# Arterial blood flow

1. Jun 17, 2009

### jturbett

Dear all,

I am trying to find a mathematical explanation for why a blood vessel's lumen, especially an artery's, expands when the heart forces blood through the vessel upon contraction of the myocardium. This expansion is clearly evident when taking a person's pulse.

I have some ideas but I am quite confused considering all of the variables.

Firstly, I took the idea of volumetric flow rate and worked from there:
$$Q=A\cdot v$$

Q blood flow rate through the vessel (volume per unit time)
A cross-sectional area of the vessel lumen
v velocity of blood flow

Now I seem to remember that (area)(velocity) = constant, though this would imply that the the vessel would constrict as the velocity of the blood increases after a heart contraction!?

I then took A, the cross-sectional area of the vessel lumen, and considered it in relation to blood pressure(from the pressure formula):
$$A=\frac{F}{p}$$

F force exerted on the vessel wall by the blood

....AND there I got stuck. It has been annoying me all day and I would quite like to find an answer for it! I seem to be unable to link my medical knowlege with my physics knowlege at this point - perhaps I'm looking at the wrong variables.

Many thanks,
James