The evaluation of heat transfer equations in the pig renal cortex

Abstract

The heat transfer mechanism in living tissues was first described by the Pennes equation derived in 1948. Recently, investigators have questioned the validity of the physical and physiological assumptions upon which the Pennes equation was developed. The questions relate to the term which Pennes used to describe the thermal contribution of the flowing blood within the tissue. Regarding this concern, Chen & Holmes and Weinbaum & Jiji proposed new equations, which are reportedly based on a more realistic vascular anatomy of the blood perfused tissue.

In the present work, the microvascular architecture in the pig renal cortex has been studied and it therefore offers an excellent opportunity to test and compare the above mentioned equations of tissue heat transfer on a more quantitative basis than has been possible till now. Temperature measurements in the alcohol preserved pig kidney have been made to examine the theoretical predictions from each equation. Results indicate that the predictions from the Pennes equation are similar to those from the Chen-Holmes equation and they are closer to the actual measurements than those predicted by the WJ equation. However, since the Pennes equation is the simplest among the three, it may still be the best one to use for describing tissue heat transfer, at least in the pig renal cortex.

In addition, the thermal effects on local temperature transients from large vessels (diameter larger than 500$\mu$m), which are usually excluded by the heat transfer equations in the living tissue, have been evaluated theoretically using a sink/source method. It has been found that there is a critical probe-vessel spacing, beyond which the vessel thermal influence can be neglected. Further, this critical spacing is negligibly affected by the local blood perfusion rate.