Medical physics

X-rays can be artificially produced using X-ray tubes. Electrons are expelled from a heater (cathode) into a vacuum via thermionic emission:

1. Thermal energy from the heater liberates electrons from their atomic nuclei.
2. The electrons are then rapidly accelerated by a high voltage electric field through the vacuum towards a target metal.
3. Finally, the electrons are rapidly decelerated by colliding with a target metal anode (e.g. tungsten).
4. Colliding with the anode makes the electrons lose most of their kinetic energy. The lost kinetic energy is converted into X-rays.

It is important to note that the internal vacuum is necessary to prevent electrons from colliding with air molecules. An external power supply creates a potential difference across the cathode and anode. A high-voltage supply is required to generate an electric field strong enough to produce X-rays.

X-rays are produced in every direction from the anode of an X-ray tube. However, in practice, the X-rays need to be guided in one direction towards a sample or object, such as a suspected broken bone. Hence, one side of the X-ray tube has a window made of a material thinner than the lead casing to allow unidirectional emission of X-rays.

The beam is directed into a series of straight, parallel metal tubes (called a collimator) that further confine the beam by absorbing any rays that are not parallel to the axis of the tubes.

Inside an X-ray tube, a heated filament (cathode) emits electrons via thermionic emission. The filament is typically made of tungsten, which can withstand high temperatures. A high external voltage of around is applied between the cathode (negative) and the anode (positive), creating an electric field. This accelerates the emitted electrons towards the anode.

A potential difference translates to a kinetic energy gain of of the electrons. It is important to note the difference in units here. This is due to the equation:

Where:

• is the energy transferred to the particle,
• is the charge (an electron has a charge of one electron volt eV), and
• is the potential difference across the X-ray tube.

When a high-speed electron is incident on the tungsten anode in an X-ray tube, X-rays are produced by two different types of interactions:

Bremsstrahlung radiation: Electrons slow down or brake when they come near the nucleus of the tungsten atoms, they lose energy in the form of X-ray photons. This type of radiation produces a broad spectrum of X-rays.

It is a broad spectrum as the electrons can have a range of kinetic energies as they accelerate through the X-ray tube. This creates a range of kinetic energy losses when they collide with the anode. Bremsstrahlung radiation is sometimes referred to as braking radiation.

Characteristic radiation: Some electrons collide with the inner shell electrons of tungsten atoms, knocking them out of their orbit. When electrons from higher energy levels drop down to fill the vacancy, they release energy in the form of X-ray photons with specific, characteristic energies.

Simple scattering is a type of X-ray attenuation mechanism and is common in the lowest energy X-rays in the range of

An incoming X-ray photon will be reflected by an electron in the material. The X-ray will be elastically scattered and change direction.

This is the simplest attenuation mechanism, and will not affect the energy or wavelength of the X-ray beam. It will not lose energy as the incoming X-ray has insufficient energy to ionise the atom.

The photoelectric effect is a type of X-ray attenuation mechanism that affects X-rays with energy less than but greater than

These X-rays can match the ionisation energy of the atoms in the material. This results in the incoming X-ray being absorbed by an orbiting electron and the emission of a photoelectron (a liberated electron from within the atom).

After the photoelectron leaves the atom, another electron may transition down to fill the now vacant position: this electron movement also releases a scattered low-energy photon as the electron moves from a higher energy state to one of lower energy.

The Compton effect is an X-ray attenuation mechanism which dominates for X-rays with energies between and

An incoming X-ray photon will inelastically scatter off an electron within a material: it is not absorbed by the atom as it has too much energy. Instead, inelastic scattering imparts some of the energy into the atom. The scattered X-ray photon will have decreased energy, and therefore an increased wavelength.

The electron involved (sometimes referred to as a Compton electron) will also be ejected from the atom, scattered in a different direction in order to conserve momentum.

Pair production is an X-ray attenuation mechanism that can occur for the highest energy X-rays over

An incoming X-ray photon will interact with the electric field of an atom and spontaneously transfer all energy into producing an electron–positron pair that travels in opposite directions to conserve momentum. The positron will then quickly collide with a different electron and annihilate. Annihilation of a particle–antiparticle pair will produce photons.

The incoming X-ray photon must have a lot of energy to produce an electron–positron pair; these energies are not used in medical imaging, so pair production normally is not observed in this context.

It is useful to note that Compton scattering is the main cause of X-ray energy loss between roughly 30 keV and a few MeV. This is because its interaction probability decreases slowly. Other processes like photoelectric absorption (at lower energies) and pair production (above 1.02 MeV) also happen, but Compton scattering is simply the most likely to occur in that middle energy range. Remember that these “ranges” overlap; they aren’t strict cut-offs.

X-rays are a form of ionising radiation: as they pass through matter they will lose energy due to attenuation. This causes a gradual decrease in the intensity of the X-ray, where intensity is defined as the power per unit of cross-sectional area and has units of

The penetrating power of the X-ray is dependent on the material it is passing through. An incoming X-ray will be attenuated based on:

• the thickness of the material,
• the density of the material, and
• the atomic number of the material.

A very thick, dense, high atomic number material will attenuate the X-ray a lot more than a thin, less dense, low atomic number material.

Different materials will attenuate X-rays to a different extent; this can be used to distinguish different materials inside the body such as bone and soft tissue.

Applying the varied attenuation abilities of different materials is vital for medical imaging. For example, an X-ray image must discern between muscle, soft tissue, and bone to diagnose potential health issues in a patient.

Bone attenuates X-rays more than soft tissue. Therefore, X-rays propagating through bone are more likely to be absorbed, and the beam is more attenuated on the other side of the bone.

Photographic film will turn from white to black if exposed to a high intensity of X-rays. Therefore, X-rays passing through bone will be attenuated and not turn the areas of the plate immediately behind the bone black. This contrast is evident in the image above. Modern digital detectors can also be used to enhance image processing, store and transfer images.

In medical X-ray imaging, barium and iodine are commonly used as contrast media.

Iodine is used as a contrast medium in liquids, for example, to observe blood flow. An organic iodine compound is injected into the bloodstream. In the X-ray image, low attenuated intensities indicate where the blood is flowing well, and areas with high attenuation (where the iodine is collecting) indicate poor blood flow.

Barium sulphate is used as a contrast medium in the digestive system. A liquid ‘barium meal’ is swallowed by the patient. Similarly, areas where the barium builds up will be highly attenuated and can locate blockages.

A computed axial tomography scan or CAT scan is a medical imaging technique that uses X-rays to analyse a patient’s body structure.

It comprises the following key elements:

• Rotating X-ray source: an X-ray tube rotates around the patient. It produces a thin, fan-shaped X-ray beam that passes through the body, targeting specific slices or sections.

• Ring of detectors: a ring of detectors encircling the patient capture the X-rays after they pass through the body. As the X-ray beam rotates, the detectors measure the amount of X-rays absorbed by different tissues, which varies based on the attenuation ability of different materials.

To generate images on a computer, software and displays are used.

• Computer software: data from the detectors is sent to a computer. Using specialised software, the computer processes this data, performing complex mathematical calculations to generate detailed images of the scanned body part.

• Display: processed data is converted into visual images that can be displayed on a monitor. These images show detailed cross-sections (slices) of the body, allowing healthcare professionals to make accurate diagnosis.

There are advantages of using CAT (computed axial tomography) scans over traditional X-ray medical imaging:

1. Cross-sectional imaging: CAT scans provide detailed cross-sectional slices of the body, offering a better view of internal structures. X-ray images are 2D, which can make it difficult to distinguish overlapping tissues.
2. Better soft tissue contrast: CAT scans are superior at visualising soft tissues, such as the brain and blood vessels, which are hard to differentiate on X-ray images.
3. Diagnostic accuracy: CAT scans can provide more extensive information for healthcare professionals to use for diagnosis, making their conclusions more accurate.

A radioisotope (or radionuclide) is an unstable isotope of an element that undergoes radioactive decay, emitting alpha, beta, or gamma radiation to achieve a more stable state.

Radioisotopes used in medical imaging must have a short half-life to ensure high activity and be detectable within the body. This allows small amounts of the radioisotope to be used to create an image, ensuring patient exposure is kept to a minimum.

Gamma-emitting isotopes are ideal for medical imaging due to their low ionisation and ability to penetrate the patient. Alpha and beta sources are not used in medical imaging because they are highly ionising, they can damage the cells in the body and lead to cancer.

Two common examples of radioisotopes used in medicine are:

• Fluorine-18: Produced in hospitals using a particle accelerator and used in PET scans.
• Technetium-99m: Produced by natural decay of molybdenum-90. Used to monitor the function of major organs, e.g. heart, lungs, brain, liver and kidneys.

The image below shows the molybdenum-90 decay chain where technetium-99m is produced:

Molybdenum-90 beta-minus decays to form technetium-99m. The ‘m’ refers to metastable, meaning the nucleus remains in a high-energy state. Technetium-99m then beta-minus decays to technetium-99, which has a very long half-life of 210,000 years.

To ensure the radioisotopes reach the desired location, they are attached to a targeting molecule using a linker (a chemical group that joins the radioisotope to the targeting molecule), which binds to the target protein on a cell membrane’s surface.

The combination of a radioisotope, linker, and targeting molecule is known as a radiopharmaceutical or a medical tracer. The diagram below shows the basic structure of a medical tracer:

It is useful to note that medical tracers can “label” a target in different ways, depending on the target molecule’s location. Some tracers bind to cell-surface receptors, whilst others are absorbed into cells by crossing the cell surface membrane. In both cases, the tracer accumulates more in the target area, making it easier to detect.

A gamma camera detects gamma photons emitted by medical tracers (usually containing Technetium-99m) injected into a patient. The diagram below shows the main components of a gamma camera:

When a gamma photon passes through the collimator and strikes the scintillator crystal (often sodium iodide), it may produce a brief flash of visible light. These light photons are detected by photomultiplier tubes, which convert the faint light into an electrical signal and amplify it.

The signals are then processed by the electrical circuits and sent to a computer, which uses them to work out where in the scintillator each gamma photon was detected. By repeating this many times, the computer builds up an image showing the distribution (concentration) of the medical tracer in the body.

The lead collimator in a gamma camera helps produce a sharp, high-resolution image by controlling the direction of incoming gamma rays. Without a collimator, gamma rays would enter from all directions, leading to a blurred, low-resolution image. The diagram below shows the basic structure of a collimator:

The collimator contains an array of small holes, allowing only gamma rays travelling along specific paths to reach the detector. It works by absorbing off-axis gamma rays, preventing them from contributing to the image:

• The smaller the holes in the collimator, the higher the resolution, but the lower the sensitivity.
• The larger the holes, the lower the resolution, but the greater the sensitivity.

The photons produced by the scintillator crystal need to be amplified and converted into an electrical signal. The diagram below shows the internal structure of a single photomultiplier tube from a gamma camera:

1. A single visible light photon from the scintillator hits the photocathode to produce a single photoelectron.
2. The photoelectron is then accelerated towards the first dynode, an electrode with a potential difference of .
3. When the photoelectron collides with the dynode, it produces additional electrons known as secondary electrons.
4. These are then accelerated to the next dynode, which is held at a higher potential difference. Each electron produces, on average, four secondary electrons at each dynode – creating an exponential growth of electrons.
5. The electrons are all collected at an anode at the end, producing a current that passes through a resistor and generates a small voltage pulse.

All particles have a corresponding antiparticle with the same mass but opposite charge and opposite values of key quantum numbers (for example, lepton number or baryon number), while other properties such as spin are the same.

When a particle and its corresponding antiparticle collide, they annihilate each other. The mass of both the particle and antiparticle is converted into energy, typically in the form of photons.

The annihilation of a positron and an electron creates two gamma photons. The gamma photons travel in opposite directions in order to conserve momentum, as shown below:

• If the particle and antiparticle are at rest in the centre-of-mass frame, the photons have equal energy and travel in opposite directions to conserve momentum.
• If the pair has net momentum in the centre-of-mass frame, the photons are still emitted so that total momentum is conserved, but not necessarily in the opposite direction.

The image below shows a basic schematic of a PET scanner:

1. The patient lies on a table surrounded by a ring of many gamma detectors. Each gamma detector comprises a sodium iodide scintillator crystal and a photomultiplier tube.
2. Every gamma photon emanating from the patient’s body that collides with the scintillator crystal produces a voltage pulse.
3. The ring of gamma detectors can determine the location of the annihilation from the difference in time at which the two gamma rays (gamma photons) strike the diametrically opposite detectors.
4. The computer receives all the voltage pulses produced at the detectors and analyses them to generate a 3-D image on a display.
5. The different concentrations of the medical tracer are highlighted in different colours and brightness on the display, allowing the analyser to determine where uptake was greatest or lowest.

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.