While the terms generally apply to arterial blood delivered to the kidneys, both RBF and RPF can be used to quantify the volume of venous blood exiting the kidneys per unit time. In this context, the terms are commonly given subscripts to refer to arterial or venous blood or plasma flow, as in RBFa, RBFv, RPFa, and RPFv. Physiologically, however, the differences in these values are negligible so that arterial flow and venous flow are often assumed equal.
This is essentially a conservation of mass equation which balances the renal inputs (the renal artery) and the renal outputs (the renal vein and ureter). Put simply, a non-metabolizable solute entering the kidney via the renal artery has two points of exit, the renal vein and the ureter. The mass entering through the artery per unit time must equal the mass exiting through the vein and ureter per unit time:
where Pa is the arterial plasma concentration of the substance, Pv is its venous plasma concentration, Ux is its urine concentration, and V is the urine flow rate. The product of flow and concentration gives mass per unit time.
As mentioned previously, the difference between arterial and venous blood flow is negligible, so RPFa is assumed to be equal to RPFv, thus
Rearranging yields the previous equation for RPF:
which is the equation for renal clearance. For PAH, this is commonly represented as
Since the venous plasma concentration of PAH is not exactly zero (in fact, it is usually 10% of the PAH arterial plasma concentration), eRPF usually underestimates RPF by approximately 10%. This margin of error is generally acceptable considering the ease with which eRPF is measured.