Question

Calculate the wave propagation speed for a 100-?m-thick blood vessel with a radius of 10 mm.
This blood vessel has a pressure of 85 mmHg and a Young’s modulus of 12.5 kPa. Under
disease conditions, the vascular wall can stiffen so that the Young’s modulus approaches 30
kPa. Calculate the change in the wave speed under these conditions. What blood vessel
property is likely to change in response to the increase in stiffness and why?

Answer 1

We know for wave propagation in blood vessel, the speed of the wave is given by:

...........EQ1

is a constant

  is the Young's modulus of the blood vessel,

is the thickness of the blood vessel,

is the radius of the blood vessel,

is the density of the blood, this is not given.

Since we cannot find absolute values of the wave speed, we can find the percentage change in wave speed, given by:

Also, we know that:

,

where is the pressure in the blood vessel,

Since rate of change of pressure with respect to radius is directly dependent on the Young's modulus. This also means that as the wave propagate there is a pressure difference at the wave front that propagates. Higher E will result in lower change or effect on the blood vessel radius or shape. This makes sense too as the blood vessel has stiffened. Also, there could be a scenario if there is partial blockage in the blood vessel, the pressure rise will be higher as blood vessel would not allow much change in radius due to stiffening.