Determination of glomerular intracapillary and transcapillary pressure gradients from sieving data. I. A mathematical model.

Determination of glomerular intracapillary and transcapillary pressure gradients from sieving data. A biomathematical model is described to calculate the intracapillary and transcapillary glomerular pressure gradients from the sieving coefficients (phi: fractional clearances/GFR) of macromolecules such as polyvinylpyrrolidone (PVP). Two differential equations have been developed. The first one calculates local values for GFR in terms of local values for PGC (intracapillary hydrostatic pressure) and pi (oncotic pressure). The second equation calculates the clearance of PVP equimolecular fractions, the sieving equations previously described (24) being used to derive the concentrations of PVP in the filtrate (c2). Two variants of the second equation have been considered, assuming the filtrate in contact with the membrane either "well stirred" or "unstirred" (constant c2 and local c2 gradient models respectively). Computer simulations have been used to illustrate how the sieving curve is modified when the five parameters on which depends the shape of the curve are changed one by one. The sieving curve relates phi to a(s) (hydrodynamically equivalent molecular radius). The determining parameters are: GFP, the mean effective glomerular filtration pressure, epsilon, the slope of the intracapillary pressure, FF, the filtration fraction, Cp0, the protein concentration in arterial plasma and r, the pore radius which is the only structural parameter involved when one assumes the glomerular membrane crossed by cylindrical pores of uniform size and length. The shape of the sieving curve is modified significantly enough by changing GFP, FF and r within reasonable limits, to make it possible to derive GFP and r from experimental sieving data for macromolecules such as PVP or dextrans.