Acoustic Impedance and Reflection

Every structure you can see on an ultrasound scan is visible only because of what happens at its boundary with the next tissue along — a partial reflection governed by a single quantity called acoustic impedance. Without a mismatch in impedance, there is no echo, and nothing to see at all.

Acoustic impedance

Ultrasound imaging works because the body is not uniform: it is made of many different tissues — fat, muscle, blood, bone, and organ walls — each with slightly different physical properties. Whenever an ultrasound pulse, travelling through one tissue, reaches a boundary with a different tissue, some of its energy reflects back the way it came, while the rest continues onward. It is these partial reflections, arriving back at the transducer at different times, that let a scanner build up a picture of what lies inside.

The physical property that determines how much reflects at a given boundary is the acoustic impedance, $Z$, of each medium, defined as:

where $\rho$ is the density of the medium and $c$ is the speed of sound within it. Acoustic impedance has units of $\text{kg m}^{-2}\text{s}^{-1}$. Different body tissues have measurably different values of $Z$, because they differ in density, in the stiffness that governs the speed of sound through them, or both — and it is precisely these differences that ultrasound imaging exploits.

The reflection formula

When an ultrasound pulse travelling through a medium of impedance $Z_1$ meets a boundary with a second medium of impedance $Z_2$, the fraction of the incident intensity $I_i$ that is reflected as intensity $I_r$ is given by:

A few important features fall directly out of this formula. Because the numerator is squared, the direction of the mismatch doesn't matter — going from a lower-impedance medium into a higher-impedance one reflects the same fraction as the reverse. If $Z_1$ and $Z_2$ are very close together (a small mismatch), the numerator is close to zero and almost nothing reflects: nearly all of the pulse's energy continues through the boundary. If $Z_1$ and $Z_2$ are very different (a large mismatch), the reflected fraction can become substantial, and in extreme cases (such as tissue meeting air) can approach the entire pulse.

Why coupling gel is essential

The reflection formula also explains a detail every ultrasound scan depends on: the layer of coupling gel spread across the skin before the transducer is applied. Air has an extremely low acoustic impedance compared to skin and soft tissue — many hundreds of times smaller. If a transducer were placed directly against dry skin, any thin layer of air trapped between the two would create an enormous impedance mismatch right at the very first boundary the pulse meets, before it has even entered the body. Using the reflection formula with such a large mismatch between $Z_1$ (air) and $Z_2$ (skin) gives a reflected fraction extremely close to 1 — in practice, almost the entire pulse would simply bounce straight back at the transducer face, and virtually nothing would be left to actually probe the body.

Coupling gel solves this by having an acoustic impedance much closer to that of skin. Smeared between the transducer and the patient, it fills in any microscopic air gaps and removes the tissue-air mismatch that would otherwise dominate. With gel in place, the first meaningful boundary the pulse meets is the gel-skin interface, where the impedances are similar and reflection is small — allowing the great majority of the pulse's energy to actually enter the body and go on to image the structures inside it.

Attenuation with depth

Reflection at boundaries is not the only thing that reduces an ultrasound pulse's intensity as it travels through the body. Even while travelling through a single, uniform tissue with no boundaries at all, a pulse's intensity progressively decreases due to attenuation — a combination of absorption (energy converted to heat within the tissue) and scattering (energy redirected in random directions by small irregularities). The further a pulse has to travel, the more its intensity has fallen by the time it reaches a given depth, and the same is true again for the returning echo travelling back out.

This has a direct practical consequence: echoes from deep structures are inherently weaker than echoes from shallow structures at the same reflecting strength, simply because the pulse and its echo have both travelled further and been attenuated more. Left uncorrected, this would make deep structures appear artificially fainter on a scan than they really are, purely as an artefact of depth rather than genuine tissue difference. Real ultrasound systems compensate for this by applying greater amplification to signals arriving from greater depths (equivalently, from later in the pulse-echo cycle) than to signals from shallow depths, correcting for the extra attenuation those deeper echoes have experienced.

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