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Talk Abstract
The Urine Concentrating Mechanism: Lessons from the Avian Kidney

Harold E. Layton
Duke University
Durham, NC 27708
layton@math.duke.edu


In the bird, concentrated urine is produced in the medullary cones, subunits of the avian kidney which are believed to contain countercurrent multiplier systems. A mathematical model of a single medullary cone was used to evaluate the countercurrent multiplier hypothesis and to investigate how concentrating capability depends on morphological and tubular transport parameters. Model simulations, using parameters based on experimental measurements, supported the countercurrent multiplier hypothesis: the model predicted a urine-to-plasma osmolality ratio of about 2.26, a value consistent with measured osmolalities. Active NaCl transport from the descending limb thick prebend segment contributed about 70% of the simulated concentrating capability. NaCl secretion and water extraction provided about 80% and 20%, respectively, of the concentrating effect in descending limbs. Parameter studies indicate that urine osmolality is very sensitive to the rate of fluid entry into descending limbs and collecting ducts at the cone base. Parameter studies also indicate 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 physiological values, urine osmolality increased only marginally, and, ultimately, urine osmolality decreased.

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1998-1999 Mathematics in Biology

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