Theoretical predication of temperature variations along paired vessels from 200 to 1000 μm diameter in skeletal muscle

It is well known that blood flow in large, thermally unequilibrated blood vessels is the main cause for temperature inhomogeneity during hyperthermia treatment. In this study a theoretical model was developed to investigate the temperature variation along the paired blood vessels from 200 to 1000 μm diameter in skeletal muscle. Scaling law was used to define a tissue cylinder surrounding these vessel pairs based on the vascular anatomy, Murray´s law and the assumption of uniform perfusion. The thermal interaction between the blood vessel pair and the surrounding tissue was solved for two vascular branching patterns. It was shown that temperature variation along these large vessel pairs strongly depends on the vascular geometry, local blood perfusion rate, as well as the local tissue temperature gradient. Results from the current research will enable one to explore the contributions of different sized vessels to the entire thermal interaction between the blood vessels and the tissue. It can provide a reasonable range of temperature variations that one would anticipate for different physiological conditions along the supply artery and vein (SAV) pairs