Development and evaluation of tissue convective energy balance equation

This work extends the derivation of Tissue Convective Energy Balance Equation (TCEBE) which is a new, theoretically rigorous, bioheat equation and evaluates its predictions in a realistic arterio-venous vessel network consisting of approximately 8000 vessels. The extension of the derivation of the TCEBE is done by developing analytical expressions for conduction shape factors that are used implicitly in the TCEBE to evaluate the blood-tissue heat transfer rates. These new conduction shape factors are derived by explicitly evaluating the heat transfer rates between the blood vessels and tissue and between the two vessels in two-dimensional (2D) tissue geometries with uniform/variable temperature boundary conditions.; The evaluation of the TCEBE is performed by comparing its temperature predictions with the predictions of the network model for two cases; one, when tissue is externally heated and the network cools the tissue, and two, when tissue is cooled from the surface and the network heats the tissue. The predictions of the TCEBE are obtained by iteratively solving this equation in the three-dimensional (3D) complete control volume using the newly developed 2D shape factor results along with the one-dimensional (1D) convective energy balance equation in the vessel network. The predictions of the network model are obtained by solving the 3D conduction energy equation in the tissue and the 1D convective energy equation in the vessel network.; Results show that the predictions of the TCEBE are very close to the predictions of the network model when axial conduction is not very important. For the cases when axial conduction is significant, the TCEBE was able to predict the general trends. Since 2D shape factor results do not include the effect of the axial conduction, these results suggest that (1) the only assumption of the TCEBE, that the effect of the local temperature fluctuations on the local volume averaged temperature is insignificant, is correct, and (2) new 3D shape factor results are needed to make the TCEBE more accurate in cases where the axial tissue conduction is significant.