Three-dimensional anatomy and renal concentrating mechanism. II. Sensitivity results.

A mathematical model has been developed to simulate hypertonic urine formation in the renal medulla. The model uses published values of membrane transport parameters, as have other models, but is unique in its representation of the three-dimensional anatomy of the medulla. The model successfully predicts measured fluid flows, osmolarities, and NaCl and urea concentrations.

Three-dimensional anatomy and renal concentrating mechanism. I. Modeling results.

Simulations were performed to test the hypothesis that the three-dimensional organization of the renal medulla is essential for formation of hypertonic urine. As in previous models, representations of loops of Henle, distal tubules, collecting ducts, and vasa recta and recent estimates of tubule characteristics were included in a simulation of NaCl, urea, and fluid transport. In addition, this model specifies the relative positions of the medullary structures.

Passive, one-dimensional countercurrent models do not simulate hypertonic urine formation.

Simulations were performed to test the ability of the countercurrent hypothesis to predict measured concentrations of NaCl and urea in the interstitium of the renal medulla. The simulations included one-dimensional representations of loops of Henle, distal tubules, collecting ducts, and vasa recta, and recent estimates of descending limb, thick ascending limb, and collecting duct transport parameters. The nonlinear two-point boundary value problem was solved numerically via quasi-linearization.

Automatic derivative evaluation in solving boundary value problems: the renal medulla.

Automatic evaluation of derivatives becomes essential when large systems of equations of many variables are to be solved. This paper presents a set of easy-to-use FORTRAN subroutines that perform automatic derivative evaluation. They were used in conjunction with the method of quasilinearization to solve a 13th-order boundary-value problem.