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An inverse algorithm for a mathematical model of an avian urine concentrating mechanism

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Abstract

A nonlinear optimization technique, in conjunction with a single-nephron, single-solute 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 free-water 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 cortico-medullary boundary; and rate of exponential CD population decrease along the medullary cone. Using a base-case parameter set and parameter bounds suggested by physiologic experiments, the optimization algorithm identified a maximum-efficiency set of parameter values that increased efficiency by 40% above base-case efficiency; a minimum-efficiency set reduced efficiency by about 41%. When maximum-efficiency 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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Authors and Affiliations

  1. Department of Mathematics, University of Puerto Rico, P.O. Box 23355, Río Piedras, Puerto Rico, 00931-3355, USA

    M. Marcano-Velázquez

  2. Department of Mathematics, Duke University, Durham, NC, 27708-0320, USA

    Harold E. Layton

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  1. M. Marcano-Velázquez
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  2. Harold E. Layton
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Correspondence to M. Marcano-Velázquez.

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Marcano-Velázquez, M., Layton, H.E. An inverse algorithm for a mathematical model of an avian urine concentrating mechanism. Bull. Math. Biol. 65, 665–691 (2003). https://doi.org/10.1016/S0092-8240(03)00029-6

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  • DOI: https://doi.org/10.1016/S0092-8240(03)00029-6

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