Appendix 2 2 - D Finite Difference Modeling of Microwave Heating in the Prostate

Accurate prediction of temperatures in the prostate undergoing thermally-based treatments is crucial to assessing efficacy and safety. A two-dimensional transient finite difference model for predicting temperatures in prostate undergoing microwave heating via a transurethral fluid-cooled catheter is presented. Unconditional stability and good accuracy are achieved by using the alternating direction implicit method. A transverse section of the prostate centered at the urethra is modeled in cylindrical coordinates. The model geometry consists of a hollow silicone cylinder, representing the catheter, surrounded by multiple regions of tissue. Cold fluid flowing through the catheter minimizes the temperature in the periurethral tissue. This flow is modeled as a convective boundary condition at the surface between the catheter lumen and wall. The outer surface of the tissue is assumed to remain at baseline temperature. Microwave heating has both a radial and angular dependence. In order to maximize the heat to the target tissue, the microwave field emitted from the transurethral catheter focuses heat away from the rectum. Different perfusion situations within the prostate are simulated. Pennes' perfusion term is assumed to model the effect of perfusion on heat transfer. Results of the numerical model are compared to phantom experiment results. The model parameters which provided the best fit for the phantom was extended to model canine prostate. Nomenclature A microwave power parameter [W] c specific heat [J/kg̊C] d microwave power offset factor [m] h convective coefficient [W/m2̊C] k thermal conductivity [W/m̊C] q ' ' power flux due to microwave heating[W/m2] q ' ' ' volumetric microwave power [W/m3] r radial position [m] Rs catheter diameter [m] Rt tissue diameter [m] s offset of microwave antenna from geometric center [m] T temperature [ ̊C] β microwave attenuation constant for uniform plane wave [m-