3D numerical simulation of real-time temperature field in a hyperthermia cancer treatment using OcTree meshes

This paper presents a computational strategy for real-time monitoring of hyperthermia treatment of cancer using nanoparticles. In this strategy, a numerical scheme based on the finite volume method is used for the simulation of heat diffusion in a synthetic biological system. This synthetic model is discretized with OcTree meshes, which can perform local refinement, allowing a good representation of complex geometries, besides having advantages on the use of computational resources. For real-time estimation of temperature in the three-dimensional model, the capture of the temperature field on the external surface of the model is simulated. With the data from these simulations, inverse problems are proposed and solved using the L-BFGS method. The damage caused by a temperature increase in healthy and diseased tissues is estimated, thus simulating a criterion for treatment safety. Numerical examples are analyzed with tumors at different depths, illustrating some particularities of this approach.