Convective uphill transport of NaCl from ascending thin limb of loop of Henle

In this paper we describe a mathematical model of the renal inner medulla based on a previously proposed model [A.S. Wexler, R.E. Kalaba, and D.J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991] in which in the inner medullary ascending thin limb of Henle's loop (ATL) and collecting duct (CD) exchange with a local capillary node with the reabsorbed water and solutes flowing radially toward a central vascular bundle. Our model differs in that ascending and descending vasa recta and surrounding interstitial space are replaced by a central core. Our analysis of the coupled ATL-CD system shows that it is theoretically capable of transporting NaCl out of the ATL into the central vascular space (approximated by the central core) against a concentration gradient, which in the absence of radial diffusion can be arbitrarily large. By numerical solution of the model with the radial diffusion coefficient (D(r)) for NaCl of 0, we find that the ATL can be more than 100 mosmol/l hypotonic with respect to the core. We also find that with restricted diffusion the osmolality of the CD at the papilla is significantly greater than that of the loop of Henle. As D(r) approaches the diffusion coefficient of NaCl in free solution, the osmolality of the loop increases and that of the CD decreases. Thus, overall, contrary to intuitive expectations, the radial separation and uphill transport of NaCl do not give any significant increase in loop concentration, which depends primarily on the quantity of urea reabsorbed from the CD.