Multiple Dipole Model Research Articles

Dipole-modeling of the visual evoked P300

We collected visual event-related potentials (ERPs) from 6 normal subjects using an “oddball” paradigm. Subjects were required to count the occurrences of matching shapes presented in the left and right visual field. Shapes matched on 20% of trials. ERPs were recorded from 20 or 43 electrodes distributed over the scalp. A multiple spatio-temporal equivalent dipole (ED) model was used to fit the early sensory and P300 component. A latency window to analyze the P300 was determined using the global field power statistic. The spatial topography of the P300 over this window was characterized by a midline positivity that decreased in amplitude with spatial distance from the peak. After sensory components were fit, the source of P300 could be accounted for by 1 or 2 EDs, which were usually located near medial temporal areas. This result is at odds with evidence from depth recordings during the oddball paradigm, showing that multiple regions of the brain are active during this interval.

Electric source localization of the auditory P300 agrees with magnetic source localization

The event-related cortical potential elicited in the context of auditory target detection tasks includes the N1, P2 and P3 components. The aim of the present study was to identify the sources of these scalp-recorded components using an electrical multiple dipole model. Nine healthy adults volunteered for the study. An auditory oddball paradigm was used. Stimuli (18% target and 82% non-target tones) were delivered through ear-phones and subjects were required to silently count the targets. Event-related potentials (ERPs) to these stimuli were recorded by 30 electrodes placed on the scalp. The identification of the sources of the ERP was attempted using the brain electric source analysis (BESA) program. The instantaneous source locations of N1, P2 and P3 reported in magnetoencephalographic (MEG) literature were used as initial starting locations for the spatio-temporal multiple dipole modeling of the EEG data. First the auditory long latency responses were modeled separately. Bilateral superior temporal plane sources with almost vertical orientations explained the first 250 msec window of the non-target tone recording including Nl P2 complex. This agrees with MEG source localization of N1 m P2 m . Two slightly deeper dipoles in superior temporal gyri and bilateral dipoles in hippocampi or parahippocampal areas explained P3 (analysis window 250–600 msec). The final model explained the complete epoch of 600 msec with 6 dipoles and the residual variances of individual models ranged from 3.83% to 7.77%. The concordance between MEG and BESA source localization results supports the notion of generators in temporal lobes for the Nl P2 complex and generators in temporal and hippocampal areas for the P3 component.

Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm

The paper describes a new algorithm for tomographic source reconstruction in neural electromagnetic inverse problems. Termed FOCUSS ( FOCal Underdetermined System Solution), this algorithm combines the desired features of the two major approaches to electromagnetic inverse procedures. Like multiple current dipole modeling methods, FOCUSS produces high resolution solutions appropriate for the highly localized sources often encountered in electromagnetic imaging. Like linear estimation methods, FOCUSS allows current sources to assume arbitrary shapes and it preserves the generality and ease of application characteristic of this group of methods. It stands apart from standard signal processing techniques because, as an initialization-dependent algorithm, it accommodates the non-unique set of feasible solutions that arise from the neuroelectric source constraints. FOCUSS is based on recursive, weighted norm minimization. The consequence of the repeated weighting procedure is, in effect, to concentrate the solution in the minimal active regions that are essential for accurately reproducing the measurements. The FOCUSS algorithm is introduced and its properties are illustrated in the context of a number of simulations, first using exact measurements in 2- and 3-D problems, and then in the presence of noise and modeling errors. The results suggest that FOCUSS is a powerful algorithm with considerable utility for tomographic current estimation.

Evaluation of abnormal low frequency magnetic activity (AL-FMA) in epilepsy

MEG attempts to define regions of epileptic pathology in patients with a seizure history are compromised by several factors. First, most studies are interictal in nature, an issue of concern to many epileptologists. Also, in some cases epileptic magnetic field patterns are highly complex and not amenable to simple single or even multiple dipole modeling. A final concern is the observation that most patients have seizures only very intermittently, with their interictal EEG often devoid of epileptic spikes and sharpwaves.

Tonotopic organization of the human auditory cortex: N100 topography and multiple dipole model analysis

The tonotopic organization of the human auditory cortex has been investigated by means of scalp potential mapping and dipole modelling of the evoked response occurring around 100 msec after the stimulus onset. The major characteristics of the topographical changes observed with increasing stimulus frequency were statistically demonstrated. Using a 3-concentric sphere head model, the scalp potential distributions can be explained in first approximation by two equivalent current dipoles, located in the supratemporal plane and mimicking the activity of both auditory cortices. To take into account the temporal aspects of the brain activities, 3 time-varying dipole strategies were tested. Frequency dependence of the dipole orientation has been evidenced in both hemispheres with the 3 models, whereas no significant change in dipole position was found. The tilt in dipole orientation could be related to the folding geometry of Heschl's gyrus, which varies with depth. In agreement with previous MEG findings, this brings new evidence for a tonotopic organization of the auditory cortical area involved in the N100 wave generation. Moreover, distinct frequency dependences of the equivalent current dipoles were observed in the early and the late parts of the N100. This study demonstrates that simple dipolar models, applied on electrical data, make it possible to reveal functionally distinct cortical areas.

Temporal dynamics of visual-evoked neuromagnetic sources: Effects of stimulus parameters and selective attention

Results are reviewed from several neuromagnetic studies which characterize the temporal dynamics of neural sources contributing to the visual evoked response and effects of attention on these sources. Different types of pattern-onset stimuli (< or = 2 degrees) were presented sequentially to a number of field locations in the right visual field. Multiple dipole models were applied to a sequence of instantaneous field distributions constructed at 10 ms intervals. Best-fitting source parameters were superimposed on Magnetic Resonance images (MRI) of each subject to identify the anatomical structure(s) giving rise to the surface patterns. At least three sources, presumably corresponding to different visual areas, were routinely identified from 80-150 ms following the onset of visual stimulation. This observation was consistent across subjects and studies. The temporal sequence and strength of activation of these sources, however, were dependent upon the specific stimulus parameters used to evoke the response (e.g., eccentricity) and on the relevance of the stimulus to the subject. In addition, our results provide evidence for the recurrence of activity in striate and extrastriate regions, following the initial cycle of responses.

Propagation of interictal epileptic activity in temporal lobe epilepsy

We recorded interictal spikes with closely spaced scalp electrodes and sphenoidal electrodes in four patients with temporal lobe epilepsy. We used multiple dipole modeling to study the number, three-dimensional intracerebral location, time activity, and functional relationship of the neuronal sources underlying the epileptic spike complexes. In all patients, we found two significant sources generating the interictal spikes which showed considerable overlap in both space and time. Source 1 was located in the mesiobasal temporal lobe and generated a restricted negativity at the ipsilateral sphenoidal electrode and a widespread positivity over the vertex. Source 2 could be attributed to the lateral temporal neocortex and was associated with a relatively restricted negativity at the ipsilateral temporal electrodes and a more widespread positivity over the contralateral hemisphere. The sources were well separated in space, with an average distance of 45 mm between them. The time activities of both sources showed similar biphasic patterns, with the mesial source leading the lateral source by approximately 40 msec, suggesting propagation of interictal epileptic activity from the mesiobasal to the lateral temporal lobe.

Spatio-temporal MEG patterns produced by spreading multiple dipoles

A spreading multiple dipole model which can describe the spatial distribution of sources is proposed. Using the source model, spatio-temporal patterns of MEGs are simulated. Effects of the spreading multiple dipoles on spatio-temporal magnetic fields are investigated. The authors showed that the topography of the peak latency is able to give important information in estimating the source in the brain.

Source analysis of generalized spike-wave complexes.

Dipole source analysis was carried out in three adults and four children with 3 c/s generalized spike-wave (SW) discharges and absence seizures. Eighty-seven SW complexes were investigated. When one regional source was used the equivalent location was always near the baso-frontal area close to the midline. It explained on the average 89% of the variance in the adults and 82% in the children. When two regional sources were used and initially constrained for symmetry, the residual variance (RV) was reduced to 7% in the adults and 9% in the children. The sources remained in the frontal areas and were on the average 2 cm from the midline. When the mirror source was freed it remained contralateral in 76% of the complexes but moved ipsilaterally to various locations in the rest. To reduce the RV to between 2 and 3% one or two additional regional sources were required. These were located in the temporal or parietal areas in the adults and occasionally one occipital region in the children. The study showed that widespread and repetitive EEG events, like the generalized SW, can lend themselves to spatio-temporal multiple dipole modeling. More precise anatomic correlates may become possible with an expanded electrode array and the verification of their locations against the patient's MRI scan.

Dipole source localization in a case of epilepsia partialis continua without premyoclonic EEG spikes

A 72-year-old woman with epilepsia partialis continua (EPC) of the right foot is presented. Rhythmic myoclonic jerks were localized to the 1st and 2nd toes of the right foot and persisted for 72 h. EEG/video monitoring did not show any epileptiform transient in association with myoclonic jerks. MRI and MRA demonstrated an arterio-venous malformation involving the left fronto-parietal parasagittal area. Using the EMG signal from the myoclonic jerk we back-averaged the EEG 640 msec before and after the onset of the twitch. A negative-positive deflection was observed preceding the myoclonic jerks by 128–188 msec. Voltage topographic mapping showed a negative maximum in the left centro-parietal region. A multiple spatio-temporal dipole model was applied to the back-averaged deflection preceding the myoclonus. The patient's MRI was used to determine the center of the best fitting sphere, and the model was corrected accordingly. The best dipole solution consisted of 3 dipoles localized in the parasagittal frontal cortex, in the location of the motor representation for the foot. The utilization of a combined technique of back-averaging from the myoclonus and dipole source localization supported the epileptogenic etiology in this case.

From EEG source localization to source imaging.

A new functional imaging technique, "FOCUS", has been developed to transform the traditional scalp EEG into an image of source activities. The image is based on multiple spatio-temporal dipole models and consists of gross spatial patterns and source waveforms reflecting the estimated activities of the different brain regions. The application of the 'FOCUS' technique to the EEG in temporal lobe epilepsy revealed the presence of different activities at the basal and lateral aspects of the temporal lobe. The source waveforms showed propagation patterns consistent with subdural recordings which were not recognizable in the scalp EEG.

Non-invasive localization of the epileptogenic focus by EEG dipole modeling.

Localization of epileptogenic foci by traditional visual inspection of EEG traces is simplistic. Voltage topography and subsequent spatio-temporal multiple dipole modeling are new techniques to assess the character of cerebral generators of EEG spikes and seizure rhythms. These predictions have been validated by intracranial monitoring. Patients with mesial temporal seizures have ipsilateral spikes and early ictal rhythms with a strong tangential (vertical) dipole component that often leads any radial source activity. This suggests propagation from baso-mesial to lateral cortex. Those with infero-lateral temporal cortical seizures have similar findings, but tangential sources are synchronous with or lag radial sources. Patients with lateral temporal cortical seizures have spikes and ictal activity that are modeled principally by radial dipoles.

Multiple current dipole estimation using simulated annealing.

A method for estimating electrical current distribution in the human brain using a multiple current dipole model is presented. A cost function for estimating multiple dipoles is proposed and a simulated annealing algorithm is used to obtain an acceptable solution. Computer simulation is used to evaluate the effectiveness of this method.

Simulation studies of multiple dipole neuromagnetic source localization: model order and limits of source resolution

Numerical simulation studies were performed using a multiple dipole source model and a spherical approximation of the head to examine how the resolution of simultaneously active neuromagnetic sources depends upon: 1) source modeling assumptions (i.e., number of assumed dipoles); 2) actual source parameters (e.g., location, orientation, and moment); and 3) measurement errors. Forward calculations were conducted for a series of source configurations in which the number of dipoles, specific dipole parameters, and noise levels were systematically varied. Simulated noisy field distributions were fit by multiple dipole models of increasing model order (1, 2, ..., 6 and alternative statistical approaches (i.e., percent of variance, reduced chi-square, and F-ratio) were compared for their effectiveness in determining adequate model order. Limits of spatial resolution were established for a variety of multi-source configurations and noise conditions. Implications for the analysis of empirical data are discussed.

Models of source currents in the brain.

Electroencephalography (EEG) and magnetoencephalography (MEG) provide signals that are weighted integrals of source currents in the brain. In addition to technical aspects, the two methods differ in their sensitivities to various cerebral sources. Moreover, it is more difficult to determine the lead fields of EEG than of MEG. If it can be assumed that only one localized source is active at a particular time, the source location, direction, and amplitude can be found with the dipole model. However, if the assumption of a single localized source is violated, erroneous results are obtained. If a few sources are responsible for the measured fields, multiple-dipole models can be used. In the general case one must start from the fundamentals of estimation theory. The use of a priori information, together with experimental data, will provide the best possible solution to the inverse problem. In the case of minimal prior information, the so-called minimum-norm solution is obtained. With the help of supplementary information, the resolution can be further improved.

Identification of the visual motion area (area V5) in the human brain by dipole source analysis.

The retinal periphery of nine healthy subjects was stimulated with computer-generated random-dot kinematograms. These stimuli provided almost isolated visual motion information and minimal position cues. Pattern-reversal stimuli at the same location in the visual field were used for control. Stimulus-related electrical brain activity was recorded from 29 scalp electrodes. Total mean and individual data were analyzed with a spatiotemporal multiple dipole model. The scalp potentials showed a different spatial distribution for motion and pattern stimulation in the time range of 160-200 ms. In this epoch, the predominant motion-related source activity was localized in the region of the contralateral occipital-temporal-parietal border. A significant ipsilateral source activity was not found. The predominant source activity related to the pattern stimulus occurred in the same epoch. The corresponding equivalent dipole was localized more medially and deeper in the brain. The orientation of these major dipole activities was markedly different. These dipoles appeared to represent activity of distinct extrastriate areas, in contrast to earlier activity which was modelled by more posterior dipoles in the occipital lobe. The latter dipoles were at comparable contralateral locations and had similar peak activities around 100 ms, suggesting an origin in the striate cortex.

Multiple dipole modeling and localization from spatio-temporal MEG data.

An array of biomagnetometers may be used to measure the spatio-temporal neuromagnetic field or magnetoencephalogram (MEG) produced by neural activity in the brain. A popular model for the neural activity produced in response to a given sensory stimulus is a set of current dipoles, where each dipole represents the primary current associated with the combined activation of a large number of neurons located in a small volume of the brain. An important problem in the interpretation of MEG data from evoked response experiments is the localization of these neural current dipoles. We present here a linear algebraic framework for three common spatio-temporal dipole models: i) unconstrained dipoles, ii) dipoles with a fixed location, and iii) dipoles with a fixed orientation and location. In all cases, we assume that the location, orientation, and magnitude of the dipoles are unknown. With a common model, we show how the parameter estimation problem may be decomposed into the estimation of the time invariant parameters using nonlinear least-squares minimization, followed by linear estimation of the associated time varying parameters. A subspace formulation is presented and used to derive a suboptimal least-squares subspace scanning method. The resulting algorithm is a special case of the well-known MUltiple SIgnal Classification (MUSIC) method, in which the solution (multiple dipole locations) is found by scanning potential locations using a simple one dipole model. Principal components analysis (PCA) dipole fitting has also been used to individually fit single dipoles in a multiple dipole problem. Analysis is presented here to show why PCA dipole fitting will fail in general, whereas the subspace method presented here will generally succeed. Numerically efficient means of calculating the cost functions are presented, and problems of model order selection and missing moments are discussed. Results from a simulation and a somatosensory experiment are presented.

Moving multiple dipole model for cardiac activity.

A single-dipole model and a two-dipole model have been examined to approximate the electrical activity of heart; positions as well as vector components of these dipoles were estimated from the body surface potential distribution that was measured with 64 electrodes arranged on the chest. The "residue" has been defined as a measure for how much potential component is left that cannot be attributed to the equivalent dipoles. A locus of the vector end of an equivalent dipole in the single-dipole model is very much like ordinary vectorcardiogram (VCG). The residue has a peak in the last half of QRS; this means that the single-dipole approximation is not valid there. Then another dipole is introduced, which is the two-dipole approximation. The residue has been greatly reduced and the peak disappears; the resultant two dipoles move around in the right and left parts of the heart with nearly opposite directions. The moving-two-dipole model for normal subjects describes the cardiac activity in QRS much better than with the moving-single-dipole model.

Effects of modeling errors on least squares error solutions to the inverse problem of electrocardiology

Modeling errors produced by differences between an actual electrical source in the heart and a model of the source have effects on least squares error (LSE) solutions for the model. These effects are analyzed using linear algebra theory and some modeling errors representative of those for actual heart measurements. It is found that increasing the number of dipoles in a multiple-dipole (MD) model increases the sensitivity of the solutions to small modeling error changes while increasing the number of terms in a multipole expansion (ME) model is likely to improve the accuracy of the solution for the dipolar terms. The results show that a MD model with more than two free-orientation dipoles will not provide accurate, useful, or reliable information for the representative modeling errors. Accurate solutions for the dipolar terms in a ME model are obtained for a model containing dipole, quadrupole, and octupole terms for these modeling errors. A new type of “average” LSE (AVL) solution for MD models with fixed-orientation dipoles is developed and compared with LSE and nonnegative LSE (NNL) solutions; the AVL solutions are found to be least sensitive to small modeling error changes but to provide misleading information for certain modeling errors. Finally, it is found that once a certain density of measurements is reached, the effects of modeling errors are nearly independent of the measurements used and, hence, no improvement in the solutions can be obtained by increasing the number of measurements.

Multiple magnetic dipole modeling and field prediction of satellites

A new method for the analysis of the dc magnetic properties of spacecraft and their subassemblies is proposed. The method, which is applicable as well to a more general variety of problems, is based on a multiple dipolar modeling of the test object; a very effective optimization procedure of the Gauss-Newton type is used to determine the dipole positions and moments of the model which reconstitute in a best manner the dc magnetic field measurements (least squares fit). Application to one subassembly and two complete spacecraft allows to appreciate the capabilities of the method to help in solving the recently more and more difficult problems in the field of dc magnetic cleanliness efforts (analysis and compensation) of spacevehicles.