Tests of the geometrical description of blood vessels in a thermal model using counter-current geometries

We have developed a thermal model, for use in hyperthermia treatment planning, in which blood vessels are described as geometrical objects; 3D curves with associated diameters. For the calculation of the heat exchange with the tissue an analytic result is used. To arrive at this result some assumptions were made. One of these assumptions is a cylindrically symmetric temperature distribution. In this paper the behaviour of the model is examined for counter-current vessel geometries for which this assumption is not valid. Counter-current vessel pairs intersecting a circular tissue slice are tested. For these 2D geometries vessel spacing, tissue radius and resolution are varied, as well as the position of the vessel pair with respect to the discretized tissue grid. The simulation results are evaluated by comparison of the different heat flow rates with analytical predictions. The tests show that for a fixed vessel configuration the accuracy is not a simple decreasing function of the voxel dimensions, but is also sensitive to the position of the configuration with respect to the discretized tissue grid.