6.5.3 - Ultrasound imaging, impedance and Doppler

Ultrasound and transducers

Ultrasound is sound, so in body tissue it travels as a longitudinal mechanical wave: particles of the medium oscillate parallel to the direction of energy transfer. The word ultrasound means the frequency is above the upper limit of human hearing.

Medical scanners use a probe called a transducer. The active part is a piezoelectric crystal. When an alternating potential difference is applied across opposite faces of the crystal, it expands and contracts rapidly, so it emits ultrasound pulses. The same crystal can also act in reverse: when an echo compresses or stretches it, a small potential difference is produced and detected by the electronics.

That dual behaviour is why one probe can both send and receive. A short pulse is sent into the body, then the probe waits for echoes from boundaries between media. The time delay tells the scanner how deep the reflecting boundary is, and the echo amplitude gives information about how strong the reflection was.

Pulse-echo A-scans and B-scans

An ultrasound pulse travels to a boundary and then the echo travels back to the transducer. If the pulse has speed $c$ in the tissue and the echo from a boundary returns after time $t$, the depth of that boundary is:

The factor of 2 is essential: the measured time is for the out-and-back journey.

An A-scan is the simplest display. It shows echo amplitude against time. Each spike represents a reflected pulse; a later spike is from a deeper boundary, and a taller spike is from a stronger reflection. OCR questions often use A-scans for measurements such as eye-lens thickness, where two echoes come from the front and back surfaces of the lens.

A B-scan builds an image from many pulse-echo measurements. The probe either sweeps across the body or uses many small transducer elements. For each scan line, echo time fixes depth and echo amplitude fixes brightness. Combining many brightness lines gives a two-dimensional section through the tissue.

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Worked example: an A-scan of an eye lens shows two echoes from the front and back of the lens. The time difference between the echoes is $5.2\,\mu\mathrm{s}$. Take the speed of ultrasound in the lens as $1.54\times 10^{3}\,\mathrm{m}\,\mathrm{s}^{-1}$.

The ultrasound travels across the lens and back between those two echoes, so:

Convert the time difference:

Substitute:

So the lens thickness is about $4.0\,\mathrm{mm}$.

A-scans are useful for precise distances between identified boundaries, such as the front and back of an eye lens. B-scans show a cross-section, useful for viewing soft tissue and fetal development in real time. Ultrasound does not use ionising photons, and a portable scanner can be comparatively inexpensive. However, air and bone can block useful transmission; a strong surface reflection can hide deeper structures. Higher frequency can resolve finer detail but is usually attenuated more strongly, limiting useful depth. The method must fit the required depth and anatomical information.

Acoustic impedance and reflection

When ultrasound reaches a boundary between two media, such as two different tissues, some intensity is reflected and the rest is transmitted. The reflection depends on the acoustic impedance of the media.

The unit follows directly from the defining equation:

If the acoustic impedances on the two sides of a boundary are $Z_1$ and $Z_2$, the fraction of incident intensity reflected at normal incidence is:

Here $I_0$ is the incident intensity and $I_r$ is the reflected intensity. This ratio has no unit. If $Z_1 = Z_2$, the numerator is zero, so there is no reflection at that boundary. If the difference between the impedances is large, a larger fraction is reflected.

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