Analytical solution of the bioheat equation for thermal response induced by any electrode array in anisotropic tissues with arbitrary shapes containing multiple-tumor nodules

Abstract

The Pennes bioheat transfer equation is the most used model to calculate the temperature induced in a tumor when physical therapies like electrochemical treatment, electrochemotherapy and/or radiofrequency are applied. In this work, a modification of the Pennes bioheat equation to study the temperature distribution induced by any electrode array in an anisotropic tissue containing several nodules (primary or metastatic) with arbitrary shape is proposed. For this, the Green functions approach is generalized to include boundaries among two or more media. The analytical solution we obtain in a very compact way, under quite general suppositions, allows calculating the temperature distributions in the tumor volumes and their surfaces, in terms of heat sources, initial temperature and calorific sources at the boundary of tumors.