An optimization study of a mathematical model of the urine concentrating mechanism of the rat kidney

Abstract

The rat kidney’s morphological and transepithelial transport properties may change in response to different physiologic conditions. To better understand those processes, we used a non-linear optimization technique to estimate parameter sets that maximize key measures that assess the effectiveness and efficiency of a mathematical model of the rat urine concentrating mechanism (UCM). We considered two related measures of UCM effectiveness: the urine-to-plasma osmolality ( U/ P) ratio and free-water absorption rate (FWA). The optimization algorithm sought parameter sets that separately maximize FWA, maximize U/ P with the constraint that the predicted urine flow rate is consistent with reported experimental value (denoted by ( U / P ) ρ ), and maximize the ratio U/ P to the total NaCl active transport (TAT) (denoted by ( U/ P)/TAT). When the principal need of the animal is to maximize the impact of its UCM on blood plasma osmolality, the kidney likely undergoes changes that increase FWA. By selecting parameter values that increase model urine flow rate (while maintaining a sufficiently high urine osmolality), the optimization algorithm identified a set of parameter values that increased FWA by 95.6% above base-case efficiency. If, on the other hand, water must be preserved, then the animal may seek to optimize U/ P instead. To study that scenario, the optimization algorithm separately sought parameter sets that attained maximum ( U / P ) ρ and ( U/ P)/TAT. Those parameter sets increased urine osmolality by 55.4% and 44.5%, respectively, above base-case value; the outer-medullary concentrating capability was increased by 64.6% and 35.5%, respectively, above base case; and the inner-medullary concentrating capability was increased by 73.1% and 70.8%, respectively, above base case. The corresponding urine flow rate and the concentrations of NaCl and urea are all within or near reported experimental ranges.