Numerical analysis of blood flow in reconstructed glomerular capillary segments

Abstract

Poiseuille's formula is conventionally used to calculate hydraulic resistance of blood capillaries. This law, however, applies to tubes with constant diameter and straight axis. Since blood capillaries, especially in the glomerular microcirculation, are far from having these features, we wanted to estimate the effect of the shape of glomerular capillary segments on the calculation of their hydraulic resistance in comparison to the values obtained with Poiseuille's formula. We studied blood flow through capillary segments of a reconstructed glomerular network from a normal Munich-Wistar rat. Geometrical parameters of capillary segments derived from serial section reconstruction of the glomerulus were used to perform numerical analysis of blood flow. Non-Newtonian properties of blood were simulated by calculating apparent blood viscosity as a function of local rheological parameters for each capillary segment. The numerically calculated hydraulic resistances were always higher than those given by the Poiseuille equation (from 22 to 99%), and this was attributed to the geometrical complexity of the reconstructed vessels. We also performed simulations of the blood flow and filtration along the glomerular network using a previously developed theoretical model that considers the topographical organization of the network structure and dimensions of individual capillary segments. Considering higher hydraulic resistances (as estimated with the numerical analysis) we found that the calculated ultrafiltration coefficient did not change appreciably, but the total network pressure drop and the fraction of filtering surface area at filtration equilibrium were higher than previously estimated.