Computational errors of the induced electric field in voxelized and tetrahedral anatomical head models exposed to spatially uniform and localized magnetic fields

Abstract

At low and intermediate frequencies, the strength of the induced electric field is used as dosimetric quantity for human protection in the International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines. To compute the induced electric field, numerical methods based on anatomically realistic voxel models are commonly used. However, grid-based models introduce staircase approximation errors when curved surfaces are discretized with voxels, particularly in correspondence of boundaries with large differences in electrical conductivity. By contrast, those kind of artefacts are absent in tetrahedral meshes. Here, we investigate the computational errors that affect voxelized and tetrahedral head models when exposed to uniform magnetic fields at 50 Hz, and localized exposure due to transcranial magnetic stimulation. Five subjects were considered, and for each of them four voxel grids and four tetrahedral meshes were reconstructed with different resolutions. The differences in the results were characterized by comparing the induced electric fields computed using those meshes/grids. The results showed modest discrepancies in the overall electric field distributions between the various grids and meshes. However, the peak electric field strengths were erroneous for both tetrahedral and voxel models. Therefore, post-processing techniques are needed to suppress those numerical artefacts. For this purpose, the 99.99th, or lower, percentile of the electric field strength was found to remove the numerical errors. In addition, we found that spatially averaging the electric fields over 2 mm cubical volumes, as described by the ICNIRP, was effective in removing most of the spuriously large electric fields. When spatial averaging was used, relative coarse head models consisting of approximately 1 mm voxels or tetrahedral meshes with 2 mm average side length were sufficient to mitigate the artefacts. Nonetheless, the additional percentile filtering might still be needed to suppress the erroneous values completely.