Estimation of state variables in the hyperthermia therapy of cancer with heating imposed by radiofrequency electromagnetic waves

One of the major difficulties in any cancer treatment is to kill the cells of the tumor without affecting healthy cells. Recently, with the advancement of nanotechnology, the localized hyperthermia treatment of cancer has again gained interest from the scientific community. In this technique, the application of electromagnetic waves, possibly even over the surface of the patient's body, causes temperature increases in the tissues. By concentrating nanoparticles in the tumorous tissues, cell damages can be inflicted mostly to the region of interest. This paper deals with numerical simulations under uncertainties of the treatment of cancer based on hyperthermia induced by radiofrequency electromagnetic waves, where the tumor is supposed to be loaded with nanoparticles. The focus of the paper is on the solution of the inverse problem dealing with the estimation of state variables, like the temperature distribution in the tissues. The state estimation problem is solved with the Particle Filter, by utilizing the Sampling Importance Resampling (SIR) algorithm. An excellent agreement between estimated and exact temperatures is obtained, which may help medical doctors in the future to prescribe treatment protocols and also opens the possibility of devising control strategies for the hyperthermia treatment of cancer.