title: An inverse algorithm for a mathematical model of an avian urine concentrating mechanism.
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.
authors.affiliation: Department of Mathematics, University of Puerto Rico, P.O. Box 23355, Río Piedras, Puerto Rico 00931-3355, USA. mmarcan1@rrpac.upr.clu.edu
authors.forename: M
authors.initials: M
authors.lastname: Marcano-Velázquez
authors.forename: Harold E
authors.initials: HE
authors.lastname: Layton
mesh_terms: D000465:Algorithms; D000818:Animals; D007671:Kidney Concentrating Ability / Q000502:physiology*; D007684:Kidney Tubules / Q000502:physiology*; D008954:Models, Biological; D009994:Osmolar Concentration; D011784:Quail / Q000652:urine*; D014867:Water / Q000502:physiology
chemical_list: D014867:Water