Three-dimensional reconstructed glomerular capillary network: blood flow distribution and local filtration.

Abstract

We developed a mathematical model to simulate blood flow and filtration in individual capillary segments of a glomerular network reconstructed from a normal Munich-Wistar (MW) rat. Three-dimensional geometric reconstruction was obtained by semithin serial sections (1 micron) of one glomerulus after perfusion fixation of kidney. Photomicrographs of each section were digitized and processed, using a computer-based image-analysis system, to derive the topological organization of the capillary network and mean diameter and length of individual capillary segments. Blood flow rate in capillary segments was calculated using a theoretical model that considers apparent viscosity of blood in small capillaries as a function of local rheological parameters, partition of cells at bifurcations, and local filtration dependent on transmembrane hydraulic and oncotic pressure gradients along the network. In accord with previous observations, the topological organization of the capillary network disclosed a three-lobular structure. The ultrafiltration coefficient (Kf) calculated for the euvolemic MW rat with the present network approach was compared with that derived from a theoretical model that assumes identical capillaries in parallel. The latter model is shown to underestimate Kf, particularly under conditions in which filtration pressure equilibrium is approached. Calculation of local blood flow and filtration along the network indicates a heterogeneous distribution of these parameters and that some parts of the capillary network operate at filtration pressure equilibrium even if the overall network operates at filtration disequilibrium.