Maximum Urine Concentrating Capability for Transport Parameters and Urine Flow within Prescribed Ranges

Abstract

In a mathematical model of the urine concentrating mechanism of the rat inner medulla, a nonlinear optimization technique was used to estimate parameter sets that maximize the urine-to-plasma osmolality ratio (U/P) and that maintain a urine flow rate within a plausible physiological range. The model assumed low solute permeabilities in the terminal part of the descending thin limb (DTL) and in the ascending thin limb of Henle’s loop. The parameters varied were: water flow and urea concentration in tubular fluid entering the DTL and collecting duct (CD) at the outer-inner medullary boundary; scaling factors for loops of Henle and CD population distributions; location and exponential increase rate of the urea permeability profile along the CD; and a scaling factor for the CD NaCl maximum active transport rate. The algorithm sought an optimum by simultaneously changing parameter values in the direction in which U/P increased. Parameters were allowed to vary within ranges suggested by physiologic experiments. The algorithm obtained a maximum U/P that increased urine osmolality by 42% above its base-case value. In the optimum case, only one parameter, CD water inflow, took on a value interior to its range; the other parameters assumed values at extrema of their ranges. This research was supported by NIH grants DK-042091 and S06GM08102, and NSF grant DMS-0340654.