Magnetic induction heating of tissue: numerical evaluation of tumor temperature distributions

A one dimensional (radial) numerical model based on the bioheat transfer equation has been developed and applied to the abdomen and pelvis heated by a concentric magnetic induction electrode. This model consists of four normal tissue regions: viscera, muscle, fat and skin. Each region is assigned thermal properties characteristic of that region and power deposition values consistent with those for this mode of heating. Tumors of 2, 4 and 7 cm thicknesses are positioned in five different radial locations ranging from the central axis to the skin surface. Two blood perfusion models of the tumor are considered: the uniformly perfused model and an annular model. Tumor temperature distributions are considered acceptable if the average tumor temperature plus and minus two standard deviations lie between 42 degrees C and 60 degrees C. To stimulate practical clinical restrictions, muscle and fat temperatures are not allowed to exceed 44 degrees C, significant portions of the viscera (except for a 1 cm thick band) are not allowed to exceed 42 degrees C, and the total absorbed power required to maintain steady state cannot exceed one kilowatt. Over 100 possible cases are presented in a compact form. A conclusion drawn from this study is that with few exceptions, only small tumors in the muscle annulus are heated adequately with this modality. Large tumors will have significant unheated portions if the specified limitations are not exceeded. While this heating modality can raise the necrotic core of a tumor to high temperatures, it cannot adequately heat well perfused regions of a deep seated tumor. These conclusions are borne out clinically and are discussed in a companion paper.