Stefano Scialó | Searcharxiv

arXiv2025

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

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, modeling the metal as thermal seeds. To overcome this limitation, a novel numerical approach that solves three-dimensional and one-dimensional coupled problems is proposed. 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. 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. The proposed method leads to improved results with respect to previous approximations by modelling the thermal diffusion through the highly conductive metallic implants.

cs.CE↗

arXiv2024

Extended Finite Elements for 3D-1D coupled problems via a PDE-constrained optimization approach

In this work, we propose the application of the eXtended Finite Element Method (XFEM) in the context of the coupling between three-dimensional and one-dimensional elliptic problems. In particular, we consider the case in which the 3D-1D coupled problem arises from the geometrical model reduction of a fully three-dimensional problem, characterized by thin tubular inclusions embedded in a much wider domain. In the 3D-1D coupling framework, the use of non conforming meshes is widely adopted. However, since the inclusions typically behave as singular sinks or sources for the 3D problem, mesh adaptation near the embedded 1D domains may be necessary to enhance solution accuracy and recover optimal convergence rates. An alternative to mesh adaptation is represented by the XFEM, which we here propose to enhance the approximation capabilities of an optimization-based 3D-1D coupling approach. An effective quadrature strategy is devised to integrate the enrichment functions and numerical tests on single and multiple segments are proposed to demonstrate the effectiveness of the approach.

math.NA↗