Modeling the Effects of Positive and Negative Feedback in Kidney Blood Flow Control

Abstract

This paper models the interactions of three key feedback mechanisms that regulate blood flow in the mammalian kidney: (1) the myogenic response, triggered by blood pressure in the afferent arteriole; (2) tubuloglomerular feedback (TGF), a negative feedback mechanism responding to chloride concentrations at the mascula densa (MD); and (3) connecting tubule glomerular feedback (CTGF), a positive feedback mechanism responding to chloride concentrations in the connecting tubule, downstream of the mascula densa. Previous models have studied the myogenic response and TGF. However, CTGF is much less well understood, and we thus aim to construct a mathematical model incorporating all three mechanisms. A bifurcation analysis was performed on this expanded model to predict the behavior of the system over a range of physiologically realistic parameters, and numerical simulations of the model equations were computed to supplement the results of the bifurcation analysis. In doing so, we seek to elucidate the interactions of all three feedback mechanisms and their effects on kidney blood flow. In particular, numerical simulations were able to confirm our hypothesis that the interactions between TGF and CTGF give rise to an experimentally observed low frequency oscillation that could not be explained by previous models incorporating TGF alone.