Simulation of Isothermal Walls of Vessels Embedded in Tissue

It is well documented in anatomical studies that large supplying arteries and veins with diameters greater than 0.5mm. are normally paired in biological systems. Investigators in bio-heat and bio-mass transfer field have recently found that the blood flow rate within these vessels is normally too high to allow the thermal equilibration to occur between blood and the local tissue. Based on studies of the thermal equilibration length of the vessel (Baish et al. 1986; Chen & Holmes, 1980; Weinbaum et al. 1984), the actual equilibration between blood and tissue takes place in vessels with diameters ranging from 0.05 to 0.5mm. Vessels in this range are viewed as thermally significant and are not always closely paired. The pairing percentage is normally tissue dependent and is about 30% in the pig kidney cortex (Xu et al. 1994). This indicates that within any given cross-sectional tissue area, a more realistic vascular model would be artery-vein pairs embedded in a tissue matrix in which single vessels are uniformly distributed.