Hydrodynamic model for renal microvascular filtration: Effects of physiological and hemodynamic changes on glomerular size-selectivity.

OBJECTIVE: The first step in renal urine formation is ultrafiltration across the glomerular barrier. The change in its nanostructure has been associated with nephrotic syndromes. Effects of physiological and hemodynamic factor alterations associated with diabetic nephropathy (DN) on glomerular permselectivity are examined through a mathematical model employing low-Reynolds-number hydrodynamics and hindered transport theory. METHODS: Glomerular capillaries are represented as networks of cylindrical tubes with multilayered walls. Glomerular basement membrane (GBM) is a fibrous medium with bimodal fiber sizes. Epithelial slit fiber spacing follows a lognormal distribution based on reported electron micrographs with the highest resolution. Endothelial fenestrae are filled with fibers the size of glycosaminoglycans (GAGs). Effects of fiber-macromolecule steric and hydrodynamic interactions are included. Focusing on diabetic nephropathy, the physiological and hemodynamic factors employed in the computation are those reported for healthy humans and patients with early-but-overt diabetic nephropathy. The macromolecule concentration is obtained as a finite element solution of the convection-diffusion equation. RESULTS: Computed sieving coefficients averaged along the capillary length agree well with ficoll sieving coefficients from studies in humans for most solute radii. GBM thickening and the loss of the slit diaphragm hardly affect glomerular permselectivity. GAG volume fraction reduction in the endothelial fenestrae, however, significantly increases macromolecule filtration. Increased renal plasma flow rate (RPF), glomerular hypertension, and reduction of lumen osmotic pressure cause a slight sieving coefficient decrease. These effects are amplified by an increased macromolecule size. CONCLUSION: Our results indicate that glomerular hypertension and the reduction in the oncotic pressure decreases glomerular macromolecule filtration. Reduction of RPF and changes in the glomerular barrier structure associated with DN, however, increase the solute sieving. Damage to GAGs caused by hyperglycemia is likely to be the most prominent factor affecting glomerular size-selectivity.

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

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.

Electrostatic and electrokinetic effects on hindered convection in pores.

The sieving of macromolecules in ultrafiltration is affected by solute and pore charge, as well as size. A large, relatively rigid molecule such as a globular protein may be viewed as a particle in an electrolyte solution. Charge may influence both its equilibrium partition coefficient and its lag coefficient (G), which is the ratio of particle to fluid velocity. Partitioning had been examined previously for spheres in cylindrical pores by using continuum double layer theory to evaluate the electrostatic potential energy (E). The present objective was to estimate G for particles and pores of like charge. Particle or fluid motion tends to distort the diffuse double layers, an effect termed "relaxation," which increases the drag on the particle. The streaming potential that arises from flow through a charged pore under open-circuit conditions also increases the drag on a confined, stationary particle. These electrokinetic effects were quantified using finite element solutions of the equations of motion, Poisson's equation, and conservation equations for small ions in the electrolyte. It was found that charge effects generally reduce G, with relaxation tending to be the more important contributor. Thus, a freely suspended, charged particle will move through a pore more slowly than an uncharged one of the same size. However, the effects of E on sieving outweigh those of the electrokinetic decrease in G. That is, charge influences sieving mainly by altering the partition coefficient.