Non-ionising imaging (3.10.4)

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.

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.

As ultrasound propagates through body tissue, its intensity decreases because some energy is absorbed by the tissue and some is scattered out of the beam.

The reduction in wave intensity as it travels through a material is known as attenuation. For a given material, equal thicknesses produce the same fractional (percentage) reduction in intensity. The reduction in wave intensity as it travels through a uniform material follows an exponential decay pattern.

For example, if the intensity decreases by 10% across the first 1 cm, it will decrease by a further 10% across the next 1 cm, and so on. This cumulative reduction results in the characteristic exponential decay curve illustrated below.

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.

An optical fibre is a very thin, flexible strand of glass with a core that can transmit light through total internal reflection. Light rays striking the inside wall of an optical fibre at an angle greater than the critical angle are totally internally reflected along the length of the cable.

In a tightly packed bundle of optical fibres, light can leak from one fibre to the other if nothing prevents it. To stop this, each fibre’s core is surrounded by a cladding, a second layer of glass with a lower refractive index.

This refractive index difference ensures that, for rays above the critical angle, total internal reflection occurs at the core–cladding boundary, keeping light confined within each fibre.

An endoscope is a medical instrument used to view the inside of the gastrointestinal tract. It is a flexible tube containing bundles of optical fibres; channels for air, water, and suction; and tools for taking tissue samples for analysis.

Light is transmitted through an incoherent bundle of glass fibres. This type of bundle cannot form an image because the ends of the fibres are randomly arranged. However, in a coherent bundle, all the fibres have the same spatial position at both ends.

A coherent bundle is capable of producing an image, as the light emitted from its ends is an exact replica of the incident light. Coherent bundles are expensive to make. Therefore, incoherent bundles are more appropriate for providing light during a medical examination.

Magnetic resonance imaging (MRI) is a type of scan that is capable of producing a cross-sectional image of a patient. The images can be used to diagnose various conditions, including brain tumours, joint injuries, and blood vessel blockages.

The main components of an MRI machine are:

• superconducting coils (very strong magnet)
• a radio frequency (RF) emitter
• RF receiver coils
• gradient coils
• a computer.

An MRI scan utilises the magnetic properties of protons. Every hydrogen atom in the body consists of a single proton as the nucleus. Protons possess their own magnetic field (i.e. they act as tiny magnets) due to their charge and spin.

Normally, protons are randomly oriented. However, in the presence of an external magnetic field , the majority of protons align themselves parallel to the field, such that their axes of spin precess (wobble) about the direction of the external magnetic field generated by the MRI machine. Antiparallel alignment means the protons point in the opposite direction to the field.

The frequency at which the axis of spin precesses is known as the Larmor frequency.

In an MRI scan, the patient lies on a table inside the bore of the superconducting magnet.

1. The magnetic field aligns the protons in the body.
2. A radio-frequency (RF) pulse at the Larmor frequency is directed at the patient. This causes the hydrogen protons to precess at a typical angle of 90° to , exciting them to a higher energy state.
3. When the RF pulse ends, protons de-excite and relax back toward equilibrium, emitting RF signals (the MR signal).
4. The signals emitted by the protons, and their duration, are detected by receiver coils and analysed by a computer to construct an image.
5. The time required for protons to relax and return to equilibrium varies across different body tissues (e.g., fat, blood, tissue). This allows the computer to identify the composition of the imaged section.

An MRI scanner needs high magnetic field strengths, about a few tesla, generated using superconducting coils. The magnetic flux density is 10,000 times that of the Earth’s magnetic field.

The gradient coils are responsible for the cross-sectional imaging of an MRI scanner. These coils are loops of wire on a cylindrical shell that lies just inside the bore.

How gradient coils work:

• Main function: They provide the necessary linear gradients to manipulate the main magnetic field, enabling the system to pinpoint the MR signal source slice by slice.

• Creating the gradient: When a current flows through a coil, it generates a secondary magnetic field. This field is superimposed on the main magnetic field, altering its strength along a specific axis.

• Spatial encoding: This variation in magnetic field strength causes hydrogen protons to precess at different frequencies depending on their location. By precisely controlling these gradients, the MRI machine can decode this frequency information to construct a 3D image of the body.

MRI scans have several advantages as well as disadvantages: