A mathematical model of the rat kidney. II. Antidiuresis

Abstract

Kidney water conservation requires a hypertonic medullary interstitium, NaCl in the outer medulla and NaCl and urea in the inner medulla, plus a vascular configuration that protects against washout. In this work, a multisolute model of the rat kidney is revisited to examine its capacity to simulate antidiuresis. The first step was to streamline model computation by parallelizing its Jacobian calculation, thus allowing finer medullary spatial resolution and more extensive examination of model parameters. It is found that outer medullary NaCl is modestly increased when transporter density in ascending Henle limbs from juxtamedullary nephrons is scaled to match the greater juxtamedullary 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 transport is powered anaerobically. Reducing vascular flows or increasing vessel permeabilities does little to further increase outer medullary solute gradients. In contrast to medullary models of others, vessels in this model have solute reflection coefficients close to zero; increasing these coefficients provides little enhancement of solute profiles but does generate high interstitial pressures, which distort tubule architecture. Increasing medullary urea delivery via entering vasa recta increases inner medullary urea, although not nearly to levels found in rats. In summary, 1) medullary Na+ and urea gradients are not captured by the model and 2) the countercurrent architecture that provides antidiuresis also produces exaggerated Pco2 profiles and is an unappreciated constraint on models of medullary function.

Restoration of proximal tubule flow–activated transport prevents cyst growth in polycystic kidney disease

“…The first concern was addressed with creation of a kidney model, which included the medullary vasculature and, thus, enabled calculation of medullary interstitial conditions ( 36 ). Tubule compliance along all segments was introduced in a revision to that model ( 37 ). It must be acknowledged that the experimental data guiding assignment of tubule compliance were scant, with few studies in rat PT ( 38 – 40 ) and 1 regarding rat distal tubule ( 38 ).…”