Three-dimensional electromagnetic power deposition in tumors using interstitial antenna arrays

Interstitial arrays of insulated antennas have shown promise for microwave hyperthermia treatment of deep-seated tumors. Available analytical techniques for predicting the electromagnetic (EM) power deposition of these antennas have been limited to the case of a homogeneous conductive medium surrounding the array. Since tumors and host tissue may differ in their electrical characteristics, it is necessary to consider the impact of this variation in electrical properties and the geometry of the tumor in the calculation of the EM field distribution and power deposition pattern when modeling interstitial antennas. In this paper a three-dimensional model of a tumor of arbitrary shape subjected to the fields of an interstitial antenna array is developed to predict the EM power deposition in an inhomogeneous tumor-tissue medium. The volume integral equation for the imbedded tumor is developed and solved by method of moments. The incident fields are calculated based on the available formulation of interstitial antennas in homogeneous media. The accuracy of the developed computer code was checked by comparing the results from the volume integral approach with the Mie solution for the special case of spherical tumors. Good comparison was obtained for tumors with properties approximately 25 percent different from those of the surrounding tissue. Comparisons of results from models of antenna arrays with and without imbedded tumors show significant differences in their predictions of the EM power deposition in the tumor. Hyperthermia protocols generally specify uniform temperature distribution within the tumor. The developed inhomogeneous model was used to examine the feasibility of controlling the uniformity of the power deposition pattern in large tumors by adjusting the amplitude or relative phase between the array elements. Results are presented to show that a phase lead of +90 degrees or relative amplitude of 4.0 on one antenna in a square array of four antennas could be used to shift the power deposition pattern to sequentially heat outer portions of a 2 cm diameter tumor, thereby achieving a more uniform time-averaged temperature distribution in the tumor.