A description of discrete vessel segments in thermal modelling of tissues

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Abstract
In hyperthermia treatment planning vessels with a diameter larger than 0.5 mm must be treated individually. Such vessels can be described as 3D curves with associated diameters. The temperature profile along the vessel is discretized one dimensionally. Separately the tissue is discretized three dimensionally on a regular grid of voxels. The vessel as well as the tissue are positioned in one global space. Methods are supplied to describe the tissue-vessel interaction, the shift of the blood temperature profile describing the flow of blood along the vessel and the calculation of the vessel wall temperature. The calculation of the interaction is based on tissue temperature samples and the blood temperature together with the distance between the centre of the vessel and the tissue temperature sample. An analytical expression for a vessel inside a coaxial tissue cylinder is then used for the calculation of the heat flow rate across the vessel wall. The basic test system is a vessel segment embedded inside a coaxial tissue cylinder. All the tests use this setup while the following simulation parameters are varied: position and orientation of the vessel relative to the tissue grid, vessel radius, sample density of the blood temperature and power deposition inside the tissue cylinder. The blood temperature profile is examined by calculation of the local estimate of the equilibration length. All tests show excellent agreement with the theory.