Analysis of interaction between TGF and the myogenic response in renal blood flow autoregulation

Abstract

The present study investigates the interaction between the tubuloglomerular feedback (TGF) response and the myogenic mechanism by use of a mathematical model. The two control mechanisms are implemented in a spatially distributed model of the rat renal juxtamedullary afferent arteriole. The model of the afferent arteriole is based on in vivo measurements of the stress-strain relation in muscle strips. Analysis of experimental data shows that the myogenic response can be modeled by a linear relation between the transmural pressure and the level of activation of the vascular smooth muscle cells. The contribution of TGF to smooth muscle activity is assumed to be a linear function of the glomerular capillary pressure. The results show that the myogenic response plays an important role in renal blood flow autoregulation. Without a myogenic response, mechanisms such as TGF that are localized in the distal segments of the microvasculature would not be able to achieve autoregulation because of passive, pressure-mediated effects in the upstream vascular segments. In addition, it is shown that a strong myogenic response may lead to both propagation and enhancement of vascular effects mediated through mechanisms located in the distal part of the afferent arteriole. An ascending myogenic response could enhance the regulatory efficiency of the TGF mechanism by increasing the open-loop gain of the system. However, such a synergistic interaction will only be observed when the two mechanisms operate on more or less separate segments of the afferent arteriole. In the case where they operate on common segments of the arteriole, the outcome of the interaction may well be antagonistic.

Synchronization phenomena in nephron–nephron interaction

“…16 Here, one observes a peak at frequencies considerably higher than the frequencies of the TGF regulation and corresponding to typical arteriolar dynamics. Based on in vitro experiments on the strain-stress relationships for muscle strips, Feldberg et al 17 have proposed a mathematical model for the reaction of the arteriolar wall in the individual nephron.…”

Bifurcation analysis of nephron pressure and flow regulation

“…Despite much research, the detailed mechanisms of this response are still unknown. Based on in vitro experiments on the strain-stress relationship for muscle strips, Feldberg et al 20,24 have proposed a mathematical model of the reaction of the arteriolar wall. This reaction is considered to consist of a passive elastic component in parallel with an active muscular component.…”

“…This representation implies that the delay is represented as a smoothed process, with 1 , 2 , and 3 being intermediate variables in the delay chain. The afferent arteriole is divided into two serially coupled sections of which the first ͑representing a fraction ␤ of the total length͒ is assumed to have a constant hemodynamic resistance, while the second ͑closer to the glomerulus͒ is capable of varying its diameter and hence the flow resistance in dependence of the tubuloglomerular feedback activation, 20 R a ϭR a0 ͓␤ϩ͑ 1Ϫ␤ ͒r Ϫ4 ͔. ͑11͒…”

“…By numerically integrating the passive and active contributions to the response across the arteriolar wall, one can establish a relation between the equilibrium pressure P eq , the normalized radius r, and the activation level . 20,24 This relation is represented by the fully drawn curves in Fig. 2.…”

“…Based on in vitro measurements of the stress-strain relationship for muscle strips, Feldberg 20 recently developed a detailed description of the myogenic regulation and of its interaction with the TGF mechanism. A characteristic feature of this model is that the afferent arteriole tends to contract in response to increasing hydrostatic pressure in the blood.…”