Pathways for glomerular macromolecule filtration: A mathematical model for transport across glomerular filtration surface, mesangium and shear-induced shunts.

A mathematical model is developed to investigate the relative contribution of macromolecule transport across the glomerular filtration surface and that across mesangial area to glomerular size-selectivity. Endothelial fenestrae are assumed to be filled with glycosaminoglycans. Glomerular basement membrane (GBM) is a hydrogel containing two types of fibers. Slit diaphragm is a row of parallel cylinders with inter-fiber spacing following a lognormal distribution. Glomerular mesangium is viewed as a Brinkman medium with solute diffusivity and convection rate calculated from hydrodynamic forces exerted on confined spheres. Comparison between calculated sieving coefficients and those of Ficolls from in vivo studies demonstrates that inclusion of fluxes across the filtration surface and mesangial area, although capable of explaining small and medium-sized solute sieving, underestimates filtration of macromolecules with radii larger than 5 nm. Based on electron micrographs displaying red blood cells escaping through openings at the junction between the filtration surface and mesangium, the location with maximum shear stress, the present study examines effects of these openings using low-Reynolds-number hydrodynamics. Even though such effects on filtration of small and moderate-sized solutes are negligible, the presence of possibly shear-induced openings amplifies sieving of large macromolecules, yielding calculated sieving coefficients that agree well with those obtained from urinalysis in healthy humans and patients with diabetic nephropathy for the entire range of solute radii. While the glomerular filtration surface is the main pathway for small and moderate-sized solutes, main passages of large macromolecules are likely to be through the shear-induced openings, explaining the "upper limit" of glomerular size-selectivity.