Renal countercurrent system: role of collecting duct convergence and pelvic urea predicted from a mathematical model

A differential equation model of the renal countercurrent system has been developed and physiological data from nephron segments were incorporated together with recently suggested urea recycling from renal pelvis to inner medulla and, particularly, an exponential reduction in the number of collecting tubules towards the renal papilla. The role of these features for the countercurrent concentrating mechanism has been studied by simulation runs. The computations, using the multiple shooting method, provide predictions about concentration profiles for salt and urea in tubes (nephron segments) and in the central core along the entire medullary countercurrent system. The results indicate that this model, without active salt or urea transport in the inner medulla, yields concentration gradients along the medullary axis compatible with those measured in the tissue.