Temperature distributions in hyperthermia by electromagnetic induction: a theoretical model for the thorax

Steady-state temperature solutions to the bioheat equation are presented for magnetic induction heating of a thoracic model consisting of a spherical tumor embedded in lung tissue which is layered by muscle and fatty tissue. Analytical solutions are presented for each of the tissue regions along with their numerical evaluations over a range of physical characteristics, including surface cooling effects. A strong dependence of tumor temperature on size and blood perfusion rate is shown to exist and can be used to optimize treatment parameters. Tendencies of the chest muscles and overlaying fatty tissue to overheat, particularly in the case of an obese patient, are discussed along with the alleviating influence of surface cooling. Healthy lung tissue, on the other hand, is shown to be safe from any significant damage in such a heating situation. Transient times required for tumors to achieve thermal equilibrium are computed and shown to depend strongly on tumor size and, to a lesser extent, on blood perfusion rate. Finally, the overall results obtained from the model are compared with available clinical data and are found to be in line with those observations.