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

Anthony S. Wexler, Robert E. Kalaba, Donald J. Marsh

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


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. By assuming that the structure of the minimum functional unit is a vascular bundle surrounded by tubules and ascending vessels, we have represented the threedimensional organization of the medulla by a cylindrically symmetric two-dimensional model. The resulting set of equations gives rise to a nonlinear boundary value problem with linear boundary conditions, which was solved numerically via quasi linearization. Compared with previous simulations, the concentrations predicted by this model more accurately match measured quantities in two regards. First, papillary tip concentrations of NaCl and urea are significantly higher, and, second, a monotonic increase in osmolarity is observed in the inner medulla. The three-dimensional organization permitted development of local concentration gradients, which are essential to the final result.

Original languageEnglish (US)
JournalAmerican Journal of Physiology - Renal Fluid and Electrolyte Physiology
Issue number3 29-3
StatePublished - 1991
Externally publishedYes


  • Loops of Henle
  • Mathematical models
  • Renal anatomy
  • Renal medulla

ASJC Scopus subject areas

  • Physiology


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