Math @ Duke

Publications [#287311] of Harold Layton
Papers Published
 MarcanoVelÃ¡zquez, M; Layton, HE, An inverse algorithm for a mathematical model of an avian urine concentrating mechanism.,
Bulletin of Mathematical Biology, vol. 65 no. 4
(July, 2003),
pp. 665691 [doi]
(last updated on 2019/06/15)
Abstract: A nonlinear optimization technique, in conjunction with a singlenephron, singlesolute mathematical model of the quail urine concentrating mechanism, was used to estimate parameter sets that optimize a measure of concentrating mechanism efficiency, viz., the ratio of the freewater absorption rate to the total NaCl active transport rate. The optimization algorithm, which is independent of the numerical method used to solve the model equations, runs in a few minutes on a 1000 MHz desktop computer. The parameters varied were: tubular permeabilities to water and solute; maximum active solute transport rates of the ascending limb of Henle and the collecting duct (CD); length of the prebend enlargement (PBE) of the descending limb; fractional solute delivery to the CD; solute concentration of tubular fluid entering the CD at the corticomedullary boundary; and rate of exponential CD population decrease along the medullary cone. Using a basecase parameter set and parameter bounds suggested by physiologic experiments, the optimization algorithm identified a maximumefficiency set of parameter values that increased efficiency by 40% above basecase efficiency; a minimumefficiency set reduced efficiency by about 41%. When maximumefficiency parameter values were computed as medullary length varied over the physiologic range, the PBE was found to make up 88% of a short medullary cone but only 8% of a long medullary cone.


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