Effect of tubular inhomogeneities on feedback-mediated dynamics of a model of a thick ascending limb

Abstract

One of the key mechanisms that mediate renal autoregulation is the tubuloglomerular feedback (TGF) system, which is a negative feedback loop in the kidney that balances glomerular filtration with tubular reabsorptive capacity. Tubular fluid flow, NaCl concentration and other related variables are known to exhibit TGF-mediated oscillations. In this study, we used a mathematical model of the thick ascending limb (TAL) of a short loop of Henle of the rat kidney to study the effects of (i) spatially inhomogeneous TAL NaCl active transport rate, (ii) spatially inhomogeneous tubular radius and (iii) compliance of the tubular walls on TGF-mediated dynamics. A bifurcation analysis of the TGF model equations was performed by deriving a characteristic equation and finding its roots. Results of the bifurcation analysis were validated via numerical simulations of the full model equations. Model results suggest that a higher TAL NaCl active transport rate or a smaller TAL radius near the loop bend gives rise to stable oscillatory solutions at sufficiently high TGF gain values, even with zero TGF delay. In addition, when the TAL walls are assumed to be compliant, the TGF system exhibits a heightened tendency to oscillate, a result that is consistent with predictions of a previous modelling study. © The Author 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.