Improved Cartesian Coordinate Finite Difference Simulations of Small Cylindrical Objects

Abstract

An analytical, cylindrical coordinate formula for the thermal resistance around small cylindrical objects has been incorporated into finite difference equations in Cartesian coordinates to improve the accuracy of the numerical simulations of hyperthermia cancer treatments. This is done by introducing a circular finite difference control volume which is centered on the cylindrical object. The temperature distributions calculated from this new formulation and from the formulation obtained from a conventional, rectangular control volume are compared to the predictions from an analytical solution. The results show that for a given Cartesian grid spacing, the new method is superior to the conventional one. This will allow more accurate numerical solutions to be obtained at larger grid spacings when the effect of blood vessels or other cylindrical objects, such as ferromagnetic implants, hot water tubes, etc., are being investigated.