Reducing the staircasing error in computational dosimetry of low-frequency electromagnetic fields

From extremely low frequencies to intermediate frequencies, the magnitude of induced electric field inside the human body is used as the metric for human protection. The induced electric field inside the body can be computed using anatomically realistic voxel models and numerical methods such as the finite-difference or finite-element methods. The computed electric field is affected by numerical errors that occur when curved boundaries with large contrasts in electrical conductivity are approximated using a staircase grid. In order to lessen the effect of the staircase approximation error, the use of the 99th percentile electric field, i.e. ignoring the highest 1% of electric field values, is recommended in the ICNIRP guidelines. However, the 99th percentile approach is not applicable to localized exposure scenarios where the majority of significant induced electric field values may be concentrated in a small volume. In this note, a method for removing the staircasing error is proposed. Unlike the 99th percentile, the proposed method is also applicable to localized exposure scenarios. The performance of the method is first verified by comparison with the analytical solution in a layered sphere. The method is then applied for six different exposure scenarios in two anatomically realistic human head models. The results show that the proposed method can provide conservative estimates for the 99th percentile electric field in both localized and uniform exposure scenarios.