Inner medullary external osmotic driving force in a 3-D model of the renal concentrating mechanism

The mechanism by which the renal medulla establishes and maintains a gradient of osmolarity along the corticomedullary axis, especially in the inner medulla, where there is no active transmural flux out of the ascending limbs of Henle, remains a source of controversy. We show here that, if realistic values of urea permeability in the inner medullary descending limbs and water permeability in the upper inner medullary section of the collecting ducts are taken into account, even a model including the three-dimensional vascular bundle structures [A. S. Wexler, R. E. Kalaba, and D. J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991] fails to explain the experimentally observed inner medullary osmolality gradient. We show here that this failure can be overcome by application of an external osmotic driving force, an idea recently revived by J. F. Jen and J. L. Stephenson (Bull. Math. Biol. 56: 491-514, 1994) in the context of a single-solute, single-loop central core model. We show that inclusion of such an external driving force with a value equivalent to at least 100 mosM of inner medullary interstitial osmolytes in the three-dimensional model of Wexler et al. accounts for a physiological osmolality gradient, even in the face of realistic permeability values. Furthermore, inclusion of the external driving force makes the model less dependent on the positions of descending and ascending limbs of Henle with respect to the collecting ducts. In an effort to assess whether there is any experimental basis for osmolytes, we show that a significant amount of extra inner medullary interstitial osmolytes is plausible, based on extrapolation from existing experimental data.