Two models of glomerular filtration rate and renal blood flow in the rat

Two mathematical models of glomerular filtration and blood flow are derived. The first is based on principles of fluid and mass conservation in individual capillaries. The model explains why the filtration rate (GFR) is strongly dependent on local hydrostatic and protein oncotic pressures, and on plasma flow rate (GCPF), but only weakly dependent on exact numbers, lengths, radii, or filtration coefficient of glomerular capillaries. The model shows that much of the increased GFR in both isooncotic plasma loading and isotonic Ringer's loading is due to increased GCPF caused by diluting erythrocytes. The second model uses several approximations and reduces to a quadratic in afferent arteriolar blood flow. When arterial pressure, hematocrit, plasma protein concentration, and afferent and efferent arteriolar resistances are specified, the model predicts GFR, afferent arteriolar blood flow, and filtration fraction. Alternatively, if any two of these three variables are known, the model predicts segmental arteriolar resistances. The model indicates that GFR and blood flow regulation must be located in the afferent arteriole, despite the strong dependence of GFR on GCPF.