Current Dipole Source Research Articles

Numerical Calculation of the Potential Distribution Due to Dipole Sources in a Spherical Model of the Head

A three-dimensional spherical model of the head was investigated numerically. The model consists of four conductive layers representing the scalp, the skull, the cerebrospinal fluid, and the cortex with a dipole current source. The potential created by the dipole was calculated using quasistatic formulation and a linear medium. The volume conduction equation was discretized by the finite volume method to ensure the conservation of fluxes and efficient solution method. The large set of algebraic equations for the electric potential was solved iteratively by the successive over relaxation method. The new formulation of the volume conduction problem was validated by comparing the numerical results with two analytical solutions. The first test-case considers a homogeneous spherical model with a dipole in the center. The potential on the outer surface, as well as within the volume conductor, was calculated and very good agreement was obtained with the analytical solution. In the second test-case, the scalp potential due to a radially oriented eccentric dipole in a four concentric spheres model was compared with an analytic solution. It was found that a grid of 90 × 90 × 90 volume elements yielded accurate results on the scalp surface with errors on the order of 1%. The present numerical model can be extended to general cases with any volume conductor shape or with any distribution or orientation of the current dipoles. Compared to other numerical methods, this approach offers enhanced accuracy for given computational resources (both in CPU time and memory). The gain might be more than one order of magnitude, allowing simulation with considerably larger meshes.

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.

Minimum-norm estimation in a boundary-element torso model

The paper deals with the bioelectric and biomagnetic inverse problems. The authors present a method to estimate primary-current distributions in a homogeneous, realistically shaped boundary-element torso model. The reconstruction surface is triangulated to keep the procedure computationally feasible. The minimum-norm estimate is computed on the basis of separate electric and magnetic signals, as well as from combined data. The method can be used both for heart and brain studies. Simulation results for current-dipole sources in a homogeneous realistic torso are discussed.

Estimation of electric fields in the conducting Earth's crust for oscillating electric current dipole sources and implications for anomalous electric fields associated with earthquakes

Electromagnetic radiation, possibly associated with earthquake occurrences in the Earth's crust, can be treated as a problem of electromagnetic induction within a conducting half-space representing the crust. We estimated the magnitude of the electric field near the Earth's surface for oscillating electric current dipole sources located at various depths. This shows that the electric field highly attenuates, as expected, and the source must be stronger than 10 5 A · m, even if it is located at a depth of several kilometers, for practically detecting signals at frequencies in the ULF (ultra-low frequency) range. We also examined the electric field near the Earth's surface for a box-car type source in uniform and non-uniform crust models. We found that the wave form of the source is rather well preserved in both models but signal amplitudes are very small and unlikely to be drastically enhanced even in a non-uniform crustal structure, although this discussion is based only on a specific non-uniform model.

Magnetic field responses to visual stimulation in human parietal association cortex

The neural activities of the parietal association cortex were studied in humans through the use of a 37-channel SQUID magnetometer system. The magnetic field responses were recorded in the parietal association cortex following visual stimulation with LED light. Main responses peaking at about 120, 170 and 220 msec after LED onset were observed. The estimated current dipole sources of the magnetic field responses at latencies of 160–190 and 210–270 msec were revealed to be located in the intraparietal sulcus. A change in the magnetic field responses with the eye position was found in the amplitude.

Non-invasive magnetocardiographic localization of ventricular pre-excitation in the Wolff-Parkinson-White syndrome using a realistic torso model.

This study was performed to evaluate the accuracy of magnetocardiography in non-invasive localization of the ventricular pre-excitation site in patients suffering from the Wolff-Parkinson-White (WPW) syndrome. Twelve WPW patients were studied, in whom the pre-excitation caused serious supraventricular arrhythmias refractory to drug therapy. Magnetocardiographic measurements were performed in a magnetically shielded room, and non-invasive localization was computed from preprocessed magnetic signals using a current dipole source in a realistically shaped digital torso. All patients underwent intra-operative multicatheter mapping and subsequent dissection of the accessory atrioventricular connection. The intra-operative localization results were marked on magnetic resonance images of the heart, where magnetocardiographic results were also superimposed to allow comparison. The average of the three-dimensional differences between the magnetocardiographic and the invasive results was 2.1 +/- 0.9 cm. In all cases, the computed localization result was in the same or adjacent anatomical region as the intra-operative result. The present results show that the magnetocardiographic method using a realistic torso model is capable of localizing pre-excitation sites with sufficient accuracy to provide extra information so that non-pharmacological therapeutic interventions can be applied.

Analysis of errors in neuromagnetic localization of multiple current dipole sources

Describes a calculation algorithm for the neuromagnetic localization of multiple current-dipole sources and a computer simulation study using the method. In the simulation, source localizations were obtained for dipolar and multipolar field patterns subject to different levels of Gaussian noises. The results show that the present algorithm is useful for localizing multiple dipoles in low signal-to-noise ratio conditions and that the location accuracy depends on the signal-to-noise ratio, the distance between dipoles and the depth of the dipoles.

Three-dimensional localization of SMA activity preceding voluntary movement

Previous studies by magnetoencephalography (MEG) failed to consistently localize the activity of the supplementary motor area (SMA) prior to voluntary movements in healthy human subjects. Based on the assumption that the SMA of either hemisphere is active prior to voluntary movements, the negative findings of previous studies could be explained by the hypothesis that magnetic fields of current dipole sources in the two SMAs may cancel each other. The present MEG study was performed in a patient with a complete vascular lesion of the right SMA. In this case it was possible to consistently localize a current dipole source in the intact left SMA starting about 1200 msec prior to the initiation of voluntary movements of the right thumb. Starting at about 600 msec prior to movement onset the assumption of a current dipole source in the left primary motor cortex was needed to account for the observed fields. Measurements of brain potentials were consistent with MEG findings of activity of the left SMA starting about 1200 msec prior to movement onset.

Cerebral magnetic fields to lingual stimulation

We recorded cerebral magnetic fields to electric stimulation of the tongue in 7 healthy adults. The two main deflections of the response peaked around 55 msec (P55m) and 140 msec (N 140 m). During both oof them the magnetic field pattern, determined with a 7- or 24-channel SQUID magnetometer, suggested a dipolar current source. The topography of P55m can be explained by a tangential dipole at the first somatosensory cortex (SI) in the posterior wall of the central sulcus. The equivalent source of N140m is, on average, about 1 cm lateral to the source of P55m. The reported method allows non-invasive determination of the cortical tongue representation area.

Orthogonal expansions: their applicability to signal extraction in electrophysiological mapping data

The applicability of orthogonal expansions (singular-value decomposition, Karhunen-Loève transform and principal-component analysis) for the purpose of identifying source distributions associated with definite electrophysiological events in the heart and brain is explored with a current dipole source model. By definition, the expansion eigenvectors are orthogonal, and as such will extract the features of one specific source only if all other secondary signals are orthogonal to that first source. The number of significant eigenvectors can be related to the number of original components forming a signal, but there is not a one-to-one correspondence between these eigenvectors and the individual components. Furthermore, many eigenvectors may be needed to faithfully represent even a single source, if that source is nonstationary. We conclude that generally it would be inappropriate to ascribe any physiological significance to the data resulting from such expansions.

Neuromagnetic fields accompanying unilateral and bilateral voluntary movements: topography and analysis of cortical sources

Movement-related magnetic fields (MRMFs) accompanying left and right unilateral and bilateral finger flexions were studied in 6 right-handed subjects. Six different MRMF components occurring prior to, and during both unilateral and bilateral movements are described: a slow pre-movement readiness field (RF, 1–0.5 sec prior to movement onset); a motor field (MF) starting shortly before EMG onset; 3 separate “movement-evoked” fields following EMG onset (MEFI at 100 msec; MEFII at 225 msec; and MEFIII at 320 msec); and a “post-movement” field (PMF) following the movement itself. The bilateral topography of the RF and MF for both unilateral and bilateral movements suggested bilateral generators for both conditions. Least-squares fitting of equivalent current dipole sources also indicated bilateral sources for MF prior to both unilateral and bilateral movements with significantly greater strength of contralateral sources in the case of unilateral movements. Differences in pre-movement field patterns for left versus right unilateral movements indicated possible cerebral dominance effects as well. A single current dipole in the contralateral sensorimotor cortex could account for the MEFI for unilateral movements and bilateral sensorimotor sources for bilateral movements. Other MRMF components following EMG onset indicated similar sources in sensorimotor cortex related to sensory feedback or internal monitoring of the movement. The results are discussed with respect to the possible generators active in sensorimotor cortex during unilateral and bilateral movement preparation and execution and their significance for the study of cortical organization of voluntary movement.

Magnetic fields of current monopoles in special volume conductors

A theory for deriving the magnetic fields generated by monopoles of current (i.e. point sources of current) located in two volume conductor shapes is presented. The solution is derived for the magnetic field exterior to a semi-infinite conducting volume and exterior to a conducting spherical volume. In both volumes, the magnetic field of the dipole volume current is shown to be a spatial derivative of the magnetic field due to a current monopole. The magnetic field exterior to the semi-infinite volume conductor is equivalent to that of a semi-infinite line current, starting at the position of the monopole, oriented perpendicular to the surface of the conducting volume, and flowing toward infinity. The field exterior to a conducting sphere is equivalent to that generated by a finite-length line current flowing from the position of the monopole to the center of the sphere. Current monopoles can be used in lieu of dipole current sources to reduce source modeling errors and to better understand the effects of volume currents.

Magnetocardiographic localisation and modelling

In our magnetocardiographic (MCG) localisation studies, two modelling approaches have been applied: (a) modelling the sources with dipole and quadrupole moments in a general multipole expansion and using a homogeneous, semi-infinite volume conductor, and (b) using a single current dipole source in a homogeneous, realistically shaped torso. Both approaches have been successfully applied in localising the premature ventricular excitation site in patients suffering from the Wolff-Parkinson-White syndrome. In addition, we have participated in developing a model of propagation of electrical activation in the ventricles. Anisotropic conductivity properties and spiral arrangement of myocardial fibres are included in the model.

Gender differences in source location for the N100 auditory evoked magnetic field

Auditory evoked magnetic fields were recorded in response to contralateral stimulation over the right hemisphere in 6 adult males and 6 adult females. The data were fit to a model of a current-dipole source in a homogeneous sphere and 5 parameters of the dipole were computed — 3 spatial coordinates, orientation, and strength. When average values for the dipole parameters were compared between sexes, it was found that the current source for the N100 m is located more than 1 cm posterior in females and is oriented pointing more downward. These findings were replicated in separate measurements sessions. Viewing of individual magnetic resonance images did not reveal a corresponding anatomical disparity in the location of the primary auditory cortex which is assumed to produce the N100 m. Therefore, functional organization of the auditory cortex may be different for the sexes.

Neuromagnetic topography of photoconvulsive response in man

The neuromagnetic method was applied to the study of photoconvulsive responses. The identification of specific magnetic field distributions over the scalp was achieved by: (a) a stimulation paradigm consisting of series of trains of flicker stimuli randomly presented to the epileptic patient, after eye closure, to get epileptic responses while avoiding seizures; (b) a novel procedure for data analysis, to select consistent responses. These patterns, when sufficiently stable in time and dipolar in shape, were used for source localization in the usual biomagnetic framework of the equivalent current dipole source representation. The results of this approach suggest that different specific cortical areas are repeatedly and randomly activated, involving mainly the frontal, occipital and temporal areas, often with a hemispheric prevalence.

Neuromagnetic fields accompanying unilateral finger movements: pre-movement and movement-evoked fields.

Neuromagnetic fields accompanying voluntary flexions of the right index finger were studied in five subjects. In all subjects, slow magnetic fields were observed over the central scalp beginning about 1 second prior to movement onset. These fields displayed a similar time course to the electrically recorded "readiness potential", but with reversals of field direction over regions of the rolandic fissure over both hemispheres. Least-squares fitting of two current dipole sources for the pre-movement fields resulted in a consistent localization of one source in the region of the rolandic fissure contralateral to the side of movement in four subjects. Ipsilateral dipole sources fitted inconsistently at deeper locations or outside the head indicating the inability of a single dipole source to account for the ipsilateral fields. A large field reversal was also observed over the contralateral (left) hemisphere, 90-130 ms after onset of EMG activity in the active muscles. In some subjects, single dipole sources could be fitted to this "movement-evoked" field at locations slightly deeper and posterior to the pre-movement source locations in the contralateral hemisphere, possibly indicating unilateral activation of somatosensory cortex related to sensory feedback during the onset of this movement. Subtraction of pre-movement field activity from post-movement fields improved the ability to fit a single contralateral rolandic source for all subjects suggesting that pre-movement sources continue to be active during movement onset. These findings confirm previous reports that voluntary finger movements are preceded by slow magnetic fields.(ABSTRACT TRUNCATED AT 250 WORDS)

SQUID tomographic neuromagnetic imaging

AbstractThe human brain emits a measurable magnetic field in response to stimulation. The aim of neuromagnetic imaging is to produce maps of the underlying neuronal activity from measurements of the emitted magnetic field. Modeling neuronal activity by dipolar current sources, we have previously reported simulation studies to reconstruct planar source distributions using the algebraic reconstruction technique, with the constraint that the sources could only have two orientations. We now present a general solution for two‐dimensionally distributed sources, which is based on measuring both the normal and tangential components of the magnetic field. Also, using a single‐channel SQUID neuromagnetometer, we present results of a tomographic imaging experiment conducted with wires carrying currents to demonstrate the potential of neuromagnetic imaging in reconstructing extended cortical sources.

Effect of radial position on volume measurements using the conductance catheter.

A finite-difference computer model has been used to determine the potential distributions arising from a dipole current source aligned parallel to the axis of bounding cylinders. The radial position of this source had large and nonlinear influence on the potentials along the dipole axis. The accuracy of the computer simulation was established from comparison with an analytic solution of a simple geometry. Measurements using a conductance catheter in saline-filled cylinders also demonstrated the dependence of the conductance on the radial position. The dependence of the potential distribution on the radial position of the dipole places limits on the ultimate accuracy of the conductance catheter technique when used for the measurement of ventricular volume. Radial movement of the catheter within the ventricular cavity, resulting in changes in the potential distribution, could explain some artefacts that appear on volume recordings from the conductance catheter.

SQUID arrays for simultaneous magnetic measurements: calibration and source localization performance

Recently developed small arrays of SQUID- (superconducting quantum interference device) based magnetic sensors can, if appropriately placed, locate the position of a confined biomagnetic source without moving the array. A technique is presented having a relative accuracy of about 2% for calibrating such sensors having detection coils with the geometry of a second-order gradiometer. The effects of calibration error and magnetic noise on the accuracy of locating an equivalent current dipole source in the human brain are investigated for five- and seven-sensor probes and for a pair of seven-sensor probes. With a noise level of 5% of peak signal, uncertainties of about 20% in source strength and depth for a five-sensor probe are reduced to 8% for a pair of seven-sensor probes, and uncertainties of about 15 mm in lateral position are reduced to 1 mm for the configuration considered. >

Magnetic determination of the spatial extent of a single cortical current source: a theoretical analysis

In this paper a model, originally developed for calculating the magnetic field produced by a single nerve fiber, is used to compare the ability of two magnetometers with different spatial resolutions to map the magnetic field distribution from a highly localized current source in the cerebral cortex. It is concluded that whenever the source-to-coil distance is much larger than the dimensions of the source it will be difficult, if not impossible, to use an inverse calculation to determine the spatial extent of the source from the magnetic field. When the source-to-coil distance is comparable to the extent of the source, an inverse calculation can provide information regarding the axial length of a localized dipolar current source.