Trends in EEG source localization

BackgroundThe aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.MethodsWhile other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.ResultsIt starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.ConclusionSolving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

To improve the EEG source localization in the brain, the conductivities used in the head model play a very important role. In this study, we focus on the modeling of the anisotropic conductivity of the white matter. The anisotropic conductivity profile can be derived from diffusion weighted magnetic resonance images (DW-MRI). However, deriving these anisotropic conductivities from diffusion weighted MR images of the white matter is not straightforward. In the literature, two methods can be found for calculating the conductivity from the diffusion weighted images. One method uses a fixed value for the ratio of the conductivity in different directions, while the other method uses a conductivity profile obtained from a linear scaling of the diffusion ellipsoid. We propose a model which can be used to derive the conductivity profile from the diffusion tensor images. This model is based on the variable anisotropic ratio throughout the white matter and is a combination of the linear relationship as stated in the literature, with a constraint on the magnitude of the conductivity tensor (also known as the volume constraint). This approach is stated in the paper as approach A. In our study we want to investigate dipole estimation differences due to using a more simplified model for white matter anisotropy (approach B), while the electrode potentials are derived using a head model with a more realistic approach for the white matter anisotropy (approach A). We used a realistic head model, in which the forward problem was solved using a finite difference method that can incorporate anisotropic conductivities. As error measures we considered the dipole location error and the dipole orientation error. The results show that the dipole location errors are all below 10 mm and have an average of 4 mm in gray matter regions. The dipole orientation errors ranged up to 66.4°, and had a mean of, on average, 11.6° in gray matter regions. In a qualitative manner, the results show that the orientation and location error is dependent on the orientation of the test dipole. The location error is larger when the orientation of the test dipole is similar to the orientation of the anisotropy, while the orientation error is larger when the orientation of the test dipole deviates from the orientation of the anisotropy. From these results, we can conclude that the modeling of white matter anisotropy plays an important role in EEG source localization. More specifically, accurate source localization will require an accurate modeling of the white matter conductivity profile in each voxel.

Electroencephalogram (EEG) source localization requires a solution to an ill-posed inverse problem. The additional challenge is to solve this problem in the context of multiple moving sources. An effective and simple technique for both separation and localization of EEG sources is therefore proposed by incorporating an algorithmically coupled blind source separation (BSS) approach. The method relies upon having a priori knowledge of the locations of a subset of the sources. The cost function of the BSS algorithm is constrained by this information, and the unknown sources are iteratively calculated. An important application of this method is to localize abnormal sources, which, for example, cause changes in attention, movement, and behavior. In this application, the Alpha rhythm was considered as the known sources. Simulation studies are presented to support the potential of the approach in terms of source localization.

Complementary with electroencephalograph (EEG), functional magnetic resonance imaging (fMRI), with high spatial resolution, is powerful at providing prior source locations based on actual brain physiology. It hereby can help improve the accuracy of EEG source localization. However, most of the current methods directly penalize the sources whose fMRI activation probability is low and estimate the sources activities at every time point. Thus, they do not account for the temporal interrelated and non-stationary features of electromagnetic brain signals, and some are too much dependent on the fMRI prior. Here, we propose a new fMRI informed EEG source localization method and is termed fMRI-informed spatio-temporal unifying tomography (FIST). It uses a mixed norm constraint defined in terms of time–frequency decomposition of the sources and combines it with fMRI prior. The Fast Iterative Shrinkage Thresholding Algorithm is employed to solve the optimization problem. Both simulated and real EEG data are applied to assess the performance of the proposed method. Compared with L2-norm constrained methods, FIST has the superiority brain source estimation both in the spatial and temporal domains. By virtue of the fMRI information as a prior, FIST has great improvement in spatial accuracy and computational efficiency, when comparing with the method which only uses mixed-norm constraint. In addition, FIST shows good ability to select the fMRI priors to get a better estimation without totally depending on the prior, when comparing with the method which also has fMRI prior information.

Electroencephalography (EEG) source localization in epileptology continues to be a challenge for neuroscientists. A number of inverse solution (IS) methodologies have been proposed to solve this problem, and their advantages and limitations have been described. In the present work, a previously developed IS approach called Bayesian model averaging (BMA) is introduced in clinical practice in order to improve the localization accuracy of epileptic discharge sources. For this study, 31 patients with the diagnosis of partial epilepsies were studied: 14 had benign childhood epilepsy with centrotemporal spikes and 17 had temporal lobe epilepsy (TLE). The underlying epileptic sources were localized using the BMA approach, and the results were compared with those expected from the clinical diagnosis. Additional comparisons with results obtained from 3 of the most commonly used distributed IS methods for these purposes (minimum norm [MN], weighted minimum norm [WMN], and low-resolution electromagnetic tomography [LORETA]) were carried out in terms of source localization accuracy and spatial resolutions. The BMA approach estimated discharge sources that were consistent with the clinical diagnosis, and this method outperformed LORETA, MN, and WMN in terms of both localization accuracy and spatial resolution. The BMA was able to localize deeper generators with high accuracy. In conclusion, the BMA methodology has a great potential for the noninvasive accurate localization of epileptic sources, even those located in deeper structures. Therefore, it could be a promising tool for clinical practice in epileptology, although additional studies in other types of epileptic syndromes are necessary.

Newton's method is one of the commonly used methods for acoustic emission partial discharge (AEPD) source localization in power transformers. The major problem in the AEPD source localization is the difficulty in accurately measuring the signal arrival time from the source to the multiple sensors. The exact instant at which the partial discharge (PD) occurs is not known. Therefore, instead of the absolute time, the time-delay in signal reception of each sensor with respect to the sensor nearest to the PD source is estimated. In the present study the effect of time-delay error on the accuracy of the PD source localization is analyzed through numerical experimentations. The solution of the Newtons's method in turn depends on the choice of the initial guess. Hence, different initial guesses are selected for Newton's method randomly. For a fixed set of coordinates for the four sensors and the PD source positions, the time-delays are theoretically calculated. The error is systematically increased in the calculated time-delay to form different groups of time-delays. The PD source is localized using each initial guess for all the groups of time-delays to analyze the effect of error in time-delay on accuracy of PD source localization. The error in time-delay greatly affects the AEPD source localization. Moreover, if Newton's method with a bad initial guess is used then the errors in AEPD source localizations are not systematic.

The brain-to-skull conductivity ratio (BSCR) is an important parameter in EEG source imaging and localization. Misspecification of this value may introduce localization errors in the estimation of brain electrical activity. However, the effect of this ratio has not been well understood despite many investigations. In the present study, we conducted a series of computer simulations to investigate the relationship between BSCR and EEG source localization accuracy. Furthermore, we have attempted to correlate the localization accuracy of epileptogenic regions with the BSCR in epilepsy patients. Our results indicate that the dipole localization errors ranged from 10 to 20 mm. The localization accuracy resulting when the conductivity ratio used in the inverse calculation was set at 20 was better than those resulting when the ratio was set at 80 in epilepsy patients with a deep tumor. Future work is needed to validate this finding by experimental investigations in a large patient population.

Passive source localization plays a critical role in understanding subsurface stress dynamics during hydraulic fracturing, assessing seismic risks, and exploring mineral resources. However, existing passive source localization methods often face challenges such as high computational costs, reliance on high‐quality data, and the need for large‐scale training data sets, which limits their practical application. To overcome these limitations, we propose a physics‐constrained deep operator network model (PhysLoc‐DeepONet) designed to address performance degradation in scenarios with sparse or low‐quality data. The model integrates physical constraints with deep learning techniques to achieve efficient and accurate source localization using limited seismic data. Compared with existing methods, PhysLoc‐DeepONet accounts for data sparsity in its network architecture and introduces innovations in training data set construction and loss function optimization, thereby maintaining high localization accuracy even under limited data conditions. Multiple numerical simulations and field tests are conducted based on microseismic monitoring scenarios to validate the effectiveness of the proposed method. Experimental results demonstrate that the model not only achieves fast ( s), high‐precision source localization in complex geological environments but also exhibits strong adaptability to various monitoring conditions and data quality levels. Further analysis indicates that incorporating additional physical information and data constraints can further enhance localization accuracy, yielding satisfactory results even under resource‐limited conditions. With its solid theoretical foundation and broad applicability, PhysLoc‐DeepONet enables efficient, accurate, and cost‐effective real‐time source localization, showing strong promise for practical implementation.

The use of audio systems that employ binaural synthesis with head tracking has become increasingly popular, particularly in virtual reality gaming systems. The binaural synthesis process uses the Head-Related Transfer Functions (HRTF) as an input required to assign the directions of arrival to sounds coming from virtual sound sources in the created virtual environments. Generic HRTFs are often used for this purpose to accommodate all potential listeners. The hypothesis of the research is that the use of individual HRTF in binaural synthesis instead of generic HRTF leads to improved accuracy and quality of virtual sound source localization, thus enhancing the user experience. A novel methodology is proposed that involves the use of dynamic virtual sound sources. In the experiments, the test participants were asked to determine the direction of a dynamic virtual sound source in both the horizontal and vertical planes using both generic and individual HRTFs. The gathered data are statistically analyzed, and the accuracy of localization is assessed with respect to the type of HRTF used. The individual HRTFs of the test participants are measured using a novel and efficient method that is accessible to a broad range of users.

Accurate localization of multiple sound sources is indispensable for the microphone array-based high quality sound capture. For single sound source localization, the CSP (cross-power spectrum phase analysis) method has been proposed. The CSP method localizes a sound source as a crossing point of sound directions estimated using different microphone pairs. However, when localizing multiple sound sources, the CSP method has a problem that the localization accuracy is degraded due to cross-correlation among different sound sources. To solve this problem, this paper proposes a new method which suppresses the undesired cross-correlation by synchronous addition of CSP coefficients derived from multiple microphone pairs. Experiment results in a real room showed that the proposed method improves the localization accuracy when increasing the number of the synchronous addition.

The orthogonal imaging method is commonly used for source localization in brachytherapy. In some cases, however, difficulty is encountered in determining the dummy sources because of the presence of either contrast materials or bony structures. We here offer a novel method for source localization utilizing a dual-energy, radiographic technique. In this approach, two sets of orthogonal radiographic images (anterior-posterior and lateral views) are obtained using two different x-ray energies. Image processing (i.e., subtraction between two image sets) is carried out to enhance the source image. In a study performed using a laboratory developed pelvic phantom, it was demonstrated that the dual-energy method could significantly enhance the image quality of the dummy sources, and improve the achievable precision and relative accuracy in localization of source positions. When directly combined with digital imaging modalities, the dual-energy method can be a useful technique to improve the accuracy in brachytherapy source localization from planar radiographs.

Background: Electroencephalography (EEG) may be used as an objective diagnosis tool for diagnosing various disorders. Recently, source localization from EEG is being used in the analysis of real-time brain monitoring applications. However, inverse problem reduces the accuracy in EEG signal processing systems. Objectives: This paper presents a new method of EEG source localization using variational mode decomposition (VMD) and standardized the low resolution brain electromagnetic tomography (sLORETA) inverse model. The focus is to compare the effectiveness of the proposed approach for EEG signals of depression patients. Method: As the first stage, real EEG recordings corresponding to depression patients are decomposed into various mode functions by applying VMD. Then, closely related functions are analyzed using the inverse modelling-based source localization procedures such as sLORETA. Simulations have been carried out on real EEG databases for depression to demonstrate the effectiveness of the proposed techniques. Results: The performance of the algorithm has been assessed using localization error (LE), mean square error and signal to noise ratio output corresponding to simulated EEG dipole sources and real EEG signals for depression. In order to study the spatial resolution for cortical potential distribution, the main focus has been on studying the effects of noise sources and estimating LE of inverse solutions. More accurate and robust localization results show that this methodology is very promising for EEG source localization of depression signals. Conclusion: It can be said that proposed algorithm efficiently suppresses the influence of noise in the EEG inverse problem using simulated EEG activity and EEG database for depression. Such a system may offer an effective solution for clinicians as a crucial stage of EEG pre-processing in automated depression detection systems and may prevent delay in diagnosis.

Background:Magnetoencephalography (MEG) based on optically pumped magnetometers (OPMs) opens up new opportunities for brain research. However, OPM recordings are associated with artifacts. We describe a new artifact reduction method, frequency specific signal space classification (FSSSC), to improve the signal-to-noise ratio of OPM recordings.Methods:FSSSC was based on time-frequency analysis and signal space classification (SSC). SSC was accomplished by computing the orthogonality of the brain signal and artifact. A dipole phantom was used to determine if the method could remove artifacts and improve accuracy of source localization. Auditory evoked magnetic fields (AEFs) from human subjects were used to assess the usefulness of artifact reduction in the study of brain function because bilateral AEFs have proven a good benchmark for testing new methods. OPM data from empty room recordings were used to estimate magnetic artifacts. The effectiveness of FSSSC was assessed in waveforms, spectrograms, and covariance domains.Results:MEG recordings from phantom tests show that FSSSC can remove artifacts, normalize waveforms, and significantly improve source localization accuracy. MEG signals from human subjects show that FSSC can reveal auditory evoked magnetic responses overshadowed and distorted by artifacts. The present study demonstrates FSSSC is effective at removing artifacts in OPM recordings. This can facilitate the analyses of waveforms, spectrograms, and covariance. The accuracy of source localization of OPM recordings can be significantly improved by FSSSC.Conclusions:Brain responses distorted by artifacts can be restored. The results of the present study strongly support that artifact reduction is very important in order for OPMs to become a viable alternative to conventional MEG.

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Equivalent dipole source localization is a well-established approach to localizing the electrical activity in electroencephalogram (EEG). So far, source localization has been used primarily in localizing the epileptic source in human epileptic patients. Currently, source localization techniques have been applied to account for localizing epileptic source among the epileptic patients. Here, we present the first application of source localization in the field of sleep spindle in mouse brain. The spatial distribution of cortical potential was obtained by high density EEG and then the anterior and posterior sleep spindles were classified based on the K-mean clustering algorithm. To solve the forward problem, a realistic geometry brain model was produced based on boundary element method (BEM) using mouse MRI. Then, we applied four different source estimation algorithms (minimum norm, eLORETA, sLORETA, and LORETA) to estimate the spatial location of equivalent dipole source of sleep spindles. The estimated sources of anterior and posterior spindles were plotted in a cine-mode that revealed different topographic patterns of spindle propagation. The characterization of sleep spindles may be better be distinguished by our novel visualization method.