On the influence of volume currents and extended sources on neuromagnetic fields: a simulation study

Limiting parameter range for cortical-spherical mapping improves activated domain estimation for attention modulated auditory response

BACKGROUND

Attention is one of the factors involved in selecting input information for the brain. We applied a method for estimating domains with clear boundaries using magnetoencephalography (the domain estimation method) for auditory-evoked responses (N100m) to evaluate the effects of attention in milliseconds. However, because the surface around the auditory cortex is folded in a complicated manner, it is unknown whether the activity in the auditory cortex can be estimated.

NEW METHOD

The parameter range to express current sources was set to include the auditory cortex. Their search region was expressed as a direct product of the parameter ranges used in the adaptive diagonal curves.

RESULTS

Without a limitation of the range, activity was estimated in regions other than the auditory cortex in all cases. However, with the limitation of the range, the activity was estimated in the primary or higher auditory cortex. Further analysis of the limitation of the range showed that the domains activated during attention included the regions activated during no attention for the participants whose amplitudes of N100m were higher during attention.

COMPARISON WITH EXISTING METHOD

We proposed a method for effectively limiting the search region to evaluate the extent of the activated domain in regions with complex folded structures.

CONCLUSION

To evaluate the extent of activated domains in regions with complex folded structures, it is necessary to limit the parameter search range. The area of the activated domains in the auditory cortex may increase by attention on the millisecond timescale.

Shamo: A Tool for Electromagnetic Modeling, Simulation and Sensitivity Analysis of the Head

Accurate electromagnetic modeling of the head of a subject is of main interest in the fields of source reconstruction and brain stimulation. Those processes rely heavily on the quality of the model and, even though the geometry of the tissues can be extracted from magnetic resonance images (MRI) or computed tomography (CT), their physical properties such as the electrical conductivity are difficult to measure with non intrusive techniques. In this paper, we propose a tool to assess the uncertainty in the model parameters, the tissue conductivity, as well as compute a parametric forward models for electroencephalography (EEG) and transcranial direct current stimulation (tDCS) current distribution.

Magnetoencephalography and electroencephalography can both detect differences in cortical responses to vibrotactile stimuli in individuals on the autism spectrum

Autism Spectrum (AS) is defined primarily by differences in social interactions, with impairments in sensory processing also characterizing the condition. In the search for neurophysiological biomarkers associated with traits relevant to the condition, focusing on sensory processing offers a path that is likely to be translatable across populations with different degrees of ability, as well as into animal models and across imaging modalities. In a prior study, a somatosensory neurophysiological signature of AS was identified using magnetoencephalography (MEG). Specifically, source estimation results showed differences between AS and neurotypically developing (NTD) subjects in the brain response to 25-Hz vibrotactile stimulation of the right fingertips, with lower inter-trial coherence (ITC) observed in the AS group. Here, we examined whether these group differences can be detected without source estimation using scalp electroencephalography (EEG), which is more commonly available in clinical settings than MEG, and therefore offers a greater potential for clinical translation. To that end, we recorded simultaneous whole-head MEG and EEG in 14 AS and 10 NTD subjects (age 15-28 years) using the same vibrotactile paradigm. Based on the scalp topographies, small sets of left hemisphere MEG and EEG sensors showing the maximum overall ITC were selected for group comparisons. Significant differences between the AS and NTD groups in ITC at 25 Hz as well as at 50 Hz were recorded in both MEG and EEG sensor data. For each measure, the mean ITC was lower in the AS than in the NTD group. EEG ITC values correlated with behaviorally assessed somatosensory sensation avoiding scores. The results show that information about ITC from MEG and EEG signals have substantial overlap, and thus EEG sensor-based ITC measures of the AS somatosensory processing biomarker previously identified using source localized MEG data have a potential to be developed into clinical use in AS, thanks to the higher accessibility to EEG in clinical settings.

Automated ictal EEG source imaging: A retrospective, blinded clinical validation study

OBJECTIVE

EEG source imaging (ESI) is a validated tool in the multimodal workup of patients with drug resistant focal epilepsy. However, it requires special expertise and it is underutilized. To circumvent this, automated analysis pipelines have been developed and validated for the interictal discharges. In this study, we present the clinical validation of an automated ESI for ictal EEG signals.

METHODS

We have developed an automated analysis pipeline of ictal EEG activity, based on spectral analysis in source space, using an individual head model of six tissues. The analysis was done blinded to all other data. As reference standard, we used the concordance with the resected area and one-year postoperative outcome.

RESULTS

We analyzed 50 consecutive patients undergoing epilepsy surgery (34 temporal and 16 extra-temporal). Thirty patients (60%) became seizure-free. The accuracy of the automated ESI was 74% (95% confidence interval: 59.66-85.37%).

CONCLUSIONS

Automated ictal ESI has a high accuracy for localizing the seizure onset zone.

SIGNIFICANCE

Automating the ESI of the ictal EEG signals will facilitate implementation of this tool in the presurgical evaluation.

Variation in Reported Human Head Tissue Electrical Conductivity Values

Electromagnetic source characterisation requires accurate volume conductor models representing head geometry and the electrical conductivity field. Head tissue conductivity is often assumed from previous literature, however, despite extensive research, measurements are inconsistent. A meta-analysis of reported human head electrical conductivity values was therefore conducted to determine significant variation and subsequent influential factors. Of 3121 identified publications spanning three databases, 56 papers were included in data extraction. Conductivity values were categorised according to tissue type, and recorded alongside methodology, measurement condition, current frequency, tissue temperature, participant pathology and age. We found variation in electrical conductivity of the whole-skull, the spongiform layer of the skull, isotropic, perpendicularly- and parallelly-oriented white matter (WM) and the brain-to-skull-conductivity ratio (BSCR) could be significantly attributed to a combination of differences in methodology and demographics. This large variation should be acknowledged, and care should be taken when creating volume conductor models, ideally constructing them on an individual basis, rather than assuming them from the literature. When personalised models are unavailable, it is suggested weighted average means from the current meta-analysis are used. Assigning conductivity as: 0.41 S/m for the scalp, 0.02 S/m for the whole skull, or when better modelled as a three-layer skull 0.048 S/m for the spongiform layer, 0.007 S/m for the inner compact and 0.005 S/m for the outer compact, as well as 1.71 S/m for the CSF, 0.47 S/m for the grey matter, 0.22 S/m for WM and 50.4 for the BSCR.

A Finite Element Solution of the Forward Problem in EEG for Multipolar Sources

Multipolar source models have been presented in the context of electro/magnetoencephalography (E/MEG) to compensate for the limitations of the classical equivalent current dipole to represent realistic generators of brain activity. Although there exist several reports accounting for the advantages of multipolar components over single dipoles, there is still no available numerical implementation in fully personalized scenarios. In this paper, we present, for the first time, a finite element framework for simulating EEG signals generated by multipolar current sources in individualized, heterogeneous, and anisotropic head models. This formulation is based on the subtraction approach, guaranteeing the existence and uniqueness of the solution. In particular, we analyze the cases of monopolar, dipolar, and quadrupolar source components, for which we study their performance in idealized and realistic head models. Numerical solutions are compared with analytical formulas in multi-layered spherical models. Such formulas are available in the case of monopolar and dipolar sources, and here derived for the quadrupolar components. We finally illustrate their advantages in the description of extended current generators using a realistic head model. The framework presented here enables further analysis towards the estimation of biophysically principled source parameters from standard E/MEG experiments.

New Strategy for Finite Element Mesh Generation for Accurate Solutions of Electroencephalography Forward Problems

The finite element method (FEM) is a numerical method that is often used for solving electroencephalography (EEG) forward problems involving realistic head models. In this study, FEM solutions obtained using three different mesh structures, namely coarse, densely refined, and adaptively refined meshes, are compared. The simulation results showed that the accuracy of FEM solutions could be significantly enhanced by adding a small number of elements around regions with large estimated errors. Moreover, it was demonstrated that the adaptively refined regions were always near the current dipole sources, suggesting that selectively generating additional elements around the cortical surface might be a new promising strategy for more efficient FEM-based EEG forward analysis.

The Discontinuous Galerkin Finite Element Method for Solving the MEG and the Combined MEG/EEG Forward Problem

In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM) EEG forward approach has been proposed as an alternative to CG-FEM (Engwer et al., 2017). It was shown that DG-FEM preserves the property of conservation of charge and that it can, in certain situations such as the so-called skull leakages, be superior to the standard CG-FEM approach. In this paper, we developed, implemented, and evaluated two DG-FEM approaches for the MEG forward problem, namely a conservative and a non-conservative one. The subtraction approach was used as source model. The validation and evaluation work was done in statistical investigations in multi-layer homogeneous sphere models, where an analytic solution exists, and in a six-compartment realistically shaped head volume conductor model. In agreement with the theory, the conservative DG-FEM approach was found to be superior to the non-conservative DG-FEM implementation. This approach also showed convergence with increasing resolution of the hexahedral meshes. While in the EEG case, in presence of skull leakages, DG-FEM outperformed CG-FEM, in MEG, DG-FEM achieved similar numerical errors as the CG-FEM approach, i.e., skull leakages do not play a role for the MEG modality. In particular, for the finest mesh resolution of 1 mm sources with a distance of 1.59 mm from the brain-CSF surface, DG-FEM yielded mean topographical errors (relative difference measure, RDM%) of 1.5% and mean magnitude errors (MAG%) of 0.1% for the magnetic field. However, if the goal is a combined source analysis of EEG and MEG data, then it is highly desirable to employ the same forward model for both EEG and MEG data. Based on these results, we conclude that the newly presented conservative DG-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches in EEG or combined MEG/EEG source analysis scenarios, which motivates a further evaluation of DG-FEM for applications in bioelectromagnetism.

Electrical Stimulation of the Human Cerebral Cortex by Extracranial Muscle Activity: Effect Quantification With Intracranial EEG and FEM Simulations

OBJECTIVE

Electric fields (EF) of approx. 0.2 V/m have been shown to be sufficiently strong to both modulate neuronal activity in the cerebral cortex and have measurable effects on cognitive performance. We hypothesized that the EF caused by the electrical activity of extracranial muscles during natural chewing may reach similar strength in the cerebral cortex and hence might act as an endogenous modality of brain stimulation. Here, we present first steps toward validating this hypothesis.

METHODS

Using a realistic volume conductor head model of an epilepsy patient having undergone intracranial electrode placement and utilizing simultaneous intracranial and extracranial electrical recordings during chewing, we derive predictions about the chewing-related cortical EF strength to be expected in healthy individuals.

RESULTS

We find that in the region of the temporal poles, the expected EF strength may reach amplitudes in the order of 0.1-1 V/m.

CONCLUSION

The cortical EF caused by natural chewing could be large enough to modulate ongoing neural activity in the cerebral cortex and influence cognitive performance.

SIGNIFICANCE

The present study lends first support for the assumption that extracranial muscle activity might represent an endogenous source of electrical brain stimulation. This offers a new potential explanation for the puzzling effects of gum chewing on cognition, which have been repeatedly reported in the literature.

Overview of MEG

Magnetoencephalography (MEG) is a method to study electrical activity in the human brain by recording the neuromagnetic field outside the head. MEG, like electroencephalography (EEG), provides an excellent, millisecond-scale time resolution, and allows the estimation of the spatial distribution of the underlying activity, in favorable cases with a localization accuracy of a few millimeters. To detect the weak neuromagnetic signals, superconducting sensors, magnetically shielded rooms, and advanced signal processing techniques are used. The analysis and interpretation of MEG data typically involves comparisons between subject groups and experimental conditions using various spatial, temporal, and spectral measures of cortical activity and connectivity. The application of MEG to cognitive neuroscience studies is illustrated with studies of spoken language processing in subjects with normal and impaired reading ability. The mapping of spatiotemporal patterns of activity within networks of cortical areas can provide useful information about the functional architecture of the brain related to sensory and cognitive processing, including language, memory, attention, and perception.

Transcranial Alternating Current and Random Noise Stimulation: Possible Mechanisms

Background. Transcranial alternating current stimulation (tACS) is a relatively recent method suited to noninvasively modulate brain oscillations. Technically the method is similar but not identical to transcranial direct current stimulation (tDCS). While decades of research in animals and humans has revealed the main physiological mechanisms of tDCS, less is known about the physiological mechanisms of tACS. Method. Here, we review recent interdisciplinary research that has furthered our understanding of how tACS affects brain oscillations and by what means transcranial random noise stimulation (tRNS) that is a special form of tACS can modulate cortical functions. Results. Animal experiments have demonstrated in what way neurons react to invasively and transcranially applied alternating currents. Such findings are further supported by neural network simulations and knowledge from physics on entraining physical oscillators in the human brain. As a result, fine-grained models of the human skull and brain allow the prediction of the exact pattern of current flow during tDCS and tACS. Finally, recent studies on human physiology and behavior complete the picture of noninvasive modulation of brain oscillations. Conclusion. In future, the methods may be applicable in therapy of neurological and psychiatric disorders that are due to malfunctioning brain oscillations.

The Role of Skull Modeling in EEG Source Imaging for Patients with Refractory Temporal Lobe Epilepsy

We investigated the influence of different skull modeling approaches on EEG source imaging (ESI), using data of six patients with refractory temporal lobe epilepsy who later underwent successful epilepsy surgery. Four realistic head models with different skull compartments, based on finite difference methods, were constructed for each patient: (i) Three models had skulls with compact and spongy bone compartments as well as air-filled cavities, segmented from either computed tomography (CT), magnetic resonance imaging (MRI) or a CT-template and (ii) one model included a MRI-based skull with a single compact bone compartment. In all patients we performed ESI of single and averaged spikes marked in the clinical 27-channel EEG by the epileptologist. To analyze at which time point the dipole estimations were closer to the resected zone, ESI was performed at two time instants: the half-rising phase and peak of the spike. The estimated sources for each model were validated against the resected area, as indicated by the postoperative MRI. Our results showed that single spike analysis was highly influenced by the signal-to-noise ratio (SNR), yielding estimations with smaller distances to the resected volume at the peak of the spike. Although averaging reduced the SNR effects, it did not always result in dipole estimations lying closer to the resection. The proposed skull modeling approaches did not lead to significant differences in the localization of the irritative zone from clinical EEG data with low spatial sampling density. Furthermore, we showed that a simple skull model (MRI-based) resulted in similar accuracy in dipole estimation compared to more complex head models (based on CT- or CT-template). Therefore, all the considered head models can be used in the presurgical evaluation of patients with temporal lobe epilepsy to localize the irritative zone from low-density clinical EEG recordings.

The role of blood vessels in high-resolution volume conductor head modeling of EEG

Reconstruction of the electrical sources of human EEG activity at high spatio-temporal accuracy is an important aim in neuroscience and neurological diagnostics. Over the last decades, numerous studies have demonstrated that realistic modeling of head anatomy improves the accuracy of source reconstruction of EEG signals. For example, including a cerebro-spinal fluid compartment and the anisotropy of white matter electrical conductivity were both shown to significantly reduce modeling errors. Here, we for the first time quantify the role of detailed reconstructions of the cerebral blood vessels in volume conductor head modeling for EEG. To study the role of the highly arborized cerebral blood vessels, we created a submillimeter head model based on ultra-high-field-strength (7T) structural MRI datasets. Blood vessels (arteries and emissary/intraosseous veins) were segmented using Frangi multi-scale vesselness filtering. The final head model consisted of a geometry-adapted cubic mesh with over 17×10(6) nodes. We solved the forward model using a finite-element-method (FEM) transfer matrix approach, which allowed reducing computation times substantially and quantified the importance of the blood vessel compartment by computing forward and inverse errors resulting from ignoring the blood vessels. Our results show that ignoring emissary veins piercing the skull leads to focal localization errors of approx. 5 to 15mm. Large errors (>2cm) were observed due to the carotid arteries and the dense arterial vasculature in areas such as in the insula or in the medial temporal lobe. Thus, in such predisposed areas, errors caused by neglecting blood vessels can reach similar magnitudes as those previously reported for neglecting white matter anisotropy, the CSF or the dura - structures which are generally considered important components of realistic EEG head models. Our findings thus imply that including a realistic blood vessel compartment in EEG head models will be helpful to improve the accuracy of EEG source analyses particularly when high accuracies in brain areas with dense vasculature are required.

Primary somatosensory contextual modulation is encoded by oscillation frequency change

OBJECTIVE

This study characterized thalamo-cortical communication by assessing the effect of context-dependent modulation on the very early somatosensory evoked high-frequency oscillations (HF oscillations).

METHODS

We applied electrical stimuli to the median nerve together with an auditory oddball paradigm, presenting standard and deviant target tones representing differential cognitive contexts to the constantly repeated electrical stimulation. Median nerve stimulation without auditory stimulation served as unimodal control.

RESULTS

A model consisting of one subcortical (near thalamus) and two cortical (Brodmann areas 1 and 3b) dipolar sources explained the measured HF oscillations. Both at subcortical and the cortical levels HF oscillations were significantly smaller during bimodal (somatosensory plus auditory) than unimodal (somatosensory only) stimulation. A delay differential equation model was developed to investigate interactions within the 3-node thalamo-cortical network. Importantly, a significant change in the eigenfrequency of Brodmann area 3b was related to the context-dependent modulation, while there was no change in the network coupling.

CONCLUSION

This model strongly suggests cortico-thalamic feedback from both cortical Brodmann areas 1 and 3b to the thalamus. With the 3-node network model, thalamo-cortical feedback could be described.

SIGNIFICANCE

Frequency encoding plays an important role in contextual modulation in the somatosensory thalamo-cortical network.

Influence of isotropic skull models on EEG source localization

We investigated the influence of using simplified skull models on electroencephalogram (EEG) source localization. The simplified skull models were derived from CT and MR images, with isotropic conductivity modeled as either heterogeneous or homogeneous. A total of four simplified head models were compared against a reference model with a skull accurately segmented with CT images. Our results show that the use of a simplified geometry for the skull, can lead to errors of approximately 1 cm for sources located in the central and temporal regions of the brain.

Influence of skull modeling approaches on EEG source localization

Electroencephalographic source localization (ESL) relies on an accurate model representing the human head for the computation of the forward solution. In this head model, the skull is of utmost importance due to its complex geometry and low conductivity compared to the other tissues inside the head. We investigated the influence of using different skull modeling approaches on ESL. These approaches, consisting in skull conductivity and geometry modeling simplifications, make use of X-ray computed tomography (CT) and magnetic resonance (MR) images to generate seven different head models. A head model with an accurately segmented skull from CT images, including spongy and compact bone compartments as well as some air-filled cavities, was used as the reference model. EEG simulations were performed for a configuration of 32 and 128 electrodes, and for both noiseless and noisy data. The results show that skull geometry simplifications have a larger effect on ESL than those of the conductivity modeling. This suggests that accurate skull modeling is important in order to achieve reliable results for ESL that are useful in a clinical environment. We recommend the following guidelines to be taken into account for skull modeling in the generation of subject-specific head models: (i) If CT images are available, i.e., if the geometry of the skull and its different tissue types can be accurately segmented, the conductivity should be modeled as isotropic heterogeneous. The spongy bone might be segmented as an erosion of the compact bone; (ii) when only MR images are available, the skull base should be represented as accurately as possible and the conductivity can be modeled as isotropic heterogeneous, segmenting the spongy bone directly from the MR image; (iii) a large number of EEG electrodes should be used to obtain high spatial sampling, which reduces the localization errors at realistic noise levels.

Tangential and radial epileptic spike activity: different sensitivity in EEG and MEG

OBJECTIVE

Observations in epileptic patients show that interictal spikes are sometimes only visible in electroencephalography (EEG) and sometimes only in magnetoencephalography (MEG). This observation cannot readily be explained by the theoretical sensitivities of EEG and MEG based on analytical models. In this context, we aimed to study the directional sensitivity of radial and tangential spike activity in numerical simulations using realistic head models.

METHODS

We calculated the signal-to-noise ratio (SNR) of simulated spikes at varying orientations and with varying background activity in 12 brain regions in 4 volunteers. Different levels of background activity were modeled by adjusting the amplitudes of several thousand dipoles distributed in the cortex.

RESULTS

For a fixed realistic background activity, we found a higher SNR for MEG spikes for spike orientations that deviated not > 30° from the tangential direction. In contrast, we found a higher SNR for EEG spikes that deviated not > 45° from the radial direction. When the radial background activity was selectively increased, the sensitivity of EEG for radially oriented spikes decreased; when the tangential background activity selectively increased, the sensitivity of MEG for tangentially oriented spikes was decreased.

CONCLUSIONS

Our simulations provide a possible explanation for the clinically observed differences in epileptic spike detection between EEG and MEG. Epileptic spike detection can be improved by analyzing a combination of EEG and MEG data.

Reconstruction of quasi-radial dipolar activity using three-component magnetic field measurements

OBJECTIVE

While standard magnetoencephalographic systems record only one component of the biomagnetic field, novel vector-biomagnetometers enable measurement of all three components of the field at each sensing point. Because information content in standard one-component magnetoencephalography (MEG) is often not adequate to reconstruct quasi-radial dipolar activity, we tested the hypothesis that quasi-radial activity can be estimated using three-component MEG.

METHODS

We stimulated the right median nerve in 11 healthy volunteers and recorded the somatosensory evoked fields over the contralateral hemisphere using a novel vector-biomagnetometer system comprised of SQUID-based magnetometer triplets. Source reconstruction for the early cortical components N20m and P25m was subsequently performed.

RESULTS

Both tangential and quasi-radial dipolar activity could be reconstructed in 10 of the 11 participants. Dipole locations were found in the vicinity of the central sulcus, and dipole orientations were predominantly tangential for N20m and quasi-radial for P25m. The mean location difference between the tangential and quasi-radial dipoles was 11.9 mm and the mean orientation difference was 97.5°.

CONCLUSIONS

Quasi-radial dipolar activity can be reconstructed from three-component magnetoencephalographic measurements.

SIGNIFICANCE

Three-component MEG provides higher information content than does standard MEG.

Source cancellation profiles of electroencephalography and magnetoencephalography

Recorded electric potentials and magnetic fields due to cortical electrical activity have spatial spread even if their underlying brain sources are focal. Consequently, as a result of source cancellation, loss in signal amplitude and reduction in the effective signal-to-noise ratio can be expected when distributed sources are active simultaneously. Here we investigate the cancellation effects of EEG and MEG through the use of an anatomically correct forward model based on structural MRI acquired from 7 healthy adults. A boundary element model (BEM) with four compartments (brain, cerebrospinal fluid, skull and scalp) and highly accurate cortical meshes (~300,000 vertices) were generated. Distributed source activations were simulated using contiguous patches of active dipoles. To investigate cancellation effects in both EEG and MEG, quantitative indices were defined (source enhancement, cortical orientation disparity) and computed for varying values of the patch radius as well as for automatically parcellated gyri and sulci. Results were calculated for each cortical location, averaged over all subjects using a probabilistic atlas, and quantitatively compared between MEG and EEG. As expected, MEG sensors were found to be maximally sensitive to signals due to sources tangential to the scalp, and minimally sensitive to radial sources. Compared to EEG, however, MEG was found to be much more sensitive to signals generated antero-medially, notably in the anterior cingulate gyrus. Given that sources of activation cancel each other according to the orientation disparity of the cortex, this study provides useful methods and results for quantifying the effect of source orientation disparity upon source cancellation.

Feasibility of Neural Stimulation With Floating-Light-Activated Microelectrical Stimulators

Neural microstimulation is becoming a powerful tool for the restoration of impaired functions in the central nervous system. Microelectrode arrays with fine wire interconnects have traditionally been used in the development of these neural prosthetic devices. However, these interconnects are usually the most vulnerable part of the neuroprosthetic implant that can eventually cause the device to fail. In this paper, we investigate the feasibility of floating-light-activated microelectrical stimulators (FLAMES) for wireless neural stimulation. A computer model was developed to simulate the micro stimulators for typical requirements of neural activation in the human white and gray matters. First, the photon densities due to a circular laser beam were simulated in the neural tissue at near-infrared (NIR) wavelengths. Temperature elevation in the tissue was calculated and the laser power was retrospectively adjusted to 325 and 250 mW/cm(2) in the gray and white matters, respectively, to limit ΔT to 0.5 °C. Total device area of the FLAMES increased with all parameters considered but decreased with the output voltage. We conclude that the number of series photodiodes in the device can be used as a free parameter to minimize the device size. The results suggest that floating, optically activated stimulators are feasible at submillimeter sizes for the activation of the brain cortex or the spinal cord.

Virtual labyrinth model of vestibular afferent excitation via implanted electrodes: validation and application to design of a multichannel vestibular prosthesis

To facilitate design of a multichannel vestibular prosthesis that can restore sensation to individuals with bilateral loss of vestibular hair cell function, we created a virtual labyrinth model. Model geometry was generated through 3-dimensional (3D) reconstruction of microMRI and microCT scans of normal chinchillas (Chinchilla lanigera) acquired with 30-48 μm and 12 μm voxels, respectively. Virtual electrodes were positioned based on anatomic landmarks, and the extracellular potential field during a current pulse was computed using finite element methods. Potential fields then served as inputs to stochastic, nonlinear dynamic models for each of 2,415 vestibular afferent axons with spiking dynamics based on a modified Smith and Goldberg model incorporating parameters that varied with fiber location in the neuroepithelium. Action potential propagation was implemented by a well validated model of myelinated fibers. We tested the model by comparing predicted and actual 3D angular vestibulo-ocular reflex (aVOR) axes of eye rotation elicited by prosthetic stimuli. Actual responses were measured using 3D video-oculography. The model was individualized for each animal by placing virtual electrodes based on microCT localization of real electrodes. 3D eye rotation axes were predicted from the relative proportion of model axons excited within each of the three ampullary nerves. Multiple features observed empirically were observed as emergent properties of the model, including effects of active and return electrode position, stimulus amplitude and pulse waveform shape on target fiber recruitment and stimulation selectivity. The modeling procedure is partially automated and can be readily adapted to other species, including humans.

Sensitivity of MEG and EEG to source orientation

An important difference between magnetoencephalography (MEG) and electroencephalography (EEG) is that MEG is insensitive to radially oriented sources. We quantified computationally the dependency of MEG and EEG on the source orientation using a forward model with realistic tissue boundaries. Similar to the simpler case of a spherical head model, in which MEG cannot see radial sources at all, for most cortical locations there was a source orientation to which MEG was insensitive. The median value for the ratio of the signal magnitude for the source orientation of the lowest and the highest sensitivity was 0.06 for MEG and 0.63 for EEG. The difference in the sensitivity to the source orientation is expected to contribute to systematic differences in the signal-to-noise ratio between MEG and EEG.

In vitro testing of floating light activated micro-electrical stimulators

Chronic tissue response to microelectrode implants stands in the way as a major challenge to development of many neural prosthetic applications. The long term tissue response is mostly due to the movement of interconnects and the resulting mechanical stress between the electrode and the surrounding neural tissue. Remotely activated floating micro-stimulators are one possible method of eliminating the interconnects. As a method of energy transfer to the micro-stimulator, we proposed to use a laser beam at near infrared (NIR) wavelengths. FLAMES of various sizes were fabricated with integrated silicon PIN photodiodes. Sizes varied from 120 (Width) x 300 (Length) x 100 (Height) microm to 200 x 500 x 100microm. Devices were bench tested using 850nm excitation from a Ti:Sapphire laser. To test this method, the voltage field of the FLAMES was experimentally tested in saline solution pulsed with a NIR laser beam. The voltage generated is around 196mV in peak at the cathodic contact as a response to a single pulse. When a train of laser pulses was applied at 100Hz, the peak voltage at the cathodic contact remained around 141mV suggesting the feasibility of this approach for applications with pulse frequencies up to 100Hz.

Modelling of cortical and thalamic 600 Hz activity by means of oscillatory networks

The purpose of this study is to investigate information processing in the primary somatosensory system with the help of oscillatory network modelling. Specifically, we consider interactions in the oscillatory 600Hz activity between the thalamus and the cortical Brodmann areas 3b and 1. This type of cortical activity occurs after electrical stimulation of peripheral nerves such as the median nerve. Our measurements consist of simultaneous 31-channel MEG and 32-channel EEG recordings and individual 3D MRI data. We perform source localization by means of a multi-dipole model. The dipole activation time courses are then modelled by a set of coupled oscillators, described by linear second-order ordinary delay differential equations (DDEs). In particular, a new model for the thalamic activity is included in the oscillatory network. The parameters of the DDE system are successfully fitted to the data by a nonlinear evolutionary optimization method. To activate the oscillatory network, an individual input function is used, based on measurements of the propagated stimulation signal at the biceps. A significant feedback from the cortex to the thalamus could be detected by comparing the network modelling with and without feedback connections. Our finding in humans is supported by earlier animal studies. We conclude that this type of rhythmic brain activity can be modelled by oscillatory networks in order to disentangle feed forward and feedback information transfer.

The cortical site of visual suppression by transcranial magnetic stimulation

In visual suppression paradigms, transcranial magnetic stimulation (TMS) applied approximately 90 ms after visual stimulus presentation over occipital visual areas can robustly interfere with visual perception, thereby most likely affecting feedback activity from higher areas (Amassian VE, Cracco RQ, Maccabee PJ, Cracco JB, Rudell A, Eberle L. 1989. Suppression of visual perception by magnetic coil stimulation of human occipital cortex. Electroencephalogr Clin Neurophysiol 74:458-462.). It is speculated that the observed effects might stem primarily from the disruption of V1 activity. This hypothesis, although under debate, argues in favor of a special role of V1 in visual awareness. In this study, we combine TMS, functional magnetic resonance imaging, and calculation of the induced electric field to study the neural correlates of visual suppression. For parafoveal visual stimulation in the lower right half of the visual field, area V2d is shown to be the likely TMS target based on its anatomical location close to the skull surface. Furthermore, isolated stimulation of area V3 also results in robust visual suppression. Notably, V3 stimulation does not directly affect the feedback from higher visual areas that is relayed mainly via V2 to V1. These findings support the view that intact activity patterns in several early visual areas (rather than merely in V1) are likewise important for the perception of the stimulus.

Nonlinear interactions of high-frequency oscillations in the human somatosensory system

OBJECTIVE

The source of somatosensory evoked high-frequency activity at about 600 Hz is still not completely clear. Hence, we aimed to study the influence of double stimulation on the human somatosensory system by analyzing both the low-frequency activity and the high-frequency oscillations (HFOs) at about 600 Hz.

METHODS

We used median nerve stimulation at seven interstimuli intervals (ISIs) with a high time resolution between 2.4 and 4.8 ms to investigate the N15, N20 and superimposed HFOs. Simultaneously, the electroencephalogram and the magnetoencephalogram of 12 healthy participants were recorded. Subsequently, the source analysis of precortical and cortical dipoles was performed.

RESULTS

The difference computations of precortical dipole activation curves showed in both the low- and high-frequency range a correlation between the ISI and the latency of the second stimulus response. The cortical low-frequency response showed a similar behavior. Contrarily, in the second response of cortical HFOs this latency shift could not be confirmed. We found amplitude fluctuations that were dependent on the ISI in the low-frequency activity and the HFOs. These nonlinear interactions occurred at ISIs, which differ by one full HFO period (1.6 ms).

CONCLUSIONS

Low-frequency activity and HFOs originate from different generators. Precortical and cortical HFOs are independently generated. The amplitude fluctuations dependent on ISI indicate nonlinear interference between successive stimuli.

SIGNIFICANCE

Information processing in human somatosensory system includes nonlinearity.

Finite element analysis of a microelectrode on a substrate

Analytical solutions for the voltage field generated by a microelectrode are available for simple electrode and volume conductor geometries. However, the practical microelectrodes fabricated on a planar substrate deviate from those simple geometries substantially. It needs to be determined in which cases the analytical methods can be employed without introducing significant errors. We developed a finite element model (FEM) to study the potential field generated in a volume conductor by a circular disk electrode etched into a planar substrate. The results were compared to that of an analytical model provided by Wiley and Webster. The peak voltage at the contact surface varies as a function of the substrate width and it reaches 90% of the maximum at about twice the contact diameter. This suggests that an FEM is required for narrow substrate widths. The effect of the intercontact distance for the bipolar electrodes is also studied.

Finite element analysis of a floating microstimulator

Analytical solutions for voltage fields in a volume conductor are available only for ideal electrodes with radially symmetric contacts and infinitely extending substrates. Practical electrodes for neural stimulation may have asymmetric contacts and finite substrate dimensions and hence deviate from the ideal geometries. For instance, it needs to be determined if the analytical solutions are adequate for simulations of narrow shank electrodes where the substrate width is comparable to the size of the contacts. As an extension to this problem, a "floating" stimulator can be envisioned where the substrate would be finite in all directions. The question then becomes how small this floating stimulator can be made before its stimulation strength is compromised by the decrease in the medium impedance between the contacts as the contacts are approaching each other. We used finite element modeling to solve the voltage and current profiles generated by these radially asymmetric electrode geometries in a volume conductor. The simulation results suggest that both the substrate size and the bipolar contact separation influence the voltage field when these parameters are as small as a few times the contact size. Both of these effects are larger for increasing elevations from the contact surface, and even stronger for floating electrodes (finite substrate in all directions) than the shank-type electrodes. Location of the contacts on the floating electrode also plays a role in determining the voltage field. The voltage field for any device size and current, and any specific resistance of the volume conductor can be predicted from these results so long as the aspect ratios are preserved.

Identifying mutual information transfer in the brain with differential-algebraic modeling: Evidence for fast oscillatory coupling between cortical somatosensory areas 3b and 1

Understanding information transfer in the brain is a major challenge in today's neurosciences. Commonly, information transfer between brain areas is analyzed with the help of correlation measures for electrophysiological data. However, such approaches cannot distinguish between mutual coupling and other mechanisms of creating correlations between responses, such as common input from other sources. Functional coupling is mandatory for information transfer. Here we propose to analyze coupling between active brain areas with the help of models described by a system of differential-algebraic equations. Comparing models with various degrees of coupling, we show that mutual information transfer can be distinguished from one-way information transfer for activated cortical areas estimated by source localization techniques. We exemplify the technique with fast oscillatory activity found in both cortical areas 3b and 1 after peripheral nerve stimulation.

A novel integrated MEG and EEG analysis method for dipolar sources

The ability of magnetoencephalography (MEG) to accurately localize neuronal currents and obtain tangential components of the source is largely due to MEG's insensitivity to the conductivity profile of the head tissues. However, MEG cannot reliably detect the radial component of the neuronal current. In contrast, the localization accuracy of electroencephalography (EEG) is not as good as MEG, but EEG can detect both the tangential and radial components of the source. In the present study, we investigated the conductivity dependence in a new approach that combines MEG and EEG to accurately obtain, not only the location and tangential components, but also the radial component of the source. In this approach, the source location and tangential components are obtained from MEG alone, and optimal conductivity values of the EEG model are estimated by best-fitting EEG signal, while precisely matching the tangential components of the source in EEG and MEG. Then, the radial components are obtained from EEG using the previously estimated optimal conductivity values. Computer simulations testing this integrated approach demonstrated two main findings. First, there are well-organized optimal combinations of the conductivity values that provide an accurate fit to the combined MEG and EEG data. Second, the radial component, in addition to the location and tangential components, can be obtained with high accuracy without needing to know the precise conductivity profile of the head. We then demonstrated that this new approach performed reliably in an analysis of the 20-ms component from human somatosensory responses elicited by electric median-nerve stimulation.

Diffusion tensor MRI-based estimation of the influence of brain tissue anisotropy on the effects of transcranial magnetic stimulation

We evaluate and discuss the relevance of fiber anisotropy in estimating the effect of transcranial magnetic stimulation (TMS) on the human brain. Finite element simulations were carried out on a three-dimensional model of the head that included anisotropic conductivity information derived from diffusion tensor imaging (DTI). The results show that anisotropy has minor effects both on the position of the main locus of activation and on its intensity. It has considerably more effect on the spatial distribution of the induced electric field, yielding differences of the order of 10% of the maximum induced field. Moreover the area affected by magnetic stimulation is slightly larger when we include fiber anisotropy in the calculations than in an isotropic model. We also show that the induced field observed in the anisotropic model does not always align with the local fiber orientation but rather follows specific patterns of parallelity. These findings will help to improve the estimation of the areas involved in magnetic stimulation.

Alpha entrainment in human electroencephalogram and magnetoencephalogram recordings

Visual stimulation by repetitive flashes of light can lead to an entrainment of the alpha rhythm in electroencephalogram recordings (also called photic driving). We report a comparison of simultaneously recorded electric and magnetic data in a photic driving experiment, adapted to the individual alpha rhythm of 10 healthy volunteers. We show that there is a stronger frequency entrainment in magnetoencephalogram than in electroencephalogram recordings in all volunteers, which indicates a possible tangential brain activity underlying the dominant entrainment effect. The entrainment in the magnetoencephalogram lasts over significantly more frequencies and is most effective in the region around the individual alpha and a half alpha. For different channels, we found different degrees of entrainment showing topological and time-varying properties.

Influence of head models on neuromagnetic fields and inverse source localizations

Background

The magnetoencephalograms (MEGs) are mainly due to the source currents. However, there is a significant contribution to MEGs from the volume currents. The structure of the anatomical surfaces, e.g., gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the MEGs and the inverse source localizations. This was examined in detail with three different human head models.

Methods

Three finite element head models constructed from segmented MR images of an adult male subject were used for this study. These models were: (1) Model 1: full model with eleven tissues that included detailed structure of the scalp, hard and soft skull bone, CSF, gray and white matter and other prominent tissues, (2) the Model 2 was derived from the Model 1 in which the conductivity of gray matter was set equal to the white matter, i.e., a ten tissuetype model, (3) the Model 3 consisted of scalp, hard skull bone, CSF, gray and white matter, i.e., a five tissue-type model. The lead fields and MEGs due to dipolar sources in the motor cortex were computed for all three models. The dipolar sources were oriented normal to the cortical surface and had a dipole moment of 100 μA meter. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. A set of 100 trial inverse runs was made covering the 3 cm cube motor cortex area in a random fashion. The Model 1 was used as a reference model.

Results

The reference model (Model 1), as expected, performed best in localizing the sources in the motor cortex area. The Model 3 performed the worst. The mean source localization errors (MLEs) of the Model 3 were larger than the Model 1 or 2. The contour plots of the magnetic fields on top of the head were also different for all three models. The magnetic fields due to source currents were larger in magnitude as compared to the magnetic fields of volume currents.

Discussion

These results indicate that the complexity of head models strongly influences the MEGs and the inverse source localizations. A more complex head model performs better in inverse source localizations as compared to a model with lesser tissue surfaces.

Influence of electricity on post-mortal body temperature

In a case of suicidal application of electricity differences between the rectal temperature of the body and the suspected time of death were observed. In order to answer the question whether an electric current from hand to hand over >30 min led to a rise in body temperature FEM-based computer simulations and animal experiments were carried out. Both resulted in a warming of the soft parts in the arm without warming the body core. Thus a temperature-based estimation of the time since death can also be used in cases with electricity as the cause of death. Besides, in the animal experiment we found a spontaneous rise in the body core temperature even without application of electricity which may be a reason for the typical temperature plateau after death.

An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging

The forward problem of electromagnetic source imaging has two components: a numerical model to solve the related integral equations and a model of the head geometry. This study is on the boundary element method (BEM) implementation for numerical solutions and realistic head modelling. The use of second-order (quadratic) isoparametric elements and the recursive integration technique increase the accuracy in the solutions. Two new formulations are developed for the calculation of the transfer matrices to obtain the potential and magnetic field patterns using realistic head models. The formulations incorporate the use of the isolated problem approach for increased accuracy in solutions. If a personal computer is used for computations, each transfer matrix is calculated in 2.2 h. After this pre-computation period, solutions for arbitrary source configurations can be obtained in milliseconds for a realistic head model. A hybrid algorithm that uses snakes, morphological operations, region growing and thresholding is used for segmentation. The scalp, skull, grey matter, white matter and eyes are segmented from the multimodal magnetic resonance images and meshes for the corresponding surfaces are created. A mesh generation algorithm is developed for modelling the intersecting tissue compartments, such as eyes. To obtain more accurate results quadratic elements are used in the realistic meshes. The resultant BEM implementation provides more accurate forward problem solutions and more efficient calculations. Thus it can be the firm basis of the future inverse problem solutions.

Inhomogeneous propagation of cortical spreading depression—detection by electro- and magnetoencephalography in rats

Spreading depression (SD) propagates in cortical regions that are different in their morphological and functional characteristics. We tested whether the propagation pattern of spreading depression was different between parts of the cortex. In six adult rats, we recorded the ECoG by a 4 x 4 electrode array that covered parts of the frontal, parietal cortex and the cingulate cortex. Simultaneously a 16-channel magnetoencephalogram was recorded to characterize the development and direction of intracortical ion movements accompanying this phenomenon. Spreading depression was initiated by occipital application of 0.3 molar KCl solution. Depolarization was observed, at first, at lateral cortical regions and then at medial cortical regions. Thereafter, the propagation velocity increased in medial cortical regions and was faster than in lateral regions. Negative potential shifts were detected by all electrodes, but the depolarization reached a maximum over lateral and caudal cortical regions. The recorded magnetic fields indicated the same orientation of currents underlying these fields, which was perpendicular to the wave front and points away from the depolarization region. Overall, the data indicated that propagation patterns of spreading depression differed between parts of the cortex and, thus, propagation was inhomogeneous. This propagation was accompanied by strong currents parallel to the cortical surface.

Localization of realistic cortical activity in MEG using current multipoles

We present a novel approach to MEG source estimation based on a regularized first-order multipole solution. The Gaussian regularizing prior is obtained by calculation of the sample mean and covariance matrix for the equivalent moments of realistic simulated cortical activity. We compare the regularized multipole localization framework to the classical dipole and general multipole source estimation methods by evaluating the ability of all three solutions to localize the centroids of physiologically plausible patches of activity simulated on the surface of a human cerebral cortex. The results, obtained with a realistic sensor configuration, a spherical head model, and given in terms of field and localization error, depict the performance of the dipolar and multipolar models as a function of variable source surface area (50-500 mm(2)), noise conditions (20, 10, and 5 dB SNR), source orientation (0-90 degrees ), and source depth (3-11 cm). We show that as the sources increase in size, they become less accurately modeled as current dipoles. The regularized multipole systematically outperforms the single dipole model, increasingly so as the spatial extent of the sources increases. In addition, our simulations demonstrate that as the orientation of the sources becomes more radial, dipole localization accuracy decreases substantially, while the performance of the regularized multipole model is far less sensitive to orientation and even succeeds in localizing quasi-radial source configurations. Furthermore, our results show that the multipole model is able to localize superficial sources with higher accuracy than the current dipole. These results indicate that the regularized multipole solution may be an attractive alternative to current-dipole-based source estimation methods in MEG.

The influence of brain tissue anisotropy on human EEG and MEG

The influence of gray and white matter tissue anisotropy on the human electroencephalogram (EEG) and magnetoencephalogram (MEG) was examined with a high resolution finite element model of the head of an adult male subject. The conductivity tensor data for gray and white matter were estimated from magnetic resonance diffusion tensor imaging. Simulations were carried out with single dipoles or small extended sources in the cortical gray matter. The inclusion of anisotropic volume conduction in the brain was found to have a minor influence on the topology of EEG and MEG (and hence source localization). We found a major influence on the amplitude of EEG and MEG (and hence source strength estimation) due to the change in conductivity and the inclusion of anisotropy. We expect that inclusion of tissue anisotropy information will improve source estimation procedures.

Evaluation of inverse methods and head models for EEG source localization using a human skull phantom

We used a real-skull phantom head to investigate the performances of representative methods for EEG source localization when considering various head models. We describe several experiments using a montage with current sources located at multiple positions and orientations inside a human skull filled with a conductive medium. The robustness of selected methods based on distributed source models is evaluated as various solutions to the forward problem (from the sphere to the finite element method) are considered. Experimental results indicate that inverse methods using appropriate cortex-based source models are almost always able to locate the active source with excellent precision, with little or no spurious activity in close or distant regions, even when two sources are simultaneously active. Superior regularization schemes for solving the inverse problem can dramatically help the estimation of sparse and focal active zones, despite significant approximation of the head geometry and the conductivity properties of the head tissues. Realistic head models are necessary, though, to fit the data with a reasonable level of residual variance.

Combined MEG and EEG source imaging by minimization of mutual information

Though very frequently assumed, the necessity to operate a joint processing of simultaneous magnetoencephalography (MEG) and electroencephalography (EEG) recordings for functional brain imaging has never been clearly demonstrated. However, the very last generation of MEG instruments allows the simultaneous recording of brain magnetic fields and electrical potentials on the scalp. But the general fear regarding the fusion between MEG and EEG data is that the drawbacks from one modality will systematically spoil the performances of the other one without any consequent improvement. This is the case for instance for the estimation of deeper or radial sources with MEG. In this paper, we propose a method for a cooperative processing of MEG and EEG in a distributed source model. First, the evaluation of the respective performances of each modality for the estimation of every dipole in the source pattern is made using a conditional entropy criterion. Then, the algorithm operates a preprocessing of the MEG and EEG gain matrices which minimizes the mutual information between these two transfer functions, by a selective weighting of the MEG and EEG lead fields. This new combined EEG/MEG modality brings major improvements to the localization of active sources, together with reduced sensitivity to perturbations on data.

Influence of skull anisotropy for the forward and inverse problem in EEG: simulation studies using FEM on realistic head models

For the sake of realism in the description of conduction from primary neural currents to scalp potentials, we investigated the influence of skull anisotropy on the forward and inverse problems in brain functional imaging with EEG. At present, all methods available for cortical imaging assume a spherical geometry, or when using realistic head shapes do not consider the anisotropy of head tissues. However, to our knowledge, no study relates the implication of this simplifying hypothesis on the spatial resolution of EEG for source imaging. In this paper, a method using finite elements in a realistic head geometry is implemented and validated. The influence of erroneous conductivity values for the head tissues is presented, and results show that the conductivities of the brain and the skull in the radial orientation are the most critical ones. In the inverse problem, this influence has been evaluated with simulations using a distributed source model with a comparison of two regularization techniques, with the isotropic model working on data sets produced by a nonisotropic model. Regularization with minimum norm priors produces source images with spurious activity, meaning that the errors in the head model totally annihilate any localization ability. But nonlinear regularization allows the accurate recovery of simultaneous spots of activity, while the restoration of very close active regions is profoundly disabled by errors in the head model. We conclude that for robust cortical source imaging with EEG, a realistic head model taking anisotropy of tissues into account should be used.

MCG simulations of myocardial infarctions with a realistic heart-torso model

Data from simulations of the anterior myocardial infarction (AMI) and inferior myocardial infarction (IMI) are presented. One infarct located in the anterior section of the left ventricle and a second one in the inferior wall of the left ventricle were modeled. A high-resolution finite element model of a heart and torso was used in this study. Differences in the normal and infarcted fields were computed. Our data suggest that the infarcted region contribution to the total magnetic field can be accounted for by an equivalent current dipole. It might also be possible to detect an infarct from these difference fields constructed for different cases of myocardial infarction. More simulations are needed to determine the relations between infarct sizes and locations and magnetic fields. These relations might then be used to detect various cases of myocardial infarction.

MCG simulations with a realistic heart-torso model

Magnetocardiograms (MCG's) simulated with a high-resolution heart-torso model of an adult subject were compared with measured MCG's acquired from the same individual. An exact match of the measured and simulated MCG's was not found due to the uncertainties in tissue conductivities and cardiac source positions. However, general features of the measured MCG's were reasonably represented by the simulated data for most, but not all of the channels. This suggests that the model accounts for the most important mechanisms underlying the genesis of MCG's and may be useful for cardiac magnetic field modeling under normal and diseased states. MCG's were simulated with a realistic finite-element heart-torso model constructed from segmented magnetic resonance images with 19 different tissue types identified. A finite-element model was developed from the segmented images. The model consists of 2.51 million brick-shaped elements and 2.58 million nodes, and has a voxel resolution of 1.56 x 1.56 x 3 mm. Current distributions inside the torso and the magnetic fields and MCG's at the gradiometer coil locations were computed. MCG's were measured with a Philips twin Dewar first-order gradiometer SQUID-system consisting of 31 channels in one tank and 19 channels in the other.

Effect of conductivity uncertainties and modeling errors on EEG source localization using a 2-D model

This paper presents a sensitivity study of electroencephalography-based source localization due to errors in the head-tissue conductivities and to errors in modeling the conductivity variation inside the brain and scalp. The study is conducted using a two-dimensional (2-D) finite element model obtained from a magnetic resonance imaging (MRI) scan of a head cross section. The effect of uncertainty in the following tissues is studied: white matter, gray matter, cerebrospinal fluid (CSF), skull, and fat. The distribution of source location errors, assuming a single-dipole source model, is examined in detail for different dipole locations over the entire brain region. We also present a detailed analysis of the effect of conductivity on source localization for a four-layer cylinder model and a four-layer sphere model. These two simple models provide insight into how the effect of conductivity on boundary potential translates into source location errors, and also how errors in a 2-D model compare to errors in a three-dimensional model. Results presented in this paper clearly point to the following conclusion: unless the conductivities of the head tissues and the distribution of these tissues throughout the head are modeled accurately, the goal of achieving localization accuracy to within a few millimeters is unattainable.