A region-based model framework for the rat urine concentrating mechanism.

The highly structured organization of tubules and blood vessels in the outer medulla of the mammalian kidney is believed to result in preferential interactions among tubules and vessels; such interactions may promote solute cycling and enhance urine concentrating capability. In this study, we formulate a new model framework for the urine concentrating mechanism in the outer medulla of the rat kidney. The model simulates preferential interactions among tubules and vessels by representing two concentric regions and by specifying the fractions of tubules and vessels assigned to each of the regions. The model equations are based on standard expressions for transmural transport and on solute and water conservation. Model equations, which are derived in dynamic form, are solved to obtain steady-state solutions by means of a stable and efficient numerical method, based on the semi-Lagrangian semi-implicit method and on Newton's method. In this application, the computational cost scales as O(N2), where N is the number of spatial subintervals along the medulla. We present representative solutions and show that the method generates approximations that are second-order accurate in space and that exhibit mass conservation.