Computation of hyperthermia-SAR distributions in three dimensions (abstract)

Abstract

Hyperthermia, the heating of tumors to greater than 42 °C, has been demonstrated to be an effective adjuvant to radiation therapy in treating cancer.1 Heating techniques using electromagnetic energy are largely employed in the clinic, at present, to produce therapeutic temperatures in the tumor. The critical parameters influencing the induced temperature distribution in the tissue are the electromagnetic power absorption rate (SAR or specific absorption rate in W/kg) and the blood perfusion rate. It is important to ensure that the SAR is high in the target volume and not harmful to healthy tissue. To this end, the general Maxwell equations have to be solved in the human body2 at a given frequency (anywhere from low to high) for an electric field applied tangential to the body (usually near the waist).3 This paper reviews the state of the methods of field computation employed today and describes the beginnings of a treatment planning system being constructed. The planning system needs to be able to construct the model of the body, solve for the fields, and show the SAR distribution. A major difficulty is encountered with the more conventional vector potential formulation. It is traditionally assumed that in the splitting of the electric field E into −jωA and −∇φ, the latter term is from externally applied power sources. While this is true in two dimensions, in three dimensions, so assuming would make E=jωA continuous across interfaces. At the same time, solving directly for E makes it difficult to impose the divergence and curl equations together because of the trial function restrictions. It is shown that the boundary-element method, where an analytical Green’s function solution is used (without the restrictions of the finite-element trial functions), will give us the best accuracy.