Renal blood flow
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Overview
In the physiology of the kidney, renal blood flow (RBF) is the volume of blood delivered to the kidneys per unit time. In humans, the kidneys together receive roughly 20% of cardiac output, amounting to 1 L/min in a 70kg adult male. RBF is closely related to renal plasma flow (RPF), which is the volume of blood plasma delivered to the kidneys per unit time.
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 RBF_{a}, RBF_{v}, RPF_{a}, and RPF_{v}. Physiologically, however, the differences in these values are negligible so that arterial flow and venous flow are often assumed equal.
Calculation
Renal blood flow calculations are based on renal plasma flow and hematocrit (HCT). This follows from the fact that hematocrit estimates the fractional volume of blood consumed (occupied) by red blood cells. Hence, the fraction of blood that is in the form of plasma is given by 1HCT.
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): RPF = RBF(1  HCT)
Alternatively:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): RBF = \frac{RPF}{1  HCT}
Renal plasma flow
Renal plasma flow is given by the Fick principle:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): RPF = \frac{U_x V}{P_a  P_v}
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 nonmetabolizable 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:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): RPF_a \times P_a = RPF_v \times P_v + U_x \times V
where P_{a} is the arterial plasma concentration of the substance, P_{v} is its venous plasma concentration, U_{x} 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 RPF_{a} is assumed to be equal to RPF_{v}, thus
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): RPF \times P_a = RPF \times P_v + U_x V
Rearranging yields the previous equation for RPF:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): RPF = \frac{U_x V}{P_a  P_v}
Measuring
Values of P_{v} are difficult to obtain in patients. In practice, PAH clearance is used instead to calculate the effective renal plasma flow (eRPF). PAH (paraaminohippurate) is freely filtered, and it is not reabsorbed by the kidney so that its venous plasma concentration is approximately zero. Setting P_{v} to zero in the equation for RPF yields
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): eRPF = \frac{U_x}{P_a} V
which is the equation for renal clearance. For PAH, this is commonly represented as
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): eRPF = \frac{U_{PAH}}{P_{PAH}} V
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.
References
 Boron, Walter F., Boulpaep, Emile L. (2005). Medical Physiology: A Cellular and Molecular Approach. Philadelphia, PA: Elsevier/Saunders. ISBN 1416023283.
 Eaton, Douglas C., Pooler, John P. (2004). Vander's Renal Physiology (8th edition ed.). Lange Medical Books/McGrawHill. ISBN 0071357289.