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It has been shown that the organization of nephrons and
vasa recta in the mammalian outer medulla is highly structured.
Nephrons and vasa recta are positioned around the vascular bundles,
which are tightly packed bundles containing descending vasa recta and
ascending vasa recta, arranged in a checkerboard pattern.
It has been proposed that this structural organization may results in
preferential interactions among nephrons and vasa recta,
which may in turn contribute to solute recycling
in the medulla and to the urine concentrating mechanism.
The goal of our study is to develop a mathematical model of the mammalian outer medulla that incorporates the findings of anatomic studies and recently obtained epithelial transport parameters. Our model is formulated as a dynamic boundary-value problem, consisting of a large system of coupled ordinary differential equations (ODEs), representing water conservation, and partial hyperbolic partial differential equations (PDEs), representing solute conservation. Unliked previous central core models, this model includes the representation of vasa recta. By representing the relative positions of the medullary structures, the model captures preferential interactions among the structures.
Our outer medulla model (see above figure) represents a short loop of Henle that reaches to the end of the outer medulla, a long loop of Henle that reaches into the inner medulla, continuously distributed vasa recta that turn at differing levels of the outer medulla, a long vas rectum that reaches into the inner medulla, a collecting duct, and two central regions of merged capillaries, interstitial spaces, and interstitial cells. The loops of Henle, vasa recta, and collecting duct interact in the central regions; two central regions are included to simulate the preferential interactions among tubules vessels that have been suggested by the complex structural features revealed in anatomical studies of the mammalian renal medulla. Such preferential interactions have been interpreted to contribute to more efficient countercurrent exchange or multiplication, to the cycling and accumulation of urea in the inner medulla, and to the sequestration of urea or NaCl in tubular segments. In most mammalian species, descending vasa recta (DVR) and ascending vasa recta (AVR) are incorporated into tightly packed vascular bundles in the inner stripe of the outer medulla. The innermost central region, denoted by R1, represents a intrabundle region. DVR on the periphery of the bundles peel off to supply the dense capillary plexus of the outer medulla. Thus, these vasa recta are represented by continuously distributed vasa recta, with a vas rectum reaching to each level of the outer medulla. Centrally located DVR traverse the axis of the bundles to supply blood flow to the inner medulla. Thus, vasa recta that are destined for the inner medulla are represented by a single vas rectum that reaches past the end of the outer medulla. |
Configuration of the Outer Medulla Model