Oscillations in the proximal intratubular pressure: a mathematical model

Abstract

This study presents a dynamic continuous time model of the regulation of the renal proximal intratubular pressure in the rat. The model integrates a functional model of the glomerulus, a tubular model, a feedback model, and an afferent arteriolar model. The model has one equilibrium solution for the dependent variables (equilibrium point) for each set of independent variables. An equilibrium point, chosen to be in accordance with experimental data from Sprague-Dawley rats, was used as the initial value for the dependent variables. The model is shown to have parameter ranges in which sustained stable oscillations in proximal pressure are present. For sustained oscillations to appear, it is necessary for the system's operating point to be located on a sufficiently steep portion of the tubuloglomerular feedback curve. The model analyses are compared with various experimental recordings of the proximal intratubular pressure. The model simulations show both spontaneous and induced oscillations in the proximal pressure in close agreement with the experimental results; but the steady-state mean pressure regulation is found to be less efficient in the model than that apparent from the experimental recordings, suggesting the involvement of additional pressure-regulating mechanisms other than those included in the present model. It is concluded that the dynamic systems approach used in the present study yields new insight into the mechanisms underlying the proximal intratubular pressure oscillations and that it can be of further value for the study of the factors regulating the proximal intratubular pressure.