Analytical and numerical solution of the one dimensional steady state bioheat transfer equation

This work describes the comparison between the analytical and numerical solution of the one dimensional (1D) bioheat transfer equation in the steady state condition along the axis of a muscle slab. Aim of the work is the definition of an analytical framework for hyperthermia devices design and optimization. Oncological hyperthermia is a medical technique aimed at generating a temperature increase in the tumour region of the patient through the application of a single frequency electromagnetic field. The absorbed electromagnetic power per unit mass is defined as specific absorption rate (SAR). The SAR and the temperature distributions inside the human tissue are related by the bioheat transfer equation. In this study a plane wave at the working frequency of 434 MHz is considered as electromagnetic source, and the analytical solution is calculated solving the bioheat equation in case of an exponential approximation of the SAR distribution, in order to evaluate and predict the temperature distribution along the axis of the tissue. Results show an optimum agreement between the analytical and numerical temperature distributions.