Tensor-based SPFD method for accurate low-frequency magnetic field dosimetry in anatomical models

<i>Objective.</i>Concerns regarding the potential adverse health effects of electromagnetic field exposure are increasing. At low frequencies, international guidelines have adopted the induced electric field within the human body as an index for safety assessment. However, because direct, non-invasive measurement of the induced field is not feasible, computational analysis using anatomically realistic human models is commonly employed. However, these models rely on tissue segmentation and are prone to numerical artifacts, particularly staircasing errors, at tissue interfaces with sharp conductivity contrast. To address this issue, we propose a novel three-dimensional scalar-potential finite-difference (SPFD) method that incorporates a tensor-conductance model and applies it to realistic human head models for the first time.<i>Approach.</i>We propose a three-dimensional SPFD method incorporating a tensor-conductance model, applied here for the first time to anatomically realistic human head models. The method was validated with multilayer spherical models and evaluated under uniform magnetic field exposure and transcranial magnetic stimulation (TMS).<i>Main Results.</i>In spherical models, the proposed method reduced root-mean-square error by up to 65% and improved agreement with theoretical values compared to the conventional method. In head models, it consistently suppressed numerical artifacts and reduced maximum electric field values by up to 22% under uniform exposure and by 5%-8% under TMS. Computational efficiency was improved using a multigrid method, achieving a 25-fold speedup without compromising accuracy.<i>Significance.</i>The tensor-based 3D SPFD method significantly improves field estimation accuracy while reducing computational artifacts in complex anatomical models. This approach may contribute to refining exposure limits and enhancing simulation fidelity for medical applications.