Hindered transport of macromolecules through a single row of cylinders: Application to glomerular filtration

The slit diaphragms of renal glomerular capillaries form an ultrafiltration barrier which may be approximated as a row of cylindrical fibers of macromolecular dimensions. To describe the hindered transport of plasma proteins and other macromolecules through this barrier, we developed an approximate hydrodynamic model for spherical, Brownian particles passing through a row of infinitely long cylinders. The selectivity of the slit diaphragm was assessed by computing concentration profiles for a wide range of molecular sizes for Pe less than or equal to 1, where Pe is a Peclet number based on the cylinder radius. The sieving coefficient the slit diaphragm was computed as theta(SD) = C-B/C-0, where C-0 was the average concentration at a specified distance upstream from the cylinders (corresponding to the location of the basement membrane), and C-B was the concentration far downstream (corresponding to Bowman's space). The results of previous experimental sieving studies using rats could be accounted for approximately by postulating a wide distribution of spacings between the fibers of the slit diaphragm. Comparing the results for theta(SD) with calculations for a model of the glomerular basement membrane suggests that the slit diaphragm is by far the more size-restrictive part of the overall barrier.