The wave speed plays a very important role in wave intensity analysis. From the theory for flow in 1-D elastic vessels, we learn that disturbances introduced into the vessel will propagate with a speed c. {mathematical details}.
This wave speed is the speed at which the waves would move if the blood velocity is zero. The waves are convected by the blood velocity (just as ripples in a river are convected with the river), so that the observed speed of propagation is U + c in the downstream direction and U - c in the upstream direction. If U > c, we get the interesting result that both waves propagate downstream with no information about the disturbance propagating upstream. This is generally known as supersonic conditions and it leads to many interesting phenomena in gas dynamics (e.g. you can't hear a supersonic plane approaching you). Only rarely, if ever, does this happen in the arteries and we will assume in this introduction that U < c.
An advantage of the method of characteristics solution is that it gives an analytical expression for c in terms of the elastic properties of the vessel.
| c2 = | 1 ρD |
where ρ is the density of blood and D = (1/A) (dA/dP) is the distensibility of the artery wall (the fractional change in area with a change in pressure). The distensibility is related to the compliance or the stiffness of the artery which are of clinical importance. Since ρ is relatively constant, the local wave speed is a direct measure of arterial stiffness; stiffer arteries have a lower distensibility and a higher wave speed.