Neonatal EEG at scalp is focal and implies high skull conductivity in realistic neonatal head models.

The potential improvements in spatial resolution of neonatal EEG used in source localization have been challenged by the insufficiencies in realistic neonatal head models. Our present study aimed at using empirical methods to indirectly estimate skull conductivity; the model parameter that is known to significantly affect the behavior of newborn scalp EEG and cause it to be markedly different from that of an adult. To this end, we used 64 channel EEG recordings to study the spatial specificity of scalp EEG by assessing the spatial decays in focal transients using both amplitudes and between-c'hannels linear correlations. The findings showed that these amplitudes and correlations decay within few centimeters from the reference channel/electrode, and that the nature of the decay is independent of the scalp area. This decay in newborn infants was found to be approximately three times faster than the corresponding decay in adult EEG analyzed from a set of 256 channel recordings. We then generated realistic head models using both finite and boundary element methods along with a manually segmented magnetic resonance images to study the spatial decays of scalp potentials produced by single dipole in the cortex. By comparing the spatial decays due to real and simulated EEG for different skull conductivities (from 0.003 to 0.3S/m), we showed that a close match between the empirical and simulated decays was obtained when the selected skull conductivity for newborn was around 0.06-0.2S/m. This is over an order of magnitude higher than the currently used values in adult head modeling. The results also showed that the neonatal scalp EEG is less smeared than that of an adult and this characteristic is the same across the entire scalp, including the fontanel region. These results indicate that a focal cortical activity is generally only registered by electrodes within few centimeters from the source. Hence, the conventional 10 to 20 channel neonatal EEG acquisition systems give a significantly spatially under sampled scalp EEG and may, consequently, give distorted pictures of focal brain activities. Such spatial specificity can only be reconciled by appreciating the anatomy of the neonatal head, especially the still unossified skull structure that needs to be modeled with higher conductivities than conventionally used in the adults.

Decrease in phase slip rates and phase cone structures during seizure evolution and epileptogenic activities derived from microgrid ECoG data.

Sudden phase changes are related to cortical phase transitions, which likely change in frequency and spatial distribution as epileptogenic activity evolves. A 100 s long section of micro-ECoG data obtained before and during a seizure was selected and analyzed. In addition, nine other short-duration epileptic events were also examined. The data was collected at 420 Hz, imported into MATLAB, downsampled to 200 Hz, and filtered in the 1-50 Hz band. The Hilbert transform was applied to compute the analytic phase, which was then unwrapped, and detrended to look for sudden phase changes. The phase slip rate (counts/s) and its acceleration (counts/s2) were computed with a stepping window of 1-s duration and with a step size of 5 ms. The analysis was performed for theta (3-7 Hz), alpha (7-12 Hz), and beta (12-30 Hz) bands. The phase slip rate on all electrodes in the theta band decreased while it increased for the alpha and beta bands during the seizure period. Similar patterns were observed for isolated epileptogenic events. Spatiotemporal contour plots of the phase slip rates were also constructed using a montage layout of 8 × 8 electrode positions. These plots exhibited dynamic and oscillatory formation of phase cone-like structures which were higher in the theta band and lower in the alpha and beta bands during the seizure period and epileptogenic events. These results indicate that the formation of phase cones might be an excellent biomarker to study the evolution of a seizure and also the cortical dynamics of isolated epileptogenic events.

Spatial patterning of the neonatal EEG suggests a need for a high number of electrodes.

There is an increasing demand for source analysis of neonatal EEG, but currently there is inadequate knowledge about i) the spatial patterning of neonatal scalp EEG and hence ii) the number of electrodes needed to capture neonatal EEG in full spatial detail. This study addresses these issues by using a very high density (2.5mm interelectrode spacing) linear electrode array to assess the spatial power spectrum, by using a high density (64 electrodes) EEG cap to assess the spatial extent of the common oscillatory bouts in the neonatal EEG and by using a neonatal size spherical head model to assess the effects of source depth and skull conductivities on the spatial frequency spectrum. The linear array recordings show that the spatial power spectrum decays rapidly until about 0.5-0.8 cycles per centimeter. The dense array EEG recordings show that the amplitude of oscillatory events decays within 4-6 cm to the level of global background activity, and that the higher frequencies (12-20 Hz) show the most rapid spatial decline in amplitude. Simulation with spherical head model showed that realistic variation in skull conductivity and source depths can both introduce orders of magnitude difference in the spatial frequency of the scalp EEG. Calculation of spatial Nyquist frequencies from the spatial power spectra suggests that an interelectrode distance of about 6-10mm would suffice to capture the full spatial texture of the raw EEG signal at the neonatal scalp without spatial aliasing or under-sampling. The spatial decay of oscillatory events suggests that a full representation of their spatial characteristics requires an interelectrode distance of 10-20mm. The findings show that the conventional way of recording neonatal EEG with about 10 electrodes ignores most spatial EEG content, that increasing the electrode density is necessary to improve neonatal EEG source localization and information extraction, and that prospective source models will need to carefully consider the neonatally relevant ranges of tissue conductivities and source depths when source localizing cortical activity in neonates.

Noninvasive localization of epileptic sites from stable phase synchronization patterns on different days derived from short duration interictal scalp dEEG.

The stochastic behavior of the phase synchronization index (SI) on different days during a hospital stay of epileptic patients was studied for noninvasive localization of the epileptogenic areas from high density (256 channel) scalp EEG recordings. The study was performed on three subjects with interictal EEG data on different days. The seizure areas were localized with subdural recordings with an 8 × 8 grid electrode array. The study was performed in low gamma (30-50 Hz) band with short duration (0-180 s), seizure-free and spike-free scalp EEG data. A detrended fluctuation analysis was used to find the averaged stochastic fluctuations in the SI. The phase synchronization was computed after taking Hilbert transform of the EEG data. Contour plots were constructed with 20 s time-frames using a montage of the layout of 256 electrode positions. It was found that the stochastic behavior of the SI was higher in epileptogenic areas on different days for each subject. Also, a stable higher pattern of SI emerged after 60-100 s in the epileptogenic areas. These findings suggest that it is possible to localize the epileptogenic areas from the short duration (60-100 s), seizure-free and spike-free high density scalp EEG recordings.

Spatiotemporal phase slip patterns for visual evoked potentials, covert object naming tasks, and insight moments extracted from 256 channel EEG recordings.

Phase slips arise from state transitions of the coordinated activity of cortical neurons which can be extracted from the EEG data. The phase slip rates (PSRs) were studied from the high-density (256 channel) EEG data, sampled at 16.384 kHz, of five adult subjects during covert visual object naming tasks. Artifact-free data from 29 trials were averaged for each subject. The analysis was performed to look for phase slips in the theta (4-7 Hz), alpha (7-12 Hz), beta (12-30 Hz), and low gamma (30-49 Hz) bands. The phase was calculated with the Hilbert transform, then unwrapped and detrended to look for phase slip rates in a 1.0 ms wide stepping window with a step size of 0.06 ms. The spatiotemporal plots of the PSRs were made by using a montage layout of 256 equidistant electrode positions. The spatiotemporal profiles of EEG and PSRs during the stimulus and the first second of the post-stimulus period were examined in detail to study the visual evoked potentials and different stages of visual object recognition in the visual, language, and memory areas. It was found that the activity areas of PSRs were different as compared with EEG activity areas during the stimulus and post-stimulus periods. Different stages of the insight moments during the covert object naming tasks were examined from PSRs and it was found to be about 512 ± 21 ms for the 'Eureka' moment. Overall, these results indicate that information about the cortical phase transitions can be derived from the measured EEG data and can be used in a complementary fashion to study the cognitive behavior of the brain.

Noninvasive epileptic seizure localization from stochastic behavior of short duration interictal high density scalp EEG data.

The stochastic behavior of the phase synchronization index (SI) in different EEG bands was examined for noninvasive localization of the epileptogenic areas from the short duration (30-60 s), seizure-free and spike-free high density (256 channel) scalp EEG data. We also examined the cross-frequency and cross-electrode coupling in different EEG bands. EEG data of four subjects was used. The seizure areas were localized with subdural recordings with an 8×8 grid electrode array. It was found that the stochastic behavior of the SI in low gamma band (30-50 Hz) was higher in epileptogenic areas. The beta (12-30 Hz) band also showed similar tendencies. The stochastic behavior in theta (3-7 Hz) band was depressed in the seizure area while it was widespread in large areas over the scalp in the alpha (7-12 Hz) band. The stochastic behavior of the cross-frequency and cross-electrode couplings in theta-gamma, alpha-gamma and beta-gamma bands were decreased in the seizure areas for all four subjects. These findings suggest that it is possible to localize the epileptogenic areas from the short duration seizure-free and spike-free high density scalp EEG data.

Cortical Pathways During Postural Control: New Insights From Functional EEG Source Connectivity.

Postural control is a complex feedback system that relies on vast array of sensory inputs in order to maintain a stable upright stance. The brain cortex plays a crucial role in the processing of this information and in the elaboration of a successful adaptive strategy to external stimulation preventing loss of balance and falls. In the present work, the participants postural control system was challenged by disrupting the upright stance via a mechanical skeletal muscle vibration applied to the calves. The EEG source connectivity method was used to investigate the cortical response to the external stimulation and highlight the brain network primarily involved in high-level coordination of the postural control system. The cortical network reconfiguration was assessed during two experimental conditions of eyes open and eyes closed and the network flexibility (i.e. its dynamic reconfiguration over time) was correlated with the sample entropy of the stabilogram sway. The results highlight two different cortical strategies in the alpha band: the predominance of frontal lobe connections during open eyes and the strengthening of temporal-parietal network connections in the absence of visual cues. Furthermore, a high correlation emerges between the flexibility in the regions surrounding the right temporo-parietal junction and the sample entropy of the CoP sway, suggesting their centrality in the postural control system. These results open the possibility to employ network-based flexibility metrics as markers of a healthy postural control system, with implications in the diagnosis and treatment of postural impairing diseases.

Increased Phase Cone Turnover in 80-250 Hz Bands Occurs in the Epileptogenic Zone During Interictal Periods.

We found that phase cone clustering patterns in EEG ripple bands demonstrate an increased turnover rate in epileptogenic zones compared to adjacent regions. We employed 256 channel EEG data collected in four adult subjects with refractory epilepsy. The analysis was performed in the 80-150 and 150-250 Hz ranges. Ictal onsets were documented with intracranial EEG recordings. Interictal scalp recordings, free of epileptiform patterns, of 240-s duration, were selected for analysis for each subject. The data was filtered, and the instantaneous phase was extracted after the Hilbert transformation. Spatiotemporal contour plots of the unwrapped instantaneous phase with 1.0 ms intervals were constructed using a montage layout of the 256 electrode positions. Stable phase cone patterns were selected based on criteria that the sign of spatial gradient did not change for a minimum of three consecutive time samples and the frame velocity was consistent with known propagation velocities of cortical axons. These plots exhibited increased dynamical formation and dissolution of phase cones in the ictal onset zones, compared to surrounding cortical regions, in all four patients. We believe that these findings represent markers of abnormally increased cortical excitability. They are potential tools that may assist in localizing the epileptogenic zone.

Similarities between simulated spatial spectra of scalp EEG, MEG and structural MRI.

Electrical dipoles oriented perpendicular to the cortical surface are the primary source of the scalp EEGs and MEGs. Thus, in particular, gyri and sulci structures on the cortical surface have a definite possibility to influence the EEGs and MEGs. This was examined by comparing the spatial power spectral density (PSD) of the upper portion of the human cortex in MRI slices to that of simulated scalp EEGs and MEGs. The electrical activity was modeled with 2,650 dipolar sources oriented normal to the local cortical surface. The resulting scalp potentials were calculated with a finite element model of the head constructed from 51 segmented sagittal MR images. The PSD was computed after taking the fast Fourier transform of scalp potentials. The PSD of the cortical contour in each slice was also computed. The PSD was then averaged over all the slices. This was done for sagittal and coronal view both. The PSD of EEG and MEG showed two broad peaks, one from 0.05 to 0.22 cycles/cm (wavelength 20-4.545 cm) and the other from 0.22 to 1.2 cycles/cm (wavelength 4.545-0.834 cm). The PSD of the cortex showed a broad peak from 0.08 to 0.32 cycles/cm (wavelength 12.5-3.125 cm) and other two peaks within the range of 0.32 to 0.9 cycles/cm (wavelength 3.125-1.11 cm). These peaks are definitely due to the gyri structures and associated larger patterns on the cortical surface. Smaller peaks in the range of 1-3 cycles/cm were also observed which are possibly due to sulci structures. These results suggest that the spatial information was present in the EEG and MEG at the spatial frequencies of gyri. This also implies that the practical Nyquist frequency for sampling scalp EEGs should be 3.0 cycles/cm and an optimal interelectrode spacing of about 3 mm is needed for extraction of cortical patterns from scalp EEGs in humans.

Safety of slow-pulsed transcranial electrical stimulation in acute spike suppression.

We examined the effects of slow-pulsed transcranial electrical stimulation (TES) in suppressing epileptiform discharges in seven adults with refractory epilepsy. An MRI-based realistic head model was constructed for each subject and co-registered with 256-channel dense EEG (dEEG). Interictal spikes were localized, and TES targeted the cortical source of each subject's principal spike population. Targeted spikes were suppressed in five subject's (29/35 treatment days overall), and nontargeted spikes were suppressed in four subjects. Epileptiform activity did not worsen. This study suggests that this protocol, designed to induce long-term depression (LTD), is safe and effective in acute suppression of interictal epileptiform discharges.

Oscillatory Patterns of Phase Cone Formations near to Epileptic Spikes Derived from 256-Channel Scalp EEG Data.

Our objective was to determine if there are any distinguishable phase cone clustering patterns present near to epileptic spikes. These phase cones arise from episodic phase shifts due to the coordinated activity of cortical neurons at or near to state transitions and can be extracted from the high-density scalp EEG recordings. The phase cone clustering activities in the low gamma band (30-50 Hz) and in the ripple band (80-150 Hz) were extracted from the analytic phase after taking Hilbert transform of the 256-channel high density (dEEG) data of adult patients. We used three subjects in this study. Spatiotemporal contour plots of the unwrapped analytic phase with 1.0 ms intervals were constructed using a montage layout of 256 electrode positions. Stable phase cone patterns were selected based on the criteria that the sign of the spatial gradient did not change for at least three consecutive time samples and the frame velocity was within the range of propagation velocities of cortical axons. These plots exhibited dynamical formation of phase cones which were higher in the seizure area as compared with the nearby surrounding brain areas. Spatiotemporal oscillatory patterns were also visible during ±5 sec period from the location of the spike. These results suggest that the phase cone activity might be useful for noninvasive localization of epileptic sites and also for examining the cortical neurodynamics near to epileptic spikes.

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 microA 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 head models on EEG simulations and inverse source localizations.

BACKGROUND: The structure of the anatomical surfaces, e.g., CSF and gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the scalp potentials and the inverse source localizations. This was examined in detail with four different human head models. METHODS: Four 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 tissue-type model, (3) the Model 3 was derived from the Model 1 in which the conductivities of gray matter and CSF were set equal to the white matter, i.e., a nine tissue-type model, (4) the Model 4 consisted of scalp, hard skull bone, CSF, gray and white matter, i.e., a five tissue-type model. How model complexity influences the EEG source localizations was also studied with the above four finite element models of the head. The lead fields and scalp potentials due to dipolar sources in the motor cortex were computed for all four models. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. The inverse analysis was performed by adding uncorrelated Gaussian noise to the scalp potentials to achieve a signal to noise ratio (SNR) of -10 to 30 dB. The Model 1 was used as a reference model. RESULTS: The reference model, as expected, performed the best. The Model 3, which did not have the CSF layer, performed the worst. The mean source localization errors (MLEs) of the Model 3 were larger than the Model 1 or 2. The scalp potentials were also most affected by the lack of CSF geometry in the Model 3. The MLEs for the Model 4 were also larger than the Model 1 and 2. The Model 4 and the Model 3 had similar MLEs in the SNR range of -10 dB to 0 dB. However, in the SNR range of 5 dB to 30 dB, the Model 4 has lower MLEs as compared with the Model 3. DISCUSSION: These results indicate that the complexity of head models strongly influences the scalp potentials 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. The CSF layer plays an important role in modifying the scalp potentials and also influences the inverse source localizations. In summary, for best results one needs to have highly heterogeneous models of the head for accurate simulations of scalp potentials and for inverse source localizations.

Synchronization analysis of the uterine magnetic activity during contractions.

BACKGROUND: Our objective was to quantify and compare the extent of synchronization of the spatial-temporal myometrial activity over the human uterus before and during a contraction using transabdominal magnetomyographic (MMG) recordings. Synchronization can be an important indicator for the quantification of uterine contractions. METHODS: The spatialtermporal myometrial activity recordings were performed using a 151-channel noninvasive magnetic sensor system called SARA. This device covers the entire pregnant abdomen and records the magnetic field corresponding to the electrical activity generated in the uterine myometrium. The data was collected at 250 samples/sec and was resampled with 25 samples/sec and then filtered in the band of 0.1-0.2 Hz to study the primary magnetic activity of the uterus related to contractions. The synchronization between a channel pair was computed. It was inferred from a statistical tendency to maintain a nearly constant phase difference over a given period of time even though the analytic phase of each channel may change markedly during that time frame. The analytic phase was computed after taking Hilbert transform of the magnetic field data. The process was applied on the pairs of magnetic field traces (240 sec length) with a stepping window of 20 sec duration which is long enough to cover two cycle of the lowest frequency of interest (0.1 Hz). The analysis was repeated by stepping the window at 10 sec intervals. The spatial patterns of the synchronization indices covering the anterior transabdominal area were computed. For this, regional coil-pairs were used. For a given coil, the coil pairs were constructed with the surrounding six coils. The synchronization indices were computed for each coil pair, averaged over the 21 coil-pairs and then assigned as the synchronization index to that particular coil. This procedure was tested on six pregnant subjects at the gestational age between 29 and 40 weeks admitted to the hospital for contractions. The RMS magnetic field for each coil was also computed. RESULTS: The results show that the spatial patterns of the synchronization indices change and follow the periodic pattern of the uterine contraction cycle. Spatial patterns of synchronization indices and the RMS magnetic fields show similarities in few window frames and also show large differences in few other windows. For six subjects, the average synchronization indices were: 0.346 +/- 0.068 for the quiescent baseline period and 0.545 +/- 0.022 at the peak of the contraction. DISCUSSION: These results show that synchronization indices and their spatial distributions depict uterine contractions and relaxations.

Efficient electromagnetic source imaging with adaptive standardized LORETA/FOCUSS.

Functional brain imaging and source localization based on the scalp's potential field require a solution to an ill-posed inverse problem with many solutions. This makes it necessary to incorporate a priori knowledge in order to select a particular solution. A computational challenge for some subject-specific head models is that many inverse algorithms require a comprehensive sampling of the candidate source space at the desired resolution. In this study, we present an algorithm that can accurately reconstruct details of localized source activity from a sparse sampling of the candidate source space. Forward computations are minimized through an adaptive procedure that increases source resolution as the spatial extent is reduced. With this algorithm, we were able to compute inverses using only 6% to 11% of the full resolution lead-field, with a localization accuracy that was not significantly different than an exhaustive search through a fully-sampled source space. The technique is, therefore, applicable for use with anatomically-realistic, subject-specific forward models for applications with spatially concentrated source activity.

Spatiotemporal phase clusters and phase synchronization patterns derived from high density EEG and ECoG recordings.

High density scalp EEG and subdural ECoG recordings provide an opportunity to map the electrical activity of the cortex with high spatial resolution. The spatial power spectral densities conform to a power law distribution with some nonlinear variations. The spatiotemporal patterns of phase derived from these data sets have unique features, such as, amplitude and phase modulation waves and also exhibited formation of spatial phase cluster patterns. These unique features represent different cognitive states and are different between normal and diseased states. Reported results show that the rate of formation of phase cluster patterns derived from the seizure-free interictal EEG data are higher in epileptogenic zones as compared with nearby normal areas of the brain.

Low-Amplitude Craniofacial EMG Power Spectral Density and 3D Muscle Reconstruction from MRI.

Improving EEG signal interpretation, specificity, and sensitivity is a primary focus of many current investigations, and the successful application of EEG signal processing methods requires a detailed knowledge of both the topography and frequency spectra of low-amplitude, high-frequency craniofacial EMG. This information remains limited in clinical research, and as such, there is no known reliable technique for the removal of these artifacts from EEG data. The results presented herein outline a preliminary investigation of craniofacial EMG high-frequency spectra and 3D MRI segmentation that offers insight into the development of an anatomically-realistic model for characterizing these effects. The data presented highlights the potential for confounding signal contribution from around 60 to 200 Hz, when observed in frequency space, from both low and high-amplitude EMG signals. This range directly overlaps that of both low γ (30-50 Hz) and high γ (50-80 Hz) waves, as defined traditionally in standatrd EEG measurements, and mainly with waves presented in dense-array EEG recordings. Likewise, average EMG amplitude comparisons from each condition highlights the similarities in signal contribution of low-activity muscular movements and resting, control conditions. In addition to the FFT analysis performed, 3D segmentation and reconstruction of the craniofacial muscles whose EMG signals were measured was successful. This recapitulation of the relevant EMG morphology is a crucial first step in developing an anatomical model for the isolation and removal of confounding low-amplitude craniofacial EMG signals from EEG data. Such a model may be eventually applied in a clinical setting to ultimately help to extend the use of EEG in various clinical roles.

The effect of volume currents due to myocardial anisotropy on body surface potentials.

Changes in anterior and posterior body surface potential maps (BSPMs) due to myocardial anisotropy were examined using a highly heterogeneous finite element model of an adult male subject constructed from segmented magnetic resonance images. A total of 23 different tissue types were identified in the whole torso. The myocardial fibre orientations in the human heart wall were mapped from the fibre orientations of a canine heart which are available in the literature using deformable mapping techniques. The current and potential distributions in the whole torso were computed using dipolar sources in the septum, apical area, left ventricular wall or right ventricular wall. For each dipole x, y, z orientations were studied. An adaptive finite element solver was used to compute currents and potential distributions in the whole torso with an element size of 0.78 x 0.78 x 3 mm in the myocardium and larger elements in other parts of the torso. For each dipole position two cases were studied. In one case the myocardium was isotropic and in the other it was anisotropic. It was found that BSPMs showed a very notable difference between the isotropic and the anisotropic myocardium for all dipole positions with the largest difference for the apical dipoles. The correlation coefficients for the BSPMs between the isotropic and anisotropic cases ranged from 0.83 for an apical dipole to 0.99 for an RV wall dipole. These results suggest that myocardial fibre anisotropy plays an important role in determining the body surface potentials.

Ellipsoidal refinement of the regularized inverse: performance in an anatomically realistic EEG model.

Functional brain imaging and source localization based on the scalp's potential field requires a solution to the inverse electrostatic problem. This is an underdetermined problem with many solutions. Minimum norm and regularization methods involving the norm are often used, but generally give solutions in which current is widely distributed. One method for reducing the spatial distribution of a solution is to apply it iteratively within the bounds of a shrinking ellipsoid. This paper compares the performance of this approach with an exhaustive search at various noise levels using a numeric simulation of the electroencephalogram in a realistic conductor model. The results show that inverting a single dipolar source with a location accuracy comparable to an exhaustive search requires in the range of 5 to 10 dB higher signal-to-noise ratio.

Dipole models for the EEG and MEG.

The current dipole is a widely used source model in forward and inverse electroencephalography and magnetoencephalography applications. Analytic solutions to the governing field equations have been developed for several approximations of the human head using ideal dipoles as the source model. Numeric approaches such as the finite-element and finite-difference methods have become popular because they allow the use of anatomically realistic head models and the increased computational power that they require has become readily available. Although numeric methods can represent more realistic domains, the sources in such models are an approximation of the ideal dipole. In this paper, we examine several methods for representing dipole sources in finite-element models and compare the resulting surface potentials and external magnetic field with those obtained from analytic solutions using ideal dipoles.