Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole

Abstract

We have formulated a mathematical model for the rat afferent arteriole (AA). Our model consists of a series of arteriolar smooth muscle cells and endothelial cells, each of which represents ion transport, cell membrane potential, and gap junction coupling. Cellular contraction and wall mechanics are also represented for the smooth muscle cells. Blood flow through the AA lumen is described by Poiseuille flow. The AA model's representation of the myogenic response is based on the hypothesis that changes in hydrostatic pressure induce changes in the activity of nonselective cation channels. The resulting changes in membrane potential then affect calcium influx through changes in the activity of the voltage-gated calcium channels, so that vessel diameter decreases with increasing pressure values. With this configuration, the model AA maintains roughly stable renal blood flow within a physiologic range of blood flow pressure. Model simulation of vasoconstriction initiated from local stimulation also agrees well with findings in the experimental literature, notably those of Steinhausen et al. (Steinhausen M, Endlich K, Nobiling R, Rarekh N, Schütt F. J Physiol 505: 493–501, 1997), which indicated that conduction of vasoconstrictive response decays more rapidly in the upstream flow direction than downstream. The model can be incorporated into models of integrated renal hemodynamic regulation.