Solution of an Inverse Heat Transfer Problem for Treatment of Tumors by Hyperthermia

Abstract

In the last decades, some treatments for different types of cancer have been proposed and studied. Among these, we can cite radiotherapy, chemotherapy, cryosurgery and hyperthermia. In general, hyperthermia is the heating of tumor region for a certain period of time so that healthy cells remain unchanged, while pathological cells are destroyed. From the mathematical point of view, the phenomenon of heat transfer in the region of interest can be represented by a partial differential equation that is dependent on characteristics related to the material used for heating and the cell properties where the carcinoma is located. This contribution aims to formulate and solve inverse problems for the determination of geometry and source term during the hyperthermia process. For this purpose, the direct problem is solved considering the Normal Collocation Method and the inverse problem is solved considering the Differential Evolution algorithm. The results obtained demonstrate that the proposed methodology is able to obtain good estimates in all the proposed case studies, proving to be an interesting alternative to solve this type of problem