The basic principle

Sound travels at 330m/s in air. It travels faster in solids and liquids, think of American Indians putting their ear to the ground to hear horses.

If you shout opposite a large wall and time how long it takes for an echo to return, you can work out how far away the wall is. E.g. the time for the echo to return is 2 seconds, so at 330m/s for 2 seconds the sound will have travelled 660m. Obviously it has gone there and back so the wall is 330m away.

v=d/t

Where v is the speed, d is the distance and t the time to cover the distance.

The speed of sound in tissues is assumed to be 1540m/s (faster than it travels in air). Differences in the speed of sound in different tissues can be ignored for now.

That is pretty much all there is to ultrasound.

A bit more detail

What is ultrasound?

Sound is a longitudinal wave. In air, the air molecules are compressed at the 'peak' and in the 'trough', there is rarefaction. There is, as with other waves, a frequency of the compression and rarefaction. Audible sound has a frequency less than 20kHz. Ultrasound has a frequency higher than this and in medicine the frequencies range from 1MHz to 15MHz.

Generation of ultrasound

Ultrasound may be produced by applying a voltage to a piezoelectric crystal. Think of the squeezy, clicky thing that you light gas ovens and bunsen burners with - this has a piezoelectric crystal in so that when you squeeze and deform it, a charge is produced. The charge can be used to produce a voltage/potential difference between two prongs so you get a spark. Ultrasound generation is the reverse. A voltage is applied to a crystal which either expands or contracts. If the voltage is varied, then the crystal vibrates accordingly. This vibration produces ultrasound. When ultrasound is reflected from tissues in the body and returns to the ultrasound probe, the reverse happens and the electrical signals generated are analysed and displayed as an image.

How ultrasound is reflected

Think about the example of shouting at a wall as described above. Why is it that we know sound travels more easily in solids, yet when we shout opposite a wall, we get an echo instead of the sound passing straight through? The reason for this is that sound is reflected when it meets an interface between two structures that have very different acoustic impedances (Z which is the product of the density and the velocity of sound in the material). Now this makes sense, but if the ultrasound beam hits a 45 degree surface, it is reflected at 90 degrees to its original path, so if this was the only way ultrasound is reflected the probe would not detect any returning echoes.  Fortunately, surfaces are not entirely smooth so some ultrasound is reflected back to the probe. In addition the small structures that make up a tissue scatter the beam in all directions, including back to the probe. This means that even though there is no tissue interface, we can still see the internal architecture of the liver.

The intensity reflection coefficient, R is given by the formula below:

The acoustic impedances, Z, with units of Kg m^-2 s^-1 are very small and very similar for most tissues and so the amount of energy reflected back is very small.

Figure 1: A B mode ultrasound image of the liver in transverse section showing the hepatic veins. Note that the skin is at the top of the image and the depth is marked in centimetres by the small diamond shapes to the right. By convention the probe is held so the left side of the screen is towards the examiner on the right or towards the head of the patient.

Amplitude (A) mode, brightness (B) mode and motion (M) mode

All you need to know: B mode is the mode you will encounter most frequently and the strength of the returning echoes is indicated by their brightness on the screen. A picture is built up by scanning and displaying many different scan lines across the screen sequentially and repeatedly. Read on if interested or skip to the next section (TGC).

These modes are different types of scanning that can be performed with ultrasound. Although you may never see it, A mode is useful to think about, as it demonstrates how a picture is built up. In this mode, only a single line of an image is built up. The probe emits a very short pulse of ultrasound which enters the tissue of interest and is reflected at tissue interfaces. The pulses are repeated rapidly, but since the duration of each pulse is very short, the probe is able to listen to the returning echoes between pulses. A returning echo is displayed as a spike on the screen at a location related to its distance. Note each echo must return before the next pulse is produced, if it doesn't then you have reached the limit of the depth you can scan.

B mode is pretty much the same as A mode except the returning echoes are represented as a shade of grey on the screen (brighter indicating a larger echo) and many adjacent scan lines are added together sequentially so that a picture is built up of bright, dark and in between spots. This is the type of image that you will be used to seeing.

In contrast, M-mode scanning can show a one dimensional (in terms of space) slice of any part of the B-mode image. This slice is then repeated across the screen over real time. In this way tissue boundaries can be seen and distances measured.  If the object being imaged is still, then a one dimensional slice is taken across it and this is repeated across the screen and can be seen to be unchanged with time. If the object is moving then, just like the B-mode image changing in real time, the one dimensional slice of the B-mode image changes in time and tissue boundaries undulate/move up and down across the screen. Making measurements (time and distance) is easy in this mode due to the isolation of one part of the B-mode image. This is particularly useful in echocardiography where movement of valves may be easily seen.

Figure 2: A diagramatic representation of M-mode scanning.

TGC

This stands for time gain compensation. As ultrasound travels deeper it is attenuated, so the echoes become smaller even if the reflecting structures are the same as those more superficially. To provide an even image, the ultrasound machine can be set to 'turn up the volume' of the deeper echoes after it has received them.

Figure 3: This is an image of a bladder. Note the curved vertical line on the right. This indicates the time gain compensation. Here it is set contrary to what you would expect, with the gain turned down for deeper structures - the curve is deviating to the left (arrow). This is to compensate for the decreased attenuation from the fluid filled bladder which would otherwise cause very bright echoes deep to it.

Doppler

This is the last bit of physics. Anything following this bit, I'll just ask you to accept, but for now you still need to think about this and make sure you understand it.

You all know how police speed guns work (or at least used to work). If not you will now. They like many other things rely on the Doppler effect. Police speed guns use radar (radio detection and ranging). Radio waves are emitted and strike a moving object. If the object is moving away from the speed gun, the reflected waves are stretched as the object moves away. The wavelength and therefore the frequency is changed. The speed gun detects the change in frequency. If, however, the object is moving towards the speed gun, the radio waves are compressed as they hit the object moving in the opposite direction. They return to the speed gun with a higher frequency. In both cases, Doppler shift has occurred.

Figure 4: The Doppler effect explained using the police speed gun as an example (note the wave is transverse in this example, but would be longitudinal if sound were being used).

The Doppler shift is the reflected frequency (f_r) subtracted from the incident frequency (f_i). Although the frequencies used in ultrasound imaging are high, the actual change between f_r and f_i is small enough to be in the audible frequency range and so can be played back through speakers. The change in frequency is related to the velocity of the object by the following equation:

c is the speed of sound in tissue (assumed to be 1540m/s), v is the velocity of the moving object (usually red blood cells) and θ is the angle of the beam to the path of the moving object.

Figure 5: Colour Doppler of the portal vein. The speed of flow is indicated by colour. See the key to the right. Flow towards the probe (at the top of the image) is red and away is blue.

Figure 6: This is the Doppler trace from the internal carotid artery. Note that the key on the right is inverted so red is now flowing away from the probe. The peak velocity is 120cm/s (indicating no significant stenosis) and this was calculated more accurately by ensuring the machine knew the angle of the flow being measured by adjusting the two short lines orientated along the course of the vessel.

Calcium, air and fluid

As stated before, where the acoustic impedances at an interface vary significantly, most of the ultrasound is reflected and very little is transmitted. So the two extremes air and bone both cause little transmission and behind these structures a shadow is cast where the ultrasound beam cannot pass. If, however, the ultrasound beam encounters a fluid filled cyst, the sound is not attenuated as much as it would be in soft tissue (the machine does not know this) and behind the cyst a bright area is seen. This may be termed increased through transmission.

Figure 7: An transverse section through a gallbladder in a patient suffering from cholecystitis secondary to gallstones. Note the shadowing behind the stones and also the increased transmission through the fluid part of the gallbladder. The gallbladder is thick walled and contains sludge as well as stones.

Figure 8: This demonstrates the shadowing behind air in the small bowel. This can be mistaken for gallstones in a contracted or packed (with stones) gallbladder.

Scan depth

An ultrasound wave travelling through a medium is attenuated in an exponential manner that is affected by the attenuation coefficient of the medium (α). The higher the frequency, the higher attenuation coefficient, so to image large distances (e.g. in an obese patient) the frequency needs to be low to ensure the wave is attenuated as little as possible. The reason for the increased attenuation is due to the absorption where as the frequency increases, more energy is converted to heat per second and scattering where the scattering increases as the frequency increases.

All you need to know: use a low frequency probe to visualise deeper structures.

High frequency vs low frequency

The advantages of using a low frequency are seen above, the disadvantage is a trade off in spatial resolution. This can be shown by the equation below:

Where Δx is the resolution, c is the speed of sound, n is the number of periods per pulse and f is the frequency. Therefore, as frequency increases, Δx, the minimum distance that can be separated, decreases (i.e. spatial resolution improves).

All you need to know: use a high frequency probe for better spatial resolution.

Orientation of the slices

If you think about how the A-mode works, this will help you orientate the images. The ultrasound probe emits the ultrasound as a slice - it is 2 dimensional, but not like a camera. The slice cuts though with echoes returning according to what the beam hits. The probe sees things through a narrow slit, but it can do what we can't and penetrate structures, so it sees everything along that slit and the image is effectively turned so we can see it displayed on the screen.

Figure 9: Although it looks like we are seeing the kidney as we do in an AP radiograph, the probe is actually seeing a narrow slice from the side and is turning it on to the screen so we can see it. If we were to look where the probe is pointing, we would only see a narrow patch of skin on the side of the body.

Figure 10: Transverse section through the gallbladder and kidney (remember we are looking from the feet up with CT).

Types of transducer

There are many types of transducer. You only really need to know their 'phenotypes'. The curved probe is called a curvilinear probe and has a frequency of around 1-4MHz. Two other types of probe are commonly used - a higher frequency linear probe (6-9MHz) and a very high frequency linear probe (10-15MHZ). Use the latter for superficial structures that you want to see in greater detail. Other probes you may encounter are endoprobes e.g. for transrectal ultrasound and echocardiography probes (1-5MHz, but with a small footprint to sit between the ribs).

Artefacts

Artefacts in ultrasound do occur since there are many assumptions being made in the formation of the image. The artefacts most easily explained are mirror artefacts, reverberation and aliasing. These shall be addressed here. For a more in depth discussion see Feldman et al¹.

Mirror artefact occurs where an object is placed superficial to a boundary where almost all ultrasound is reflected e.g. diaphragm/lung. Here some ultrasound is reflected from the object and some passes through, after which it may either be reflected off the boundary and returned to the probe or reflected off boundary and bounced between and the object and the boundary again before returning to the probe. In this case the ultrasound will have travelled an additional distance and the machine will assume these echoes are truly originating from a more deep structure.

Figure 11: The image you see here is mostly mirror artefact. The actual object lies very superficially (at the end of the yellow arrow). The object is actually an olive and the highly reflective surface is the bottom of a glass bowl. The yellow arrows represent US reflected from the deep border of the olive. The white arrows represent US reflected from the glass bowl. The red arrows represent the US travelling down and bounced between the olive and the bottom of the bowl. Since this US has travelled further the machine thinks it is coming from a structure deeper than the bottom of the glass bowl, hence the mirror image.

Figure 12: Mirror image where a branch of the portal vein is seen to lie apparently within the lungs (arrow). The diaphragm is clearly seen (arrowheads).

Reverberation artefact can also be seen in the figure 11. This occurs where ultrasound is bounced between two very reflective surfaces in a similar manner to mirror artefact. This can be seen as echogenic bands deep to the reflective surfaces and these represent the ultrasound that has travelled further by bouncing between the surfaces.

Aliasing occurs in Doppler where the pulses are not sufficiently frequent to allow accurate estimation of the velocity. If the pulses are not repeated (the pulse repetition frequency, PRF indicates this frequency) at least twice every cycle of the highest frequency returned from the moving object, then it follows that if the probe is not emitting pulses with short enough intervals, it is also not sampling at the necessary intervals to determine the frequency of the Doppler signal. This is partially explained by figure 13.

Figure 13: The lower wave is not sampled at sufficient intervals (vertical lines) to determine its frequency. If this scenario were to occur in colour doppler, the high frequency would erroneously be depicted as a very low frequency (see trace mapped by black dots) and the colour would 'wrap around' to the other side of the scale.

Safety

The biophysical effects that give rise to safety issues in ultrasound scanning are heating and mechanical damage (cavitation). The first is easy to understand in that energy is being transmitted in to the body and as a result, some of that energy is dissipated as heat. The second effect is the concept that a mechanical wave (ultrasound) can a result in mechanical effects in the tissue. Since mechanical waves cause compression and rarefaction they can cause the formation of bubbles in a tissue that then burst (cavitation). Both of these effects may cause local cell damage.

The effects are indicated in modern scanners by indices. The thermal index indicates the ratio between the power a tissue is exposed to and the power required to cause a 1^oC rise in temperature at any point along the path of the ultrasound. Higher values obviously indicate a higher potential for temperature rise. The mechanical index is a calculation of the greatest amplitude of the pressure pulse caused by the ultrasound.

All you need to know: ultrasound doesn't use ionising radiation and is therefore 'safe'. There can be safety concerns, however, when scanning heat sensitive structures such as the foetus.

Further reading

1. Feldman MK, Katyal S, Blackwood MS. US Artifacts. Radiographics. 2009;29(4):1179-1189.

2. Dendy PP, Heaton B. Physics for Diagnostic Radiology. 2nd ed. Taylor & Francis; 1999.

3. Allisy-Roberts Penelope, Williams Jerry. Farr's Physics for Medical Imaging. 2nd ed. Saunders Ltd.; 2007.