Renal Plasma Flow
In practice, it is difficult to measure RPF directly.
Instead, it is estimated from the effective renal plasma flow (ERPF), which is the amount of plasma cleared of p-aminohippuric acid (PAH) per unit time.
The formula for RPF comes from the Fick relation, which is really a mass balance calculation.
"Flow in = flow out"
"renal artery input = renal vein output + ureter output"
RPF × P_a = RPF × P_v + U × V
where
P_a and P_v "= arterial and venous plasma concentrations of PAH"
U "= urine concentration of PAH"
V "= urine flow rate"
Rearranging gives:
color(blue)(bar(ul(|color(white)(a/a)RPF = (UV)/(P_a-P_v)color(white)(a/a)|)))" "
Almost all the PAH is cleared through the ureter.
![PAH Flow]()
(From slideplayer.com)
Setting P_v = 0 gives
color(blue)(bar(ul(|color(white)(a/a)ERPF = (UV)/P_acolor(white)(a/a)|)))" "
Renal Blood Flow
RBF is the measure of blood (plasma + RBCs) that passes through the kidneys.
"blood = plasma + hematocrit"
Let Hct = "fraction of blood that is RBCs"
Then "fraction that is plasma" = 1 - Hct and
RBF(1-Hct) =ERPF
color(blue)(bar(ul(|color(white)(a/a) RBF = (ERPF)/(1-Hct)color(white)(a/a)|)))" "
Sample Problem
Calculate RBF for a patient with the following: U "= 650 mg/mL"; V "= 1 mL/min"; P_a "= 1.2 mg/mL"; Hct "= 0.45".
Solution
ERPF = (UV)/P_a = (650 color(red)(cancel(color(black)("mg/mL"))) "× 1 mL/min")/(1.2 color(red)(cancel(color(black)("mg/mL")))) = "542 mL/min"
RBF = (ERPF)/(1-Hct) = "542 mL/min"/(1 - 0.45) = "542 mL/min"/0.55 = "985 mL/min"
