Principles of Doppler Ultrasound

Published on 06/02/2015 by admin

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Last modified 06/02/2015

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Principles of Doppler Ultrasound

Jonathan Kraidin, Steven Ginsberg, William Jian and Kevin A. Jian

Doppler works with sound. Sound is a mechanical, longitudinal wave that alternates between expanding and compressing the medium through which it propagates. This is analogous to a wave moving through the water. Normally, the ear perceives sounds up to 20 KHz. Higher frequencies are referred to as ultrasound, and unless you are a dog or bat you are not going to hear them. The rapid vibration of a piezoelectric crystal produces the ultrasound waves. The properties that describe the wave are ¹:

1. the period is the duration of each cycle

2. the frequency is the number of times the waves cycle per second (this is the reciprocal of the period)

3. the wavelength is the distance between two wave crests of the sinusoidal wave

4. the propagation speed, which is the speed the wave travels through the medium as it compresses and expands

Doppler echocardiography allows the non-invasive assessment of blood flow, velocity and direction.² It is based on the principle that a moving target will shift the reflected frequency higher or lower depending on whether it is moving toward or away from the transmitter. Using this principle, if one knows the frequency shift one can determine the velocity and direction of the blood flow.

Waves of energy, such as light and sound, can be defined by the wavelength and frequency. This gives us a third parameter, which is the propagation speed through the medium.

The equation is

in which f is the frequency, λ is the wavelength and c is the speed of sound in tissue, which is 1540 m/sec.

When a pure frequency of sound hits a stationary object, the sound bounces back at the same frequency. If the object is moving when the sound hits, the returning wave will have a slightly different frequency. The difference in the outgoing and incoming frequency is called the Doppler shift.

You can see the derivation of the Doppler Shift equation in the section, Derivation of the Doppler Shift Equation.

The Doppler Shift Equation

For a returning signal the equation is:

Let us break this equation down:

f₀ is the original frequency of the ultrasound wave, v is the velocity of the object hit by the wave, and c is the speed of the wave as it propagates through the medium. Theta (θ) is the incident angle the beam makes with the axis of flow.

This is not just theoretical physics. This stuff really happens. Recall the sound of an approaching train. When the train is coming towards us, the pitch is higher (v is positive); when the train is moving away from us the pitch is lower (v is negative).

Let’s look at some real numbers:

v (of blood) = 2 m/sec

f₀ = 2 500 000 Hz (this is a typical frequency for the beam)

F_shift = 2 500 000 * cos(0)*2*2/1540

F_shift = 6493 Hz

What can we do with this information? By knowing the Doppler shift, we can use the equation in reverse and determine the velocity of the blood:

How is such a small change in the frequency measured? The truth is that the frequency is not measured. The machine actually measures the phase shift between the outgoing and incoming signal. The phase difference correlates with the Doppler shift as a first-order approximation.³

So, now that we have an understanding of the Doppler shift equation and how the machine makes measurements, what can we do with this information?

Basic Principle for Tissue Reconstruction Using Ultrasound

A sound wave is emitted from the transducer. When this wave encounters differences in density it gets reflected back. If you scream over the ocean shore you don’t hear your voice reflected off of the air because it has a constant density. If you scream across a canyon you hear an echo because the sound encounters a change of density when it hits the rocks, resulting in the sound getting reflected back. The amount of sound that gets reflected not only depends on the change in density at the interface, but on the orientation of the object. The orientation can scatter the sound in different directions. Software analyzes the amplitude of the sound at different times in order to reconstruct the tissue density at a specific depth from the probe, giving an image.

B-Mode

This was originally called brightness mode. The brightness shown on the display corresponds to the amplitude of the returning echo, and the location is related to the position of the reflected tissue. Highly echogenic objects reflect more of the signal back; this is represented by a brighter point on the screen.

M-Mode

Once upon a time this stood for time-motion mode. It was shortened to M-mode for motion mode. M-mode is multiple B-mode dots plotted on a straight line. The amplitude of the signal is recorded at various times; each time corresponds to a different distance from the probe. A vertical line is constructed where the brightness of each pixel corresponds to the strength of the echo at each point. The constructed line is moved leftwards and a new scan line is created up to 1000 times/sec. Using this methodology, time is represented on the x-axis and the distance of the tissue from the probe is on the y-axis. This is useful for watching anatomical motion of the myocardium and valves along a single line of sight. This is useful for timing the movement of valve leaflets when assessing regurgitant blood flow.

Two-Dimensional Imaging

This is one line of B-mode swept through an arc. The result is a sector of tissue called a frame. The frame image is rapidly refreshed between 30 to 60 times/sec allowing one to see motion of the tissue within the frame. The frame rate, and thus the quality of the moving image, is affected by sector width and depth.

The figure below sums this all up.

Color Doppler

Remember the theory about Doppler shift? By sending a beam of sound at moving blood cells one obtains blood velocities. The velocities are represented by colors. If the object is moving towards the probe the machine tags it with a shade of red; if it is moving away it gets tagged with a shade of blue (BART: blue away red towards). A jet of blood moving toward the probe will appear as a red flame. The fastest part will be a bright red, which will fade to a duller red as the velocity slows down. If the blood is swirling (turbulent flow) the color will appear as a mosaic pattern because the velocity and direction are rapidly changing. The color will jump from red to blue, and all the shades in between these two colors. The color representation of the velocities is superimposed on a 2-D image of the underlying tissue.

Color Doppler allows one to get a rapid understanding of the blood flow in a window of interest. One can determine that blood is moving in the wrong direction, if the flow is laminar or turbulent, or if there is flow where there should be none such as through a defect.

Continuous Wave Doppler

Continuous wave (CW) Doppler allows one to measure fast blood velocities. CW Doppler is exactly as the name describes: a transducer continuously transmits a beam of sound while a receiver continuously measures the returning signal. As the transducer emits sound, the beam encounters moving blood cells at varying points. The returning sound contains multiple shifted frequencies because it bounces off of blood cells at different depths, moving at different velocities. CW Doppler is unable to tell where these velocities are occurring; it can only report a range of velocity values. These velocities are all mixed together in a velocity envelope and occur along the line of sight of the probe.

How does this help if the machine is getting back a myriad of velocities? One uses CW when there is an interest in measuring fast velocities. True, all of the velocities are mixed together, but the operator only cares about the fastest velocity. The peak of the envelope represents the fastest velocity; everything inside the envelope represents all other velocities, which one ignores. For example, if one is looking at a stenotic aortic valve, the jet of blood traveling through the valve will give the fastest velocity. Even though the CW Doppler does not know where the fastest velocity is coming from, the operator knows the fastest velocity measured must be coming from the jet going through the stenotic valve.

Pulse Wave Doppler

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