University of Puerto Rico, Río Piedras Campus
December 16, 2014
Two modes of urine formation in neonatal rat kidney by means of optimization problems
At birth, the rat’s kidney has not completed the process of nephron formation. The immature kidney is capable of producing diluted urine, but its concentrating ability is very limited. This could put at risk a newborn that is under dehydration.
We developed a mathematical model of a neonatal rat kidney. Model parameters consist of membrane transport rates of water and solute, boundary values, and the decay rate of nephron distribution. Parameter values for the diluting mode were computed by maximizing the amount of water excreted by the kidney, whereas for the concentrating mode, the parameters were obtained by maximizing the amount of water conserved by the kidney. Further, by extending the ranges of key parameters, an optimum that gives a more concentrated urine is obtained for the immature kidney.