A Mathematical Model of the Rat Kidney. II. Antidiuresis

Abstract

Water conservation by the kidney requires a hypertonic medullary interstitium, NaCl in outer medulla (OM) and both NaCl and urea in inner medulla (IM), along with a vascular configuration that protects against washout. A multi‐solute mathematical model of the rat kidney, which includes the important acid‐base species, was developed and used first to examine K+‐induced natriuresis (Am. J. Physiol. 312:F925, 2017). In the present work, model computation has been streamlined by parallelizing the calculation of the model Jacobian, and this has allowed finer medullary spatial resolution, along with more extensive examination of model parameters. Tubule compliance is now represented along the whole nephron, and this attenuates pressure swings due to variations in urine flow. OM NaCl is modestly increased when transporter density in ascending Henle limbs (AHL) from juxtamedullary nephrons (JM), is scaled to match the greater JM nephron solute flow. However, higher NaCl transport produces greater CO2 generation, and by virtue of countercurrent vascular flows, establishment of high medullary pCO2. This CO2 gradient can be mitigated, by assuming that a fraction of medullary AHL and collecting duct transport is powered anaerobically. Reduction of vascular flows or increasing vessel permeabilities does little to further increase OM solute gradients. In contrast to the medullary models of others, vessels in this model all have solute reflection coefficients close to zero; increasing these coefficients provides no substantive enhancement of solute profiles, but does generate high interstitial hydrostatic pressures, which distort tubule architecture. As others have noted, increasing medullary urea delivery via entering vasa recta, enhances IM urea, although not nearly to levels found in rats. In sum, (1) the magnitudes of medullary gradients of Na+, urea, and ammonia are still not captured by the model; and (2) the countercurrent architecture that provides antidiuresis also produces exaggerated pCO2 profiles and appears to be an unappreciated constraint on models of medullary function.Support or Funding InformationNIH RO1‐DK‐29857