The transport equation describing the flow of solute across a membrane has been modified on the basis of theoretical studies calculating the drag of a sphere moving in a viscous liquid undergoing Poiseuille flow inside a cylinder. It is shown that different frictional resistance terms should be introduced to calculate the contributions of diffusion and convection. New sieving equations are derived to calculate r and A,/Ax (respectively, the pore radius and the total area of the pores per unit of path length). These equations provide a better agreement than the older formulas between the calculated and the experimental glomerular sieving coefficients for [6I]polyvinylpyrrolidone (PVP) fractions with a mean equivalent radius between 19 and 37 A. From r and A,/Ax, the mean effective glomerular filtration pressure has been calculated, applying Poiseuille's law. A value of 15.4 mm Hg has been derived from the mean sieving curve obtained from 23 experiments performed on normal anesthetized dogs.In 1951, Pappenheimer et al. developed the so-called "pore theory" to account for the transcapillary transport of uncharged, lipid-insoluble solutes in mammalian muscles (24). According to this theory, convective flow and net diffusion contribute to solute flow across the membrane, in this case the capillary walls, both processes being impeded by the steric hindrance at the entrance of the "pores" (supposed to exist between the cells) and by frictional forces within the pores (20,22,23,25).The solute flow due to diffusion was calculated as D(c -c 2 )AW/Ax X A,/A, where D is the free diffusion coefficient, cl and c 2 , respectively, the solute concentrations in filtrand and filtrate and A,/Ax the pore area freely available to water per unit of length. The term A,/A, describes the restriction to the motion and can be calculated as 1/K 1 X SD where SD = [1 -(a,/r)]2 is the steric hindrance term (a, is the radius of the solute molecules

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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.

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The effects of the intrarenal infusion of synthetic Asn1, val 5 angiotensin II (AII) (from 0.38 to 1 mug min-1) on the determinants of glomerular filtration have been studied. The intracapillary and transcapillary pressure gradients along the capillaries, together with 2 parameters characterizing the porosity of the membrane in terms of pore theory (r, radius of the pores and Ap/1, total pore area per unit of path length) were calculated from the analysis of the sieving curve of I125 PVP molecules (polyvinylpyrrolidone) according to a biomathematical model previously described. AII increased PGC, the intracapillary hydrostatic pressure, but more at the efferent end of the capillaries. Filtration pressure equilibrium was maintained. AII also decreased the water permeability coefficient, Kf. by decreasing Ap/1, r remaining constant. Our results were compared to those obtained from the direct measurements of PGC, using micropuncture techniqles in hydropenic and plasma loaded rats. The complete agreement between the two approaches confirms the validity of the method based on the analysis of the sieving data of neutral macromolecules to calculate the determinants of GFR.

The two theoretical models proposed previously to calculate the intracapillary and transcapillary glomerular pressure gradients from the sieving of macromolecules such as PVP have been used to analyse in 22 normotensive dogs the sieving curve relating the sieving coefficients, phi, to molecular size (phi: glomerular clearance of PVP fractions/GFR). Neither the "local c2" model-filtrate unmixed at the outer face of the capillaries walls--nor the constant c2 model-filtrate well mixed--allowed to obtain realistic values for the hemodynamical parameters. Indeed with the local c2 model, the best fit between calculated and experimental sieving curves could be obtained only by reversing the intracapillary pressure gradient; conversely the constant c2 model obliged to decrease the intracapillary pressure so abruptly along the capillaries, that retrofiltration took place in the distal parts of the vessels. This difficulty has been overcome by combining the two models; the so-called "hybrid model" considers that the filtrate is well mixed in the vicinity of the urinary pole only. The following results were obtained: 1. PGCa and PGCe (intracapillary pressures at the afferent and efferent extremities of the capillaries) equal to 49.7 +/- 1.03 and 41.8 +/- 1.00 mm Hg respectively. 2. Pressure equilibrium is generally reached at the efferent extremity of the vessels. 3. The slope of PGC (see article) varies inversely to FF. (filtration fraction). 4. The model, however, does not allow to rule out the possibility of retrofiltration.

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