Simulation of hyperthermia treatment using the edge-based smoothed finite-element method

Hyperthermia treatment is an effective tool of cancer therapy. The main feature of hyperthermia treatment is to use thermal energy to kill the cancer cells without minimum damage to surrounding tissue [1-31, 2, 3]. In such treatment, it is essential to predict the temperature distribution accurately for a given supply of heat at the cancer cells. In this article, an edge-based smoothed finite-element method (ES-FEM) in 2-D and face-based smoothed finite-element method (FS-FEM) in 3-D are presented to improve the accuracy of the finite-element method (FEM) without much change to the FEM setting. In the ES-FEM, the discretized equations are established using the smoothed Galerkin weak form with edge-based smoothing domains. Compared with the FEM that behaves overly-stiff, the ES-FEM model possesses a close-to-exact stiffness. Thus, ES-FEM can provide much more accurate result than the FEM using the same mesh. Numerical examples, including 2-D and 3-D of hyperthermia treatment have been analyzed using ES-FEM and FS-FEM, respectively. The results have demonstrated that ES-FEM (FS-FEM) significantly outperform the FEM using the same mesh.