ANALYTICAL SOLUTIONS IN THE MODELING OF THE LOCAL RF ABLATION

Abstract

Coupled mathematical models for the radiofrequency (RF) ablation performed in biomedical sciences have been developed based on the bioheat transfer theory. The heat exchange problem is important to be analytically studied in order to control the size of the necrosis zone caused by RF ablation. This lesion size in the tissue may be predicted by the knowledge of the internal tissue temperature. We propose an analytical solution for the Pennes heat transfer equation in bi- and tri-region domains, applicable to the RF ablation of cancerigeneous tissue — a clinical relevant problem. The model consists of two partial differential equations describing the spatio-temporal interactions between the electric and thermic effects. The aim is to find simple algebraic expressions of analytical solutions that may allow to generate quantitative results which in turn may be interpreted (including uncertainties). The dependence of the temperature as function of the electrothermal parameters in both diseased and surrounding healthy tissues is pointed out. Two cases, namely the tumor–tissue and tumor–tissue–skin systems, are graphically computed, and important findings include the fact that the presence of tissue with smaller value parameters protects somehow healthy cells. Moreover, the graphical representations are conducted to highlight the link of the profile of current density distribution in the physiological problem with the (neither oval nor circular) shape of the temperature isoclinic lines.