An Optimization Algorithm for a Distributed-Loop Model of an Avian Urine Concentrating Mechanism

Abstract

To better understand how the avian kidney's morphological and transepithelial transport properties affect the urine concentrating mechanism (UCM), an inverse problem was solved for a mathematical model of the quail UCM. In this model, a continuous, monotonically decreasing population distribution of tubes, as a function of medullary length, was used to represent the loops of Henle, which reach to varying levels along the avian medullary cones. A measure of concentrating mechanism efficiency - the ratio of the free-water absorption rate (FWA) to the total NaCl active transport rate (TAT) - was optimized by varying a set of parameters within bounds suggested by physiological experiments. Those parameters include transepithelial transport properties of renal tubules, length of the prebend enlargement of the descending limb (DL), DL and collecting duct (CD) inflows, plasma Na(+) concentration, length of the cortical thick ascending limbs, central core solute diffusivity, and population distribution of loops of Henle and of CDs along the medullary cone. By selecting parameter values that increase urine flow rate (while maintaining a sufficiently high urine-to-plasma osmolality ratio (U/P)) and that reduce TAT, the optimization algorithm identified a set of parameter values that increased efficiency by approximately 60% above base-case efficiency. Thus, higher efficiency can be achieved by increasing urine flow rather than increasing U/P. The algorithm also identified a set of parameters that reduced efficiency by approximately 70% via the production of a urine having near-plasma osmolality at near-base-case TAT. In separate studies, maximum efficiency was evaluated as selected parameters were varied over large ranges. Shorter cones were found to be more efficient than longer ones, and an optimal loop of Henle distribution was found that is consistent with experimental findings.

Maximum Urine Concentrating Capability in a Mathematical Model of the Inner Medulla of the Rat Kidney

“…As we have previously noted (Marcano-Velázquez and Layton, 2003; Marcano et al, 2006), one can distinguish between those model studies on the UCM that have sought to investigate sensitivity to parameters by varying one parameter at a time (e.g., Layton et al (2000), Layton and Layton (2005b), Layton et al (2004), and Wexler et al (1991)), and those that have incorporated algorithms that allow multiple parameters to vary simultaneously in an attempt to optimize a measure of model performance (e.g., Breinbauer (1988), Breinbauer and Lory (1991), Kim and Tewarson (1996), Tewarson (1993b), Tewarson (1993a), and Tewarson and Marcano (1997)). In the present study, as in our studies of the avian UCM (Marcano-Velázquez and Layton, 2003; Marcano et al, 2006), we applied the latter approach, because it allows one to identify the synergistic, and perhaps nonlinear effects of interacting parameters, which an organism may be able to adjust and coordinate to meet its functional objectives.…”

“…In the present study, as in our studies of the avian UCM (Marcano-Velázquez and Layton, 2003; Marcano et al, 2006), we applied the latter approach, because it allows one to identify the synergistic, and perhaps nonlinear effects of interacting parameters, which an organism may be able to adjust and coordinate to meet its functional objectives. In the avian kidney, where only one solute, NaCl, is believed to play a fundamental role in the UCM, concentrating capability is modest relative to that in most mammals, and the principles of the UCM are believed to be well-understood (Layton et al, 2000).…”

Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla

“…Other loop bends have a transverse segment that labels for ClC-K1 and that may deliver a NaCl flux that is nearly transversely localized within a narrow band of the corticomedullary axis (54). Mathematical models have indicated that such localized delivery is optimal for concentrating efficacy (38,41,46). However, this efficacy may be further enhanced by a three-dimensional feature common to many of the transverse segments: they wrap around nearby CDs (54).…”

Modeling Transport and Flow Regulatory Mechanisms of the Kidney

“…While birds and mammals can regulate blood plasma osmolality by producing a concentrated urine when deprived of water, the avian kidney differs from the mammalian one in that all the ascending limbs of the avian loop of Henle have active transepithelial transport of NaCl, whereas only the thick ascending limbs in the outer medulla of the mammalian kidney have significant active NaCl transport. Thus, the avian urine concentrating mechanism is relatively well understood, and the mathematical models [68–70] predicted tubular fluid concentrations that are consistent with experimental measurements in Gambel’s quail [71]. In contrast, the thin ascending limbs found in the inner medulla have no significant active transepithelial transport of NaCl or of any other solute [72–75].…”

“…The central core formulation was used in urine concentrating mechanism models of the rat kidney [58–67] and of the avian (quail) kidney [68–70]. While birds and mammals can regulate blood plasma osmolality by producing a concentrated urine when deprived of water, the avian kidney differs from the mammalian one in that all the ascending limbs of the avian loop of Henle have active transepithelial transport of NaCl, whereas only the thick ascending limbs in the outer medulla of the mammalian kidney have significant active NaCl transport.…”