Pointwise antennas design in hyperthermia therapy

Abstract

Abstract This work deals with pointwise antennas design in hyperthermia treatment. Hyperthermia is a non-invasive therapy usually combined with chemotherapy and/or radiotherapy, which consists in heating the diseased tissue in an attempt to kill the cancerous cells. In particular, we want to find the optimal values of current densities passing through each antenna to selectively heat a specified target. The forward problem is governed by the steady-state heat equation in living tissues which is coupled with the Helmholtz problem modeling the electromagnetism phenomenon. An objective functional measuring the difference between the target temperature and the solution to the model problem is minimized with respect to the current densities by using the topological derivative method. The resulting sensitivities are used to devise first and second order antenna design algorithms as well as a third one that combines both the previous algorithms. Numerical experiments are presented showing different features of the proposed methodology, including its capability in selectively heating the target up to the desired temperature. Finally, a selected result is used in a full transient analysis, where the hot spots are keeping over the diseased tissues during the whole heating process.