Mathematical model of an avian urine concentrating mechanism

Abstract

A mathematical model was used to investigate how concentrated urine is produced within the medullary cones of the quail kidney. Model simulations were consistent with a concentrating mechanism based on single-solute countercurrent multiplication and on NaCl cycling from ascending to descending limbs of loops of Henle. The model predicted a urine-to-plasma (U/P) osmolality ratio of ∼2.26, a value consistent with maximum avian U/P osmolality ratios. Active NaCl transport from descending limb prebend thick segments contributed 70% of concentrating capability. NaCl entry and water extraction provided 80 and 20%, respectively, of the concentrating effect in descending limb flow. Parameter studies indicated that urine osmolality is sensitive to the rate of fluid entry into descending limbs and collecting ducts at the cone base. Parameter studies also indicated that the energetic cost of concentrating urine is sensitive to loop of Henle population as a function of medullary depth: as the fraction of loops reaching the cone tip increased above anatomic values, urine osmolality increased only marginally, and, ultimately, urine osmolality decreased.