An Electric Field Induced in the Retina and Brain at Threshold Magnetic Flux Density Causing Magnetophosphenes

For magnetic field exposures at extremely low frequencies, the electrostimulatory response with the lowest threshold is the magnetophosphene, a response that corresponds to an adult exposed to a 20 Hz magnetic field of nominally 8.14 mT. In the IEEE standard C95.6 (2002), the corresponding in situ field in the retinal locus of an adult-sized ellipsoidal was calculated to be 53 mV m(-1). However, the associated dose in the retina and brain at a high level of resolution in anatomically correct human models is incompletely characterized. Furthermore, the dose maxima in tissue computed with voxel human models are prone to staircasing errors, particularly for the low-frequency dosimetry. In the analyses presented in this paper, analytical and quasi-static finite-difference time-domain (FDTD) solutions were first compared for a three-layer sphere exposed to a uniform 50 Hz magnetic field. Staircasing errors in the FDTD results were observed at the tissue interface, and were greatest at the skin-air boundary. The 99th percentile value was within 3% of the analytic maximum, depending on model resolution, and thus may be considered a close approximation of the analytic maximum. For the adult anatomical model, TARO, exposed to a uniform magnetic field, the differences in the 99th percentile value of in situ electric fields for 2 mm and 1 mm voxel models were at most several per cent. For various human models exposed at the magnetophosphene threshold at three orthogonal field orientations, the in situ electric field in the brain was between 10% and 70% greater than the analytical IEEE threshold of 53 mV m(-1), and in the retina was lower by roughly 50% for two horizontal orientations (anterior-posterior and lateral), and greater by about 15% for a vertically oriented field. Considering a reduction factor or safety factors of several folds applied to electrostimulatory thresholds, the 99th percentile dose to a tissue calculated with voxel human models may be used as an estimate of the tissue's maximum dose.