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 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 (EEG's) since the numerically computed surface EEG's are severely affected by the relatively low conductivity of the compartment representing the skull.
SummaryThe magnetic field distribution around the head is simulated using a realistically shaped compartment model of the head. The model is based on magnetic resonance images. The 3 compartments describe the brain, the skull and the scalp. The source is represented by a current dipole situated in the visual cortex. The magnetic field distribution due to the source and that due to the volume currents are calculated separately. The simulations are carried out in order to ascertain which matrix of grid points is suitable as a measuring grid. The possibilities studied are grid points situated in a plane, in a surface which follows the contours of the head and in a sphere. This sphere is taken concentric to the sphere which is the best possible fit for the head. Taking into account the relative contribution of the volume currents and the possible accuracy in the positioning of the magnetic field detector, it can be concluded that the best choice is to measure the normal component of the magnetic field at points which are situated in the spherical surface. The results of this study also show that the magnetic field distribution based on a realistically shaped compartment model differs from that based on a compartment model consisting of concentric spheres. In the spherical model of the head no contribution of the volume currents to the component of the field normal to the sphere can be expected. The difference between the results obtained with these two volume conductor models increases with source depth.Key words: magnetoencephalography; visual cortex; simulation; volume conductor shape; recording surfacesThe accuracy of source localization within the brain based on magnetoencephalographic (MEG) measurements around the head depends on the adequacy of the models used to represent both the source and the volume conductor (i.e., the head). The most commonly used model for a source is a single-current dipole or a current dipole layer. Up to now mathematical models of the head have been confined to spherical models (Cohen and Cuffin 1983), although the influence of the shape of an isolated human skull on the magnetic field was measured by Weinberg et al. (1984) and Barth et al. (1986).In some cases the adequacy of a model used for the localization of a source may be confirmed, for instance, by X-ray tomographs in studies of focal epilepsy (Barth et al. 1984). However, in most other cases such a confirmation cannot be obtained. Although not conclusive, a model inspires confidence when source localization, using this model, leads to the same results when the localization is based on the measured EEG distribution as in the case where the localization is based on the measured MEG distribution.For sources in the visual cortex the estimated source location based on the visual evoked potentials did not coincide with the location based on the visual evoked magnetic fields (Stok et al. 1984). The model used for the computations consisted of 4 concentric spheres, where the spheres were fitted in the section of the head near the vi...
I n t r o d u c t i o nTo BE ABLE to compute the potential distribution on the scalp due to brain activity (as reflected in EEGs) and the distribution of a component of the magnetic field (as reflected in MEGs), both the source and the volume conductor (i.e., the head) have to be modelled. Dipolar current sources are commonly used as a model for brain activity.In the past it was common practice to describe the head by models for which an analytical solution exists. Usually, the head is described by a set of concentric spheres (CUFFIN and COHEN, 1979; COI-mN and CUEFIN, 1983; ROMAN[ et al., 1985). Using this model, the active regions within the brains have been localised from the measured magnetic field data. These studies have been reviewed by OKADA (1983). The localisation of human focal epilepsy from measured magnetic field data is of clinical importance (SuTHERLING et al., 1984;BARTH et al. 1984;RICCI et al., 1984). Such a localisation will guide the neurosurgeon in those cases which are appropriate for surgical intervention. The use of a realistically shaped volume conductor model of the head (MEIJS et al., 1985), rather than a set of concentric spheres is not discussed in this paper. However, for this work we use the boundary element method for solving the associate forward problem of both the electrical potential and the magnetic field distribution. In the numerical computations some errors are to be expected in the approximate solution. These errors never proved to be a limitation in similar simulations of the cardiac electrical potential distribution and the cardiac magnetic field distribution (PETERS et al., 1983). Realistically chosen conduc-
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