DYNAMIC BEHAVIOR ANALYSIS OF THE GLOMERULO-TUBULAR BALANCE MEDIATED BY THE EFFERENT BLOOD VISCOSITY

International audienceA mathematical model of the dynamics of a single nephron function relating glomerulo-tubular balance, tubule-glomerular feedback, and peritubular blood viscosity is developed. Based upon experimental data, the model shows that complex behaviors of the nephron can be modulated by changes in the efferent arteriole blood viscosity. The main hypothesis is that the reabsorbed mass flow is modulated by the hematocrit of the efferent arteriole, in addition to the Starling forces. From a mathematical perspective, these behaviors can be explained by a bifurcation diagram analysis where the efferent blood viscosity is taken as the bifurcation parameter. This analytical description allows to predict changes in proximal convoluted tubule reabsorption, following changes in peritubular capillary viscosity generated by periodic changes in the glomerular filtration rate. Thus, the model links the tubule-glomerular feedback with the glomerular tubular balance

Cerebral autoregulation: an overview of current concepts and methodology with special focus on the elderly.

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Coupling-induced complexity in nephron models of renal blood flow regulation

Tubular pressure and nephron blood flow time series display two interacting oscillations in rats with normal blood pressure. Tubuloglomerular feedback (TGF) senses NaCl concentration in tubular fluid at the macula densa, adjusts vascular resistance of the nephron's afferent arteriole, and generates the slower, larger-amplitude oscillations (0.02–0.04 Hz). The faster smaller oscillations (0.1–0.2 Hz) result from spontaneous contractions of vascular smooth muscle triggered by cyclic variations in membrane electrical potential. The two mechanisms interact in each nephron and combine to act as a high-pass filter, adjusting diameter of the afferent arteriole to limit changes of glomerular pressure caused by fluctuations of blood pressure. The oscillations become irregular in animals with chronic high blood pressure. TGF feedback gain is increased in hypertensive rats, leading to a stronger interaction between the two mechanisms. With a mathematical model that simulates tubular and arteriolar dynamics, we tested whether an increase in the interaction between TGF and the myogenic mechanism can cause the transition from periodic to irregular dynamics. A one-dimensional bifurcation analysis, using the coefficient that couples TGF and the myogenic mechanism as a bifurcation parameter, shows some regions with chaotic dynamics. With two nephrons coupled electrotonically, the chaotic regions become larger. The results support the hypothesis that increased oscillator interactions contribute to the transition to irregular fluctuations, especially when neighboring nephrons are coupled, which is the case in vivo