Dipole Fitting Research Articles

Partially Constrained Blind Source Separation for Localization of Unknown Sources Exploiting Non-homogeneity of the Head Tissues

A new brain source localization technique using electroencephalograms (EEGs) is investigated in this paper. The information which describes the location of certain known sources is used as the constraint within the proposed blind source separation (BSS) algorithm and leads to a solution to the ill-posed inverse problem of source localization. Non-homogeneity of the head tissues, on the other hand, is exploited by introducing a realistic model of the mixing system. This model is used to better identify the location of the unknown sources within the brain from projection of the separated independent components on to the scalp. A separate procedure is employed to highlight the rhythmic EEG sources such as Alpha rhythm as the known sources. The performance of the scheme is shown on real EEG measurements and compared with that of "conventional dipole fitting algorithm".

Study of conducting volume boundary influence on source localization using a realistic MEG phantom

In order to gauge the applicability of a source reconstruction technique in MEG it is necessary to assess the overall accuracy and precision of the method. Computer simulation is useful in this regard, but it is inherently limited in the extent that it can model factors such as sensor performance and environmental noise accurately. We have designed a realistically shaped physical phantom with moveable dipole sources to examine the influence of the conductor boundary used in forward model generation on localization accuracy. The scalp and inner skull surfaces were compared using single sphere and overlapping-sphere models in both dipole fitting and event-related beamforming (ERB) techniques. Over all source locations and methods, the mean localization error when using the inner skull boundary was significantly lower than when using the scalp surface (scalp/inner skull = 9.08 mm/6.76 mm P < 0.0002). As expected, the difference was largest in inferior regions where the curvature of the skull diverges greatly from that of the outer scalp.

Continuous head localization and data correction in MEG

Abstract We describe a system that monitors head movement continuously and corrects the data to remove the effects of motion. Head position is monitored by real-time analysis of signals of three small coils mounted on the subject's head. Data correction is done off-line. Tests of the system with both dipole fitting and SAM beamformer analysis show that it allows correction of errors in source locations due to head movement to ∼ 1 mm.

Localization accuracy and temporal resolution of MEG: A phantom experiment

Abstract. Recent phantom studies have demonstrated localization accuracy of 1.4–3 mm for single trial recordings of dipole positions representing the somatosensory area, and of 14 mm for deeper locations. The duration of the dipole activation in these studies was too long and the stimulus was too strong to validate MEG's accuracy in localizing weak spikes of high frequency. It was recently demonstrated that such “MEG spikes” are widely distributed across the cortex, cerebellum and brainstem. The present study demonstrates MEG's ability to localize weak, transient brain activation in both single trials and averaged data. MEG data were collected using the CTF whole head system. A saline-filled spherical phantom was used with a dipole placed in one of three different locations. The dipole was activated with a train of 360 spikes. The data were analyzed using an Equivalent Current Dipole (ECD) and the Synthetic Aperture Magnetometry (SAM). On the cortex, dipole analysis fitted single trial data with localization error of 3.6 and 15 mm for dipole strengths of 80 and 9 nA-m, respectively. The averaged data for the same superficial locations were localized with accuracy between 1 and 2 mm. For deeper dipoles acceptable localization was only obtained for the averaged data. SAM analysis produced slightly better results than ECD. These results demonstrate that dipole fitting of average MEG data and SAM analysis can localize focal sources with an accuracy of 2 mm or better in the human cortex, and about 5 mm in deeper areas.

Concordance between routine interictal magnetoencephalography and simultaneous scalp electroencephalography in a sample of patients with epilepsy.

Both electroencephalography (EEG) and magnetoencephalography (MEG) localize epileptiform activity but may yield different results. This discordance may arise from different detection capabilities or from different data collection and interpretation techniques. Comparisons of MEG and EEG have focused on detection of individual spikes. However, side-by-side comparisons of results as used in the clinical setting is lacking. In this report, we present our empirical comparison. We reviewed 58 simultaneous MEG-EEG recordings (35 paired-sensors, 23 whole-head) from a diverse epilepsy population, comparing previous clinical MEG interpretations with new blinded EEG interpretations, noting lobar concordance of readers' judgments of regional abnormalities. A second-pass unblinded analysis, using all available clinical data, assessed the relative contribution and plausibility of the results of each technique. Concordance was high (85%) overall. Discordance was sometimes caused by constraints imposed by MEG dipole fitting techniques. Even when results of the techniques did not match, MEG often disambiguated the clinical scenario, especially when combined with imaging information. Thoughtful analysis of combined MEG-EEG datasets, beyond algorithm-based interictal spike detection, can help guide clinical decision-making even when concordance between techniques is imperfect. In some cases, EEG and MEG are synergistic and provide complementary information.

High‐resolution electroencephalography and source localization in neonates

Although Electroencephalography (EEG) source localization is being widely used in adults, this promising technique has not yet been applied to newborns because of technical difficulties, such as lack of data concerning the newborn skull conductivity, thickness, and homogeneity. Using a new type of EEG headcap molded on each baby's head, we aimed to determine whether this technique could be adapted to neonates, and to evaluate the importance of these technical difficulties. We carried out EEG source reconstruction of the recordings of five neonates using dipole fit algorithm. We used four different head models for each neonate, obtained from individual MRI scans: normal skull thickness and conductivity of 0.0042 S/m; normal thickness and conductivity of 0.33 S/m; increased thickness and conductivity of 0.0042 S/m; and normal thickness and conductivity with a modeled bregma fontanel. Dipole locations were consistent with MRI and clinical data. The mean difference between the dipole locations in the 0.0042 and the 0.33 S/m skull layer models was 11.6 +/- 2.5 mm, with an average 29.7% decrease in magnitude for the 0.33 S/m model but no significant changes for the dipoles orientation. Skull layer thickness had a large influence on magnitude, but no significant effect on position and orientation. The mean difference between the dipole locations induced by the modeled fontanel was 2.0 +/- 2.1 mm, with an average 2.1% increase in magnitude. Our results show that EEG source localization is feasible in neonates. With further development, the technique may prove useful for neurological evaluation of neonates.

Abnormal slow wave mapping (ASWAM)—A tool for the investigation of abnormal slow wave activity in the human brain

Slow waves in the delta and theta frequency range, normal signs of deactivated networks in sleep stages, are considered ‘abnormal’ when prominent in the waking state and when generated in circumscribed brain areas. Structural cortical lesions, e.g. related to stroke, tumors, or scars, generate focal electric and magnetic slow wave activity in the penumbra. Focal concentrations of slow wave activity exceeding those of healthy subjects have also been found in individuals suffering from psychiatric disorders without obvious structural brain damage. Hence, identification and mapping of abnormal slow wave activity might contribute to the investigation of cortical indications of psychopathology. Here I propose a method for abnormal slow wave mapping (ASWAM), based on a 5 min resting magnetoencephalogramm (MEG) and equivalent current dipole fitting to sources in the 1–4 Hz frequency band (delta) in anatomically defined cortical regions. The method was tested in a sample of 116 healthy subjects (59 males), with the aim to provide a basis for later comparison with patient samples. As to be expected, delta dipole density was low in healthy subjects. However, its distribution differed between genders with fronto-central > posterior dipole density in male and posterior dominance in female participants, which was not significantly related to either age or headsize. Results suggest that this method allows the identification of ASWA, so that comparison against Z-scores from a larger normal control group might assist diagnostic purposes in patient groups. As specific distributions seem to reflect differences between genders, this should be considered also in the analysis of patient samples.

Searching for the best model: ambiguity of inverse solutions and application to fetal magnetoencephalography

Fetal brain signals produce weak magnetic fields at the maternal abdominal surface. In the presence of much stronger interference these weak fetal fields are often nearly indistinguishable from noise. Our initial objective was to validate these weak fetal brain fields by demonstrating that they agree with the electromagnetic model of the fetal brain. The fetal brain model is often not known and we have attempted to fit the data to not only the brain source position, orientation and magnitude, but also to the brain model position. Simulation tests of this extended model search on fetal MEG recordings using dipole fit and beamformers revealed a region of ambiguity. The region of ambiguity consists of a family of models which are not distinguishable in the presence of noise, and which exhibit large and comparable SNR when beamformers are used. Unlike the uncertainty of a dipole fit with known model plus noise, this extended ambiguity region yields nearly identical forward solutions, and is only weakly dependent on noise. The ambiguity region is located in a plane defined by the source position, orientation, and the true model centre, and will have a diameter approximately 0.67 of the modelled fetal head diameter. Existence of the ambiguity region allows us to only state that the fetal brain fields do not contradict the electromagnetic model; we can associate them with a family of models belonging to the ambiguity region, but not with any specific model. In addition to providing a level of confidence in the fetal brain signals, the ambiguity region knowledge in combination with beamformers allows detection of undistorted temporal waveforms with improved signal-to-noise ratio, even though the source position cannot be uniquely determined.

Estimation of number of independent brain electric sources from the scalp EEGs.

In electromagnetic source analysis, many source localization strategies require the number of sources as an input parameter (e.g., spatio-temporal dipole fitting and the multiple signal classification). In the present study, an information criterion method, in which the penalty functions are selected based on the spatio-temporal source model, has been developed to estimate the number of independent dipole sources from electromagnetic measurements such as the electroencephalogram (EEG). Computer simulations were conducted to evaluate the effects of various parameters on the estimation of the source number. A three-concentric-spheres head model was used to approximate the head volume conductor. Three kinds of typical signal sources, i.e., the damped sinusoid sources, sinusoid sources with one frequency band and sinusoid sources with two separated frequency bands, were used to simulate the oscillation characteristics of brain electric sources. The simulation results suggest that the present method can provide a good estimate of the number of independent dipole sources from the EEG measurements. In addition, the present simulation results suggest that choosing the optimal penalty function can successfully reduce the effect of noise on the estimation of number of independent sources. The present study suggests that the information criterion method may provide a useful means in estimating the number of independent brain electrical sources from EEG/MEG measurements.

Source analysis of epileptic discharges using multiple signal classification analysis

Multiple signal classification is an alternative to the traditional dipole fitting source analysis methods. Our aim was to assess the clinical usefulness of this algorithm and to compare the localization of the epileptiform electroencephalography discharges with the regions of altered cerebral blood flow in 10 patients with complex partial seizures undergoing preoperative investigation. We performed multiple signal classification analysis of ictal and interictal discharges, and registered single-photon emission computed tomography. Localization of the ictal, but not the interictal discharges, as determined by multiple signal classification analysis was consistent with the regions showing perfusion changes on the single-photon emission computed tomography. Multiple signal classification analysis is a promising tool in localizing foci in patients with complex partial seizures and may contribute to the preoperative evaluation.

Automated localization of magnetoencephalographic interictal spikes by adaptive spatial filtering

Objective Automated adaptive spatial filtering techniques can be applied to magnetoencephalographic (MEG) data collected from people with epilepsy. Source waveforms estimated by these methods have higher signal-to-noise ratio (SNR) than spontaneous MEG data, allowing identification and location of interictal spikes. The software tool SAM( g 2) provides an adaptive spatial filtering algorithm for MEG data that yields source images of excess kurtosis and provides source time-courses in voxels exhibiting high excess kurtosis. The sensitivity and specificity of SAM( g 2) in epilepsy is unknown. Methods Interictal MEG data from 36 patients with intractable epilepsy were analyzed using SAM( g 2), and results compared with equivalent current dipole (ECD) fit procedures. Results When SNR of interictal spikes was high (compared to background) with a clear single focus, in most cases there was good agreement between ECD and SAM( g 2). With multiple foci, there was typically overlap but imperfect concordance between results of ECD and SAM( g 2). Conclusions SAM( g 2) may in some cases be equivalent to manual ECD fit for localizing interictal spikes with single locus and good SNR. Further studies are required to validate SAM( g 2) with multiple foci or poor SNR. Significance In some cases, SAM( g 2) might eventually assist or replace manual ECD analysis of MEG data.

Combining fMRI and MEG increases the reliability of presurgical language localization: A clinical study on the difference between and congruence of both modalities

To avoid neurological impairment during surgery near language-related eloquent brain areas, we performed presurgical functional brain mapping with functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) in 172 patients using language tasks. For MEG localizations, we used either a moving equivalent-current dipole fit or a current–density reconstruction using a minimum variance beamformer with a spatial filter algorithm. We localized the Wernicke and Broca language areas for every patient. We integrated the results into a frameless stereotaxy system. To visualize the results in the navigation microscope during surgery, we superimposed the fMRI and MEG findings on the brain surface. MEG and fMRI results differed in 4% of cases, and in 19%, one modality showed activation but not the other. In the vicinity of large gliomas, the BOLD (blood oxygenation level-dependent) effect was suppressed in 53% of our patients. Of the 124 patients who had surgery, only 7 patients (5.6%) experienced a transient language deterioration, which resolved in all cases. We used MEG and fMRI to show different aspects of brain activity and to establish validation between MEG and fMRI. We conclude that measurement by both MEG and fMRI increases the degree of reliability of language area localization and that the combination of fMRI and MEG is useful for presurgical localization of language-related eloquent cortex.

Efficient Localization of Synchronous EEG Source Activities Using a Modified RAP-MUSIC Algorithm

Synchronization across different brain regions is suggested to be a possible mechanism for functional integration. Noninvasive analysis of the synchronization among cortical areas is possible if the electrical sources can be estimated by solving the electroencephalography inverse problem. Among various inverse algorithms, spatio-temporal dipole fitting methods such as RAP-MUSIC and R-MUSIC have demonstrated superior ability in the localization of a restricted number of independent sources, and also have the ability to reliably reproduce temporal waveforms. However, these algorithms experience difficulty in reconstructing multiple correlated sources. Accurate reconstruction of correlated brain activities is critical in synchronization analysis. In this study, we modified the well-known inverse algorithm RAP-MUSIC to a multistage process which analyzes the correlation of candidate sources and searches for independent topographies (ITs) among precorrelated groups. Comparative studies were carried out on both simulated data and clinical seizure data. The results demonstrated superior performance with the modified algorithm compared to the original RAP-MUSIC in recovering synchronous sources and localizing the epileptiform activity. The modified RAP-MUSIC algorithm, thus, has potential in neurological applications involving significant synchronous brain activities.

MEG and EEG Source Localization in Beamspace

Beamspace methods are applied to EEG/MEG source localization problems in this paper. Beamspace processing involves passing the data through a linear transformation that reduces the data dimension prior to applying a desired statistical signal processing algorithm. This process generally reduces the data requirements of the subsequent algorithm. We present one approach for designing beamspace transformations that are optimized to preserve source activity located within a given region of interest and show that substantial reductions in dimension are obtained with negligible signal loss. Beamspace versions of maximum likelihood dipole fitting, MUSIC, and minimum variance beamforming source localization algorithms are presented. The performance improvement offered by the beamspace approach with limited data is demonstrated by bootstrapping somatosensory data to evaluate the variability of the source location estimates obtained with each algorithm. The quantitative benefits of beamspace processing depend on the algorithm, signal to noise ratio, and amount of data. Dramatic performance improvements are obtained in scenarios with low signal to noise ratio and a small number of independent data samples.

Bayesian analysis of the neuromagnetic inverse problem with ℓp-norm priors

Magnetoencephalography (MEG) allows millisecond-scale non-invasive measurement of magnetic fields generated by neural currents in the brain. However, localization of the underlying current sources is ambiguous due to the so-called inverse problem. The most widely used source localization methods (i.e., minimum-norm and minimum-current estimates (MNE and MCE) and equivalent current dipole (ECD) fitting) require ad hoc determination of the cortical current distribution ( ℓ 2-, ℓ 1-norm priors and point-sized dipolar, respectively). In this article, we perform a Bayesian analysis of the MEG inverse problem with ℓ p -norm priors for the current sources. This way, we circumvent the arbitrary choice between ℓ 1- and ℓ 2-norm prior, which is instead rendered automatically based on the data. By obtaining numerical samples from the joint posterior probability distribution of the source current parameters and model hyperparameters (such as the ℓ p -norm order p) using Markov chain Monte Carlo (MCMC) methods, we calculated the spatial inverse estimates as expectation values of the source current parameters integrated over the hyperparameters. Real MEG data and simulated (known) source currents with realistic MRI-based cortical geometry and 306-channel MEG sensor array were used. While the proposed model is sensitive to source space discretization size and computationally rather heavy, it is mathematically straightforward, thus allowing incorporation of, for instance, a priori functional magnetic resonance imaging (fMRI) information.

Gluon distributions and fits using dipole cross sections

I investigate the relationship between the gluon distribution obtained using a dipole model fit to low-x data on F_2(x,Q^2) and standard gluons obtained from global fits with the collinear factorization theorem at fixed order. I stress the necessity to do fits of this type carefully, and in particular to include the contribution from heavy flavours to the inclusive structure function. I find that the dipole cross-section must be rather steeper than the gluon distribution, which at least partially explains why dipole model fits produce dipole cross-sections growing quite strongly at small x, while DGLAP based fits have valence-like, or even negative, small-x gluons as inputs. However, I also find that the gluon distributions obtained from the dipole fits are much too small to match onto the conventional DGLAP gluons at high Q^2, i.e. approx 50 GeV^2, where the two approaches should coincide. The main reason for this discrepancy is found to be the large approximations made in converting the dipole cross-sections into structure functions using formulae which are designed only for asymptotically small x. The shortcomings in this step affect the accuracy of the extracted dipole cross-sections in terms of size and shape, and hence also in terms of interpretation, at all scales.

Human posterior auditory cortex gates novel sounds to consciousness.

Life or death in hostile environments depends crucially on one's ability to detect and gate novel sounds to awareness, such as that of a twig cracking under the paw of a stalking predator in a noisy jungle. Two distinct auditory cortex processes have been thought to underlie this phenomenon: (i) attenuation of the so-called N1 response with repeated stimulation and (ii) elicitation of a mismatch negativity response (MMN) by changes in repetitive aspects of auditory stimulation. This division has been based on previous studies suggesting that, unlike for the N1, repetitive "standard" stimuli preceding a physically different "novel" stimulus constitute a prerequisite to MMN elicitation, and that the source loci of MMN and N1 are different. Contradicting these findings, our combined electromagnetic, hemodynamic, and psychophysical data indicate that the MMN is generated as a result of differential adaptation of anterior and posterior auditory cortex N1 sources by preceding auditory stimulation. Early ( approximately 85 ms) neural activity within posterior auditory cortex is adapted as sound novelty decreases. This alters the center of gravity of electromagnetic N1 source activity, creating an illusory difference between N1 and MMN source loci when estimated by using equivalent current dipole fits. Further, our electroencephalography data show a robust MMN after a single standard event when the interval between two consecutive novel sounds is kept invariant. Our converging findings suggest that transient adaptation of feature-specific neurons within human posterior auditory cortex filters superfluous sounds from entering one's awareness.

Localization of auditory N1 in children using MEG: source modeling issues

Techniques for localizing auditory (AEF) sources are a topic of on-going discussion and this is particularly pertinent in pediatric research. Smaller head sizes are: (1) subject to bilateral temporal lobe source interference from both temporal lobes; and (2) further from MEG sensors resulting in poorer signal-to-noise ratios. An additional consideration in children is that the components of the AEF have distinct contributions along the development spectrum resulting in an ever-changing morphology for the pediatric AEF. These factors present a complicated picture for dipole fitting and raise the question of the most effective fitting strategy. We examined the AEF localizations in five children from 151, 70 and 47 MEG channels of data. We found evidence that bilateral source interaction could result in localization errors along the medial–lateral axis of up to 1 cm. We suggest that any modeling strategy needs to sufficiently account for this interaction and more precise models allowing for multiple sources need to be developed.

Quasi-Elastic Electron-Deuteron Scattering and Calculation of Neutron Electromagnetic Form Factors at Q2 = 1.75 to 4.00 (GeV/c)2

Electric and Magnetic form factors of neutron are calculated via electron-deuteron scattering at 5.507 GeV energy using SLAC group data. Our results show that the neutron electric form factor is not equal to zero; rather it has a small value, indicating that in spite of the fact that total charge is almost neutral, there is a nonuniform charge distribution within the neutron, and that magnetic form factor follows the dipole fit.

The Permanent and Inductive Magnetic Moments of Ganymede

Data acquired by the Galileo magnetometer on five passes by Ganymede have been used to characterize Ganymede's internal magnetic moments. Three of the five passes were useful for determination of the internal moments through quadrupole order. Models representing the internal field as the sum of dipole and quadrupole terms or as the sum of a permanent dipole field upon which is superimposed an induced magnetic dipole driven by the time varying component of the externally imposed magnetic field of Jupiter's magnetosphere give equally satisfactory fits to the data. The permanent dipole moment has an equatorial field magnitude 719 nT. It is tilted by 176° from the spin axis with the pole in the southern hemisphere rotated by 24° from the Jupiter-facing meridian plane toward the trailing hemisphere. The data are consistent with an inductive response of a good electrical conductor of radius approximately 1 Ganymede radius. Although the data do not enable us to establish the presence of an inductive response beyond doubt, we favor the inductive response model because it gives a good fit to the data using only four parameters to describe the internal sources of fields, whereas the equally good dipole plus quadrupole fit requires eight parameters. An inductive response is consistent with a buried conducting shell, probably liquid water with dissolved electrolytes, somewhere in the first few hundred km below Ganymede's surface. The depth at which the ocean is buried beneath the surface is somewhat uncertain, but our favored model suggests a depth of the order of 150 km. As both temperature and pressure increase with depth and the melting temperature of pure ice decreases to a minimum at ∼170 km depth, it seems possible that near this location, a layer of water would be sandwiched between layers of ice.