24.1 - Ultrasound generation and imaging

One crystal can send and receive sound

How can the same ultrasound probe both make a sound pulse and hear its echo? Its piezoelectric crystal works in both directions: electrical changes deform it, and mechanical deformation generates an electrical signal.

A p.d. applied across a suitable crystal changes its shape. An alternating p.d. repeatedly changes the deformation, making the crystal vibrate. In contact with a medium, those vibrations set neighbouring particles oscillating and launch a longitudinal sound wave. The particles move back and forth; they do not travel through the patient with the pulse.

Ultrasound has frequency above the upper limit of normal human hearing, about $20\,\mathrm{kHz}$. Imaging commonly uses frequencies in the megahertz range. For example, at $4.0\,\mathrm{MHz}$, a crystal is driven through four million cycles each second. The electrical driving frequency determines the sound frequency, with efficient vibration near a suitable resonance of the transducer.

Receiving reverses the chain. A returning pressure wave makes the crystal vibrate and change shape. That deformation generates a changing e.m.f. across the crystal. Electronics detect and process this signal. A transducer converts energy between electrical and mechanical forms; it is not a microphone listening to an electrical echo travelling through tissue.

The scanner drives a short burst, then listens. Continuing to drive a large signal while trying to detect a weak echo would hide information. Damping reduces prolonged crystal vibration so separate short pulses and echoes can be distinguished.

Echo delay locates a tissue boundary

A boundary between tissues can reflect part of an ultrasound pulse. The returned signal carries two different clues: its delay locates the boundary, while its strength depends on the boundary and the losses along the path.

The delay is measured from emission to reception. For a boundary directly along the beam at depth $d$, sound travels to the boundary and back. In one uniform medium, the distance is $2d$.

[DIAGRAM: asset_name: Ultrasound paths and echo delays; asset_slug: pulse-echo-paths; caption: Each echo delay includes the outward and return sound paths; description: A probe sends a pulse along a straight beam towards two planar tissue boundaries. Outward and return arrows are separated for clarity but represent the same beam path. A companion signal trace shows emission at zero and echoes at 78 and 100 microseconds. Depths are measured one way from the probe.]

Scanning the beam across the body builds up boundary positions. Echo signals can be displayed as brightness at their inferred depths to form an image. A single line of echo delays is not already a complete cross-sectional picture.

Short pulses also help distinguish boundaries close together along the beam. If a pulse lasts $\Delta t_p$, echoes with delays differing by much less than this overlap. In a simple pulse-length model, axial separation needs to be about $c\Delta t_p/2$ or greater. A $1.0\,\mathrm{\mu s}$ pulse in a medium with speed $1540\,\mathrm{m\,s^{-1}}$ corresponds to about $0.77\,\mathrm{mm}$ separation. This is a pulse-length estimate, not a complete model of scanner resolution.

Impedance mismatch controls reflection

Why does gel help sound enter the body? An air gap gives a very large mismatch between the acoustic properties on its two sides, so nearly all the incident intensity is reflected. Coupling gel removes that gap and provides a much closer match to tissue.