Thermal Distributions in Spherical Regions with Variable Thermal Conductivity

Abstract

A method for predicting relative temperature distributions in acoustically homogeneous regions heated by acoustic sources is pre- sented. A generalized approach is presented in which thermal distor- tions, produced by variable conduction andlor perfusion cooling, are approximated as an effective conductivity term in a heat-diffusion equation. Calculated acoustic intensity distributions are input into the calculation for annularly focused sources. Sample calculations are com- pared with measurements in homogeneous rat mammary tumors and in normal pig muscle. More complex situations and implications for lo- cal hyperthermia treatment planning are presented. VER THE PAST few years the widespread use of both local and regional hyperthermia has inspired the development of a variety of tools for delivering heat, rang- ing from interstitially implanted radio-frequency (rf) or microwave antennae to external application of RF, micro- waves, magnetic induction and ultrasound. Among the early results of clinical and experimental evaluation of localized hyperthermia is the finding that temperature distribution and minimum tumor temperature (l)-(3) are key factors in tumor response prognosis. A variety of methods for thermal dosimetry (3)-(6) have subsequently arisen to help provide a framework for quan- titative therapeutic analyses. The principal deficiency in those evaluations is the quality of accessible tempera- ture distribution data, which is usually difficult to obtain clinically. To help bridge the gap between accessible data and com- prehensive knowledge of the temperature distributions, a growing number of sophisticated numerical methods (7)- (9) have been applied to the solution of bio-heat type equa- tions. These methods should be capable of producing rea- sonable estimates of temperature profiles in tissues where the thermal conductivities and blood perfusion character- istics, as well as the thermal source distributions. are known. Ultrasound, as a heating source, has been shown to be useful for a number of soft tissue cancers and tumors not too closely associated with bone or air pockets (lo)-( 121. In particular, the capability of focusing ultrasound (13)- ( 151 and calculating the resulting acoustic intensity distri-