Blood flow

From Wikipedia, the free encyclopedia

Blood flow is the flow of blood in the cardiovascular system. The discovery that blood flows is attributed to William Harvey.

Mathematically, blood flow is described by Darcy's law (which can be viewed as the fluid equivalent of Ohm's law) and approximately by Hagen-Poiseuille's law (as it is accurate only for Newtonian fluids, while blood flow is not Newtonian and its flow can be described as laminar only in smaller vessels, elsewhere it is turbulent). The first equation below is Darcy's law, the second is the Hagen-Poiseuille law:

$F = \frac{\Delta P}{R}$

$R = (\frac{\nu L}{r^4})(\frac{8}{\pi})$

where:

F = blood flow

P = pressure

R = resistance

ν = fluid viscosity

L = length of tube

r = radius of tube

In the last equation it is important to note that blood flow changes with the fourth power with change of radius. This is important in angioplasty, as it enables the increase of blood flow with balloon catheter to the deprived organ significantly with only a small increase in radius of a vessel.