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

ICNIRP and IEEE publish standards/guidelines for exposures to low-frequency electromagnetic fields and their associated in situ electric fields. Two methods are prescribed for spatially averaging the in situ electric field to evaluate compliance: averaging (1) over a 2 mm × 2 mm × 2 mm volume (ICNIRP) and (2) along a 5 mm linear segment of neural tissue (IEEE). However, detailed calculation procedures for these two schemes are not provided, particularly when the averaging volume/line straddles a tissue/air or tissue/tissue interface. This study proposes detailed schemes for implementing the volume- and line-averaging in such cases, applying them to both a spherical model of layered tissues and a human anatomical model. To extend the applicability of the proposed averaging schemes to the voxels at the tissue boundaries, a parameter, p
_max
, is introduced and defined as the maximum permissible percentage of air/other tissues in the averaging volume/line. For most inner-tissue voxels results show good agreement between the two averaging schemes, in general. Excluding skin, the relative differences between the two averaging schemes were less than 9% for the 99
^th
percentile in situ electric field, and these differences decrease as p
_max
increases. Results indicate that around 20-30% inclusion of air or other tissues for volume averaging of internal tissues provides stable percentile values; less stability is observed across p
_max
for linear averaging. Invoking the suggestion of ICNIRP (2010) that the averaging cube for skin “may extend to subcutaneous tissue,” ≥10% inclusion of air results in stable averaged induced electric fields.