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# What is the difference between renal blood flow and renal plasma flow?

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Sep 30, 2016

Renal blood flow ($R B F$) is the volume of blood delivered to the kidneys per unit time. Renal plasma flow ($R P F$) is the volume of plasma delivered to the kidneys per unit time.

#### Explanation:

Renal Plasma Flow

In practice, it is difficult to measure $R P F$ directly.

Instead, it is estimated from the effective renal plasma flow ($E R P F$), which is the amount of plasma cleared of p-aminohippuric acid ($P A H$) per unit time.

The formula for $R P F$ comes from the Fick relation, which is really a mass balance calculation.

$\text{Flow in = flow out}$

$\text{renal artery input = renal vein output + ureter output}$

RPF × P_a = RPF × P_v + U × V

where

${P}_{a} \mathmr{and} {P}_{v} \text{= arterial and venous plasma concentrations of PAH}$
$U \text{= urine concentration of PAH}$
$V \text{= urine flow rate}$

Rearranging gives:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} R P F = \frac{U V}{{P}_{a} - {P}_{v}} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Almost all the $P A H$ is cleared through the ureter.

(From slideplayer.com)

Setting ${P}_{v} = 0$ gives

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} E R P F = \frac{U V}{P} _ a \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Renal Blood Flow

$R B F$ is the measure of blood (plasma + RBCs) that passes through the kidneys.

$\text{blood = plasma + hematocrit}$

Let $H c t = \text{fraction of blood that is RBCs}$

Then $\text{fraction that is plasma} = 1 - H c t$ and

$R B F \left(1 - H c t\right) = E R P F$

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} R B F = \frac{E R P F}{1 - H c t} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Sample Problem

Calculate $R B F$ for a patient with the following: $U \text{= 650 mg/mL}$; $V \text{= 1 mL/min}$; ${P}_{a} \text{= 1.2 mg/mL}$; $H c t \text{= 0.45}$.

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"

$R B F = \frac{E R P F}{1 - H c t} = \text{542 mL/min"/(1 - 0.45) = "542 mL/min"/0.55 = "985 mL/min}$

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