Analysis of pulsatile pressures and flows in glomerular filtration

Abstract

Previous mathematical models of glomerular filtration have ignored the pulsatility of the glomerular capillary pressure, using only steady-state equations and time-averaged pressures and flows. Because the actual pressure pulses are rapid and of large amplitude and because the governing equations are nonlinear, it is questionable whether the effects of the pressure pulses average out in the manner that has been assumed. We have developed a model that includes sinusoidal variations in the glomerular transcapillary hydraulic pressure (delta P) and the afferent arteriolar plasma flow rate over each cardiac cycle. The analysis suggests that the previously ignored time derivatives in the luminal mass balance equations are not negligible. The amplitude of the oscillations in delta P was found to be sufficient to reverse the direction of the transmural fluxes over part of each cardiac cycle, at the more efferent locations in a capillary. However, the time-averaged values of single-nephron glomerular filtration rate and sieving coefficients for macro-molecules from the pulsatile model differed from that for a steady-state formulation by less than 0.1 and less than or equal to 10%, respectively. We conclude that use of the usual steady-state assumption introduces negligible errors in calculating glomerular membrane parameters from experimental data.