Mathematical Models of Renal Physiology

Anita Layton and Harold Layton


Kidney Image
The formation of hypertonic urine in mammals during periods of water deprivation is provided by the kidney's urine concentrating mechanism: water is aborbed, in excess of solute, from the collecting ducts into the vasculature of the renal medulla, thus increasing the osmolality of the urine. In the outer medulla, this absorption of water is maintained by the active absorption of NaCl from the water-impermeable thick ascending limbs. This active transport favors the absorption of water from the water-permeable descending limbs and collecting ducts, and results in a ``single effect'', which is then multiplied by the countercurrent arrangement of renal tubules and blood vessels in the outer medulla.

While the hypothesis of the countercurrent multiplication for the outer medulla is believed to be well established, the urine concentrating mechanism in the inner medulla remains controversial. In the inner medulla, the thin ascending limbs appear to have no significant active NaCl transport. The most popular hypothesis for the inner medullary concentrating mechanism is the passive mechanism, proposed independently by Stephenson and Kokko and Rector in 1972. According to the passive mechanism, urea is absorbed from the highly urea-permeable inner medullary collecting ducts, increasing the urea concentration and osmolality in the interstitial fluid. This also results in an transmural gradient favoring the absorption of water from the water-permeable collecting ducts and descending limbs, thus increasing the osmolality of the collecting duct fluid (and eventually, urine) and the NaCl concentration in the descending limbs. Thus, the fluid entering the thin ascending limbs has a high NaCl concentration relative to urea; consequently, NaCl diffuses down the gradient from the ascending limbs into the interstitium.

The passive mechanism requires low urea and NaCl permeabilities in the descending limbs, so that the concentration difference in urea and NaCl in the descending limbs is not dissipated before the fluid reaches the ascending limbs. However, experiments have reported moderately large urea and NaCl permeabilities in the descending limbs. When these values are used in model studies, no concentration gradient is generated in the inner medulla. Thus, the underlying concentrating mechanism in the inner medulla remains to be elucidated.




Last updated: November 4, 2004.