Doppler shift

SPEAKER: An important type of ultrasound imaging uses the Doppler effect. But what is Doppler and what information does it give?

The Doppler effect has been discovered by Christian Doppler in the 19th century. It can be defined as a change in frequency of a wave for an observer moving relative to the source of the wave. Actually, the Doppler effect is commonly heard in our daily life. For instance, if a police car approaches you with a siren on and it passes nearby, you hear a change of the pitch of the siren. And that’s because it’s a source moving to you and then moving away from you.

If the source moves towards you, the pitch that hear is slightly higher than the original pitch. And that’s because each next wave emitted by the sound source has to travel a shorter distance to you.

The frequency difference is equal to the original frequency times the velocity of the source, divided by the speed of sound.

And this, again, is equal to the velocity of the source divided by the wave length of the sound.

And in the same way, if the source of the sound moves away from you, then the pitch is lower than the original pitch. And the amount that is lower is, again, given by these equations.

In Doppler ultrasound, of course, the source is not moving and the observer is not moving. But actually, it’s the red blood cells, which act as reflecting objects. It’s a 2-step process. And in the first step, the moving red blood cells are hit by the nearby passing waves of the ultrasound and a red blood cell experiences a Doppler shift equal to this amount.

And the second step of the process is that the red blood cells re-emit the received ultrasound. So now they become a source of ultrasound, which is moving. And that creates, again, a Doppler shift equal to the first amount. So in total we now have twice the original Doppler shift. So the total Doppler shift, the total Doppler frequency is now two times the velocity of the moving object, divided by the wavelength of the sound.

Now one more complication might be that red blood cell does not move towards you as an observer or away from you, but under an angle. And in this case, it is only the component of velocity in the direction of the sound beam, which determines the total Doppler shift. And in the equation, describing the Doppler shift, we now get an extra factor cosinus theta, in which theta is the angle between the velocity and the beam of sound.

The consequence is that the measuring the flow in a blood vessel, the orientation of the probe is very important. Suppose that you want to measure the flow in an artery or a vein running parallel to the skin, in that case, don’t place your probe under 90 degrees with the blood vessel, because in that case, the Doppler frequency is zero. Instead, you have to place the probe under an angle so you get a non-zero Doppler shift.

This is how a Doppler image may look like, the so-called colour Doppler. The orientation of the probe is indicated by the green line. And the blood moving towards the probe is indicated in red, while the blood moving away from the probe, is indicated in blue.

So Doppler ultrasound allows you to measure both the velocity of the flow and its direction. Doppler ultrasound makes ultrasound imaging a richer technology, because it does not only provide you the structure of the tissue, but also functions such as blood flow.