Dynamic Behavior Analysis of the Glomerulo-Tubular Balance Mediated by the Efferent Blood Viscosity

Abstract

In this paper, a mathematical model of the dynamics of a single-nephronfunction relating glomerulo-tubular balance, tubule-glomerular feedback, and peritubularblood viscosity is developed. Based upon experimental data, the modelshows that complex behaviors of the nephron can be modulated by changes in theefferent arteriole blood viscosity. The main hypothesis is that the reabsorbed massflow is modulated by the hematocrit of the efferent arteriole, in addition to the Starlingforces. From a mathematical perspective, these behaviors can be explained by abifurcation diagram analysis where the efferent blood viscosity is taken as the bifurcationparameter. This analytical description allows to predict changes in proximalconvoluted tubule reabsorption, following changes in peritubular capillary viscositygenerated by periodic changes in the glomerular filtration rate. Thus, the modellinks the tubule-glomerular feedback with the glomerular tubular balance.