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

Abstract

ICNIRP and IEEE publish standards/guidelines for exposures to low-frequency electromagnetic fields and their associated <italic>in situ</italic> electric fields. Two methods are prescribed for spatially averaging the <italic>in situ</italic> electric field to evaluate compliance: averaging (1) over a 2 mm <inline-formula> <tex-math notation= LaTeX >$\\times 2$ </tex-math></inline-formula> mm <inline-formula> <tex-math notation= LaTeX >$\\times 2$ </tex-math></inline-formula> 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, <inline-formula> <tex-math notation= LaTeX >$p_{\\mathrm {max}}$ </tex-math></inline-formula>, 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 <italic>in situ</italic> electric field, and these differences decrease as <inline-formula> <tex-math notation= LaTeX >$p_{\\mathrm {max}}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation= LaTeX >$p_{\\mathrm {max}}$ </tex-math></inline-formula> for linear averaging. Invoking the suggestion of ICNIRP (2010) that the averaging cube for skin “<italic>may extend to subcutaneous tissue</italic>,” ≥10% inclusion of air results in stable averaged induced electric fields.