An ultrasound image is a map of echoes. A probe sends a short pulse of sound into the body, at a few megahertz, far above the 20 kHz the ear can hear (hence ultra), and then listens. Where a strong echo comes back the pixel is bright; where nothing comes back it is dark. The time the echo takes tells the scanner how deep it came from. Strong echoes come from boundaries between tissues, such as a vessel wall or the surface of an organ. Bone reflects part of the pulse and absorbs the rest, so the image stops behind it. Fluid contains almost nothing that scatters sound, so the bladder, a cyst and blood appear black. Almost every ultrasound image is a 2D slice. 3D probes do exist but are rare.
Ultrasound images from three different types of probes. Left: thyroid with a linear array (rectangle). Middle: a 12-week fetus with a curvilinear array (sector with a curved top). Right: the heart in the apical four-chamber view with a phased array (narrow-topped sector). Nevit Dilmen, Wolfgang Moroder, Fruehaufsteher2; Wikimedia Commons, CC BY-SA 3.0.
An ultrasound image consists of a thin cross-section in the plane of the probe, rendered with the probe face at the top of the picture. Depth into the body increases downward. Bright lines are boundaries between tissues and black regions are fluid. The gray grain that fills everything else is speckle, echoes from structures too small to be resolved. Clinicians call grayscale ultrasound images B-mode (brightness mode) and describe a region relative to its surroundings as hyperechoic (brighter), hypoechoic (darker) or anechoic (black).
Ultrasound is one of the most common imaging examinations. It images the fetus, the heart (echocardiography), the liver, gallbladder and kidneys, vessels (thrombosis, carotid narrowing), the thyroid, breast, muscles and tendons, free fluid after trauma and the lung in emergency medicine, and it guides needles and catheters. An important benefit of ultrasound is that it can render in real time.
It is also attractive because it has no ionizing radiation and the transducer costs a small fraction of an MRI system and fits in a hand. The downsides are that each image depends on whoever holds the probe, the same image is hard to take twice, the probe position is not recorded, the pixel values have no unit, and image quality falls with depth.
The probe contains a transducer. A transducer is both source and detector. It emits a pulse a few cycles long, then listens. An echo arriving after time $t$ comes from depth
$$ d=\frac{c\,t}{2}\tag{2.7.1} $$
where $c$ is the speed of sound, and the 2 is for the round trip. An echo from 15 cm deep arrives after 195 µs. One pulse-and-listen cycle gives the echo strength along one line into the body, as depicted below. An ultrasound image is composed of many such lines side by side.
Left: a tissue cross-section and a single transducer. Right: received 1-D signal. The pulse is partly reflected at each interface. Echoes arrive in order of depth. The strong reflection at bone leaves nothing to echo behind it.
Sound is a pressure wave in a medium, and its speed depends on how stiff and how dense that medium is, $c=\sqrt{K/\rho}$ with $K$ the bulk modulus and $\rho$ the density: a stiffer medium carries sound faster. The quantity that decides how much of a wave bounces off a boundary is the acoustic impedance
$$ Z=\rho\,c\tag{2.7.2} $$
$Z$ is the ratio of the pressure in the wave to the velocity it gives the particles of the medium: the pressure it takes to set the medium moving at a given speed. Bone has a high $Z$, air a very low one. Soft tissues differ little from one another, and the scanner assumes $c=1540$ m/s for all of them (values from Duck, 1990; 1 MRayl = 10⁶ kg m⁻² s⁻¹).
| Material | Density $\rho$ (g/cm³) | Speed of sound $c$ (m/s) | Impedance $Z$ (MRayl) |
|---|---|---|---|
| Air | 0.0012 | 343 | 0.0004 |
| Fat | 0.92 | 1450 | 1.34 |
| Water | 1.00 | 1480 | 1.48 |
| Soft tissue (scanner assumption) | 1.06 | 1540 | 1.63 |
| Blood | 1.06 | 1570 | 1.66 |
| Muscle | 1.07 | 1580 | 1.70 |
| Cortical bone | 1.9 | 3500 to 4000 | 7 to 8 |
When the pulse meets a flat boundary head-on (normal incidence), with impedance $Z_1$ on the near side and $Z_2$ on the far side, the reflected fraction of the sound wave (pressure amplitude) is
$$ R=\frac{Z_2-Z_1}{Z_2+Z_1}\tag{2.7.3} $$
R is the fraction of the wave's pressure that bounces back. The fraction of its reflected energy is $R^2$. This makes measurements very small: R = 0.1 means only 1% of the energy returns. If the two media have the same impedance, R is zero and there is no echo at all.
The bigger the jump in impedance, the stronger the echo. The table below works Eq. 2.7.3 out for three common boundaries.