discarding spurious coupling. Comparison with existing methodsRecent techniques look at time delays in the activity between two locations to discard spurious interactions, while we propose a linear mixing model and demonstrate its relationship with symmetry aspects of cross-covariance matrices. ConclusionsOur tests indicate the benefits of the CCA approach in connectivity studies, as it allows the simultaneous evaluation of several possible combinations of cross-frequency interactions in a single statistical test.

A three domain covariance framework for EEG/MEG data

In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG–fMRI experiments in which the correlation between EEG and fMRI signals is investigated.We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets.

Self-Consistent MUSIC: An approach to the localization of true brain interactions from EEG/MEG data

MUltiple SIgnal Classification (MUSIC) is a standard localization method which is based on the idea of dividing the vector space of the data into two subspaces: signal subspace and noise subspace. The brain, divided into several grid points, is scanned entirely and the grid point with the maximum consistency with the signal subspace is considered as the source location. In one of the MUSIC variants called Recursively Applied and Projected MUSIC (RAP-MUSIC), multiple iterations are proposed in order to decrease the location estimation uncertainties introduced by subspace estimation errors. In this paper, we suggest a new method called Self-Consistent MUSIC (SC-MUSIC) which extends RAP-MUSIC to a self-consistent algorithm. This method, SC-MUSIC, is based on the idea that the presence of several sources has a bias on the localization of each source. This bias can be reduced by projecting out all other sources mutually rather than iteratively. While the new method is applicable in all situations when MUSIC is applicable we will study here the localization of interacting sources using the imaginary part of the cross-spectrum due to the robustness of this measure to the artifacts of volume conduction. For an odd number of sources this matrix is rank deficient similar to covariance matrices of fully correlated sources. In such cases MUSIC and RAP-MUSIC fail completely while the new method accurately localizes all sources. We present results of the method using simulations of odd and even number of interacting sources in the presence of different noise levels. We compare the method with three other source localization methods: RAP-MUSIC, dipole fit and MOCA (combined with minimum norm estimate) through simulations. SC-MUSIC shows substantial improvement in the localization accuracy compared to these methods. We also show results for real MEG data of a single subject in the resting state. Four sources are localized in the sensorimotor area at f=11Hz which is the expected region for the idle rhythm.

Sparse weightings for collapsing inverse solutions to cortical parcellations optimize M/EEG source reconstruction accuracy

Source-reconstructed magneto- and electroencephalography (M/EEG) are promising tools for investigating the human functional connectome. To reduce data, decrease noise, and obtain results directly comparable to magnetic resonance imaging (MRI), M/EEG source data can be collapsed into a cortical parcellation. For most collapsing approaches, however, it remains unclear if collapsed parcel time series accurately represent the coherent source dynamics within each parcel. We introduce a collapse-weighting-operator optimization approach that maximizes parcel fidelity, i.e., the phase correlation between original source dynamics and collapsed parcel time series, and thereby the accuracy with which the source dynamics are retained in forward and inverse modeling. The sparse, optimized weighting operator increased parcel fidelity 57-73% and true positive rate of interaction mapping from 0.33 to 0.84 in comparison to a non-sparse weighting approach. These improvements were robust for variable source topographies and parcellation resolutions. Critically, in real inverse-modeled MEG data, the optimized operator yielded close-to-perfect intra-parcel coherence. Previous suggestions for obtaining parcel time series include averaging all source time series within each anatomical parcel or using exclusively the time series of the voxel with maximum power. These methods are sensitive to signal heterogeneity and outlier sources. The approach advanced here avoids these problems. The optimized operator is suitable for collapsing real source-reconstructed M/EEG data into any cortical parcellation. The enhanced time series reconstruction fidelity yields improved accuracy of subsequent analyses of both local dynamics and large-scale interaction mapping.

Multi-session statistics on beamformed MEG data

Beamforming has been widely adopted as a source reconstruction technique in the analysis of magnetoencephalography data. Most beamforming implementations incorporate a spatially-varying rescaling (which we term weights normalisation) to correct for the inherent depth bias in raw beamformer estimates. Here, we demonstrate that such rescaling can cause critical problems whenever analyses are performed over multiple sessions of separately beamformed data, for example when comparing effect sizes between different populations. Importantly, we show that the weights-normalised beamformer estimates of neural activity can even lead to a reversal in the inferred sign of the effect being measured. We instead recommend that no weights normalisation be carried out; any depth bias is instead accounted for in the calculation of multi-session (e.g. group) statistics. We demonstrate the severity of the weights normalisation confound with a 2-D simulation, and in real MEG data by performing a group statistical analysis to detect differences in alpha power in eyes-closed rest compared with continuous visual stimulation.

Mutual information spectrum for selection of event-related spatial components. Application to eloquent motor cortex mapping

Spatial component analysis is often used to explore multidimensional time series data whose sources cannot be measured directly. Several methods may be used to decompose the data into a set of spatial components with temporal loadings. Component selection is of crucial importance, and should be supported by objective criteria. In some applications, the use of a well defined component selection criterion may provide for automation of the analysis. In this paper we describe a novel approach for ranking of spatial components calculated from the EEG or MEG data recorded within evoked response paradigm. Our method is called Mutual Information (MI) Spectrum and is based on gauging the amount of MI of spatial component temporal loadings with a synthetically created reference signal. We also describe the appropriate randomization based statistical assessment scheme that can be used for selection of components with statistically significant amount of MI. Using simulated data with realistic trial to trial variations and SNR corresponding to the real recordings we demonstrate the superior performance characteristics of the described MI based measure as compared to a more conventionally used power driven gauge. We also demonstrate the application of the MI Spectrum for the selection of task-related independent components from real MEG data. We show that the MI spectrum allows to identify task-related components reliably in a consistent fashion, yielding stable results even from a small number of trials. We conclude that the proposed method fits naturally the information driven nature of ICA and can be used for routine and automatic ranking of independent components calculated from the functional neuroimaging data collected within event-related paradigms.

Convolution models for induced electromagnetic responses

In Kilner et al. [Kilner, J.M., Kiebel, S.J., Friston, K.J., 2005. Applications of random field theory to electrophysiology. Neurosci. Lett. 374, 174–178.] we described a fairly general analysis of induced responses—in electromagnetic brain signals—using the summary statistic approach and statistical parametric mapping. This involves localising induced responses—in peristimulus time and frequency—by testing for effects in time–frequency images that summarise the response of each subject to each trial type. Conventionally, these time–frequency summaries are estimated using post‐hoc averaging of epoched data. However, post‐hoc averaging of this sort fails when the induced responses overlap or when there are multiple response components that have variable timing within each trial (for example stimulus and response components associated with different reaction times). In these situations, it is advantageous to estimate response components using a convolution model of the sort that is standard in the analysis of fMRI time series. In this paper, we describe one such approach, based upon ordinary least squares deconvolution of induced responses to input functions encoding the onset of different components within each trial. There are a number of fundamental advantages to this approach: for example; (i) one can disambiguate induced responses to stimulus onsets and variably timed responses; (ii) one can test for the modulation of induced responses—over peristimulus time and frequency—by parametric experimental factors and (iii) one can gracefully handle confounds—such as slow drifts in power—by including them in the model. In what follows, we consider optimal forms for convolution models of induced responses, in terms of impulse response basis function sets and illustrate the utility of deconvolution estimators using simulated and real MEG data.

Raviart–Thomas-type sources adapted to applied EEG and MEG: implementation and results

This paper studies numerically electroencephalography and magnetoencephalography (EEG and MEG), two non-invasive imaging modalities in which external measurements of the electric potential and the magnetic field are, respectively, utilized to reconstruct the primary current density (neuronal activity) of the human brain. The focus is on adapting a Raviart–Thomas-type source model to meet the needs of EEG and MEG applications. The goal is to construct a model that provides an accurate approximation of dipole source currents and can be flexibly applied to different reconstruction strategies as well as to realistic computation geometries. The finite element method is applied in the simulation of the data. Least-squares fit interpolation is used to establish Cartesian source directions, which guarantee that the recovered current field is minimally dependent on the underlying finite element mesh. Implementation is explained in detail and made accessible, e.g., by using quadrature-free formulae and the Gaussian one-point rule in numerical integration. Numerical results are presented concerning, for example, the iterative alternating sequential inverse algorithm as well as resolution, smoothness and local refinement of the finite element mesh. Both spherical and pseudo-realistic head models, as well as real MEG data, are utilized in the numerical experiments.