MBI Publications

MBI Publications for Renal Hemodynamics (1)

• P. Grajdeanu and L. Moore
Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop
Mathematical BiosciencesVol. 209 No. 2 (2007) pp. 564-592

Abstract

We used a simple mathematical model of rat thick ascending limb (TAL) of the loop of Henle to predict the impact of spatially inhomogeneous NaCl permeability, spatially inhomogeneous NaCl active transport, and spatially inhomogeneous tubular radius on luminal NaCl concentration when sustained, sinusoidal perturbations were superimposed on steady-state TAL flow. A mathematical model previously devised by us that used homogeneous TAL transport and fixed TAL radius predicted that such perturbations result in TAL luminal fluid NaCl concentration profiles that are standing waves. That study also predicted that nodes in NaCl concentration occur at the end of the TAL when the tubular fluid transit time equals the period of a periodic perturbation, and that, for non-nodal periods, sinusoidal perturbations generate non-sinusoidal oscillations (and thus a series of harmonics) in NaCl concentration at the TAL end. In the present study we find that the inhomogeneities transform the standing waves and their associated nodes into approximate standing waves and approximate nodes. The impact of inhomogeneous NaCl permeability is small. However, for inhomogeneous active transport or inhomogeneous radius, the oscillations for non-nodal periods tend to be less sinusoidal and more distorted than in the homogeneous case and to thus have stronger harmonics. Both the homogeneous and non-homogeneous cases predict that the TAL, in its transduction of flow oscillations into concentration oscillations, acts as a low-pass filter, but the inhomogeneities result in a less effective filter that has accentuated non-linearities.