# Producing an ultrasound beam

### Piezoelectric effect

A transducer with piezoelectric crystals is used to produce the ultrasound beam. This is a material in which mechanical energy is converted into electrical energy and vice versa. This means that transmitting an electric voltage through the material will cause it to vibrate, producing a sound wave. Similarly, the returning echo sound wave vibrates the crystals producing an electric voltage that can be measured. In this way, the material acts as a receiver and a transmitter. The intensity of the sound wave, or the pressure changes, is proportional to the amount of voltage. The system can, therefore, represent the intensity of the returning echoes as points of brightness (B-mode imaging) based on the voltage produced.

### Natural / resonant frequency If two sound waves of the same wavelength cross in the same phase, they combine and are reinforced (constructive interference). If, however, they are in different phases they cancel each other out (destructive interference).

A transducer produces its largest output when the frequency produces a wavelength equal to 2x the thickness of the piezoelectric disc. This is because as the material pulses backwards and forwards it reinforces the waves due to them being exactly in-phase. Therefore, the crystals are cut to half the thickness of the desired wavelength.

*** Thickness of piezoelectric disc = 1/2 λ (desired wavelength) ***

#### Pulse duration Once the transducer is pushed it continues to vibrate for a short time with exponentially decreasing intensity (damping). The mechanical coefficient (Q value) reflects how quickly the signal is dampened.

Materials with a higher Q-value vibrate for a long time i.e. have a light dampening effect, and the pulse persists for a longer time. Materials with a low Q-value dampen the vibration quickly and the pulse lasts for a shorter time.

#### Pulse Repetition Frequency (PRF)

The scan line density is the number of beams sent out by the transducer to sample the patient's tissues per frame.

The typical number is 100 lines per frame. To allow adequate real-time image a sufficiently large number of frames must be scanned per second. The rate at which these frames are repeated is measured by the pulse repetition frequency (PRF). It depends upon the velocity of sound (which is assumed to be ~1500 m/s), the depth of the structure being imaged and the number of pulses sent out per frame.

PRF = frame rate x lines per frame

e.g. 30 frames per second each of 100 lines per frame requires a PRF of 3 kHz

Longer PRF caused by:

• Deeper structures being imaged (the longer it takes to go and come back, the longer the listen phase of the pulse has to be)
• More lines per frame

#### Depth of view

In each pulse the beam has to be transmitted, reach the structure to be imaged, and the echo returned to the transducer before the next pulse can be generated. The time taken to reach a structure, the distance the beam travels and the speed of the beam are related to each other by the equation below.

Distance = time x velocity x 0.5

(divide by 2 for journey there and back)

Each pulse has to go to the deepest tissue then return to the transducer before the next pulse is generated. The depth of tissues that can be imaged with a particular PRF can be calculated by the equation below:

Depth of view = 0.5 x sound velocity / PRF

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## Transducer array

#### Single Transducer When a single transducer produces a beam it starts off as a parallel beam (near field). This is the most useful part of the beam. Then, the beam diverges (far field). The length of this near field depends on the width of the transducer. The wider the transducer the longer the near field.

Near field distance = D2 / 4λ
where:
D = diameter of transducer
λ = wavelength

To get as long a near field distance as possible we would have to make the transducer wider. However, the resolution will be reduced and the width of the whole transducer array will be much larger. To overcome this, a stepped linear array is used.

#### Stepped linear array Many small transducers are placed next to each other. They are then activated as a group to widen the beam and produce a longer near field distance. The initial transducer is then inactivated and the next transducer activated, moving the beam along. In this way many more wide beams can be produced in a smaller space than could be produced with wide transducers activated individually. This linear array can also be used to focus the beam electronically. The outermost transducers are activated first, then the two inner, then the innermost etc. In this way the transmitted beam is focused to a specific point. The order in which transducers receive echoes can also be focused to preferentially receive signals from a particular depth. This is what happens when the focus is set on the ultrasound machine.

Σ Summary
• Piezoelectric effect is a property of the transducer crystals. An electric current produces movement and vice versa.
• Thickness of piezoelectric crystal = 1/2 x desired λ
• Mechanical coefficient (Q value) of backing material
• High Q value = low dampening, long pulse
• Low Q value = heavy dampening, short pulse
• Pulse repetition frequency (PRF) = frame rate x lines per frame
• Distance travelled by beam = time x velocity x 0.5
• Depth of view = 0.5 x sound velocity / PRF
• Near field distance = (diameter of transducer)2 / 4λ
• Stepped linear array increases near field distance and can be used to electronically focus the beam

#### Next page: Image properties 