Analysis of PCO2 variations in the renal cortex. II. Countercurrent exchange

L. J. Atherton, D. A. Maddox, F. J. Gennari and W. M. Deen Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge 02139. In an effort to explain the relatively high values of CO2 partial pressure (PCO2) that have been measured in the superficial renal cortex of the rat, we developed a mathematical model based on the concept of countercurrent exchange between blood vessels. The model includes the possibility of exchange of CO2 between interlobular arteries and veins throughout the cortex, and between "terminal" arterioles and venules (those associated with the most superficial nephrons). The effect of countercurrent exchange is to amplify the increases in PCO2 that occur in the microcirculation of individual nephrons, which are due to the addition of metabolic CO2 and reabsorbed HCO3- and CO2 to peritubular capillaries. The model is formulated in terms of correlations that describe blood buffering equilibria in peritubular capillaries and in interlobular arteries and veins, and steady-state mass balances for the interlobular vessels. By use of physically reasonable vascular permeability values, simulations for the normal euvolemic Munich-Wistar rat yielded values of the surface-to-arterial PCO2 difference (delta PCO2) comparable to previously measured values. Predicted variations in delta PCO2 with afferent arteriolar blood flow rate and systemic arterial PCO2 were also in accord with available data. These results suggest that the amplifying effect of countercurrent exchange is in fact adequate to explain the high values of PCO2 measured in surface structures. The solutions to the mass balance equations are in closed analytical form and can be readily adapted to describe countercurrent exchange in the renal cortex of solutes other than CO2.