Transport of Spherical Particles Through Fibrous Media and a Row of Parallel Cylinders: Applications to Glomerular Filtration

Abstract

Viewed in renal physiology as a refined filtration device, the glomerulus filters large volumes of blood plasma while keeping proteins within blood circulation. Effects of macromolecule size and macromolecule hydrodynamic interaction with the nanostructure of the cellular layers of the glomerular capillary wall on the glomerular size selectivity are investigated through a mathematical simulation based on an ultrastructural model. The epithelial slit, a planar arrangement of fibers connecting the epithelial podocytes, is represented as a row of parallel cylinders with nonuniform spacing between adjacent fibers. The mean and standard deviation of gap half-width between its fibers are based on values recently reported from electron microscopy. The glomerular basement membrane (GBM) is represented as a fibrous medium containing fibers of two different sizes: the size of type IV collagens and that of glycosaminoglycans (GAGs). The endothelial cell layer is modeled as a layer full of fenestrae that are much larger than solute size and filled with GAGs. The calculated total sieving coefficient agrees well with the sieving coefficients of ficolls obtained from in vivo urinalysis in humans, whereas the computed glomerular hydraulic permeability also falls within the range estimated from human glomerular filtration rate (GFR). Our result indicates that the endothelial cell layer and GBM significantly contribute to solute and fluid restriction of the glomerular barrier, whereas, based on the structure of the epithelial slit obtained from electron microscopy, the contribution of the epithelial slit could be smaller than previously believed.