A fast and simple algorithm has been presented for the calculation of time-dependent temperature distributions in inhomogeneous vascularized tissue. Three-dimensional anatomical data of tissues and vessel structures are decomposed into elementary cubic nodes by a special digitizing routine with vessels represented by connected strings of vessel nodes. Vessel cross sections may be irregular shaped and/or tapered. Conductive and convective heat transfer was calculated through use of the heat balance technique on each cubic node resulting in an explicit finite difference computational scheme. Employing a three time level scheme, the Fourier stability criterion is circumvented allowing arbitrary time steps to be defined in the algorithm. Time steps as large as 100 times the Fourier restricted one still result in stable and convergent calculations of the stationary temperature distribution. Vessels with different flows and diameters are incorporated by performing a vessel specific second discretization step in time. Using the new algorithm as a mathematical tool the thermal equilibration length of vessel segments have been established under a broad range of geometrical and flow conditions. Validation followed from comparing transient and stationary temperature distributions derived by the proposed algorithm to those from an accurate cylindrical numerical model. Predicted values for the thermal equilibration lengths are compared to an analytical expression and phantom experiments. The algorithm is incorporated in a thermal model being the main part of our hyperthermia treatment planning system.
Accurate treatment planning is necessary for the successful application of hyperthermia in the clinic. The validity of four different bioheat models or combinations of models is evaluated: the conventional bioheat transfer equation, the limited effective conductivity model, a mixed heat sink-effective conductivity model and a discrete vessel model. The heat balance for the heated volume, and especially the ratio between conductive heat removal and heat escape through the veins, is different for each of these models. Model predictions were compared with results from experiments on isolated perfused bovine tongues. Tongues were suspended in a water-filled container and heated by conduction. The steady state temperature distribution and heat balance were determined at various blood flow rates. Increased blood flow was found to lower the mean tissue temperature and to enhance both conductive and venous heat removal. This result agrees only with the mixed heat sink-effective conductivity and the discrete vessel model predictions. At low flow rates a modified heat sink term should be used because the venous efflux temperature was significantly lower than the mean tissue temperature.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.