A Generic Tissue Convective Energy Balance Equation: Part I—Theory and Derivation

Abstract

A new equation for calculating temperatures in living tissues, the tissue convective energy balance equation (TCEBE), is derived using only a few assumptions. The resulting equation is basic, general and applicable to any tissue. The (unsolved) TCEBE is used: (a) to relate both Pennes’ BHTE perfusion-related parameter (W) and the effective thermal conductivity equation’s perfusion-related parameter (keff ) to the true capillary perfusion Ṗcap , and (b) to show that both W and keff are defined, nonphysiological variables, which are only related to Ṗcap in a problem-dependent manner. Finally, the derivation of the relationship between W and Ṗcap provides a complete derivation of Pennes’ BHTE, something that has not been previously done.