A systematic evaluation of the spherical model accuracy in EEG dipole localization

This paper presents a study of the intrinsic localization error bias due to the use of a spherical geometry model on EEG simulated data obtained from realistically shaped models. About 2000 dipoles were randomly chosen on the segmented cortex surface of a particular subject. Forward calculations were performed using a uniformly meshed model for each dipole located at a depth greater than 20 mm below the brain surface, and locally refined models were used for shallower dipoles. Inverse calculations were performed using four different spherical models and another uniformly meshed model. It was found that the best spherical model lead to localization errors of 5–6 mm in the upper part of the head, and of 15–25 mm in the lower part. The influence of the number of electrodes upon this intrinsic bias was also studied. It was found that using 32 electrodes instead of 19 improves the localization by 2.7 mm on average, while using 63 instead of 32 electrodes lead to improvements of less than 1 mm. Finally, simulations involving two simultaneously active dipoles (one in the vicinity of each auditory cortex) show localization errors increasing by about 2–3 mm.     

A study of dipole localization accuracy for MEG and EEG using a human skull phantom

Objective: To investigate the accuracy of forward and inverse techniques for EEG and MEG dipole localization.Design and Methods: A human skull phantom was constructed with brain, skull and scalp layers and realistic relative conductivities. Thirty two independent current dipoles were distributed within the `brain' region and EEG and MEG data collected separately for each dipole. The true dipole locations and orientations and the morphology of the brain, skull and scalp layers were extracted from X-ray CT data. The location of each dipole was estimated from the EEG and MEG data using the R-MUSIC inverse method and forward models based on spherical and realistic head geometries. Additional computer simulations were performed to investigate the factors affecting localization accuracy.Results: Localization errors using the relatively simpler locally fitted sphere approach are only slightly greater than those using a BEM approach. The average localization error over the 32 dipoles was 7–8 mm for EEG and 3 mm for MEG.Conclusion: The superior performance of MEG over EEG appears to be because the latter is more sensitive to errors in the forward model arising from simplifying assumptions concerning the conductivity of the skull, scalp and brain.     

A standardized boundary element method volume conductor model.

OBJECTIVES: We used a 3-compartment boundary element method (BEM) model from an averaged magnetic resonance image (MRI) data set (Montreal Neurological Institute) in order to provide simple access to realistically shaped volume conductor models for source reconstruction, as compared to individually derived models. The electrode positions were transformed into the model's coordinate system, and the best fit dipole results were transformed back to the original coordinate system. The localization accuracy of the new approach was tested in a comparison with simulated data and with individual BEM models of epileptic spike data from several patients. METHODS: The standard BEM model consisted of a total of 4770 nodes, which describe the smoothed cortical envelope, the outside of the skull, and the outside of the skin. The electrode positions were transformed to the model coordinate system by using 3-5 fiducials (nasion, left and right preauricular points, vertex, and inion). The transformation consisted of an averaged scaling factor and a rigid transformation (translation and rotation). The potential values at the transformed electrode positions were calculated by linear interpolation from the stored transfer matrix of the outer BEM compartment triangle net. After source reconstruction the best fit dipole results were transformed back into the original coordinate system by applying the inverse of the first transformation matrix. RESULTS: Test-dipoles at random locations and with random orientations inside of a highly refined reference BEM model were used to simulate noise-free data. Source reconstruction results using a spherical and the standardized BEM volume conductor model were compared to the known dipole positions. Spherical head models resulted in mislocation errors at the base of the brain. The standardized BEM model was applied to averaged and unaveraged epileptic spike data from 7 patients. Source reconstruction results were compared to those achieved by 3 spherical shell models and individual BEM models derived from the individual MRI data sets. Similar errors to that evident with simulations were noted with spherical head models. Standardized and individualized BEM models were comparable. CONCLUSIONS: This new approach to head modeling performed significantly better than a simple spherical shell approximation, especially in basal brain areas, including the temporal lobe. By using a standardized head for the BEM setup, it offered an easier and faster access to realistically shaped volume conductor models as compared to deriving specific models from individual 3-dimensional MRI data.     

The influence of electrode location errors on EEG dipole source localization with a realistic head model.

OBJECTIVES: Inaccurate information about the electrode locations on the scalp will introduce errors in electroencephalogram dipole source localization results. The present study uses computer simulations to evaluate such errors in a realistic head model and in the context of noise. METHODS: A realistic head model was constructed from magnetic resonance imaging scans and 29 electrodes placed on the head according to the 10-20 International System. Twenty sets of electrode displacements, with a mean value of 5 mm, were generated and 200 single dipoles evenly located in the brain were used as test sources. The boundary element method was employed for the forward calculation and dipole fitting was carried out at different noise levels. RESULTS: For a noise-free signal, the source localization error due to electrode misplacement is about 5 mm, whereas it is about 2 mm for normal noisy signals. CONCLUSIONS: For realistic head models, dipole estimation error due to electrode misplacement is negligible compared with errors caused by noise.     

Experimental tests of EEG source localization accuracy in spherical head models.

OBJECTIVES: The locations of electrical sources in the brain can be calculated using EEG data. However, the accuracy of these calculations is not well known because it is usually not possible to compare calculated source locations with actual locations since little accurate location information is available about most sources in the brain. METHODS: In this study, sources at known locations are created by injecting current into electrodes implanted in the brains of human subjects. The locations of the implanted and scalp EEG electrodes are determined from CTs. The EEG signals produced by these dipolar sources are used to calculate source locations in spherical head models containing brain, skull, and scalp layers. The brain and scalp layers have the same electrical conductivity while 3 different skull conductivity ratios of 1/80th, 1/40th, and 1/20th of brain and scalp conductivity are used. Localization errors have been determined for 177 sources in 13 subjects. RESULTS: An average localization error of 10.6 (SD=5.5) mm for all 177 source was obtained for a skull conductivity ratio of 1/40. The average errors for the other ratios are only a few millimeters larger. The average localization error for 108 sources at superior locations in the brain is 9.2 (4.4) mm. The average error for 69 inferior location sources is 12.8 (6.2) mm. There are no significant differences in localization accuracy for deep and superficial sources. CONCLUSIONS: These results indicate that the best average localization that can be achieved using a spherical head model is approximately 10 mm. More realistic head models will be required for greater localization accuracy.     

Source reconstruction of mesial-temporal epileptiform activity: comparison of inverse techniques

PURPOSE: To evaluate whether advanced source reconstruction such as current density reconstruction (CDR) provides additional hints for clinical presurgical evaluation, different source reconstruction techniques with idealized spherical as well as realistically shaped head models (boundary element method, BEM) were applied on interictal and ictal epileptiform activity in presurgical evaluated patients with temporal lobe epilepsy. It is discussed whether CDR and BEM give additional information for presurgical evaluation compared to "conventional" strategies, such as single moving, and spatio-temporal dipole modeling with spherical head models. METHODS: A variety of source reconstruction procedures were applied to the data of five patients with pharmacoresistent temporal lobe epilepsy with probable mesial origin: (1) single-moving dipole in a spherical head model and (2) in BEM, (3) spatio-temporal dipole modeling in a spherical head model and (4) in BEM; and (5) deconvolution with fixed locations and orientations and (6) with cortically constrained L1-norm CDR in BEM. In addition, simulated sources of temporal lobe origin were calculated in each subject with CDR to prove the basic feasibility of this technique in the particular application. RESULTS: Source activity was correctly localized within the affected temporal lobe by all source reconstruction techniques used. Neither single moving dipole, spatio-temporal modeling, nor CDR was able to localize sources at a sublobar level. In the case of two sources, single moving dipole solutions showed changes in dipole orientation in time and spatio-temporal modeling separated two sources, whereas CDR at the peak latency failed to distinguish among different origins. BEM enhanced localization accuracy. CONCLUSION: There was no advantage of using CDR. Single moving dipole as well as spatio-temporal dipole modeling in BEM leads to more precise localization within the individual anatomy and provides a simple algorithm, which is capable of indicating both the time course and the number of sources.     

Modeling of post-surgical brain and skull defects in the EEG inverse problem with the boundary element method.

OBJECTIVES: In order to obtain accurate EEG inverse solutions in patients subjected to surgery, we have studied the feasibility and influence of incorporating brain and skull defects in realistic head models. METHODS: We first measured the conductivity of the methacrylate used for cranioplasty. Then, we designed realistic boundary element method head models with a skull burr hole, a methacrylate plug or a temporal-lobe resection. We simulated the potentials that would be produced at 71 electrode locations (10/10 system) by dipoles located near the defects. Then, we fitted dipoles on these potentials using a defect-free head model. We also ran simulations in a noisy situation and with higher skull and cerebrospinal fluid (CSF) conductivity. RESULTS: The largest errors were found for burr holes, with a localization error up to 20 mm for a radial dipole located 30 mm below the hole and an amplification factor of 8. Methacrylate plugs lead to errors up to 5 mm and 0.5; the resection only lead to errors of 2 mm and 1.3. Results obtained with noise were consistent with those obtained without noise. Doubling the skull conductivity led to errors that were reduced by 10-20%, while doubling CSF conductivity increased the errors by up to 31%. CONCLUSIONS: We have shown that it is important to incorporate skull defects in realistic head models when sources are located near the defects and precision is sought. Brain cavities of the size of a typical anterior temporal lobe resection may be omitted without a significant impact on dipole localization.     

Interictal spike localization using a standard realistic head model: simulations and analysis of clinical data.

OBJECTIVES: In this paper realistic and standard realistic head models were applied to neural source localization. METHODS: Three different triangulated head structures; the brain, the skull and the scalp were constructed from MRI information of each patient. For each subject the exact positions of the electrodes were digitized. RESULTS: The influence of the number of triangles and of the skull conductivity on the accuracy of the method was tested. The use of a standard realistic head model instead of spherical models is proposed in cases where detailed MRI information is not available, and the accuracy of this procedure is tested with dipole simulations. These techniques were applied also to EEG signals from 3 patients with focal epilepsy. In all cases the neural activity was assumed to be confined to a small portion of cortical tissue, so that the neural generator was approximated to a current dipole. The realistic head model localization is discussed on the basis of neuroimaging information. CONCLUSIONS: We show that the standard realistic head model is two or 3 times better than the spherical model for dipole localization and we propose it as a good alternative to the spherical model for EEG data processing, in cases where full MRI information is not available.     

The 3D topography of MEG source localization accuracy: effects of conductor model and noise.

OBJECTIVE: To evaluate the effect that different head conductor models have on the source estimation accuracy of magnetoencephalography (MEG) under realistic conditions. METHODS: Magnetic fields evoked by current dipoles were simulated using a highly refined 3-layer realistically shaped conductor model. Noise from a real MEG measurement was added to the simulated fields. Source parameters (location, strength, orientation) were estimated from the noisy signals using 3 spherically symmetric models and several one- and 3-layer realistically shaped boundary-element models. The effect of different measurement sensors (gradiometers, magnetometers) was also tested. RESULTS: The noise typically present in brain signals masked the errors due to the different conductor models so that in most situations the models gave comparable results. Active cortical areas around the vertex and in the temporal, frontoparietal, and occipital regions were typically found with 2-4 mm accuracy, whereas source localization in several anterior frontal lobe and deep brain structures yielded errors exceeding 2 cm. Localization in anterior frontal regions may benefit most from the use of realistically shaped models. CONCLUSIONS: The traditionally used sphere model is an adequate model for most research purposes. Any means that increase the signal-to-noise ratio are of highest importance in attempting to improve the source estimation accuracy.     

Experimental tests of EEG source localization accuracy in realistically shaped head models

OBJECTIVES: To determine the accuracy with which electrical sources in the human brain can be located using realistically shaped boundary element models of the head and to compare this accuracy with that using spherical head models. METHODS: In a previous study, electroencephalographs (EEGs) produced by sources at known locations in the brains of human subjects were recorded. The sources were created by injecting current into implanted depth electrodes. The locations of the implanted depth and scalp EEG electrodes and head shape were determined from computerized tomography images. The EEGs were used to calculate source locations in spherical head models and localization accuracy was determined by comparing the calculated and actual locations. In this study, these same EEGs are used to determine localization accuracy in realistically shaped head models. RESULTS: An average localization error of 10.5 (SD=5.4) mm was obtained in the realistically shaped models for all 176 sources in 13 subjects. This compares with 10.6 (5.5) mm in the spherical models. The average localization error for 105 sources at superior locations in the brain is 9.1 (4.2) mm. The average error for 71 inferior location sources is 12.4 (6.4) mm. The corresponding values for the spherical models are 9.2 (4.4) and 12.8 (6.2) mm. CONCLUSIONS: The realistically shaped head boundary element models used in this study produced very nearly the same localization accuracy as spherical models.     

Spatial relationship of source localizations in patients with focal epilepsy: Comparison of MEG and EEG with a three spherical shells and a boundary element volume conductor model

Epilepsy surgery is an option for patients with pharmacoresistant focal epilepsies, but it requires a precise focus localization procedure. Magnetoencephalography (MEG) and electroencephalography (EEG) can be used for analysis of interictal activity. The aim of this prospective study was to compare clusters of source localization results with MEG and EEG using a three spherical shells (3SS) and a boundary element method (BEM) volume conductor model. The study was closed when 100 patients met the inclusion criteria. Simultaneous MEG and EEG were recorded during presurgical evaluation. Epileptiform signals were analyzed using an equivalent current dipole model. Centroids of source localizations from MEG, EEG, 3SS, and BEM in their respective combinations were compared. In a 3SS model, MEG source localizations were 5.6 mm inferior to those obtained by EEG, while in a BEM model MEG source localizations were 6.3 mm anterior and 4.8 mm superior. The mean scattering of source localizations between both volume conductor models was 19.5 mm for EEG and 9.6 mm for MEG. For MEG no systematic difference between BEM and 3SS source localizations was found. For EEG, source localizations with BEM were 5.9 mm posterior and 11.7 mm inferior to those determined using 3SS. No differences were found between the 46 temporal and the 54 extratemporal lobe epilepsy patients. The observed systematic differences of source localizations of epileptic spikes due to the applied source signal modality and volume conductor model should be considered in presurgical evaluation when only one source signal and volume conductor model is available.     

Accuracy of EEG dipole source localization using implanted sources in the human brain.

OBJECTIVES: The location of electrical sources in the brain can be estimated by calculating inverse solutions in which the location, amplitude and orientation of the electrical sources are fitted to the scalp EEG. To assess localization accuracy of the moving dipole inverse solution algorithm (ISA), we studied two patients who had depth electrodes implanted for presurgical planning of epilepsy surgery. METHODS: Artificial dipoles were created by connecting a single sine wave pulse generator to different pairs of electrodes in multiple orientations and depths. Surface EEG recordings of the resulting pulses were evaluated with the ISA using a 4-shell spherical head model and plotted on the subjects' MRI. Dipole localization errors were evaluated with respect to the number of averaged pulses, different electrode montages and different dipole locations and orientations. RESULTS: Dipoles located at 40-57 mm from the scalp surface had localization errors that were greater than those located at 62-85 mm. Localization accuracy improved with increasing numbers of pulses and recording electrodes. Results with a standard 10-20 array of 21 electrodes showed an average localization error of 17 mm, whereas 41 electrodes improved this to 13 mm. Mean angular errors were 31 and 30 degrees, respectively. CONCLUSIONS: The ISA was able to differentiate between tangential and radial dipoles. We conclude that our implementation of the ISA is a useful and sound method for localizing electrical activity in the brain.     

Improving lesion conductivity estimate by means of EEG source localization sensitivity to model parameter.

EEG-based source localization techniques use scalp-potential data to estimate the location of underlying neural activity. EEG source location reconstruction requires the assumption of a source model and the assumption of a conductive head model. Brain lesions can present conductivity values that are dramatically different from those of surrounding normal tissues and have to be included in head models for accurate neural source reconstruction. It is therefore necessary to analyze subjects' anatomic images (using MRI or computed tomography) to identify lesion type and to assign the appropriate conductivity value. Source localization accuracy may be influenced by uncertainties in tissue conductivity assignment during head model construction. The authors present a sensitivity study quantifying the effect of uncertainty in brain lesion conductivity assignment on EEG dipole source localization. They adopted an eccentric-spheres head model in which an eccentric bubble approximated the effects of actual brain lesions. After simulating EEG signal measurement in 64 different pathologic situations, an inverse dipole fitting procedure was carried out, assuming an incorrect lesion conductivity assignment ranging from a half to twice the real value. Incorrect lesion conductivity assignment led to markedly wrong source reconstruction for highly conductive lesions like liquid-filled ones (localization errors as much as 1.7 cm). Conversely, low sensitivity to uncertainties in conductivity assignment was found for lesions with low conductivity like calcified tumors. The authors propose a method based on residual error analysis to improve the lesion conductivity estimate. This procedure can identify lesion tissue conductivity with only a few percent error and guarantees source localization errors less than 5 mm.     

Relationship of EEG sources of neonatal seizures to acute perinatal brain lesions seen on MRI: A pilot study

Even though it is known that neonatal seizures are associated with acute brain lesions, the relationship of electroencephalographic (EEG) seizures to acute perinatal brain lesions visible on magnetic resonance imaging (MRI) has not been objectively studied. EEG source localization is successfully used for this purpose in adults, but it has not been sufficiently explored in neonates. Therefore, we developed an integrated method for ictal EEG dipole source localization based on a realistic head model to investigate the utility of EEG source imaging in neonates with postasphyxial seizures. We describe here our method and compare the dipole seizure localization results with acute perinatal lesions seen on brain MRI in 10 full‐term infants with neonatal encephalopathy. Through experimental studies, we also explore the sensitivity of our method to the electrode positioning errors and the variations in neonatal skull geometry and conductivity. The localization results of 45 focal seizures from 10 neonates are compared with the visual analysis of EEG and MRI data, scored by expert physicians. In 9 of 10 neonates, dipole locations showed good relationship with MRI lesions and clinical data. Our experimental results also suggest that the variations in the used values for skull conductivity or thickness have little effect on the dipole localization, whereas inaccurate electrode positioning can reduce the accuracy of source estimates. The performance of our fused method indicates that ictal EEG source imaging is feasible in neonates and with further validation studies, this technique can become a useful diagnostic tool. Hum Brain Mapp 34:2402–2417, 2013. © 2012 Wiley Periodicals, Inc.     

Spatial mislocalization of EEG electrodes -- effects on accuracy of dipole estimation.

OBJECTIVE: The estimation of cortical current activity from scalp-recorded potentials is a complicated mathematical problem that requires fairly precise knowledge of the location of the scalp electrodes. It is expected that spatial mislocalization of electrodes will introduce errors in this estimation. The present study uses simulated and real data to quantify these errors for dipole current sources in a spherical head model. METHODS: A 3-dimensional digitizer was used to locate the positions of 31 scalp electrodes placed on the head according to the 10-20 system in 10 normal subjects. Dipole localizations were performed on auditory evoked potentials (AEPs) collected from these subjects. RESULTS: Computer simulations with several dipole source configurations suggest that errors in locations and orientations on the order of 5 mm and 5 degrees, respectively, are possible for electrode mislocalizations of about 5 degrees. In actual experimental settings, digitized electrode positions were typically mislocalized by an average of about 4 degrees from their standard 10-20 positions on a spherical model. These differences in electrode positions translated to mean differences of about 8 mm in dipole locations and 5 degrees in dipole orientations. CONCLUSIONS: Dipole estimation errors due to electrode mislocalizations are within the limits of errors due to other modeling approximations and noise.     

A computationally efficient method for accurately solving the EEG forward problem in a finely discretized head model.

OBJECTIVE: Solution of the forward problem using realistic head models is necessary for accurate EEG source analysis. Realistic models are usually derived from volumetric magnetic resonance images that provide a voxel resolution of about 1 mm3. Electrical models could, therefore contain, for a normal adult head, over 4 million elements. Solution of the forward problem using models of this magnitude has so far been impractical due to issues of computation time and memory. METHODS: A preconditioner is proposed for the conjugate-gradient method that enables the forward problem to be solved using head models of this magnitude. It is applied to the system matrix constructed from the head anatomy using finite differences. The preconditioner is not computed explicitly and so is very efficient in terms of memory utilization. RESULTS: Using a spherical head model discretized into over 4 million volumes, we have been able to obtain accurate forward solutions in about 60 min on a 1 GHz Pentium III. L2 accuracy of the solutions was better than 2%. CONCLUSIONS: Accurate solution of the forward problem in EEG in a finely discretized head model is practical in terms of computation time and memory. SIGNIFICANCE: The results represent an important step in head modeling for EEG source analysis.     

Fast realistic modeling in bioelectromagnetism using lead-field interpolation

The practical use of realistic models in bioelectromagnetism is limited by the time-consuming amount of numerical calculations. We propose a method leading to much higher speed than currently available, and compatible with any kind of numerical methods (boundary elements (BEM), finite elements, finite differences). Illustrated with the BEM for EEG and MEG, it applies to ECG and MCG as well. The principle is two-fold. First, a Lead-Field matrix is calculated (once for all) for a grid of dipoles covering the brain volume. Second, any forward solution is interpolated from the pre-calculated Lead-Fields corresponding to grid dipoles near the source. Extrapolation is used for shallow sources falling outside the grid. Three interpolation techniques were tested: trilinear, second-order Bézier (Bernstein polynomials), and 3D spline. The trilinear interpolation yielded the highest speed gain, with factors better than x10,000 for a 9,000-triangle BEM model. More accurate results could be obtained with the Bézier interpolation (speed gain approximately 1,000), which, combined with a 8-mm step grid, lead to intrinsic localization and orientation errors of only 0.2 mm and 0.2 degrees. Further improvements in MEG could be obtained by interpolating only the contribution of secondary currents. Cropping grids by removing shallow points lead to a much better estimation of the dipole orientation in EEG than when solving the forward problem classically, providing an efficient alternative to locally refined models. This method would show special usefulness when combining realistic models with stochastic inverse procedures (simulated annealing, genetic algorithms) requiring many forward calculations.     

Boundary element method volume conductor models for EEG source reconstruction.

OBJECTIVES: The boundary element method (BEM) approximates the different compartments of volume conductor models by closed triangle meshes with a limited number of nodes. The shielding effect of the weakly conducting skull layer of the human head leads to decreasing potential gradients from the inside to the outside. Thus, there may be an optimum distribution of nodes to the compartments for a given number of nodes corresponding to a fixed computational effort, resulting in improved accuracy as compared to standard uniform distributions. METHODS: Spherical and realistically shaped surfaces are approximated by 500, 1000, 2000, and 3000 nodes, each leading to BEM models with 1500-9000 nodes in total. Electrodes are placed on extended 10/20-system positions. Potential distributions of test-dipoles at 4000 random positions within the innermost compartment are calculated. Dipoles are then fitted using 192 different models to find the optimum node distribution. RESULTS: Fitted dipole positions for all BEM models are evaluated to show the dependency of the averaged and maximum localization errors on their node distributions. Dipoles close to the innermost boundary exhibit the largest localization errors, which mainly depend on the refinement of this compartment's triangle mesh. CONCLUSIONS: More than 500 nodes per compartment are needed for reliable BEM models. For a state-of-the-art model consisting of 6000 nodes overall, the best model consists of 3000, 2000, and 1000 nodes from the inside to the outside.     

MEG versus EEG localization test using implanted sources in the human brain

It is believed that the magnetoencephalogram (MEG) localizes an electrical source in the brain to within several millimeters and is therefore more accurate than electroencephalogram (EEG) localization, reported as 20 mm. To test this belief, the localization accuracy of the MEG and EEG were directly compared. The signal source was a dipole at a known location in the brain; this was made by passing a weak current pulse simulating a neural signal through depth electrodes already implanted in patients for seizure monitoring. First, MEGs and EEGs from this dipole were measured at 16 places on the head. Then, computations were performed on the MEG and EEG data separately to determine the apparent MEG and EEG source locations. Finally, these were compared with the actual source location to determine the MEG and EEG localization errors. Measurements were made of four dipoles in each of three patients. After MEGs with weak signals were discounted, the MEG average error of localization was found to be 8 mm, which was worse than expected. The average EEG error was 10 mm, which was better than expected. These results suggest that the MEG offers no significant advantage over the EEG in localizing a focal source. However, this does not diminish other uses of the MEG.