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A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity

Department of Mathematics, Duke University, Durham, North Carolina

Submitted 29 September 2003 ; accepted in final form 17 May 2005

In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1346–F1366, 2005), a region-based mathematical model was formulated for the urine concentrating mechanism (UCM) in the outer medulla (OM) of the rat kidney. In the present study, we quantified the sensitivity of that model to several structural assumptions, including the degree of regionalization and the degree of inclusion of short descending limbs (SDLs) in the vascular bundles of the inner stripe (IS). Also, we quantified model sensitivity to several parameters that have not been well characterized in the experimental literature, including boundary conditions, short vasa recta distribution, and ascending vasa recta (AVR) solute permeabilities. These studies indicate that regionalization elevates the osmolality of the fluid delivered into the inner medulla via the collecting ducts; that model predictions are not significantly sensitive to boundary conditions; and that short vasa recta distribution and AVR permeabilities significantly impact concentrating capability. Moreover, we investigated, in the context of the UCM, the functional significance of several aspects of tubular segmentation and heterogeneity: SDL segments in the IS that are likely to be impermeable to water but highly permeable to urea; a prebend segment of SDLs that may be functionally like thick ascending limb (TAL); differing IS and outer stripe Na⁺ active transport rates in TAL; and potential active urea secretion into the proximal straight tubules. Model calculations predict that these aspects of tubular of segmentation and heterogeneity generally enhance solute cycling or promote effective UCM function.

kidney; short loops of Henle; vascular bundle; vasa recta; Na⁺ transport; urea transport

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				A. T. Layton and H. E. Layton A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results Am J Physiol Renal Physiol, December 1, 2005; 289(6): F1346 - F1366. [Abstract] [Full Text] [PDF]