Bulletin of Mathematical Biology

, Volume 65, Issue 4, pp 665–691 | Cite as

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

  • M. Marcano-VelázquezEmail author
  • Harold E. Layton


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.


Collect Duct Inverse Algorithm Macula Densa Urine Concentrate Mechanism Thin Descend Limb 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Society for Mathematical Biology 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Puerto RicoRío Piedras, Puerto RicoUSA
  2. 2.Department of MathematicsDuke UniversityDurhamUSA

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