An Optimal Mathematical Model for the Urine Concentrating Process of Neonatal Rats

Abstract

Immature rats have limited abilities to concentrate the urine. A mathematical model for the concentrating mechanism in the neonatal rat medulla was formulated. A nonlinear optimization method was used to identify model parameter sets that maximize a model efficiency measure, which was taken as the ratio of free‐water absorption rate to total active solute transport rate. The optimization method systematically changes the parameter values within their prescribed ranges, seeking maximal efficiency. The variable parameters were: NaCl and urea concentration in the cortico‐medullary junction of descending limbs of Henle (DLH) and collecting ducts (CD); urea permeability in DLH, ascending limbs (ALH) and inner medullary CD (IMCD); NaCl maximum active transport rates in ALH and IMCD; CD water permeability; and the exponential decrease rates of loops of Henle and CD population. Parameter baseline values were obtained from reported means in physiological experiments or estimated using physiological assumptions. By allowing most parameters to fluctuate by ± 25% from baseline values the maximal model efficiency was 15% above baseline, resulting in only 5% increase in urine osmolality. This is consistent with experimental data from animals and isolated CD from immature rats.