### FRCR Physics Notes

#### FRCR physics notes contents

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# Image properties

## Spatial resolution

#### Axial resolution

The ability to differentiate between two objects in the axial plane, i.e. along the path of the ultrasound beam, depends on the length of the ultrasound pulse and the wavelength. The resolution is increased by:

• Low Q value of backing material (shorter pulse length)
• Shorter wavelength i.e. increased frequency

#### Lateral resolution

The lateral resolution is measured perpendicular to the direction of the ultrasound beam and depends on the beam width which, in turn, depends on the diameter of the PZT crystals and the focusing. To differentiate between two objects, you need at least three beams to interact, one on each object and then one in the space between the two objects. Lateral resolution is always worse than axial resolution and it corresponds to ~1/3 of the transducer diameter.

Beam width = focal length x λ / D
where:
λ = wavelength
D = diameter

#### Slice thickness

The higher the frequency the smaller the slice thickness. It is usually larger than the beam width. For standard 2D transducers the slice thickness is fixed.

## Temporal resolution

This is the ability of the system to display events occurring at different times as separate images. It is measured in frames per second. It is reduced by:

• Greater number of focal zones
• Having doppler on
• Deeper object (echo takes longer to reach object and return
• Large sector width (more space to scan)

Each pulse of a transmitter contains a transmit (during which the ultrasound wave is produced) and a receive (during which the transducer “listens” for the returning echo) phase. The pulse repetition frequency (PRF) is the number of pulses of ultrasound sent out by the transducer per second. It depends on the velocity of sound and the depth of the tissue being imaged – the deeper the tissue, the longer the transducer has to wait for the echoes to come back i.e. lower PRF.

## Harmonics

At higher intensities the speed of sound is slightly faster in the high pressure (compression) parts than in the low pressure (rarefaction) which skews the normal sinusoidal wave.

• The leading edge of the sinusoidal wave becomes deeper
• Effect increases the deeper the wave travels
• This degrades the image at depth

When you perform a Fourier analysis of the returning wave, the frequencies returned are harmonic i.e. if a 2 MHz pulse is sent out, the harmonic frequencies returned are 4 MHz, 6 MHz and 8 MHz etc.

When turning on the harmonics function on the ultrasound machine an electronic filter or pulse inversion technique ensures the fundamental frequency is not returned and the harmonic frequencies are used to build up the picture.

• Higher frequencies generated at the tissue interface have less distance to travel (only travel one way, not there and back)
• Contains fewer reverberation artefacts. The harmonics used to develop the picture are developed at deeper structures whereas reverberation comes from shallow structures.
• Better resolution at deeper structures

#### When to use it

• Cardiac work: reduces reverberation from ribs. Reduces movement artefacts from tachycardia and respiration.
• Fluid-filled structures: reduces reverberation artefacts. Improves contrast.
• Improved edge enhancement
• Obese patients
• Carotid arteries: measuring wall thickness and atheroma

#### Limitations

• Not so useful in superficial structures
• Effects lost in very deep structures
• Safety: need high power USS

## Compound imaging

This utilises a phenomenon known as “beam steering” in which the angle of the ultrasound beam is altered. In compound imaging the beam is transmitted at up to 9 different angles per sweep. The same object is imaged at different angles. This means that some beams will reach behind the object and return echoes.

• Advantages: useful when examining small parts and superficial structures.

### Σ  Summary

• Axial resolution improved by:
• Shorter wavelength (higher frequency)
• Shorter length of pulse (lower Q-value of backing material)
• Lateral resolution improved by:
• Smaller beam width
• Temporal resolution worsened by:
• Smaller PRF
• Deeper structures
• More focal zones
• Doppler
• Larger sector width
• Harmonics used in obese patients and to improve movement/reverberation artefacts
• Compound imaging useful for small/superficial structures but removes acoustic shadow