Convective thermal model formulation of a three dimensional vascular system with simplified blood flow paths: Temperature distributions during hyperthermia

Abstract

The development and verification of thermal models for use in hyperthermia treatment planning is essential for obtaining accurate predictions of temperature fields. This thesis presents a three-dimensional blood vessel network constructed from connected straightline segments. The geometry of this convective thermal model is an (approximate) cube. The model contains seven levels of different size arterial vessels. The calculations of the mean blood temperature inside the vessels are based on the convective energy balance equation for the bulk fluid temperature. The adjacent tissue temperature calculations are based on either pure conduction heat transfer or the bioheat transfer equation of Pennes (22). The validity of the convective thermal model is checked by comparing it's predictions to those of an analytical solution for a single vessel, and by checking the energy balance calculations of the whole control volume. The results show that the level-7 arteries still contribute a large percentage of the total heat transfer rate between the blood vessels and the surrounding tissues; and values of the Nusselt number being either 10% higher or 10% lower than 4 do not strongly affect the temperature field.