Maximum Urine Concentrating Capability in a Mathematical Model of the Inner Medulla of the Rat Kidney

Abstract

In a mathematical model of the urine concentrating mechanism of the inner medulla of the rat kidney, a nonlinear optimization technique was used to estimate parameter sets that maximize the urine-toplasma osmolality ratio (U/P) while maintaining the urine flow rate within a plausible physiologic range. The model, which used a central core formulation, represented loops of Henle turning at all levels of the inner medulla and a composite collecting duct (CD). The parameters varied were: water flow and urea concentration in tubular fluid entering the descending thin limbs and the composite CD at the outer-inner medullary boundary; scaling factors for the number of loops of Henle and CDs as a function of medullary depth; location and increase rate of the urea permeability profile along the CD; and a scaling factor for the maximum rate of NaCl transport from the CD. The optimization algorithm sought to maximize a quantity E that equaled U/P minus a penalty function for insufficient urine flow. Maxima of E were sought by changing parameter values in the direction in parameter space in which E increased. The algorithm attained a maximum E that increased urine osmolality and inner medullary concentrating capability by 37.5% and 80.2%, respectively, above base-case values; the corresponding urine flow rate and the concentrations of NaCl and urea were all within or near reported experimental ranges. Our results predict that urine osmolality is particularly sensitive to three parameters: the urea concentration in tubular fluid entering the CD at the outer-inner medullary boundary, the location and increase rate of the urea permeability profile along the CD, and the rate of decrease of the CD population (and thus of surface area) along the cortico-medullary axis.

New insights into urea and glucose handling by the kidney, and the urine concentrating mechanism

“…1 However, the mechanism by which urine is concentrated remains incompletely understood and is not satisfactorily simulated by the most sophisticated mathematical models designed so far. [2][3][4][5] The active transport that occurs in the thick ascending limb of Henle's loops and in the collecting duct (CD) in the cortex and outer medulla (OM) provide osmotic energy that accounts for the rise in urine osmolality within these zones, but the further concentration that is observed in the inner medulla (IM) remains largely unexplained.…”

A mathematical model of the rat kidney. II. Antidiuresis

“…While reduction of urine volume may obviously enhance free water reabsorption, the free water clearance captures the fact that solute excretion also figures into the defense of plasma osmolality. In this regard, in an analysis of models of inner medullary water conservation, Marcano et al (12) identified distinct optimal parameter configurations, depending on whether one asked for the most concentrated urine or the greatest free water absorp-tion. These aspects of water conservation are assessed from measurements of whole kidney function, and data from three prior medullary models is shown in Table 12, along with the performance of the model of this paper.…”

Lack of urea transporters, UT-A1 and UT-A3, increases nitric oxide accumulation to dampen medullary sodium reabsorption through ENaC

“…Although the erythrocyte lysis-based assay is well suited for high-throughput screening, the resulting UT-B inhibitors identified are not ideal urearetics. Transgenic mouse data (32) and computational models (37) predict that inhibition of UT-A is more likely to induce diuresis and UT-A inhibition would have fewer side effects because of tissue localization specific to the renal medulla unlike UT-B, which is expressed in all erythrocytes. Seeing this need, the Verkman group developed a screening assay to identify small-molecule UT-A inhibitors (11).…”

“…Urea accumulation in the inner medullary interstitium is dependent on urea transporters (UTs) to allow for facilitated urea movement across the endothelial cells of the vasa recta (UT-B) and tubular epithelial cells (UT-A) (50). Transgenic mouse data (32) and computational models (37) predict that inhibition of UT-A is more likely to induce diuresis. Currently, there are three known isoforms of UT-A expressed in the kidney medulla, UT-A1, UT-A2, and UT-A3 (50).…”