Transfer Function Analysis of Dynamic Blood Flow Control in the Rat Kidney

Abstract

Renal blood flow is regulated by the myogenic response (MR) and tubuloglomerular feedback (TGF). Both mechanisms function to buffer not only steady pressure perturbations but also transient ones. In this study, we develop two models of renal autoregulation—a comprehensive model and a simplified model—and use them to analyze the individual contributions of MR and TGF in buffering transient pressure perturbations. Both models represent a single nephron of a rat kidney together with the associated vasculature. The comprehensive model includes detailed representation of the vascular properties and cellular processes. In contrast, the simplified model represents a minimal set of key processes. To assess the degree to which fluctuations in renal perfusion pressure at different frequencies are attenuated, we derive a transfer function for each model. The transfer functions of both models predict resonance at 45 and 180 mHz, which are associated with TGF and MR, respectively, effective autoregulation below ~100 mHz, and amplification of pressure perturbations above ~200 mHz. The predictions are in good agreement with experimental findings.

A Multicellular Vascular Model of the Renal Myogenic Response

“…Characteristic simulations show that at physiologic blood pressure, the model predicts spontaneous oscillations (Figure 4) in cytosolic [Ca 2+ ] and in vascular diameter consistent with numerous experimental and theoretical findings, for example [2][3][4]26]. Those oscillations arise from the dynamic exchange of Ca 2+ between the cytosol and the sarcoplasmic reticulum, coupled to the stimulation of Ca 2+ -activated potassium and chloride channels, and the modulation of voltage-activated L-type channels [29,30].…”

“…Figure 4B shows the cytosolic Ca 2+ concentration, which varies between approximately 200 and 360 nM, a somewhat larger range than as predicted in [29,30]. The frequency of the oscillations is 0.15 Hz, the same as in [30] and slightly smaller compared to [29], but well within the range of experimental measurements, for example see [26]. Figure 4C shows the local vascular diameter in the proximity of the first cell of the afferent arteriole, which has an average of 19.7 µm with an oscillation amplitude of 0.6 µm.…”

“…Independently of the myogenic response which is triggered by local blood pressure perturbations, tubuloglomerular feedback is triggered by salt reabsorption in the downstream nephron that, in turn, depends on filtration rate. As the triggering signals of the two mechanisms are largely independent but interrelated through blood flow which influences both local pressure and filtration rate, highly non-trivial interactions among the two mechanisms are developed [4,7,26,77]. A potential extension of the present afferent arteriole model would be to include a model of nephron transport (e.g., [78][79][80][81][82]) and tubuloglomerular feedback (e.g., [7,[83][84][85]).…”

“…Thus, for smaller inflow frequencies f , the sinusoidal perturbation leads to irregular oscillations in the local vascular diameters and outflow pressure, and for large inflow frequencies f , the perturbation leads to sustained vasoconstriction [6,20,21,55]. According to the analyses in [26], this behavior is expected since, due to absence of tubuloglomerular feedback (TGF) in the present formulation, dynamic autoregulation at low frequencies f is not incorporated.…”

“…However, theoretically a deeper understanding of the involved processes is lacking which limits our ability to investigate in silico realistic scenarios under health or disease conditions. For example, although several models accurately represent the myogenic response at the vascular or supravascular levels [2,7,11,[19][20][21][22][23][24][25][26][27][28], and few even at the cellular level [6,29,30], none of the existing models attempt to model the myogenic response across multiple scales.…”