Thermal Modelling of Laser Hyperthermia in the Vicinity of a Large Blood Vessel

Abstract

In treating cancer with hyperthermia, an understanding of the heat losses associated with the presence of a large functioning blood vessel in or proximal to a treatment area is needed in order to optimize any protocol. A three-dimensional computer model based on the Bioheat transfer equation (BHTE) has been developed to account for temperature changes in and around functioning blood vessels during laser-induced hyperthermia. The light source is modelled using an approximation to the transport theory solution for an isotropic point source in an infinite homogeneous tissue medium with anistropic scattering. The derived BHTE's for tissue, vessel and blood are solved for temperature using the implicit finite differences method. The validity of the model was tested by comparing predicted temperatures to measured temperatures from a series of dynamic phantom studies using two vessel diameters and three flow rates. Large experimental temperature variations were observed and increased proportionally with increasing thermal gradients. The model consistently over-estimates (~ 1-2C) absolute temperatures close to the source and under-estimates (~ 1-2C) them far from the source. This could be due to uncertainties associated with the estimated thermal conductivity and measured optical properties of the tissue material. Both model and experiments show a small convective heat loss due to the presence of a blood vessel. The model predicts that at high flow rates, temperature reductions of 2C or greater are limited to distances less than 0.3 cm from the surface of a 0.144 cm (outer diameter) vessel and less than 0.8 cm from the surface of a 0.40 cm vessel. The vessel has a negligible effect on temperatures at distances greater than ~ 1.75 cm. The predicted temperature change due to blood flow and the measured change agree to within experimental errors. There was better agreement with the larger diameter vessel.