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 (TMS). 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.

Effect of Electrical Conductivity Uncertainty in the Assessment of the Electric Fields Induced in the Brain by Exposure to Uniform Magnetic Fields at 50 Hz

“…However, the results derived here using the Gabriel and Dimbylow data sets were 37% and 33% lower than the above value used as basis for developing the ICNIRP guidelines [1], [6]. Considering the identical (Dimbylow) or rather similar (Gabriel) conductivity values, these differences can be explained by the lower resolution (approximately 2 mm) used in [6], that can overestimate the electric fields compared to finer resolutions [17]. Regarding the McCann data set, this difference becomes even more significant and it is in the order of 50%.…”

“…A recent ICNIRP knowledge gap document [14] highlighted the necessity of further characterizing this uncertainty, and called for new studies focused on measuring the tissue conductivities. In the LF range, most of the dosimetric investigations [12], [13], [15], [16], [17], [18] used the values employed by Dimbylow in two studies that were used as a basis for developing the ICNIRP guidelines [6], [7]. This set of electrical conductivities was derived from a list of values for frequency below 100 Hz, which was published in a technical report released by Gabriel [19] after a series of investigations in the field [20]- [22].…”

Review on biophysical modelling and simulation studies for transcranial magnetic stimulation

“…al. (2019) and Soldati and Laakso (2020) obtained similar results, showing how the error in the EFs calculated using the FEM diminished when the resolution of the mesh (tetrahedral or cubical elements) was refined. These findings indicate that the numerical errors can be controlled.…”

Spatial Averaging Schemes of In Situ Electric Field for Low-Frequency Magnetic Field Exposures

“…Below the 99 th percentile, the 2-mm cubic and 5-mm linear averaged in situ electric fields were comparable (data not shown). A recent study [33] suggested that 99.99 th percentile is a computationally stable metric for the same model using different numerical methods. Nonetheless, only limited data are available with which to recommend an optimal percentile estimate of maximum dose to tissue from magnetic field exposure.…”

“…Historically, the 99 th percentile value of the current density or in situ electric field was introduced to exclude computational artefacts [29], [30]. In low-frequency dosimetry, artefacts may include i) segmentation error in an anatomical model, which may include the quality of medical images acquired in millimeter resolution [31], ii) discretization error in modeling tissue with a finite grid resolution [32], and iii) potential error in the computations themselves, which may also partly originate in discretization error [33].…”