Using ultrasound (6.5.3)

Sound waves are a type of mechanical wave. When a sound wave propagates through a medium, the particles oscillate in a direction parallel to the wave’s propagation and energy transfer. Hence, sound waves are categorised as longitudinal waves.

A longitudinal wave is a series of compressions, where the particles are close together, and rarefactions, where the particles are spread out.

Sound waves can have frequencies ranging from a few hertz (Hz) to multiple gigahertz (GHz).

Humans can only hear sound between and this range is called audible sound.

Sound waves that lie below the audible range (i.e. below ) are called infrasound, and the ones that lie above the audible range (i.e. above ) are called ultrasound.

The generation and detection of ultrasound waves, mainly used by medical devices, depend on the piezoelectric effect.

The piezoelectric effect is the ability of certain piezoelectric crystals, such as quartz and certain ceramics, to generate an electric potential difference in response to mechanical stress (compression or extension).

The effect is reversible. So, a piezoelectric crystal will deform when a potential difference is applied.

• When stress is applied to a piezoelectric crystal, mechanical energy is converted into electrical energy.

• When a potential difference is applied to a piezoelectric crystal, electrical energy is converted into mechanical energy.

The diagram below shows the molecules of a piezoelectric crystal.

• Under no stress, the molecules are randomly oriented and no charge is observed at either end of the crystal.
• When the crystal is compressed, the molecules orient themselves so that the crystal becomes electrically polarised.
• However, when the crystal is stretched, the polarisation is reversed.

For example, in the diagram above, compressing the piezoelectric crystal may induce a positive charge at the upper end of the crystal and a negative charge at the lower end, while stretching the crystal has the opposite result.

When a power source is used to apply an alternating potential difference to the ends of the piezoelectric crystal, it compresses and expands so that the molecules of the crystal align with the external electric field, as shown below.

1. Applying an alternating voltage at frequency to the piezoelectric crystal would compress and expand, or vibrate, the crystal at that frequency.
2. As the crystal vibrates, it disturbs the surrounding air particles, thus producing sound waves of frequency

By applying an alternating potential difference with a frequency greater than ultrasound waves are produced.

A device that converts energy back and forth between mechanical energy and electrical energy by utilising the piezoelectric effect is called a piezoelectric transducer.

A piezoelectric transducer that is used in ultrasound imaging is shown below.

A transducer consists of a thin slice of piezoelectric crystal protected by an insulating case. An acoustic lens at the front is used to converge the ultrasound beam.

The crystal is backed by a damping layer, usually epoxy resin, to quickly stop its vibrations after emitting the ultrasound pulse. This reduces interference between the emitted and reflected pulses.

To maximise the efficiency of a transducer, the frequency of the waves must match the resonant frequency of the crystal. The thickness of the crystal should be about half the wavelength of the emitted ultrasound.

• To generate ultrasound, the transducer converts an alternating potential difference into sound waves.
• To detect ultrasound, the transducer converts the sound waves into an alternating potential difference.

The simplest type of ultrasound imaging is called an A-scan, or amplitude scan:

• They utilise a single transducer to emit a signal and subsequently receive the reflected signal.

• A-scans are one-dimensional, determining the depth of internal structures.

The depth to the subject of the scan from the skin is calculated by measuring the time delay between the signal generation and reception.

In A-scans, ultrasound waves are typically reflected at the boundary between two media.

Examples of A-scan usage include:

• measuring the length of the eye,
• identifying the presence of tumours.

A-scans provide depth measurements only and do not produce images.

The depth or distance to a target in the body can be calculated using an A-scan.

For a time delay between the generation and reception of the ultrasound, and by knowing the speed of ultrasound in the tissue, the depth of the target can be calculated from:

The factor of is due to how the ultrasound pulse must travel from the transducer to the boundary of the target and then back again, so the measured time corresponds to twice the one-way distance.

A B-scan image shows the reflected ultrasound intensity at each point on the sensor; for example, high-intensity ultrasound appears as white, while no reflected signal appears black.

• B-scans are primarily used for diagnostic purposes, such as visualising bones, muscles, and organs or monitoring a foetus’s development.

• To enhance image clarity, pulsed ultrasound waves are employed to ensure that reflected waves are received without interference.

• Shorter wavelengths are used to provide greater detail, allowing sound waves to navigate around finer internal structures.

The table below highlights the key differences between an A-scan and a B-scan.

The speed of sound in a material depends on both the elasticity and the density of the material.

• Gases have low densities, and ultrasound travels more slowly in gases than in other states of matter. Therefore, their acoustic impedance is low.

• Conversely, solids are generally denser, and ultrasound travels fastest in solids. As a result, the acoustic impedance of solids is high.

When a collimated beam of ultrasound is incident on a boundary between two media, it is partially reflected, and the rest is transmitted into the next medium.

The ratio of the reflected beam intensity to the incident beam intensity depends on the acoustic impedances, and of Medium 1 and Medium 2.

During an ultrasound examination, a transducer is typically placed on the patient’s abdomen or chest. If air pockets are trapped between the transducer and the skin, a significant difference in acoustic impedance is created.

As a result, a large portion of the incident ultrasound beam is reflected back, with only a small amount transmitted into the body. This can make studying the internal structure of the human body difficult.

To counteract this effect, a special gel, known as a coupling gel, is placed between the skin and the transducer. An example of this is shown in the diagram below, during the study of a lesion.

When ultrasound reflects off a moving object, its frequency changes. This is known as the Doppler effect.

Doppler ultrasound is a non-invasive medical technique that utilises ultrasound reflections from iron-rich blood cells. This helps doctors evaluate blood flow through major arteries and veins, including those in the arms, legs, neck, and heart.

Applications of Doppler ultrasound:

• Reveal blood clots.
• Identify the narrowing of vessel walls resulting from the accumulation of fatty deposits.
• Evaluate blood flow to transplanted kidneys or livers.

In Doppler ultrasound, the change in frequency as a fraction of the initial frequency is equal to:

Where:

• is the speed of blood,
• is the speed of the ultrasound, and
• is the angle between the ultrasound receiver and the line along which the blood is travelling.