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.

In recent years, human exposure to electromagnetic fields (EMF) at intermediate frequencies (300 Hz–10 MHz) has risen, mainly due to the growth of technologies using these fields. The current safety guidelines/standards defined by international bodies (e.g. ICNIRP and IEEE) established basic restrictions for limiting EMF exposure. These limits at intermediate frequencies are derived from threshold values of the internal electric field that may produce transient effects, such as the stimulation of the nervous system. However, there are some discrepancies between the basic restrictions of those guidelines/standards. The aim of this study is to investigate the excitation thresholds of the nervous system exposed to intermediate-frequency electromagnetic fields, with the purpose of extrapolating the threshold-frequency curves which are compared with existing basic restrictions prescribed by the international guidelines/standards. Our investigation was based on transcranial magnetic stimulation (TMS) experiments, physiological measurements, and individualized MRI-based computer simulations for the determination of brain stimulation thresholds. The combined approach with established biological axon models enabled the extrapolation of the measured thresholds for sinusoidally varying electric fields. The findings reveal that the exposure limits are significantly conservative for the brain, especially at frequencies in the range of 300 Hz–5 kHz.

Objective. Transcranial magnetic stimulation (TMS) can be used to safely and noninvasively activate brain tissue. However, the characteristic parameters of the neuronal activation have been largely unclear. In this work, we propose a novel neuronal activation model and develop a method to infer its parameters from measured motor evoked potential signals. Approach. The connection between neuronal activation due to an induced electric field and a measured motor threshold is modeled. The posterior distribution of the model parameters are inferred from measurement data using Bayes' formula. The measurements are the active motor thresholds obtained with multiple stimulating coil locations, and the parameters of the model are the location, preferred direction of activation, and threshold electric field value of the activation site. The posterior distribution is sampled using a Markov chain Monte Carlo method. We quantify the plausibility of the model by calculating the marginal likelihood of the measured thresholds. The method is validated with synthetic data and applied to motor threshold measurements from the first dorsal interosseus muscle in five healthy participants. Main results. The method produces a probability distribution for the activation location, from which a minimal volume where the activation occurs with 95% probability can be derived. For eight or nine stimulating coil locations, the smallest such a volume obtained was approximately 100 mm 3 . The 95% probability volume intersected the pre-central gyral crown and the anterior wall of the central sulcus, and the preferred direction was perpendicular to the central sulcus, both findings being consistent with the literature. Furthermore, it was not possible to rule out if the activation occurred either in the white or grey matter. In one participant, two distinct activations sites were found while others exhibited a unique site. Significance. The method is both generic and robust, and it lays a foundation for a framework that enables accurate analysis and characterization of TMS activation mechanisms.

The International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines and the Institute of Electrical and Electronics Engineers (IEEE) standard establish safety limits for human exposure to electromagnetic fields. At low frequencies, only a limited number of computational body models or simplified geometrical shapes are used to relate the internal induced electric fields and the external magnetic fields. As a consequence, both standard/guidelines derive the exposure reference levels for the external magnetic field without considering the variability between individuals. Here we provide quantitative data on the variation of the maximum electric field strengths induced in the brain of 118 individuals when exposed to uniform magnetic fields at 50 Hz. We found that individual characteristics, such as age and skull volume, as well as incident magnetic field direction, have a systematic effect on the peak electric field values. Older individuals show higher induced electric field strengths, possibly due to age-related anatomical changes in brain. Peak electric field strengths are found to increase for larger skull volumes, as well as for incident magnetic fields directed along the lateral direction. Moreover, the maximum electric fields provided by the anatomical models used by ICNIRP for deriving exposure limits are considerably higher than those obtained here. On the contrary, the IEEE elliptical exposure model produces a weaker peak electric field strength. Our findings are useful for the revision and harmonization of the current exposure standard and guidelines. The present investigation reduces the dosimetric uncertainty of the induced electric field among different anatomical induction models. The obtained results can be used as a basis for the selection of appropriate reduction factors when deriving exposure reference levels for human protection to low-frequency electromagnetic exposure.

International exposure standard/guidelines establish limits for external electromagnetic field strengths. At low frequencies, these maximum allowable exposure levels are derived from the limits defined for internal electric field strengths which have been set to avoid adverse health effects. In the IEEE International Committee on Electromagnetic Safety standard, the relationship between internal and external fields was obtained through homogeneous elliptical models without considering the dielectric properties of tissues. However, the International Commission on Non-Ionizing Radiation Protection guidelines were established using computational dosimetry on realistic anatomical models. In this case, variability in the electrical conductivity of the tissues represents a major source of uncertainty when deriving allowable external field strengths. Here we characterized this uncertainty by studying the effect of different tissue conductivity values on the variability of the peak electric field strengths induced in the brain of twenty-five individuals exposed to uniform magnetic fields at 50 Hz. Results showed that the maximum electric field strengths computed with new estimations of brain tissue conductivities were significantly lower than those obtained with commonly used values in low-frequency dosimetry. The lower strengths were due to the new brain conductivity values being considerably higher than those usually adopted in dosimetry modeling studies. A sensitivity analysis also revealed that variations in the electrical conductivities of the grey and white matter had a major effect on the peak electric field strengths in the brain. Our findings are intended to lessen dosimetric uncertainty in the evaluation of the electric field strengths due to electrical properties of the biological tissues.INDEX TERMS Anatomical head models, dosimetry, electromagnetic field exposure, induced electric field, low frequency, tissue conductivity.