How to apply a discrete vessel model in thermal simulations when only incomplete vessel data are available

For accurate predictions of the temperature distribution during hyperthermia treatment a thermal model should incorporate the individual impact of discrete vessels. In clinical practice not all vessels can be reconstructed individually. This paper investigates five possible strategies to model the thermal impact of these missing vessels. A tissue volume with a detailed, realistic, counter-current discrete vasculature is heated and the steady-state temperature distribution is calculated using our DIscrete VAsculature (DIVA) thermal model. To mimic incomplete discrete vasculatures the full tree is gradually stripped, that is, the number of discretely described vessels is reduced in four steps until no discrete vessels are left. At each strip level the steady state temperature distribution is calculated for five different strategies to model the missing vessels. The strategies all use a local or global heat sink model in addition to the discrete vasculature. The resulting temperature distributions are compared with the full tree simulation. With increasing strip level the correspondence with the full tree simulation deteriorated for all strategies. An optimal strategy was found to model the missing vessels depending on the available angiographic data. It was also found that simulations with a decreased number of discrete vessels, or no vessels at all, yield temperatures which are too high. Theoretically this can be compensated by increasing the thermal conductivity; finding the optimal value is done empirically.