3D–1D modelling of cranial mesh heating induced by low or medium frequency magnetic fields

Background and Objective: Safety assessment of patients with one-dimensionally structured passive implants, like cranial meshes or stents, exposed to low or medium frequency magnetic fields, like those generated in magnetic resonance imaging or magnetic hyperthermia, can be challenging, because of the different length scales of the implant and the human body. Most of the methods used to estimate the heating induced near such implants neglect the presence of the metallic materials within the body, modelling the metal as thermal seeds. To overcome this limitation, a novel numerical approach that solves three-dimensional and one-dimensional coupled problems is proposed. Methods: The proposed method is compared with measurements performed on a cranial mesh exposed to the magnetic field generated by a gradient coil system for magnetic resonance imaging. Then, it is applied to a magnetic hyperthermia case study in which a patient with a cranial mesh is exposed to the magnetic field generated by a collar-type magnetic hyperthermia applicator for neck tumour treatment. Results: The experimental comparison of the proposed method predictions and the measurement data shows an improved accuracy near the maximum temperature increase up to 25 % with respect to the method based on thermal seeds. The application of the proposed method applied to the magnetic hyperthermia case study leads to a prediction of the maximum temperature increase that is 10 % lower than the one overestimated by relying on thermal seeds. At the same time, the proposed method corrects the underestimation of the thermal seeds in the regions where the electromagnetic power is not directly deposited and the temperature increase is only due to heat transfer. Conclusions: The proposed method leads to improved results with respect to previous approximations by modelling the thermal diffusion through the highly conductive metallic implants without affecting the anatomical human model discretization based on voxels.