Bart Vanrumste

Dipole location errors in electroencephalogram source analysis due to volume conductor model errors

An examination is made of dipole location errors in electroencephalogram (EEG) source analysis, due to not incorporating the ventricular system (VS), omitting a hole in the skull and underestimating skull conductivity. The simulations are performed for a large number of test dipoles in 3D using the finite difference method. The maximum dipole location error encountered, utilising 27 and 53 electrodes is 7.6 mm and 6.1 mm, respectively when omitting the VS, 5.6 mm and 5.2 mm, respectively when neglecting the hole in the skull, and 33.4 mm and 28.0 mm, respectively when underestimating skull conductivity. The largest location errors due to neglecting the VS can be found in the vicinity of the VS. The largest location erros due to omitting a hole can be found in the vicinity of the hole. At these positions the fitted dipoles are found close to the hole. When skull conductivity is underestimated, the dipole is fitted close to the skull-brain border in a radial direction for all test dipoles. It was found that the location errors due to underestimating skull conductivity are typically higher than those found due to neglecting the VS or neglecting a hole in the skull.

The Validation of the Finite Difference Method and Reciprocity for Solving the Inverse Problem in EEG Dipole Source Analysis

The performance of the finite difference reciprocity method (FDRM) to solve the inverse problem in EEG dipole source analysis is investigated in the analytically solvable three-shell spherical head model for a large set of test dipoles. The location error for a grid with 2 mm and 3 mm node spacing is in general, not larger than twice the internode distance, hence 4 mm and 6 mm, respectively. Increasing the number of scalp electrodes from 27 to 44 only marginally improves the location error. The orientation error is always smaller than 4° for all the test dipoles considered. We have also compared the sensitivity to noise using FDRM in EEG dipole source analysis with the sensitivity to noise using the analytical expression for the forward problem. FDRM is not more sensitive to noise than the method using the analytical expression.

Ictal Source localization in presurgical patients with refractory epilepsy

Summary Source localization of epileptic foci using ictal spatiotemporal dipole modeling (ISDM) yields reliable anatomic information in presurgical candidates. It requires substantial resources from EEG and neuroimaging laboratories. The profile and number of patients who may benefit from it are currently unknown. The purpose of this study is to demonstrate the clinical usefulness of source localization in a prospectively analyzed series. One hundred patients (51 male and 49 female patients) with mean age of 31 years (range, 2 to 63 years) and mean duration of refractory epilepsy of 20 years (range, 1 to 49 years) were enrolled consecutively in a presurgical protocol. Ictal EEG was available in 93 patients. ISDM was performed when suitable ictal EEG files were available. The clinical applicability of ISDM was examined in three patients groups: 37 patients in whom ictal EEG recording and MRI were congruent (group I), 30 patients in whom results were not completely congruent but not incongruent (group II), and 26 patients in whom the results were incongruent (group III). ISDM could be performed in 31 of 100 patients: 11 in group I, 8 in group II, and 12 in group III. ISDM influenced decision making in none of the patients in group I, in 4 of 8 patients in group II, and in 10 of 12 patients in group III. Typically, the results of ISDM directed avoiding intracranial EEG recordings in what appeared to be unsuitable candidates for resection by clearly confirming the incongruency between ictal EEG and MRI findings. In this series of 100 presurgical candidates, ictal source localization could be performed in 31% of patients. In 14% of patients, it proved to be a key element in the surgical decision process.

Influence of measurement noise and electrode mislocalisation on EEG dipole-source localisation

Measurement noise in the electro-encephalogram (EEG) and inaccurate formation about the locations of the EEG electrodes on the head induce localisation errors in the results of EEG dipole source analysis. These errors are studied by performing dipole source localisation for simulated electrode potentials in a spherical head model, for a range of different dipole locations and for two different numbers (27 and 148) of electrodes. Dipole source localisation is performed by iteratively minimising the residual energy (RE), using the simplex algorithm. The ratio of the dipole localisation error (cm) to the noise level (%) of Gaussian measurement noise amounts to 0.15 cm/% and 0.047 cm/% for the 27 and 148 electrode configurations, respectively, for a radial dipole with 40% eccentricity The localisation error due to noise can be reduced by taking into account multiple time instants of the measured potentials. In the case of random displacements of the EEG electrodes, the ratio of dipole localisation errors to electrode location errors amounts to 0.78 cm−1 cm and 0.27 cm−1 cm for the 27 and 148 electrode configurations, respectively. It is concluded that it is important to reduce the measurement noise, and particularly the electrode mislocalisation, as the influence of the latter is not reduced by taking into account multiple time instants.

Comparison of performance of spherical and realistic head models in dipole localization from noisy EEG

The performance of a three-shell spherical head model versus the performance of a realistic head model is investigated when solving the inverse problem with a single dipole, in the presence of noise. This is evaluated by calculating the average dipole location error for 1000 noisy scalp potential sets, originating from the same test dipole and having the same noise level. The average location errors are obtained utilizing a local linearization, which is validated with a Monte-Carlo simulation. When the difference between the average location error utilizing a spherical and a realistic head model, represented by deltaR, is large for a large number of test dipoles, then it is worth using the more computationally demanding realistic head model. However, if deltaR is small for a large number of test dipoles, then it does not matter which model is used. For 27 electrodes, an electroencephalogram (EEG) epoch of one time sample and spatially white Gaussian noise, we found that the importance of the realistic head model over the spherical head model reduces by increasing the noise level. We further found that increasing the number of scalp electrodes from 27 to 44 has limited impact on the importance of the realistic head model over the spherical head model in EEG dipole source analysis. By increasing the number of time samples to six, the performance of the realistic head model in the inverse calculation gains importance compared with the three-shell spherical head model. Finally, we used spatially and temporally correlated background EEG instead of Gaussian noise. The advantage of the realistic head model over the spherical head model is reduced when applying correlated noise compared to Gaussian noise.

EEG dipole source localization using artificial neural networks

Localization of focal electrical activity in the brain using dipole source analysis of the electroencephalogram (EEG), is usually performed by iteratively determining the location and orientation of the dipole source, until optimal correspondence is reached between the dipole source and the measured potential distribution on the head. In this paper, we investigate the use of feed-forward layered artificial neural networks (ANNs) to replace the iterative localization procedure, in order to decrease the calculation time. The localization accuracy of the ANN approach is studied within spherical and realistic head models. Additionally, we investigate the robustness of both the iterative and the ANN approach by observing the influence on the localization error of both noise in the scalp potentials and scalp electrode mislocalizations. Finally, after choosing the ANN structure and size that provides a good trade off between low localization errors and short computation times, we compare the calculation times involved with both the iterative and ANN methods. An average localization error of about 3.5 mm is obtained for both spherical and realistic head models. Moreover, the ANN localization approach appears to be robust to noise and electrode mislocations. In comparison with the iterative localization, the ANN provides a major speed-up of dipole source localization. We conclude that an artificial neural network is a very suitable alternative for iterative dipole source localization in applications where large numbers of dipole localizations have to be performed, provided that an increase of the localization errors by a few millimetres is acceptable.

Comparing iterative solvers for linear systems associated with the finite difference discretisation of the forward problem in electro-encephalographic source analysis

Model-based reconstruction of electrical brain activity from electro-encephalographic measurements is of growing importance in neurology and neurosurgery. Algorithms for this task involve the solution of a 3D Poisson problem on a realistic head geometry obtained from medical imaging. In the model, several compartments with different conductivities have to be distinguished, leading to a problem with jumping coefficients. Furthermore, the Poisson problem needs to be solved repeatedly for different source contributions. Thus efficient solvers for this subtask are required. Experience with different iterative solvers is reported, i.e. successive over-relaxation, (preconditioned) conjugate gradients and algebraic multigrid, for a discretisation based on cell-centred finite differences. It was found that: first, the multigrid-based solver performed the task 1.8–3.5 times faster, depending on the platform, than the second-best contender; secondly, there was no need to introduce a reference potential that forced a unique solution; and, thirdly, neither the grid-nor matrix-based implementation of the solvers consistently gave a smaller run time.

Automatic localization of EEG electrode markers within 3D MR data

The electrical activity of the brain can be monitored using ElectroEncephaloGraphy (EEG). From the positions of the EEG electrodes, it is possible to localize focal brain activity. Thereby, the accuracy of the localization strongly depends on the accuracy with which the positions of the electrodes can be determined. In this work, we present an automatic, simple, and accurate scheme that detects EEG electrode markers from 3D MR data of the human head.

Detection of focal epileptiform activity in the EEG: an SVD and dipole model approach

An algorithm has been developed for detection of epileptiform activity in the EEG. The EEG is divided into overlapping epochs, which undergo two steps. The first is singular value decomposition (SVD) which identifies the number of uncorrelated active sources in an epoch. In the second step, EEG dipole source analysis, using a single dipole model, is applied to the EEG. This yields dipole parameters and a relative residual energy (RRE). The detection algorithm triggers an EEG epoch when SVD indicates a dominant source and the RRE is low. The algorithm is applied to simulated EEG generated by two sources which are synchronously and asynchronously active. For the synchronous case the critical measure is the RRE whereas for the asynchronous case both the SVD and RRE are critical. The algorithm has also been applied to real EEG containing two spikes and an eye-blink artifact. The SVD indicated a dominant active source and the RRE was low for all three events. These preliminary results demonstrate the potential of the method for detection of spikes and seizures with a focal origin.

Inverse calculations in EEG source analysis applying the finite difference method, reciprocity and lead fields

The advances in computer power and memory make the finite difference method (FDM) attractive to solve the Poison differential equation. To reduce the calculation time of the inverse procedure in EEG source analysis, the concept of lead fields in combination with the reciprocity theorem are utilized. First the accuracy of the finite difference method is evaluated in a three-shell spherical head model. The potentials at the 27 EEG scalp electrodes are obtained using the FDM in a cubic grid with node spacing of 2.5 mm. The inverse problem is solved applying the analytical expression. The mean localization error is 2 mm (ranging from 0.3 to 4.5 mm for 18 dipoles). Next, the potentials at the electrodes are given by the analytical expression. The inverse fit is then done utilizing 26 lead fields calculated numerically in a cubic grid with node spacing of 4 mm. The mean localization error is 4.1 mm (ranging from 1.2 mm to 7 mm for 18 dipoles). Finally a realistic head model is used. The potentials at the electrodes, obtained numerically in a grid with node spacing of 2.5 mm, are brought in the inverse procedure. 26 lead fields calculated numerically in a grid with node spacing of 4 mm, are then applied to perform the inverse calculations. The mean localization error is 4 mm (ranging from 0.9 to 7.2 mm for 12 dipoles). These result suggest that the FDM in combination with the lead field concept can be used for EEG source analysis.