Optimization of the hyperthermia treatment of a skin tumor containing nanoparticles

This paper deals with the optimization of the hyperthermia treatment of skin cancer, with gold nanoshells loaded in the tumor. The physical problem involves a one-dimensional bioheat transfer problem, coupled to a radiation problem for the laser propagation within a multi-layered medium that includes several tissues. The corresponding bioheat transfer problem is governed by Pennes' equation, while the laser radiation propagation in the tissues is modelled with the diffusion δ-P1 approximation. The solution of the direct problem was obtained by finite volumes and verified with an analytic solution, as well as with the Matlab function pdepe. The thermal decomposition in the tissues was modelled with an Arrhenius equation, while the objective function was given by a quadratic form involving the difference between the predicted and the desired spatial variation of the thermal damage at a specific final time. Both the Levenberg-Marquardt and the Particle Swarm methods were implemented and provided similar results for the two design variables of interest in this work: the volume fraction of nanoparticles within the tumor and the laser power, by considering a fixed duration of 10 minutes for the treatment. The results obtained in this work also show that more than one treatment session is required for the total eradication of the tumor