The Bleed Off Perfusion Term in the Weinbaum-Jiji Bioheat Equation

The microvascular organization and thermal equilibration of the primary and secondary arteries and veins that comprise the bleed off circulation to the muscle fibers from the parent countercurrent supply artery and veins are analyzed. The blood perfusion heat source term in the tissue energy equation is shown to be related to this vascular organization and to undergo a fundamental change in behavior as one proceeds from the more peripheral tissue, where the perfusion term is proportional to the Ta - Tv difference in the parent supply vessels, to the deeper tissue layers where the bleed off vessels themselves form a branching countercurrent system for each muscle tissue cylinder and the venous return temperature can vary between the local tissue temperature and Ta. The consequences of this change in behavior are examined for the Weinbaum-Jiji bioheat equation and a modified expression for the effective conductivity of perfused tissue is derived for countercurrent bleed off exchange.

Effectiveness of a salt transport cascade in the renal medulla: computer simulations

Based on morphological observations, it has been concluded that the upper parts of the long descending limbs of Henle's loops should be able to secrete salts into the tubular fluid (Kriz, W. Federation Proc. 42:2379-2385, 1983). In the same article, a hypothesis is given depicting how this active transport in concert with certain characteristics of the medullary architecture might produce a transport cascade toward the papillary tip, thus supporting the accumulation of salts in this region. The effectiveness of the proposed mechanism can be judged by a mathematical model only. The computer simulations of the present study demonstrate that this mechanism indeed leads to an increase of the concentrating capability of the renal countercurrent system.