On the influence of volume currents and extended sources on neuromagnetic fields: a simulation study

Volume conduction effects in EEG and MEG

Volume conductor models that are commonly used to describe the EEG and MEG neglect holes in the skull, lesions, the ventricles, and anisotropic conductivity of the skull. To determine the influence of these features, simulations were carried out using the finite element method. The simulations showed that a hole in the skull will have a large effect on the EEG, and as one of the consequences localisation errors up to 15 mm may occur. The effect on the MEG is negligible. The presence of a lesion may cause the shape and magnitude of the EEG and MEG to change. Hence, a lesion has to be taken into account, if the active neurones are close to it. Moreover, a localisation procedure may fail if the lesion is not included in the volume conductor model. Inclusion of the ventricles in the volume conductor model is necessary only if sources are in their vicinity or if their sizes are unusually large. Anisotropic conductivity of the skull has a smearing effect on the EEG but does not influence the MEG.

[Effect of boundary element discretization on forward calculation and the inverse problem in electroencephalography and magnetoencephalography]

Modelling in magnetoencephalography (MEG) and electroencephalography (EEG) is increasingly based on the boundary element method (BEM). We quantify the influence of boundary element discretization on the neuromagnetic and neuroelectric forward and inverse problem for different dipole depths, brain regions and the quasispherical correction. In particular we derive standards for the general use of BEM models in MEG/EEG source localization. For this purpose simulation with single current dipoles, and source reconstructions from somatosensory evoked potentials and magnetic fields were employed. It was found that both local and global discretization influence source reconstruction. Only at a minimum triangle side length of 10 mm was it possible to achieve stable results for MEG and EEG. In order to obtain acceptable errors within the stable region, the ratio of dipole depth to triangle side length must not be less than 0.5. The results obtained from a comparison of the different brain regions indicate that the similarity to spherical geometry might well have an influence on the estimated dipole location, but not so much on its strength. Source reconstruction employing quasispherical correction was found to be the most stable, in particular in the case of coarse BEM discretization.

Influence of tissue resistivities on neuromagnetic fields and electric potentials studied with a finite element model of the head

Modeling in magnetoencephalography (MEG) and electroencephalography (EEG) requires knowledge of the in vivo tissue resistivities of the head. The aim of this paper is to examine the influence of tissue resistivity changes on the neuromagnetic field and the electric scalp potential. A high-resolution finite element method (FEM) model (452,162 elements, 2-mm resolution) of the human head with 13 different tissue types is employed for this purpose. Our main finding was that the magnetic fields are sensitive to changes in the tissue resistivity in the vicinity of the source. In comparison, the electric surface potentials are sensitive to changes in the tissue resistivity in the vicinity of the source and in the vicinity of the position of the electrodes. The magnitude (strength) of magnetic fields and electric surface potentials is strongly influenced by tissue resistivity changes, while the topography is not as strongly influenced. Therefore, an accurate modeling of magnetic field and electric potential strength requires accurate knowledge of tissue resistivities, while for source localization procedures this knowledge might not be a necessity.

Computational aspects of finite element modeling in EEG source localization

A comparison is made of two different implementations of the finite element method (FEM) for calculating the potential due to dipole sources in electroencephalography (EEG). In one formulation (the direct method) the total potential is the unknown that is solved for and the dipole source is directly incorporated into the model. In the second formulation (the subtraction method) the unknown is the difference between the total potential and the potential due to the same dipole in an infinite region of homogeneous conductivity, corresponding to the region where the dipole is located. Both methods have the same FEM system matrix. However, the subtraction method requires an additional calculation of flux integrations along the edges of the elements in the computation of the right-hand side (RHS) vector. It is shown that the subtraction method is usually more accurate in the forward modeling, provided the flux integrations are computed accurately. Errors in calculating the flux integrations may result in large errors in the forward solution due to the ill-conditioned nature of the FEM system matrix caused by the Neumann boundary condition. To minimize the errors, closed-form expressions for the flux integrations are used for both linear and quadratic triangular elements. It is also found that FEM forward modeling errors may cause false extrema in the least-square objective function obtained from the boundary potential, near boundaries between media of differing conductivity. Multiple initial guesses help eliminate the possibility of the solution getting trapped in these false extrema.

Effects of tissue conductivity variations on the cardiac magnetic fields simulated with a realistic heart-torso model

Cardiac magnetic fields with varying tissue conductivities are simulated. A high-resolution finite-element torso model composed of 19 tissue types and with a voxel resolution of 1.5 mm x 1.5 mm x 3 mm is used. It has a detailed description of tissue geometries and therefore is well suited for analysing the effects of tissue conductivities on the cardiac magnetic fields. The computed results show the greatest sensitivity of the magnetic fields to the changes in the conductivity of blood and myocardium, and less significant sensitivity to the conductivity of the lungs, muscle, fat and other tissues. These results are relevant to future modelling of magnetocardiograms and solving the inverse problem. They also emphasize the importance of careful modelling of the blood and heart regions, and suggest that less attention needs to be directed to bone or fat tissue.