A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres

Fast and Accurate EEG/MEG BEM-Based Forward Problem Solution for High-Resolution Head Models

A BEM (boundary element method) based approach is developed to accurately solve an EEG/MEG forward problem for a modern high-resolution head model in approximately 60 seconds using a common workstation. The method utilizes a charge-based BEM with fast multipole acceleration (BEM-FMM) and a "smart" mesh pre-refinement (called b-refinement) close to the singular source(s). No costly matrix-filling or direct solution steps typical for the standard BEM are required; the method generates on-skin voltages as well as MEG magnetic fields for high-resolution head models in approximately 60 seconds after initial model assembly. The method is verified both theoretically and experimentally.

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling

This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

How to assess the accuracy of volume conduction models? A validation study with stereotactic EEG data

Introduction

Volume conduction models of the human head are used in various neuroscience fields, such as for source reconstruction in EEG and MEG, and for modeling the effects of brain stimulation. Numerous studies have quantified the accuracy and sensitivity of volume conduction models by analyzing the effects of the geometrical and electrical features of the head model, the sensor model, the source model, and the numerical method. Most studies are based on simulations as it is hard to obtain sufficiently detailed measurements to compare to models. The recording of stereotactic EEG during electric stimulation mapping provides an opportunity for such empirical validation.

Methods

In the study presented here, we used the potential distribution of volume-conducted artifacts that are due to cortical stimulation to evaluate the accuracy of finite element method (FEM) volume conduction models. We adopted a widely used strategy for numerical comparison, i.e., we fixed the geometrical description of the head model and the mathematical method to perform simulations, and we gradually altered the head models, by increasing the level of detail of the conductivity profile. We compared the simulated potentials at different levels of refinement with the measured potentials in three epilepsy patients.

Results

Our results show that increasing the level of detail of the volume conduction head model only marginally improves the accuracy of the simulated potentials when compared to in-vivo sEEG measurements. The mismatch between measured and simulated potentials is, throughout all patients and models, maximally 40 microvolts (i.e., 10% relative error) in 80% of the stimulation-recording combination pairs and it is modulated by the distance between recording and stimulating electrodes.

Discussion

Our study suggests that commonly used strategies used to validate volume conduction models based solely on simulations might give an overly optimistic idea about volume conduction model accuracy. We recommend more empirical validations to be performed to identify those factors in volume conduction models that have the highest impact on the accuracy of simulated potentials. We share the dataset to allow researchers to further investigate the mismatch between measurements and FEM models and to contribute to improving volume conduction models.

Multi-compartment head modeling in EEG: Unstructured boundary-fitted tetra meshing with subcortical structures

This paper introduces an automated approach for generating a finite element (FE) discretization of a multi-compartment human head model for electroencephalographic (EEG) source localization. We aim to provide an adaptable FE mesh generation tool for EEG studies. Our technique relies on recursive solid angle labeling of a surface segmentation coupled with smoothing, refinement, inflation, and optimization procedures to enhance the mesh quality. In this study, we performed numerical meshing experiments with the three-layer Ary sphere and a magnetic resonance imaging (MRI)-based multi-compartment head segmentation which incorporates a comprehensive set of subcortical brain structures. These experiments are motivated, on one hand, by the sensitivity of non-invasive subcortical source localization to modeling errors and, on the other hand, by the present lack of open EEG software pipelines to discretize all these structures. Our approach was found to successfully produce an unstructured and boundary-fitted tetrahedral mesh with a sub-one-millimeter fitting error, providing the desired accuracy for the three-dimensional anatomical details, EEG lead field matrix, and source localization. The mesh generator applied in this study has been implemented in the open MATLAB-based Zeffiro Interface toolbox for forward and inverse processing in EEG and it allows for graphics processing unit acceleration.

EEG-based source localization with enhanced virtual aperture using second order statistics

For the past few decades source localization, based on EEG modality, has been a very active area of research. EEG signal provides temporal resolution in millisecond range that can capture rapidly changing patterns of brain activity but it has a low spatial resolution as compared to techniques like fMRI, PET, CT scan, etc. So, one of the motives of this research is to improve the spatial resolution of the EEG signal. Many successful attempts have been made to localise the active neural sources using EEG signals with the introduction of techniques like MNE, LORETA, sLORETA, FOCUSS, etc. But these techniques require a large number of electrodes for correct localization of a few sources. This paper aims at providing a new method for the localization of EEG sources with a fewer electrode. This is achieved by exploiting the second-order statistics to enhance the aperture and solve the EEG localization problem. The comparison of the proposed method with the state-of-the-art methods is done by observing the localization error with variation in SNR, number of snapshots (time samples), number of active sources, and number of electrodes. The results show that the proposed method can detect a greater number of sources with fewer electrodes and with higher accuracy as compared to methods available in the literature. Real -time EEG signal during an arithmetic task is considered and the proposed algorithm clearly shows a sparse activity in the frontal region.

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.

Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes

Objective. To formulate, validate, and apply an alternative to the finite element method (FEM) high-resolution modeling technique for electrical brain stimulation-the boundary element fast multipole method (BEM-FMM). To include practical electrode models for both surface and embedded electrodes.Approach. Integral equations of the boundary element method in terms of surface charge density are combined with a general-purpose fast multipole method and are expanded for voltage, shunt, current, and floating electrodes. The solution of coupled and properly weighted/preconditioned integral equations is accompanied by enforcing global conservation laws: charge conservation law and Kirchhoff's current law.Main results.A sub-percent accuracy is reported as compared to the analytical solutions and simple validation geometries. Comparison to FEM considering realistic head models resulted in relative differences of the electric field magnitude in the range of 3%-6% or less. Quantities that contain higher order spatial derivatives, such as the activating function, are determined with a higher accuracy and a faster speed as compared to the FEM. The method can be easily combined with existing head modeling pipelines such as headreco or mri2mesh.Significance.The BEM-FMM does not rely on a volumetric mesh and is therefore particularly suitable for modeling some mesoscale problems with submillimeter (and possibly finer) resolution with high accuracy at moderate computational cost. Utilizing Helmholtz reciprocity principle makes it possible to expand the method to a solution of EEG forward problems with a very large number of cortical dipoles.

A comprehensive study on electroencephalography and magnetoencephalography sensitivity to cortical and subcortical sources

Signal-to-noise ratio (SNR) maps are a good way to visualize electroencephalography (EEG) and magnetoencephalography (MEG) sensitivity. SNR maps extend the knowledge about the modulation of EEG and MEG signals by source locations and orientations and can therefore help to better understand and interpret measured signals as well as source reconstruction results thereof. Our work has two main objectives. First, we investigated the accuracy and reliability of EEG and MEG finite element method (FEM)-based sensitivity maps for three different head models, namely an isotropic three and four-compartment and an anisotropic six-compartment head model. As a result, we found that ignoring the cerebrospinal fluid leads to an overestimation of EEG SNR values. Second, we examined and compared EEG and MEG SNR mappings for both cortical and subcortical sources and their modulation by source location and orientation. Our results for cortical sources show that EEG sensitivity is higher for radial and deep sources and MEG for tangential ones, which are the majority of sources. As to the subcortical sources, we found that deep sources with sufficient tangential source orientation are recordable by the MEG. Our work, which represents the first comprehensive study where cortical and subcortical sources are considered in highly detailed FEM-based EEG and MEG SNR mappings, sheds a new light on the sensitivity of EEG and MEG and might influence the decision of brain researchers or clinicians in their choice of the best modality for their experiment or diagnostics, respectively.

Why do humans have unique auditory event-related fields? Evidence from computational modeling and MEG experiments

Auditory event-related fields (ERFs) measured with magnetoencephalography (MEG) are useful for studying the neuronal underpinnings of auditory cognition in human cortex. They have a highly subject-specific morphology, albeit certain characteristic deflections (e.g., P1m, N1m, and P2m) can be identified in most subjects. Here, we explore the reason for this subject-specificity through a combination of MEG measurements and computational modeling of auditory cortex. We test whether ERF subject-specificity can predominantly be explained in terms of each subject having an individual cortical gross anatomy, which modulates the MEG signal, or whether individual cortical dynamics is also at play. To our knowledge, this is the first time that tools to address this question are being presented. The effects of anatomical and dynamical variation on the MEG signal is simulated in a model describing the core-belt-parabelt structure of the auditory cortex, and with the dynamics based on the leaky-integrator neuron model. The experimental and simulated ERFs are characterized in terms of the N1m amplitude, latency, and width. Also, we examine the waveform grand-averaged across subjects, and the standard deviation of this grand average. The results show that the intersubject variability of the ERF arises out of both the anatomy and the dynamics of auditory cortex being specific to each subject. Moreover, our results suggest that the latency variation of the N1m is largely related to subject-specific dynamics. The findings are discussed in terms of how learning, plasticity, and sound detection are reflected in the auditory ERFs. The notion of the grand-averaged ERF is critically evaluated.

Validation of Numerical Simulation for Transcranial Direct Current Stimulation with Spherical Phantom

Transcranial direct current stimulation (tDCS) is a promising brain modulation technique in clinical application. Computational models of brain current flow have been used to provide better insights into determining the stimulation parameters, but there are only a few studies to validate the numerical simulation model. The purpose of this study is to validate the simulation model of tDCS. A one-/three-layered spherical phantom model was constructed to mimic the human head. The tDCS-induced voltages were measured at different depth in the spherical phantom model with stereotactic-EEG (s-EEG) electrodes. Comparing the measured values with the simulation data from the computational models, we found that the computational and empirically measured electric field distributions on the brain surface is similar and that the deviation between the predicted and measured electric field value becomes larger near the electrode.

Super-Resolution for Improving EEG Spatial Resolution using Deep Convolutional Neural Network-Feasibility Study

Electroencephalography (EEG) has relatively poor spatial resolution and may yield incorrect brain dynamics and distort topography; thus, high-density EEG systems are necessary for better analysis. Conventional methods have been proposed to solve these problems, however, they depend on parameters or brain models that are not simple to address. Therefore, new approaches are necessary to enhance EEG spatial resolution while maintaining its data properties. In this work, we investigated the super-resolution (SR) technique using deep convolutional neural networks (CNN) with simulated EEG data with white Gaussian and real brain noises, and experimental EEG data obtained during an auditory evoked potential task. SR EEG simulated data with white Gaussian noise or brain noise demonstrated a lower mean squared error and higher correlations with sensor information, and detected sources even more clearly than did low resolution (LR) EEG. In addition, experimental SR data also demonstrated far smaller errors for N1 and P2 components, and yielded reasonable localized sources, while LR data did not. We verified our proposed approach’s feasibility and efficacy, and conclude that it may be possible to explore various brain dynamics even with a small number of sensors.

Wearable neuroimaging: Combining and contrasting magnetoencephalography and electroencephalography

One of the most severe limitations of functional neuroimaging techniques, such as magnetoencephalography (MEG), is that participants must maintain a fixed head position during data acquisition. This imposes restrictions on the characteristics of the experimental cohorts that can be scanned and the experimental questions that can be addressed. For these reasons, the use of 'wearable' neuroimaging, in which participants can move freely during scanning, is attractive. The most successful example of wearable neuroimaging is electroencephalography (EEG), which employs lightweight and flexible instrumentation that makes it useable in almost any experimental setting. However, EEG has major technical limitations compared to MEG, and therefore the development of wearable MEG, or hybrid MEG/EEG systems, is a compelling prospect. In this paper, we combine and compare EEG and MEG measurements, the latter made using a new generation of optically-pumped magnetometers (OPMs). We show that these new second generation commercial OPMs, can be mounted on the scalp in an 'EEG-like' cap, enabling the acquisition of high fidelity electrophysiological measurements. We show that these sensors can be used in conjunction with conventional EEG electrodes, offering the potential for the development of hybrid MEG/EEG systems. We compare concurrently measured signals, showing that, whilst both modalities offer high quality data in stationary subjects, OPM-MEG measurements are less sensitive to artefacts produced when subjects move. Finally, we show using simulations that OPM-MEG offers a fundamentally better spatial specificity than EEG. The demonstrated technology holds the potential to revolutionise the utility of functional brain imaging, exploiting the flexibility of wearable systems to facilitate hitherto impractical experimental paradigms.

Fractal dimension analysis of states of consciousness and unconsciousness using transcranial magnetic stimulation

BACKGROUND AND OBJECTIVE

Knowing whether a subject is conscious or not is a current challenge with a deep potential clinical impact. Recent theoretical considerations suggest that consciousness is linked to the complexity of distributed interactions within the corticothalamic system. The fractal dimension (FD) is a quantitative parameter that has been extensively used to analyse the complexity of structural and functional patterns of the human brain. In this study we investigate FD to assess whether it can discriminate between consciousness and different states of unconsciousness in healthy individuals.

METHODS

We study 69 high-density electroencephalogram (hd-EEG) measurements after transcranial magnetic stimulation (TMS) in 18 healthy subjects progressing from wakefulness to non-rapid eye movement (NREM) sleep and sedation induced by different anaesthetic agents (xenon and propofol). We quantify the integration of thalamocortical networks by calculating the FD of a spatiotemporal voxelization obtained from the locations of all sources that are significantly activated by the perturbation (4DFD). Moreover, we study the temporal evolution of the evoked spatial distributions and compute a measure of the differentiation of the response by means of the Higuchi FD (HFD). Finally, a Fractal Dimension Index (FDI) of perturbational complexity is computed as the product of both quantities: integration FD (4DFD) and differentiation FD (HFD).

RESULTS

We found that FDI is significantly lower in sleep and sedation when compared to wakefulness and provides an almost perfect intra-subject discrimination between conscious and unconscious states.

CONCLUSIONS

These results support the combination of FD measures of cortical integration and cortical differentiation as a novel paradigm of tracking complex spatiotemporal dynamics in the brain that could provide further insights into the link between complexity and the brain's capacity to sustain consciousness.

Handling anisotropic conductivities in the EEG forward problem with a symmetric formulation

The electroencephalography (EEG) forward problem, the computation of the electric potential generated by a known electric current source configuration in the brain, is a key step of EEG source analysis. In this problem, it is often desired to model the anisotropic conductivity profiles of the skull and of the white matter. These profiles, however, cannot be handled by standard surface integral formulations and the use of volume finite elements is required. Leveraging on the representation theorem using an anisotropic fundamental solution, this paper proposes a modified symmetric formulation for solving the EEG forward problem by a surface integral equation which can take into account anisotropic conductivity profiles. A set of numerical results is presented to corroborate theoretical treatments and to show the impact of the proposed approach on both canonical and real case scenarios.

Assessing recurrent interactions in cortical networks: Modeling EEG response to transcranial magnetic stimulation

BACKGROUND

The basic mechanisms underlying the electroencephalograpy (EEG) response to transcranial magnetic stimulation (TMS) of the human cortex are not well understood.

NEW METHOD

A state-space modeling methodology is developed to gain insight into the network nature of the TMS/EEG response. Cortical activity is modeled using a multivariariate autoregressive model with exogenous stimulation parameters representing the effect of TMS. An observation equation models EEG measurement of cortical activity. An expectation-maximization algorithm is developed to estimate the model parameters.

RESULTS

The methodology is used to assess two different hypotheses for the mechanisms underlying TMS/EEG in wakefulness and sleep. The integrated model hypothesizes that recurrent interactions between cortical regions are the source of TMS/EEG, while the segregated model hypothesizes that the TMS/EEG results from excitation of independent cortical oscillators. The results show that the relatively simple EEG response to TMS recorded during non-rapid-eye-movement sleep is described equally well by either the integrated or segregated model. However, the integrated model fits the more complex TMS/EEG of wakefulness much better than the segregated model.

COMPARISON WITH EXISTING METHOD(S)

Existing methods are limited to small numbers of cortical regions of interest or do not represent the effect of TMS. Our results are consistent with previous studies contrasting the complexity of TMS/EEG in wakefulness and sleep.

CONCLUSION

The new method strongly suggests that effective feedback connections between cortical regions are required to produce the TMS/EEG in wakefulness.

Empirical Comparison of Distributed Source Localization Methods for Single-Trial Detection of Movement Preparation

The development of technologies for the treatment of movement disorders, like stroke, is still of particular interest in brain-computer interface (BCI) research. In this context, source localization methods (SLMs), that reconstruct the cerebral origin of brain activity measured outside the head, e.g., via electroencephalography (EEG), can add a valuable insight into the current state and progress of the treatment. However, in BCIs SLMs were often solely considered as advanced signal processing methods that are compared against other methods based on the classification performance alone. Though, this approach does not guarantee physiological meaningful results. We present an empirical comparison of three established distributed SLMs with the aim to use one for single-trial movement prediction. The SLMs wMNE, sLORETA, and dSPM were applied on data acquired from eight subjects performing voluntary arm movements. Besides the classification performance as quality measure, a distance metric was used to asses the physiological plausibility of the methods. For the distance metric, which is usually measured to the source position of maximum activity, we further propose a variant based on clusters that is better suited for the single-trial case in which several sources are likely and the actual maximum is unknown. The two metrics showed different results. The classification performance revealed no significant differences across subjects, indicating that all three methods are equally well-suited for single-trial movement prediction. On the other hand, we obtained significant differences in the distance measure, favoring wMNE even after correcting the distance with the number of reconstructed clusters. Further, distance results were inconsistent with the traditional method using the maximum, indicating that for wMNE the point of maximum source activity often did not coincide with the nearest activation cluster. In summary, the presented comparison might help users to select an appropriate SLM and to understand the implications of the selection. The proposed methodology pays attention to the particular properties of distributed SLMs and can serve as a framework for further comparisons.

Primary Sensorimotor Cortex Drives the Common Cortical Network for Gamma Synchronization in Voluntary Hand Movements

Background: Gamma synchronization (GS) may promote the processing between functionally related cortico-subcortical neural populations. Our aim was to identify the sources of GS and to analyze the direction of information flow in cerebral networks at the beginning of phasic movements, and during medium-strength isometric contraction of the hand.

Methods: We measured 64-channel electroencephalography in 11 healthy volunteers (age: 25 ± 8 years; four females); surface electromyography detected the movements of the dominant hand. In Task 1, subjects kept a constant medium-strength contraction of the first dorsal interosseus muscle, and performed a superimposed repetitive voluntary self-paced brisk squeeze of an object. In Task 2, brisk, and in Task 3, constant contractions were performed. Time-frequency analysis of the EEG signal was performed with the multitaper method. GS sources were identified in five frequency bands (30–49, 51–75, 76–99, 101–125, and 126–149 Hz) with beamformer inverse solution dynamic imaging of coherent sources. The direction of information flow was estimated by renormalized partial directed coherence for each frequency band. The data-driven surrogate test, and the time reversal technique were performed to identify significant connections.

Results: In all tasks, we depicted the first three common sources for the studied frequency bands that were as follows: contralateral primary sensorimotor cortex (S1M1), dorsolateral prefrontal cortex (dPFC) and supplementary motor cortex (SMA). GS was detected in narrower low- (∼30–60 Hz) and high-frequency bands (>51–60 Hz) in the contralateral thalamus and ipsilateral cerebellum in all three tasks. The contralateral posterior parietal cortex was activated only in Task 1. In every task, S1M1 had efferent information flow to the SMA and the dPFC while dPFC had no detected afferent connections to the network in the gamma range. Cortical-subcortical information flow captured by the GS was dynamically variable in the narrower frequency bands for the studied movements.

Conclusion: A distinct cortical network was identified for GS in voluntary hand movement tasks. Our study revealed that S1M1 modulated the activity of interconnected cortical areas through GS, while subcortical structures modulated the motor network dynamically, and specifically for the studied movement program.

EEG for Current With Two-Dimensional Support

OBJECTIVE

The inverse problem of computing the neuronal current density from scalp EEG is highly ill-posed. In part, this is due to the nonuniqueness of the mapping between current sources and scalp potentials. We develop an explicit formula for the scalp EEG for sources constrained to the cortical surface in terms only of the components of the current that affect the EEG signal.

METHODS

Starting from the quasi-static form of Maxwell's equations, we develop a formula that involves only the "visible" part of the current (i.e., the part of the current that affects the EEG measurements), as well as certain auxiliary functions that depend on the topology and conductivity of the 3-D domains $\Omega _c$ , $\Omega _f$, $\Omega _b$, and $\Omega _s$, which model the spaces occupied by the cerebrum, cerebrospinal fluid, bone, and scalp, respectively.

RESULTS

we derive expressions for the scalp potential for a general nested topology, as well as for the special case of spherical and ellipsoidal surfaces. We verify that the resulting scalp potential, in the case that the current resides in a spherical shell in the cerebrum of thickness $2\delta$, agrees with the potential obtained via the 3-D formulation for $\delta =10^{-8}\text{m}$.

CONCLUSION

The "visible" part of the current can be explicitly characterized and consists of a combination of its component normal to the surface and of a certain function generating the remaining tangential components of the current.

SIGNIFICANCE

The resulting ability to restrict the source space greatly reduces the degree of ambiguity in the inverse solutions, offering the potential for more stable inverse solutions, since the auxiliary functions that define the mapping can be computed efficiently using standard numerical methods.

SEEG dipole source localization based on an empirical Bayesian approach taking into account forward model uncertainties

Electromagnetic brain source localization consists in the inversion of a forward model based on a limited number of potential measurements. A wide range of methods has been developed to regularize this severely ill-posed problem and to reduce the solution space, imposing spatial smoothness, anatomical constraint or sparsity of the activated source map. This last criteria, based on physiological assumptions stating that in some particular events (e.g., epileptic spikes, evoked potential) few focal area of the brain are simultaneously actives, has gained more and more interest. Bayesian approaches have the ability to provide sparse solutions under adequate parametrization, and bring a convenient framework for the introduction of priors in the form of probabilistic density functions. However the quality of the forward model is rarely questioned while this parameter has undoubtedly a great influence on the solution. Its construction suffers from numerous approximation and uncertainties, even when using realistic numerical models. In addition, it often encodes a coarse sampling of the continuous solution space due to the computational burden its inversion implies. In this work we propose an empirical Bayesian approach to take into account the uncertainties of the forward model by allowing constrained variations around a prior physical model, in the particular context of SEEG measurements. We demonstrate on simulations that the method enhance the accuracy of the source time-course estimation as well as the sparsity of the resulting source map. Results on real signals prove the applicability of the method in real contexts.

A novel volume integral equation for solving the Electroencephalography forward problem

In this paper, a novel volume integral equation for solving the Electroencephalography forward problem is presented. Differently from other integral equation methods standardly used for the same purpose, the new formulation can handle inhomogeneous and fully anisotropic realistic head models. The new equation is obtained by a suitable use of Green's identities together with an appropriate handling of all boundary conditions for the EEG problem. The new equation is discretized with a consistent choice of volume and boundary elements. Numerical results shows validity and convergence of the approach, together with its applicability to real case models obtained from MRI data.

Validation of Computational Studies for Electrical Brain Stimulation With Phantom Head Experiments

BACKGROUND

Although computational studies of electrical brain stimulation (EBS) have received attention as a cost-effective tool, few studies have validated the technique, particularly in invasive cortical stimulation.

OBJECTIVE

In order to validate such studies, we used EBS to compare electric potential distributions generated by both numerical simulations and empirical measurements in three phantom head models (one-/three-layered spherical heads and MRI-based head).

METHODS

We constructed spherical phantom heads that consisted of one or three layers, and an anatomical, MRI-based phantom that consisted of three layers and represented the brain or brain/skull/scalp in order to perform both numerical simulations using the finite element method (FEM) and experimental measurements. Two stimulation electrodes (cathode and anode) were implanted in the phantoms to inject regulated input voltage, and the electric potential distributions induced were measured at various points located either on the surface or deep within the phantoms.

RESULTS

We observed that both the electric potential distributions from the numerical simulations and experiments behaved similarly and resulted in average relative differences of 5.4% (spherical phantom) and 10.3% (MRI-based phantom).

CONCLUSIONS

This study demonstrated that numerical simulation is reasonably consistent with actual experimental measurements; thus, because of its cost-effectiveness, EBS computational studies may be an attractive approach for necessary intensive/extensive studies.

Synthetic neuronal datasets for benchmarking directed functional connectivity metrics

Background. Datasets consisting of synthetic neural data generated with quantifiable and controlled parameters are a valuable asset in the process of testing and validating directed functional connectivity metrics. Considering the recent debate in the neuroimaging community concerning the use of these metrics for fMRI data, synthetic datasets that emulate the BOLD signal dynamics have played a central role by supporting claims that argue in favor or against certain choices. Generative models often used in studies that simulate neuronal activity, with the aim of gaining insight into specific brain regions and functions, have different requirements from the generative models for benchmarking datasets. Even though the latter must be realistic, there is a tradeoff between realism and computational demand that needs to be contemplated and simulations that efficiently mimic the real behavior of single neurons or neuronal populations are preferred, instead of more cumbersome and marginally precise ones. Methods. This work explores how simple generative models are able to produce neuronal datasets, for benchmarking purposes, that reflect the simulated effective connectivity and, how these can be used to obtain synthetic recordings of EEG and fMRI BOLD signals. The generative models covered here are AR processes, neural mass models consisting of linear and nonlinear stochastic differential equations and populations with thousands of spiking units. Forward models for EEG consist in the simple three-shell head model while the fMRI BOLD signal is modeled with the Balloon-Windkessel model or by convolution with a hemodynamic response function. Results. The simulated datasets are tested for causality with the original spectral formulation for Granger causality. Modeled effective connectivity can be detected in the generated data for varying connection strengths and interaction delays. Discussion. All generative models produce synthetic neuronal data with detectable causal effects although the relation between modeled and detected causality varies and less biophysically realistic models offer more control in causal relations such as modeled strength and frequency location.

Effects of head models and dipole source parameters on EEG fields

Head model and an efficient method for computing the forward EEG (electroencephalography)problem are essential to dipole source localization(DSL). In this paper, we use less expensive ovoid geometry to approximate human head, aiming at investigating the effects of head shape and dipole source parameters on EEG fields. The application of point least squares (PLS) based on meshless method was introduced for solving EEG forward problem and numerical simulation is implemented in three kinds of ovoid head models. We present the performances of the surface potential in the face of varying dipole source parameters in detail. The results show that the potential patterns are similar for different dipole position in different head shapes, but the peak value of potential is significantly influenced by the head shape. Dipole position induces a great effect on the peak value of potential and shift of peak potential. The degree of variation between sphere head model and non-sphere head models is seen at the same time. We also show that PLS method with the trigonometric basis is superior to the constant basis, linear basis, and quadratic basis functions in accuracy and efficiency.

Intra-cortical propagation of EEG alpha oscillations

The most salient feature of spontaneous human brain activity as recorded with electroencephalography (EEG) are rhythmic fluctuations around 10Hz. These alpha oscillations have been reported to propagate over the scalp with velocities in the range of 5-15m/s. Since these velocities are in the range of action potential velocities through cortico-cortical axons, it has been hypothesized that the observed scalp waves reflect cortico-cortically mediated propagation of cortical oscillations. The reported scalp velocities however, appear to be inconsistent with those estimated from local field potential recordings in dogs, which are <1m/s and agree with the propagation velocity of action potentials in intra-cortical axons. In this study, we resolve these diverging findings using a combination of EEG data-analysis and biophysical modeling. In particular, we demonstrate that the observed scalp velocities can be accounted for by slow traveling oscillations, which provides support for the claim that spatial propagation of alpha oscillations is mediated by intra-cortical axons.

Localization of coherent sources by simultaneous MEG and EEG beamformer

Simultaneous magnetoencephalography (MEG) and electroencephalography (EEG) analysis is known generally to yield better localization performance than a single modality only. For simultaneous analysis, MEG and EEG data should be combined to maximize synergistic effects. Recently, beamformer for simultaneous MEG/EEG analysis was proposed to localize both radial and tangential components well, while single modality analyses could not detect them, or had relatively higher location bias. In practice, most interesting brain sources are likely to be activated coherently; however, conventional beamformer may not work properly for such coherent sources. To overcome this difficulty, a linearly constrained minimum variance (LCMV) beamformer may be used with a source suppression strategy. In this work, simultaneous MEG/EEG LCMV beamformer using source suppression was formulated firstly to investigate its capability over various suppression strategies. The localization performance of our proposed approach was examined mainly for coherent sources and compared thoroughly with the conventional simultaneous and single modality approaches, over various suppression strategies. For this purpose, we used numerous simulated data, as well as empirical auditory stimulation data. In addition, some strategic issues of simultaneous MEG/EEG analysis were discussed. Overall, we found that our simultaneous MEG/EEG LCMV beamformer using a source suppression strategy is greatly beneficial in localizing coherent sources.

Reduction of the impact of multiple uncertain conductivity values on EEG dipole source analysis

It is well known that the uncertain knowledge of the conductivity values of the head tissues has an important impact upon the accuracy of the electroencephalogram source reconstruction. Assuming a certain value of the conductivity often leads to high reconstruction error values when solving the inverse problem. It is possible to quantify the impact of multiple uncertain conductivity values on the localization accuracy. We propose an approach that reduces the impact of these multiple uncertainties on the reconstruction accuracy of the dipole parameters. This paper elaborates the numerical method and shows results of localization accuracy in a five-shell spherical head model. Sensitivity analysis, when considering multiple layers in the head model, shows the different scales of the influence of the various uncertain conductivity values on the potential values. We propose a cost function that reduces the impact of multiple uncertainties of the conductivity value on the electroencephalogram dipole reconstruction and two strategies for selecting potential values on the basis of the sensitivity analysis. Numerical simulations, when considering multiple uncertainties in the model, provide results with higher reconstruction accuracy compared with the case where only a single uncertainty is taken into account.

Locating the STN-DBS electrodes and resolving their subsequent networks using coherent source analysis on EEG

The deep brain stimulation (DBS) of the subthalamic nucleus (STN) is the most effective surgical therapy for Parkinson's disease (PD). The first aim of the study was to locate the STN-DBS electrode by applying source analysis on EEG. Secondly, to identify tremor related areas which are associated with the STN. The Dynamic imaging of coherent sources (DICS) was used to find the coherent sources in the brain. The capability of the source analysis to detect deep sources like STN in the brain using EEG data was tested with two model dipole simulations. The simulations were concentrated on two aspects, the angle of the dipole orientation and the disturbance of the cortical areas on locating subcortical regions. In all the DBS treated Parkinsonian tremor patients the power spectrum showed a clear peak at the stimulated frequency and followed by there harmonics. The DBS stimulated frequency constituted a network of primary sensory motor cortex, supplementary motor area, prefrontal cortex, diencephalon, cerebellum and brainstem. Thus the STN was located in the region of the diencephalon. The resolved network may give better understanding to the pathophysiology of the effected tremor network in PD patients with STN-DBS.

Subject position affects EEG magnitudes

EEG (electroencephalography) has been used for decades in thousands of research studies and is today a routine clinical tool despite the small magnitude of measured scalp potentials. It is widely accepted that the currents originating in the brain are strongly influenced by the high resistivity of skull bone, but it is less well known that the thin layer of CSF (cerebrospinal fluid) has perhaps an even more important effect on EEG scalp magnitude by spatially blurring the signals. Here it is shown that brain shift and the resulting small changes in CSF layer thickness, induced by changing the subject's position, have a significant effect on EEG signal magnitudes in several standard visual paradigms. For spatially incoherent high-frequency activity the effect produced by switching from prone to supine can be dramatic, increasing occipital signal power by several times for some subjects (on average 80%). MRI measurements showed that the occipital CSF layer between the brain and skull decreases by approximately 30% in thickness when a subject moves from prone to supine position. A multiple dipole model demonstrated that this can indeed lead to occipital EEG signal power increases in the same direction and order of magnitude as those observed here. These results suggest that future EEG studies should control for subjects' posture, and that some studies may consider placing their subjects into the most favorable position for the experiment. These findings also imply that special consideration should be given to EEG measurements from subjects with brain atrophy due to normal aging or neurodegenerative diseases, since the resulting increase in CSF layer thickness could profoundly decrease scalp potential measurements.

A new method for localizing the sources of correlated cross-frequency oscillations in human brains

Anatomically distributed areas are dynamically linked to form functional networks for processing and integrating the different modalities of information in the human brain. A part of such networks is considered to be realized with synchronization of neuronal activities, which can generate correlated neural oscillation at the same and/or different frequency bands. To investigate the networks with the synchronization, analysis of connectivity between not only same frequency oscillation but also different frequency (i.e. cross-frequency) is needed. For source estimation with electroencephalogram (EEG) or magneto-encephalogram (MEG) signals, a spatial filtering technique is recently applied as an alternative method for equivalent current dipole (ECD) estimation technique. Non-adaptive type of spatial filtering technique, such as the Standardized low-resolution brain electromagnetic tomography (sLORETA), is reported to discriminate correlated sources. However, it may lead to inaccurate results due to its low spatial resolution. In the present study, we proposed a new systematic approach for localizing the sources of correlated cross-frequency oscillations. The method we propose can overcome the limitation of the non-adaptive spatial filtering technique by proactively using identified information in sensor level analysis (e.g. cross-correlation map and correlation topography), which allow us to focus on target sources. The performance of our proposed method is evaluated with simulated EEG signals, and is compared with traditional method.

Neuronal networks in west syndrome as revealed by source analysis and renormalized partial directed coherence

West syndrome is a severe epileptic encephalopathy of infancy with a poor developmental outcome. This syndrome is associated with the pathognomonic EEG feature of hypsarrhythmia. The aim of the study was to describe neuronal networks underlying hypsarrhythmia using the source analysis method (dynamic imaging of coherent sources or DICS) which represents an inverse solution algorithm in the frequency domain. In order to investigate the interaction within the detected network, a renormalized partial directed coherence (RPDC) method was also applied as a measure of the directionality of information flow between the source signals. Both DICS and RPDC were performed for EEG delta activity (1-4 Hz) in eight patients with West syndrome and in eight patients with partial epilepsies (control group). The brain area with the strongest power in the given frequency range was defined as the reference region. The coherence between this reference region and the entire brain was computed using DICS. After that, the RPDC was applied to the source signals estimated by DICS. The results of electrical source imaging were compared to results of a previous EEG-fMRI study which had been carried out using the same cohort of patients. As revealed by DICS, delta activity in hypsarrhythmia was associated with coherent sources in the occipital cortex (main source) as well as the parietal cortex, putamen, caudate nucleus and brainstem. In patients with partial epilepsies, delta activity could be attributed to sources in the occipital, parietal and sensory-motor cortex. In West syndrome, RPDC showed the strongest and most significant direction of ascending information flow from the brainstem towards the putamen and cerebral cortex. The neuronal network underlying hypsarrhythmia in this study resembles the network which was described in previous EEG-fMRI and PET studies with involvement of the brainstem, putamen and cortical regions in the generation of hypsarrhythmia. The RPDC suggests that brainstem could have a key role in the pathogenesis of West syndrome. This study supports the theory that hypsarrhythmia results from ascending brainstem pathways that project widely to basal ganglia and cerebral cortex.

Anisotropic spherical head model and its application to imaging electric activity of the brain

This study reports on a solution to Poisson's equation describing an electric potential and field generated by a dipolar current source positioned inside a set of concentric spherical shells characterized by a homogeneous anisotropic conductivity inside each shell. Formulas giving a unique continuation of potentials and fields between the shells are derived. The formulas are applied to a spherical model of the human head to show that (i) real human skulls comprising isotropic compact and cancellous bone layers can be closely approximated by a single shell with radial-tangential conductivity anisotropy ~1:2 and radial conductivity equal to 1/30 of the brain/scalp conductivity; (ii) errors due to the spherical approximation of the head shape are of the same magnitude as errors due to poorly known electrical properties of the modeled head tissues; (iii) commonly used electroencephalography (EEG) average reference contributes 15% of the signal (on the average) and, therefore, makes EEG measurements significantly nonlocal; and (iv) the surface Laplacian of EEG measurements closely approximates electric currents at the skull-scalp interface, providing a parameter-free (up to a constant factor) deblurring and dereferencing of EEG data. These results can be useful for localization of sources underlying electric activity of the brain.

The effect of volume conductor modeling on the estimation of cardiac vectors in fetal magnetocardiography

Previous studies based on fetal magnetocardiographic (fMCG) recordings used simplified volume conductor models to estimate the fetal cardiac vector as an unequivocal measure of the cardiac source strength. However, the effect of simplified volume conductor modeling on the accuracy of the fMCG inverse solution remains largely unknown. Aiming to determine the sensitivity of the source estimators to the details of the volume conductor model, we performed simulations using fetal-maternal anatomical information from ultrasound images obtained in 20 pregnant women in various stages of pregnancy. The magnetic field produced by a cardiac source model was computed using the boundary-element method for a piecewise homogeneous volume conductor with three nested compartments (fetal body, amniotic fluid and maternal abdomen) of different electrical conductivities. For late gestation, we also considered the case of a fourth highly insulating layer of vernix caseosa covering the fetus. The errors introduced for simplified volume conductors were assessed by comparing the reconstruction results obtained with realistic versus spherically symmetric models. Our study demonstrates the significant effect of simplified volume conductor modeling, resulting mainly in an underestimation of the cardiac vector magnitude and low goodness-of-fit. These findings are confirmed by the analysis of real fMCG data recorded in mid-gestation.

Source analysis of beta-synchronisation and cortico-muscular coherence after movement termination based on high resolution electroencephalography

We hypothesized that post-movement beta synchronization (PMBS) and cortico-muscular coherence (CMC) during movement termination relate to each other and have similar role in sensorimotor integration. We calculated the parameters and estimated the sources of these phenomena.

We measured 64-channel EEG simultaneously with surface EMG of the right first dorsal interosseus muscle in 11 healthy volunteers. In Task1, subjects kept a medium-strength contraction continuously; in Task2, superimposed on this movement, they performed repetitive self-paced short contractions. In Task3 short contractions were executed alone. Time-frequency analysis of the EEG and CMC was performed with respect to the offset of brisk movements and averaged in each subject. Sources of PMBS and CMC were also calculated.

High beta power in Task1, PMBS in Task2-3, and CMC in Task1-2 could be observed in the same individual frequency bands. While beta synchronization in Task1 and PMBS in Task2-3 appeared bilateral with contralateral predominance, CMC in Task1-2 was strictly a unilateral phenomenon; their main sources did not differ contralateral to the movement in the primary sensorimotor cortex in 7 of 11 subjects in Task1, and in 6 of 9 subjects in Task2. In Task2, CMC and PMBS had the same latency but their amplitudes did not correlate with each other. In Task2, weaker PMBS source was found bilaterally within the secondary sensory cortex, while the second source of CMC was detected in the premotor cortex, contralateral to the movement. In Task3, weaker sources of PMBS could be estimated in bilateral supplementary motor cortex and in the thalamus.

PMBS and CMC appear simultaneously at the end of a phasic movement possibly suggesting similar antikinetic effects, but they may be separate processes with different active functions. Whereas PMBS seems to reset the supraspinal sensorimotor network, cortico-muscular coherence may represent the recalibration of cortico-motoneuronal and spinal systems.

Representation and propagation of epileptic activity in absences and generalized photoparoxysmal responses

Although functional imaging studies described networks associated with generalized epileptic activity, propagation patterns within these networks are not clear. In this study, electroencephalogram (EEG)-based coherent source imaging dynamic imaging of coherent sources (DICS) was applied to different types of generalized epileptiform discharges, namely absence seizures (10 patients) and photoparoxysmal responses (PPR) (eight patients) to describe the representation and propagation of these discharges in the brain. The results of electrical source imaging were compared to EEG-functional magnetic resonance imaging (fMRI) which had been obtained from the same data sets of simultaneous EEG and fMRI recordings. Similar networks were described by DICS and fMRI: (1) absence seizures were associated with thalamic involvement in all patients. Concordant results were also found for brain areas of the default mode network and the occipital cortex. (2) Both DICS and fMRI identified the occipital, parietal, and the frontal cortex in a network associated with PPR. (3) However, only when PPR preceded a generalized tonic-clonic seizure, the thalamus was involved in the generation of PPR as shown by both imaging techniques. Partial directed coherence suggested that during absences, the thalamus acts as a pacemaker while PPR could be explained by a cortical propagation from the occipital cortex via the parietal cortex to the frontal cortex. In conclusion, the electrical source imaging is not only able to describe similar neuronal networks as revealed by fMRI, including deep sources of neuronal activity such as the thalamus, but also demonstrates interactions interactions within these networks and sheds light on pathogenetic mechanisms of absence seizures and PPR.

Multi-Space Competitive DGA for Model Selection and its Application to Localization of Multiple Signal Sources

In this paper, a new optimization method, which is effective for the problems that the optimum solution should be searched in several solution spaces, is proposed. The proposed method is an extension of Distributed Genetic Algorithm (DGA), in which each subpopulation searches a solution in the corresponding solution space. Through the competition between the sub-populations, population sizes are adequately and gradually changed. By the change of the population size, the appropriate sub-population attracts many individuals. The changing population size yield the efficient search for the problems of searching for solutions in multiple spaces. In order to evaluate the proposed method, it is applied to a polynomial curve fitting and signal source localization, in which the number of sources is preliminarily unknown. Simulation results show the effectiveness of the proposed method.

Anatomically constrained minimum variance beamforming applied to EEG

Neural activity as measured non-invasively using electroencephalography (EEG) or magnetoencephalography (MEG) originates in the cortical gray matter. In the cortex, pyramidal cells are organized in columns and activated coherently, leading to current flow perpendicular to the cortical surface. In recent years, beamforming algorithms have been developed, which use this property as an anatomical constraint for the locations and directions of potential sources in MEG data analysis. Here, we extend this work to EEG recordings, which require a more sophisticated forward model due to the blurring of the electric current at tissue boundaries where the conductivity changes. Using CT scans, we create a realistic three-layer head model consisting of tessellated surfaces that represent the cerebrospinal fluid-skull, skull-scalp, and scalp-air boundaries. The cortical gray matter surface, the anatomical constraint for the source dipoles, is extracted from MRI scans. EEG beamforming is implemented on simulated sets of EEG data for three different head models: single spherical, multi-shell spherical, and multi-shell realistic. Using the same conditions for simulated EEG and MEG data, it is shown (and quantified by receiver operating characteristic analysis) that EEG beamforming detects radially oriented sources, to which MEG lacks sensitivity. By merging several techniques, such as linearly constrained minimum variance beamforming, realistic geometry forward solutions, and cortical constraints, we demonstrate it is possible to localize and estimate the dynamics of dipolar and spatially extended (distributed) sources of neural activity.

The M100 component of evoked magnetic fields differs by scaling factors: implications for signal averaging

MEG and EEG studies of event-related responses often involve comparisons of grand averages, requiring homogeneity of the variances. Here, we examine the possibility, implied by the nature of neural sources and the measuring principles involved, that the M100 component of auditory-evoked magnetic fields of different subjects, hemispheres, to different stimuli, and at different sensors differs by scaling factors. Such a multiplicative model predicts a linear increase in the standard deviation with the mean, and thus would have important implications for averaging and comparing such data. Our analyses, at the sensor and the source level, clearly show that the multiplicative model applies. We therefore propose geometric, rather than arithmetic, averaging of the M100 component across subjects and suggest a novel and superior normalization procedure. Our results question the justification of the common practice of subtracting arithmetic grand averages.