M.J. Peters

On the numerical accuracy of the boundary element method (EEG application)

The numerical accuracy of the boundary element (BE) method used to solve the volume conduction problem of nested compartments, each having a homogeneous conductivity, is studied. The following techniques for improving this accuracy are discussed: the handling of the auto solid angle element Omega /sup ii/, the overall refinement of the level of discreteness, the use of a locally refined discrete grid, the isolated problem approach, and an adaptive refined computation of the discrete surface integrals involved in the BE method. The effects of these techniques on the numerical accuracy of the computed electrical potentials are illustrated by taking a volume conductor consisting of four concentric spheres representing the head since for this model an analytical (exact) solution is available. The techniques are of importance for numerically computed electroencephalograms (EEGs) since the numerically computed surface EEGs are severely affected by the relatively low conductivity of the compartment representing the skull.<<ETX>>

A fast method to compute the potential in the multisphere model (EEG application)

A series expansion is derived for the potential distribution, caused by a dipole source in a multilayered sphere with piecewise constant conductivity. When the radial coordinate of the source approaches the radial coordinate of the field point the spherical harmonics expansion converges only very slowly. It is shown how the convergence can be improved by first calculating an asymptotic approximation of the potential and using the so-called addition-subtraction method. Since the asymptotic solution is an approximation of the true solution, it gives some insight on the dependence of the potential on the conductivities. The formulas are given in Cartesian coordinates, so that difficulties with coordinate transformations are avoided. Attention is paid to the (fast) computation of the partial derivatives of the potential, which is useful for inverse algorithms.<<ETX>>

The EEG and MEG, Using a Model of Eccentric Spheres to Describe the Head

Two spherical models describing the head are used to compute EEGs and MEGs for current dipolar sources located in the visual cortex area. In one of the models, the spheres are concentric, in the other eccentric, fitting the compartment boundaries of the head best in the source area. In forward computations, a strong dependency on the volume conductor model is found for the EEGs, but not for the MEGs. The dependency of the EEG due to realistic values of the eccentricities of the spheres is in accordance with experiments described in the literature. All spheres are obtained by means of a least squares fitting algorithm in which the points on the surface boundaries, used to fit the sphere, may move within an interval determined by the measuring inaccuracy. This strategy used in the fitting algorithm is shown to give considerably better results than the one normally used.

The Influence of Model Parameters on the Inverse Solution Based on MEGs and EEGs

The influence of parameters describing the head on the localization of two simultaneous active dipoles is studied. The head is described by a set of five concentric anisotropic spheres. The uncertainties in the conductivity parameters and their effects on the dipole parameters are discussed. Finally the applicability of EEG and MEG is compared.

The use of the asymptotic expansion to speed up the computation of a series of spherical harmonics

When a function is expressed as an infinite series of spherical harmonics the convergence can be accelerated by subtracting its asymptotic expansion and adding it in analytically closed form. In the present article this technique is applied to two biophysical cases: to the potential distribution in a spherically symmetric volume conductor and to the covariance matrix of biomagnetic measurements.

Anesthetic Block of Pain-related Cortical Activity in Patients with Peripheral Nerve Injury Measured by Magnetoencephalography

Background:This study examined whether chronic neuropathic pain, modulated by a local anesthetic block, is associated with cortical magnetic field changes. Methods:In a group of 20 patients with pain caused by unilateral traumatic peripheral nerve injury, a local block with lidocaine 1% was administered and the cortical effects were measured and compared with a control group. The global field power (GFP), describing distribution of cortical activation after median and ulnar nerve stimulation, was plotted and calculated. The effects on the affected hemisphere and the unaffected hemisphere (UH) before and after a block of the injured nerve were statistically evaluated. Results:Major differences based on the GFP curves, at a component between 50 ms - 90 ms (M70), were found in patients: in the affected hemisphere the M70 GFP peak values were statistically significantly larger in comparison with the UH, and the GFP curves differed morphologically. Interestingly, the mean UH responses were reduced in comparison with the control group, a finding suggesting that the UH is also part of the cortical changes. At M70, the GFP curves and values in the affected hemisphere were modulated by a local block of the median or the ulnar nerve. The most likely location of cortical adaptation is in the primary somatosensory cortex. Conclusions:Cortical activation is enhanced in the affected hemisphere compared with the UH and is modulated by a local block. The UH in neuropathic pain changes as well. Evoked fields may offer an opportunity to monitor the effectiveness of treatments of neuropathic pain in humans.

On mesh refinement and accuracy of numerical solutions

This paper investigates mesh refinement and its relation with the accuracy of the boundary element method (BEM) and the finite element method (FEM). TO this end an isotropic homogeneous spherical volume conductor, for which the analytical solution is available, wag used. The numerical results obtained with the BEM and FEM were compared with the results of the andytical solution. The results show that the accuracy of the numerical solutions is improved by enriching a mesh only if the enriched mesh not only incorporates a greater number of nodes but also follows more closely the actual geometry of the volume conductor involved.

Sensory handedness is not reflected in cortical responses after basic nerve stimulation: a MEG study

Motor dominance is well established, but sensory dominance is much less clear. We therefore studied the cortical evoked magnetic fields using magnetoencephalography (MEG) in a group of 20 healthy right handed subjects in order to examine whether standard electrical stimulation of the median and ulnar nerve demonstrated sensory lateralization. The global field power (GFP) curves, as an indication of cortical activation, did not depict sensory lateralization to the dominant left hemisphere. Comparison of the M20, M30, and M70 peak latencies and GFP values exhibited no statistical differences between the hemispheres, indicating no sensory hemispherical dominance at these latencies for each nerve. Field maps at these latencies presented a first and second polarity reversal for both median and ulnar stimulation. Spatial dipole position parameters did not reveal statistical left–right differences at the M20, M30 and M70 peaks for both nerves. Neither did the dipolar strengths at M20, M30 and M70 show a statistical left–right difference for both nerves. Finally, the Laterality Indices of the M20, M30 and M70 strengths did not indicate complete lateralization to one of the hemispheres. After electrical median and ulnar nerve stimulation no evidence was found for sensory hand dominance in brain responses of either hand, as measured by MEG. The results can provide a new assessment of patients with sensory dysfunctions or perceptual distortion when sensory dominance occurs way beyond the estimated norm.