Diagnostic imaging is facilitated with the use of ionising and non-ionising radiations. Ionising radiations involve X- and gamma rays. Non-ionising radiations involve radiofrequency and sound. The body is partly transparent to these radiations, but not completely, and the interactions of these radiations with the body elements and compounds yield diagnostic imaging.

Atomic Structure

Matter is composed of atoms. Each atom is defined by its central nucleus. This contributes the majority of the mass. The nucleus is composed of nucleons: protons and neutrons. Protons have a relative mass of 1, with a +1 charge. Neutrons have a relative mass of 1, with 0 charge. Each nucleus is held together by a strong nuclear force.

The nucleons combine to yield the mass number of the atom. The number of protons determines the atomic number. This further defines the position of an atom in the periodic table and is synonymous with the name of the element. The number of associated neutrons can vary, yielding isotopes. These atoms have the same atomic number (number of protons) but a different number of neutrons. Some of these isotopes are unstable and decay with the emission of ionising radiation or particles (or both), called radioisotopes (see section on Radioactivity further on).

1H is hydrogen. This contains only a proton with no neutron (see Fig. 1.1). 2H (deuterium) and 3H (tritium) are isotopes of hydrogen with neutrons.

12C, 13C, and 14C are all carbon atoms with six protons (see Fig. 1.2). The 12C diagram shows 6 orbiting electrons but in a specific arrangement. This arrangement is defined by the electron shells.

The nucleus is surrounded by shells of orbiting electrons. Each electron has a relative mass of 0.0005, with a −1 charge. The number of electrons usually matches the number of protons to balance the charge in the atom. There is a specific arrangement to electron shells. The innermost shell is termed the K-shell and can hold two electrons. Next is the L-shell, which holds eight electrons. The next shell, M, can hold 18 electrons, with the N shell holding 32 electrons. An example of sodium/Na is shown in Fig. 1.3.

Each of these shells has a varying number of subshells contributing to the overall shell, which also can influence the behaviour of electrons, but that is beyond the scope of this book [Further reading: Aufbau principle].

The outermost electron shell is referred to as the valence shell. The valence shell defines the chemical, thermal, optical, and electrical properties of the element. For many main-group elements, a filled outer shell follows an octet arrangement; this simple rule has exceptions, particularly among transition elements.

Metals often have 1–3 valence electrons which can be easily detached from the atom, yielding positive metal ions in a ‘sea of delocalised electrons.’ They are good conductors of heat and electricity (see Fig. 1.4).

Silver bromide forms an ionic crystal lattice whose oppositely charged ions are held together by electrostatic attraction (Fig. 1.5).

Electrons are bound to shells based on binding energy. This binding energy is required to remove the electron from the attractive force of the nucleus (expressed in electronvolts, eV). Each shell has different binding energies, with EK > EL > EM, etc. Each binding energy is fixed for a given element and shell level. When an inner shell electron is excited through the external deposition of energy, it can be raised to a higher electron shell. When the electron returns to its original shell, the excess energy is reemitted as a photon. The energy value of the photon is consistent for each element, yielding characteristic photons (termed X-rays).

See Tables 1.1 and 1.2

Electromagnetic Radiation

This is the umbrella term for energy travelling across empty space. All forms of electromagnetic (EM) radiation travel at the same velocity as light when in vacuo (2.98 × 10⁸ m/s, similar in air).

EM radiation is considered to have both wave and particle-like properties, determined from the double slit experiment.

From the quantum aspect, EM radiation can be considered as particles, represented as photons (quantised packets of energy).

From the wave aspect, EM radiation can also be considered as sinusoidally varying electric and magnetic fields. The electric and magnetic vectors are perpendicular to each other and perpendicular to the direction of the wave. Fig. 1.6 shows a wave of field strength vs time (can be considered a sine wave), where A = amplitude and T = time interval between successive wave crests. This yields:

Frequency f = 1/T

λf = c

where λ = wavelength, f = frequency, and c = constant (usually velocity). The EM spectrum is divided based on wavelength and frequency (see Table 1.3).

Combining particle and wave properties:

E = hf

where E = photon energy, h = Planck’s constant, and f = frequency. Using λf = c:

E = hc/λ

showing that photon energy is inversely proportional to wavelength:

E (keV) ≈ 1.240/λ (nm). For example, blue light at 400 nm has E ≈ 3.10 eV; an X-ray with λ = 0.1 nm has E ≈ 12.4 keV.

Intensity

EM radiation irradiates all directions from a point source, with each ‘ray’ travelling in a straight line. Collimation of these rays allows for a beam in a given direction. The perpendicular cross-section of this beam allows for further characterisation. The main facets of a beam are photon fluence, energy fluence, beam intensity, and air kerma. Photon fluence (see Fig. 1.7a) is the number of photons that pass through a specified cross-section. Energy fluence is the sum energy of all photons passing this cross-section over a given time. Beam intensity indicates the energy

fluence rate (W/mm2), including over time, but is difficult to measure in reality. Air kerma (kinetic energy released to matter) yields an indirect measurement of energy fluence.

Inverse square law (see Fig. 1.7b): The dimensions of a beam are proportional to distance. The area of a beam is

proportional to the square of the distance from a point source. This relies on two assumptions: 1. Point source 2. There is no absorption or scatter between source and

point of measurement

X-Ray Tube and X-Ray Beam

X-rays are produced when fast-moving electrons undergo interaction with a metal target. The kinetic energy of the electrons is converted to X-rays (approximately 1%) and heat (approximately 99%).

X-ray Tube Overview

Production Overview The cross-section of the X-ray tube anode/cathode is shown in Fig. 1.8. To generate electrons, the tungsten filament within the cathode is heated until incandescent. This enables thermionic emission to occur. This is the process through which a fraction of the free electrons can overcome the positive attraction of the metal anions. These free electrons are then focussed via the cup and attracted to the anode target (the degree of which is determined by the voltage). The electrons travel within a vacuum so that there is nothing else to interact with.

The electrical energy sources should have independently adjustable kilovoltage (kV) and milliamperage (mA) input settings.

The kV governs the accelerating voltage between anode and cathode (30–150 kV). It is determined by the waveform. High-frequency generators are used to maintain a near constant waveform (1% ripple). Previously varying types of rectification were used (see Fig. 1.9 and Box 1.2). The constant waveform has multiple advantages, including increased X-ray output and lower patient dose. The mA governs the tube current (energy and quantity of electrons flowing between anode and cathode). It is usually between 0.5 and 1000 mA.

(A)

kV

Target Interactions

Electrons hit the target surface with kinetic energy (in keV) equivalent to the kV of the accelerating voltage. This yields one of two interactions:

Heat Production

(approximately 99%) This is secondary to multiple small interactions and involves the outer electrons of target atoms.

X-ray Production

(approximately 1%) This is secondary to interactions with:

Inner shell electrons: photoelectric effect and characteristic X-ray (see Fig. 1.10). A bombarding electron displaces an inner shell electron. This K-shell vacancy is filled by an L-shell electron (or, less likely, an M-shell electron). Characteristic photons are produced depending on which electrons fill the K-shell and the anode material. This line spectrum depends on the target atom (see Fig. 1.11 for tungsten). • Effective energy: photon energy of a monoenergetic beam with the same attenuation (HVL) in a specified material as the actual polyenergetic beam • Peak energy: most common photon energy

For tungsten: • K-shell energy is 70 keV • L-shell is 12 keV (Kα ≈ 59 keV) • M-shell is 2 keV (Kβ ≈ 68 keV)

Field of the nucleus: the production of Bremsstrahlung (braking radiation), which accounts for 80% of produced X-rays (see Fig. 1.12). A bombarding electron passes through the electron shells and is deflected by the nucleus, losing some energy as radiation. This process yields a continuous spectrum of photon energies, dependent on tube voltage (see Fig. 1.11, dashed line).

Controlling the X-ray Spectrum

The modification of the following factors affects the X-ray spectrum (see Figs. 1.13–1.15):

kV
• Increased kV shifts the spectrum upwards and to the right
• Increased maximum and effective energy
• Increased total number of photons

mA
• Increased mA increases the quantity of photons only

Filtration
• Moves the continuous spectrum to the right
• Increases minimum and effective energy
• Reduces the total number of photons
• Increases the receptor:skin ratio (exit dose:entry dose)

Waveform
• Uniform constant current allows for an increased quantity of photons and effective energy

Atomic Number of Target
• Varies the amount of Bremsstrahlung and energy of characteristic photons

Filtration

Filtration involves the removal of lower-energy photons before they reach the patient. Lower-energy photons mostly contribute to the dose and have little impact on image formation.

The total filtration for a system is equivalent to the sum of inherent and additional filtration. For general radiology, this is 2.5 mm aluminium equivalent and removes X- rays <20 keV.

Inherent filtration in the system, equivalent to 1 mm aluminium. This is contributed by the target material itself (e.g. anode heel effect (see Ch. 3)) and the X-ray tube housing window.

Additional filtration from a flat sheet placed between tube and patient, usually composed of aluminium.

The choice of filter material is determined by atomic number (Z). This needs to be high enough to make the process of photoelectric absorption predominant. Aluminium (Z = 13, EK = 1.6 keV) is most common.

The effects of filtration are demonstrated in Fig. 1.14 Filtration attenuates lower-energy X-rays more than higher-energy X-rays:
• Increases the half-value layer (HVL)/penetrating power
• Reduces intensity
• Reduces skin dose

Increasing the filtration has the following effects:
• Shrinks the overall continuous X-ray spectrum
• Right-shifts the X-ray spectrum
• Increases the minimum and effective photon energies
• Reduces overall output of X-rays
• Can increase the required exposure time

Specific filters include:
• The K-edge filter is used extensively in mammography. It removes both high- and low-energy X-rays (see Fig. 1.15)
• The wedge filter is shaped to create a more uniform exposure across a radiograph

Matter Interactions

X-rays/Gamma Rays There are different possible outcomes for each photon as it travels through matter (see Fig. 1.16):

Transmission e Photon passes through unaffected as primary radiation and is the principal photon in X-ray image formation

Absorption e Photon transfers all energy to the matter, and the photon disappears

Scatter e Diverted in a new direction with or without the loss of energy, as secondary radiation

Each of these outcomes is a stochastic process governed by the statistical laws of chance. The outcome of any given photon is impossible to predict. The overall outcome of a beam with a large number of photons can be accurately predicted.

Attenuation

There are fewer photons present in a beam after it has passed through material than when it entered due to absorption and scatter. Overall, this process is called attenuation. Attenuation of a narrow, monoenergetic beam of X-rays is governed by:

I = I₀ exp(−μd)

where I = intensity, I0 = incident X-ray intensity, m = linear attenuation coefficient (see below), and d = thickness of the material (see Fig. 1.17).

The HVL is the thickness of a given material that will halve the intensity of a narrow beam of X-radiation (dashed lines in Fig. 1.17). The reduction in intensity is governed by 2x (where x is the number of HVLs). Three HVLs would equate to 23 = 8; 10 HVLs would equate to 210 = 1024.

The linear attenuation coefficient (m in cm 1) is specific to each material. It quantifies attenuating properties and indicates the probability of a photon interacting in a given material.

μ = ln(2)/HVL

Mass attenuation coefficient (MAC) indicates the rate of energy loss through an area of material and is independent of density:

MAC = μ/ρ

HVL decreases / LAC increases:
• Increased density of material
• Increased atomic number of material
• Decreased incident photon energy

The width of the beam impacts upon the attenuation, with there being an increased contribution of scatter on a detector with a wider beam (see Fig. 1.18). The measured HVL, in this case, would be increased.

Heterogeneous Beam Attenuation

X-ray tubes produce polyenergetic beams (rather than monoenergetic). Lower-energy photons are removed proportionally more than high-energy photons, yielding beam hardening. The more a beam passes through a material, the less heterogeneous it becomes, with an increased proportion of higher-energy photons. The second HVL is larger than the first HVL as the hardened beam has more high-energy photons. The exponential attenuation curve can still be applied to produce approximate HVL thicknesses.

Compton Effect

X-ray interaction with a loosely bound or free electron, yielding inelastic/non-coherent scattering is known as Compton effect. The electron absorbs some of the photon energy as kinetic energy (see Fig. 1.19). The recoil electron is projected forwards or sideways with higher energy. There is scatter of the incident photon in a new direction with reduced energy. The scatter angle q between the incident and scattered photon determines energy transfer (in the diagnostic energy range, ≤20% is transferred to an electron). As q increases:

• Increased kinetic energy imparted to the recoil electron (increased range)
• Decreased energy of the scattered photon (with increased wavelength)

Compton attenuation contributes to the total linear attenuation coefficient. Its probability depends primarily on electron density and photon energy; mass attenuation by Compton scattering is nearly independent of atomic number for most biological materials. Compton interaction probability generally falls as photon energy rises in the diagnostic range.

Photoelectric Effect

An incident X-/gamma ray photon collides with a bound K-shell electron allowing ejection of the electron (photoelectron); see Fig. 1.20. The energy of the incident photon is completely absorbed in this process.

Kinetic energy of electron = photon energy −Ek

Part of the energy is required to release the energy from the atom (binding energy, Ek). Sometimes the photon interacts with an electron in the L-shell with binding energy EL

Each ejected photoelectron leaves a hole in the electron shell that is filled by a higher-energy level electron, releasing characteristic radiation. This characteristic

radiation is low energy and is absorbed immediately with the release of an Auger electron (very low energy).

Photoelectric absorption in low atomic number material (e.g. human tissue) yields complete absorption of incident photon energy.

μ_total = μ_Compton + μ_photoelectric

where s = Compton linear attenuation coefficient and s = photoelectric linear attenuation coefficient.

μ_photoelectric ∝ ρZ³/E³

where r = density; Z = atomic number and E = incident photon energy.

The probability of photoelectric absorption decreases with increased incident photon energy (1/E3) and increases with the increased atomic number of the material (Z3); see Fig. 1.21

Absorption edges indicate the sudden increase in the probability of photoelectric absorption as incident photon energy reaches K/L/M-shell binding energies (see Fig. 1.11).

Different interactions predominate over different ranges of photon energies (see Fig. 1.22). In most radiology applications, photon energies are <1 MeV, so only photoelectric and Compton effects are considered.

Secondary Electrons These encompass recoil electrons and photoelectrons. These are both directly ionising and tend to interact with the outer shells of atoms: • Excite the atom: ~3 eV • Ionise the atom: ~10 eV • Mean energy expended per ion pair in air: ~34 eV

The range of a secondary electron is the distance it can travel before losing its initial excitation energy and is inversely proportional to the density of the material. The

excitations and ionisations of secondary electrons can cause a number of effects:

• Ionisation of air/gas makes them electrically conducting
• Ionisation of atoms in cells causes biological damage
• Photographic effect
• Blackening of silver and bromine in photographic film
• Plain film radiography
• Excitation of phosphors allows for luminescence/ fluorescence
• Excitation allows increased molecular motion causing heating

Charged Particles This section entails a brief overview of some of the interactions of charged particles (other than electrons) with matter. The more detailed explanations are very equation heavy and beyond the scope of this book, but an overview of how charged particles interact is important. Charged particles behave differently from photons due to mass and charge. Charged particles have a surrounding electrostatic field (coulomb field). Interactions with matter yield the concept of stopping power:
• Collision e energy deposited locally
• Radiative e energy dispersed as photons

Charged particles have a range, an ultimate depth within matter (unlike photons which undergo exponential decay). The range is dependent upon the initial energy and particle type (see Fig. 1.23).

Some of the main types of interactions are:
• Soft collisions: - Atom can be excited or ionised (valence shell electron ejected) - Most probable type
• Hard collisions: - Interaction with an individual electron that gets ejected as a delta ray - Characteristic X-ray or Auger electron also produced
• Nuclear field interaction: - Deflection (almost elastic scattering) - Bremsstrahlung Heavy particle nuclear interactions:
• Inelastic
• Expulsion of nucleons (intranuclear cascade)
• Deposition of energy to the nucleus causing excitation and subsequent evaporation of particles and gamma rays

Luminescence

Luminescence is the process through which a material absorbs energy and then re-emits this energy in the form of visible photons. This occurs in relatively cool materials, differing from incandescence (e.g. burning wood). In

radiology, we are concerned with photoluminescence (the energy source is EM radiation).

Luminescence depends on the electron shells present in a molecule. In a stable molecule, the valence electron shell is completely filled to facilitate stability. The next highest electron shell, which is empty at ground state, is called the conduction band. When energy is deposited in the material, the valence shell electrons excite and move into the conduction band. Within the conduction band, there are multiple energy states for the excited electron to occupy; the electron can also move freely within the material whole. As the excited electron loses some energy through non-radiative decay (vibrational energy or heat), it drops between the individual layers of the conduction band. As the excited electron drops from the valence shell, the energy is released as a photon, often of lower energy and longer wavelength than the incident EM radiation (see Fig. 1.24).

Fluorescence involves the emission of the photon(s) nearly instantaneously (time scale 10⁻¹⁰ to 10⁻⁷ s). Phosphorescence involves delayed emission of the photon(s). This is facilitated by the introduction of impurities in compounds. These impurities are additional elements that can form part of the main material but have differing energy shell levels (referred to as electron traps). To reach one of these electron traps, the excited electron first loses some energy through intersystem crossing (to reach the impurity element). Then the electron can drop into an electron trap [Further reading: triplet state]. To return from here to the native valence shell, the energy shell is now considered ‘forbidden’ due to the conservation of angular momentum. Even though transitions from the electron trap to the valence energy are forbidden, they still occur, just at a much slower rate than fluorescence, hence the time delay to phosphorescence (10 6 to 10 s). Some electron traps are stable and do not facilitate transition without further energy input.

Thermoluminescence enables the transition of the electrons and hence the emission of photons via heating. In photostimulable luminescence, the irradiated phosphor is exposed to light. If the incident photon is of the same energy as the photon resulting from fluorescence, this is termed resonance excitation. This only occurs when monochromatic light is used and yields a luminescence efficiency of 100%. The majority of luminescence is not at 100% (solid phosphors at w20%, electroluminescence at w10%). The intensity of the light emitted by phosphorescence is proportional to the incident energy absorbed. In radiology, this is proportional to the intensity of the radiation beam itself.

Radioactivity

Stable Nuclei Nuclides are atoms with specific numbers of protons and neutrons in their nucleus. There are over 300 naturally occurring nuclides on earth, of which around 250 are stable, and around 90 are unstable (radioactive). The stable nuclei of the lighter elements contain approximately equal numbers of protons and neutrons, except hydrogen, which has only a single proton in its nucleus. Nuclei heavier than calcium-40 (40Ca) have a greater proportion of neutrons to maintain the optimal spacing arrangement for the interactions of the strong nuclear force within the nucleus.

Isotopes Nuclides containing the same number of protons and different numbers of neutrons are isotopes of an element. These will have the same atomic number and chemical properties but will have different atomic mass numbers, density, and other physical properties.

For example, carbon has four isotopes, the nuclei of which all contain six protons. Three occur naturally: the stable isotopes carbon-12 (12C), with six neutrons, and carbon-13 (13C), with seven neutrons, and the unstable, radioactive isotope carbon-14 (14C). This has a neutron

excess, having eight neutrons. The final isotope carbon-11 (11C) is also unstable and radioactive and can only be produced artificially. It is neutron deficient, having only five neutrons.

Radionuclides Radionuclides have an unstable configuration of protons and neutrons in their nucleus, either deficit or excess, and undergo nuclear transformations (also called decay) to alter the balance between these. This is achieved by the emission of any combination of alpha, beta, and gamma radiation, and the process will continue until the nucleus reaches a stable configuration.

Radionuclide Production There are three main methods of production of the radionuclides used in medical imaging. These are using
• A cyclotron
• A nuclear reactor
• A radionuclide generator

Cyclotron

Cyclotrons produce radionuclides by bombarding stable nuclei with highly energetic charged particles, typically

protons. These force neutrons out of the target nuclei, leaving these in an unstable configuration with a neutron deficit. In this case, the mass number is unchanged, but the atomic number is increased by one, meaning a change to a new element.

The most common example is the production of fluorine-18 (18F) which is used in positron emission tomography (PET).

18O + p/18F + n

Oxygen-18 undergoes proton bombardment and produces the required fluorine-18. The resulting neutron flux complicates the shielding requirements for these facilities. There is a range of minicyclotrons which have been developed for the on-site generation of short-lived radionuclides for PET. These are generally sited at, or close to, the hospitals that require the radionuclides, although the high capital costs of these facilities, at least partly due to the complex shielding requirements, mean that many hospital sites rely upon commercial suppliers rather than having their own facility.

The radionuclides produced in cyclotrons can be obtained at high purities as they can be separated from the original stable nuclides relatively simply due to their different chemical properties, which result from their differing atomic numbers.

Nuclear Reactor

There are two methods of radionuclide production which can be achieved using reactors.

The simplest is the extraction of fission products from the spent fuel rods, which can be achieved to high purities due to their different chemical forms. The commonest fission product is iodine-131 (131I) which is used for therapeutic treatments.

238U / 131I + other fission products

The second method is the bombardment of stable nuclei by neutrons from the high neutron flux prevalent in reactor cores. This creates unstable radionuclides with a neutron excess. The most common radionuclide produced by this method is molybdenum-99 (99Mo), which is used in the production of technetium-99m (99Tcm).

98Mo + n/99Mo

The similar chemical properties of the different forms of molybdenum make separation of these problematic, and it is difficult to obtain very high purity samples.

Radionuclide Generator

These are generally used to produce shorter-lived radionuclides which cannot be produced in a cyclotron but can be produced from the decay of a longer-lived radionuclide. The longer-lived radionuclides are referred to as parent radionuclides, and the shorter-lived products are known as daughter radionuclides. Commonly available daughter products include 99mTc from a 99Mo (99Tcm/99Mo) generator and krypton-81m (81Krm) from a rubidium-81 (81Krm/81Rb) generator.

New Production Developments The nuclear reactors used for radionuclide production are not the power generation reactors commonly found around the world but are smaller research reactors which are less common. Many of these are approaching, or have already passed, their planned operating lifetimes and require higher maintenance requirements to keep them operational. In recent years, this has led to a number of unplanned shutdowns and failures of different facilities, resulting in major disruption to the global supply of 99Mo and consequent impacts on nuclear medicine departments worldwide. For this reason, considerable investment has been made to develop alternative methods of production of 99Mo or methods of direct production of 99Tcm

One method under development is the use of neutron generators to bombard 98Mo for the production of 99Mo. The neutron generators are often based around small linear particle accelerators, which fuse isotopes of hydrogen to produce the neutrons.

Another approach is the direct production of 99Tcm

using cyclotrons. Unfortunately, the power requirements needed to achieve this precludes the use of the common medical cyclotrons and requires specialist facilities to achieve this. Another drawback of this approach is the higher levels of contaminants in the 99Tcm produced, as this tends to contain numerous additional radioisotopes of technetium. This increases the radiation dose to the patient from a specific administered dose of 99Tcm and can affect the labelling efficiency of pharmaceutical kits for the production of radiopharmaceuticals.

There have also been a small number of new research reactors commissioned around the world, which have

increased the capacity for irradiation of molybdenum and, to some extent, alleviated the immediate problem. One example of this is the Open Pool Australian Lightwater reactor in the southern suburbs of Sydney, Australia.

Radioactive Decay

The decay (or transformation) method of a particular radionuclide depends on the balance of protons and neutrons within its nucleus. Each radionuclide emits a unique combination of alpha, beta, and gamma radiations with energies characteristic of that radionuclide.

Radionuclides with a Neutron Excess Radionuclides with too many neutrons for stability decay by beta decay (sometimes referred to as beta minus decay (b decay) to differentiate it from positron (b+ decay). In beta decay, a neutron is converted into a proton and an electron. The electron is emitted from the nucleus in the form of a beta particle.

n → p + β− + antineutrino

The daughter nuclide thus has the same mass number as the parent, with the atomic number increased by 1.

A ZParent / A Z+1Daughter + b

Generally, the daughter nucleus is produced in an excess energy state and returns immediately to its ground, or minimum energy, state by releasing a number of gamma photons.

Isomeric Transition

Metastable radionuclides decay by isomeric transition. These do not return to their ground state instantaneously but exist for longer periods before decaying to the ground state. The energy difference between the excited and ground states is emitted as gamma radiation. The mass number and atomic number are unchanged by isomeric transitions so that the parent and daughter radionuclides are identical in all respects other than their energy states and half-lives. The parent and daughter radionuclides are referred to as isomers

The most widely known metastable radionuclide is 99Tcm, which decays to technetium-99 (99Tc) with the emission of 140 keV gamma rays. This pure gamma emission makes 99Tcm ideally suited as an imaging

radionuclide as all the emitted radiation contributes to the formation of a useable image, which is not the case where there are particulate emissions of beta or alpha particles.

The decay scheme for 99Tcm can then be written as:

g 99

b g 99

b g 99

99 42Mo →

43Tcm/

43Tc →

44Ru

where ruthenium-99 is the stable nuclide at the end of the decay chain.

Beta Emission

The spectrum of beta-emitting radionuclides does not exhibit the characteristic photopeak(s) of gamma-emitting radionuclides but instead covers a continuous spectrum up to a maximum value, Emax, which is characteristic of the radionuclide. The average energy of the beta particles is approximately Emax/3. Irrespective of their charge, when the moving electrons of beta emissions travel through a substance, they will interact with the outer shell electrons of adjacent atoms, causing ionisation. This leads the track of the beta particles to be dotted with ion pairs.

The beta particle will lose energy during these interactions until it has depleted its initial energy, at which point it reaches the end of its range. The range depends upon the initial energy of the beta particle and the density of the material through which it is travelling. Typically, this is a few millimetres in tissue.

Radionuclides with a Neutron Deficit These can also be described as having a proton excess, which can be resolved by the conversion of a proton into a neutron and a positive electron. This is released from the nucleus as a high-energy, positive beta particle, commonly referred to as a positron. Positrons are a type of antimatter. Antimatter particles have an opposite charge to their matching particle. Positrons are the antimatter equivalent of electrons.

p → n + β+ + neutrino

The atomic number thus reduces by one, and the mass number stays the same. As with negative beta decay, the daughter nucleus may be left in an excited state, releasing gamma energy until the ground state is reached.

An alternative means of decay for nuclei with a proton excess is the capture of an inner (K) shell electron, facilitating the conversion of a proton into a neutron. This is known as electron capture and leads to outer shell electrons cascading down to fill the vacancy in the K-shell, with the

emission of characteristic X-rays. If left in an excited state, the daughter nucleus may also emit gamma rays.

p + e /n

Again, the atomic number reduces by one, and the mass number is unchanged. A commonly found example in nuclear medicine is iodine-123 (123I) which decays purely by electron capture with the emission of 160 keV gamma and 28 keV X-rays.

Positron Emitters A positron emitted by a neutron deficient nucleus is antimatter, the antiparticle of a negative electron, and therefore exists for only a very short time before interacting with a free electron. The mattereantimatter particles cannot coexist, and both disappear, with their mass being converted to energy. From Einstein’s famous equation E = mc2, it is relatively straightforward to calculate that the mass of a positron has an energy equivalence of 511 keV. A positroneelectron pair has an energy equivalence of 1.02 MeV, and this is the threshold energy difference between parent and daughter nuclear energy levels for radionuclides to be able to decay by positron emission. The energy is emitted in the form of two 511 keV gamma rays travelling collinearly in opposite directions. This 511 keV gamma radiation, sometimes known as annihilation radiation, is the basis of PET image formation.

Internal Conversion

Some radionuclides undergo internal conversion where the emitted gamma rays from the nucleus are absorbed by K- shell electrons which are then ejected from the atom via the photoelectric effect. This results in the emission of characteristic X-rays and photoelectrons, which make these radionuclides generally unsuitable for imaging as the X-rays are of insufficient energy to escape the body and only contribute unnecessary radiation dose to the patient.

Processes of Radioactive Decay Radioactive decay is a random process which obeys Poisson statistics. This means that it is impossible to determine when any particular unstable nucleus will disintegrate, but when there are large numbers of nuclei, the rate at which they will decay is predictable.

The amount of radioactive decay is known as radioactivity or simply activity. The activity of a radionuclide is the number of nuclear transformations per second. It may also be referred to as the number of disintegrations per

second or becquerels (Bq). The becquerel is the SI unit of activity, but in imaging, we generally use megabecquerels (1 MBq = 106 Bq) and gigabecquerels (1 GBq = 109 Bq).

Once a nucleus has decayed, then it cannot do it again. Thus, the number of atoms available to decay continuously decreases with time. The time taken to decay depends on the instability of the radionuclide and is characterised by its half-life.

After one half-life (t1/2), the activity is reduced to one half of its original value. After n half-lives, the activity will have been reduced by a factor of 2n. Mathematically radioactive decay is an exponential process, with the radioactivity of a sample being proportional to the number of radioactive atoms present.

For a given element, the nucleus has the same probability of decaying per second, l. So if we have N atoms, the number of decays per second, i.e. the activity:

A = λN

Thus, we can write mathematically:

N = N₀ exp(−λt)

where N0 is the number of parent nuclei at time t = 0, N is the number of undecayed nuclei t seconds later and l is the probability of decay or decay constant. This is related to the halflife (t1⁄2) by the formula:

λ = ln(2)/t½ ≈ 0.693/t½

The activity can be seen to also follow an exponential relationship and can be written as:

A = A₀ exp(−λt)

This can be plotted graphically, as seen in Fig. 1.25, using linear axes, which demonstrates the characteristic exponential curve shape. This also clearly demonstrates that the activity never falls to zero.

If the activity is instead plotted on a logarithmic scale (see Fig. 1.26), the resultant decay curve is a straight line of slope −l and with an intercept of lnA0

Curves of this form make it comparatively straightforward to determine how long radioactive waste must be stored before it can be safely disposed of. These can also be used to calculate the amount of activity that must be prepared to have a particular amount available a given number of hours later.

The correct definition for the half-life which we have been describing here is the physical half-life, tphys, which is

an immutable property of the radionuclide. These can range from fractions of a second to trillions of years. Bismuth-209 has a physical half-life more than a billion times greater than the current age of the universe.

From an imaging point of view, we also need to consider the physiological clearance of the pharmaceutical compound to which any radionuclide has been joined,

which is known as labelling. This determines the clearance of the pharmaceutical from the body tissues and can again be described using an exponential model. As such, it also has a half-life to define the clearance rate, and this is known as the biological half-life, tbiol

In the body, the clearance of any combination of a pharmaceutical and a radionuclide is determined by the combined effects of the radioactive decay and the physiological clearance. This will be shorter than the physical or biological half-lives as both occur simultaneously. It will also vary subtly amongst any population group as the physiological processes are unique to each individual and may be affected by any current pathology.

This combined clearance can be said to be occurring with a half-life known as the effective half-live, teff. This is defined mathematically as:

1/t_eff = 1/t_phys + 1/t_biol

Characteristics of an Ideal Radionuclide Any radionuclide being considered for use in imaging should have as many as possible of a group of desirable properties which allow optimisation of imaging parameters whilst minimising radiation exposure to the patient and staff. These are:
• A physical half-life which is similar in length to the total time of the imaging examination from the preparation of the product to the end of the imaging. This is generally a few hours
• Emission of gamma rays only, with no particulate emissions or low-energy gamma and X-rays, as these only contribute dose to the patient with no imaging benefit. This indicates that decay by isomeric transition or electron capture are preferable
• Emission of monoenergetic gamma rays as this allows simpler exclusion of scattered radiation
• Gamma rays with sufficient energy to easily leave the patient’s body but low enough to be easily detected by the imaging system. The optimal energy is around 150 keV, but energies between 50–400 keV can be tolerated
• Decay to a stable daughter product or one with a halflife which is sufficiently longer than the average human lifespan
• Should be chemically versatile to allow simple labelling to any required pharmaceutical with no significant detriment to its biological behaviour
• Should be easily available, ideally with a means of production on the site of the imaging facility

The radionuclide that comes closest to these ideal parameters and is the most commonly used in nuclear

medicine is 99Tcm. This decays by isomeric transition with a 6 hours half-life and produces monoenergetic 140 keV gamma rays. It can be produced on-site using a 99Mo generator and, as a transition metal, is chemically versatile.

Radiopharmaceuticals

The combination of radionuclides labelled with pharmaceutical preparations used as diagnostic or therapeutic agents are known as radiopharmaceuticals. If we can find a pharmaceutical that is trapped in or handled by a particular organ of interest, we can image any organ system in the body.

The ideal radiopharmaceutical should have the following properties:
• Be specific to the pathology of interest, i.e. localise predominantly in the organ system of interest
• Have a short biological half-life, such that the majority is excreted from the body shortly after the conclusion of the imaging
• Be non-toxic or of very low toxicity
• Be stable both in vitro and in vivo
• Be readily available and economic

Preparation of Radiopharmaceuticals There are three commonly used basic methods of production of radiopharmaceuticals:
• Substitution of a stable nuclide with a radionuclide
• Addition of a radionuclide to a chemical compound
• Incorporation of a radionuclide onto autologous blood cells

Substitution of a Stable Nuclide This is used to image processes involving biologically useful elements where the stable form can be replaced by a radionuclide of suitable characteristics. The most common example is the use of 123I to image the thyroid. In practice, all radiopharmaceuticals produced by this method are prepared by a commercial manufacturer and distributed to the user in sterile vials with stated activity, volume, and reference time.

Addition to a Chemical Compound This is the method used for the production of most radiopharmaceuticals in nuclear medicine departments. 99Tcm labelled radiopharmaceuticals are prepared on a daily basis in a radiopharmacy facility. This may be on the hospital site or, in larger urban centres, a central facility

may transport the prepared products out to the different hospital sites.

The unlabelled pharmaceutical material and required chemicals are generally supplied as a freeze-dried powder in a sterile vial. These are often known as radiopharmaceutical kits. The user adds the required activity of sterile eluate (sodium pertechnetate, NaTcO4) from the 99Tcm

generator to the kit vial. Usually, labelling is completed in a few minutes with little intervention except agitation to ensure mixing. Further steps, such as immersion in a boiling water bath for a short period, are required for some preparations.

Blood Cell Labelling Autologous blood cell labelling is one of the most complex procedures undertaken in radiopharmacies. The patient’s blood is centrifuged to separate the component cells of the blood then the required cells can be extracted for labelling. White blood cells and platelets are labelled in vitro and then resuspended in the extracted plasma or a saline solution for injection back into the patient. In vitro labelling of cells must be performed in separate facilities from those used for general radiopharmaceutical production due to the high level of sterility required and the risk of crossinfection.

Red blood cells can be labelled in vitro, but for imaging purposes using 99Tcm are generally labelled in vivo by prior injection of a reducing agent, stannous chloride (SnCl2). This adheres to the surface of the red cells, and when a subsequent injection of sodium pertechnetate is administered, the pertechnetate ion adheres strongly to the stannous ion. This provides a simple method of cell labelling with a very high labelling efficiency, generally over 95%.

Advantages of Kit Preparation The advantages of kit preparation of radiopharmaceuticals which ensures it is the most commonly used method are:
• Rapid and easy preparation of the product
• Low radiation hazard to the operator as handling time is minimised
• Radiopharmaceutical product is stable, sterile, and pyrogen-free
• Radiopharmaceutical product is reproducible and reliable
• The unlabelled kit material has a long shelf life, generally a few months, which simplifies stock control and allows for the use of regular standing orders
• The kits are generally readily available and economical to procure as there is a robust market with sufficient competition to ensure competitive pricing

Most radiopharmaceuticals are administered by injection (usually intravenous) and therefore must be sterile. This does not apply to radiopharmaceuticals that are administered orally or by inhalation. The radiopharmaceutical may be diluted with saline in the preparation vial to give an appropriate concentration.

The prepared radiopharmaceutical with the appropriate activity may be dispensed into sterile syringes for patient administration or decanted into further sterile vials, which are sent to the hospital nuclear medicine department. The required volume can then be drawn up from the vial into a syringe just prior to injection to ensure the correct activity is administered. This method gives greater flexibility than the direct distribution of preprepared syringes as the department can easily adjust if the patient arrives early or late. Once labelled, radiopharmaceuticals generally have a limited shelf life of typically 4–8 hours, or more practically, the end of the working day on the day of production.

Radiopharmaceuticals

for injection must be produced in a sterile, pyrogen-free environment. The required standards of air cleanliness for the preparation of sterile products are classified as Grades A, B, C, and D under the Good Manufacturing Practice1 (GMP) guidelines. All aseptic operations should be in a workstation with a controlled work environment conforming to GMP Grade A. This can be provided by a laminar flow cabinet in a cleanroom or an isolator with a filtered air supply. If using a laminar flow cabinet, the cleanroom must conform to at least Grade B standard. Blood cell labelling must be conducted in a laminar flow cabinet or isolator in a separate room from other radiopharmaceutical production.

Laminar flow cabinets are similar to fume hoods but of considerably higher performance and specification. The work area is flushed with a nonturbulent, unidirectional downflow of filtered high-efficiency particulate air, which can be recycled. Cleanrooms are positively pressurised, environmentally controlled workrooms, where entry and egress are through a cascading, positively pressurised three-stage changing area. Isolators have integral lead shielding and allow the operator to manipulate materials within via an integrated glove system. They are generally negatively pressurised to mitigate against leaks and provide very high rates of air exchange.

Quality Control All radiopharmaceutical production must be compliant with the appropriate local legislation, which in the UK includes the Medicines Act2 and IRR3 and requires appropriate permissions from the MHRA. A major part of all legislation and licencing is the maintenance of adequate

quality control. Therefore, all radiopharmaceuticals produced undergo a number of quality checks which include:

Radionuclide Activity This is to ensure that the correct, required amount of activity is being produced and is measured using an air ionisation chamber. These are often known as radionuclide or dose calibrators. Syringes or vials can be measured by sitting them in a holder which drops into the well of the calibrator. An electric current is generated by the ionisation of the air in the chamber, which is proportional to the radioactivity of the selected radionuclide. Preset buttons are generally available for common radionuclides, or bespoke radionuclides can be measured if the correct calibration value is known. The measured activity is indicated on a digital display, usually in megabecquerels, and some now have touchscreen displays to minimise space requirements.

Radionuclide Purity This test measures the proportion of the radioactivity present, which is in the stated radionuclide form. A possible contaminant in 99Tcm radiopharmaceuticals is 99Mo from the generator column if this has washed off during elution of the generator. Testing should be carried out daily for molybdenum breakthrough by placing the freshly eluted sodium pertechnetate solution vial in a 6-mm thick lead container and measuring the ionisation current in the calibrator. This is then repeated with the vial only, removing the lead container. The lead will absorb virtually all of the 140 keV gamma rays from the 99Tcm, but only 50% of the 740 keV gamma rays from the 99Mo. Comparing the ionisation current readings allows calculation of the level of 99Mo present in the eluate. The maximum permitted level of 99Mo in the sample is one part per 1000.

Radiochemical Purity This measures the proportion of the total activity present in the stated chemical form. Possible contaminants in 99Tcm labelled radiopharmaceuticals are free pertechnetate, 99TcmO4, and reduced forms of 99Tcm. The purity is measured using thin-layer chromatography.
• A drop of the radiopharmaceutical is applied at the bottom of the chromatogram
• This is placed in a solvent, ensuring that the origin is not immersed
• As the solvent migrates along the chromatogram, different chemical species in the radiopharmaceutical are separated

The chromatogram is then analysed to calculate the percentage of bound, free, and reduced 99Tcm in the preparation. For radiopharmaceuticals, radiochemical purity should be >95%.

Chemical Purity This measures the fraction of the total mass present in the sample, which is in the stated chemical form. The main possible chemical contaminant of 99Tcm is Al3+ from the alumina column in the generator. Aluminium concentration is tested on the first elution of the generator using a commercially available kit. This contains Al3+ indicator papers and a standard Al3+ solution of 10 μg/mL. A drop of the standard is placed on the indicator paper next to a drop from the eluate. The intensity of the colour produced by the eluate should be less than that produced by the standard.

Sterility All substances for patient injection must be tested to ensure sterility. Surplus eluate (after decay) and samples of each radiopharmaceutical (after decay) are sent to bacteriology for testing. Due to the short shelf life of 99Tcm

radiopharmaceuticals, preparations have to be released prior to the results of sterility testing being known. Testing can only show that the product was sterile at the time of testing, not at the time of use. Testing for pyrogens may also be carried out. Pyrogens are polysaccharides which may be the metabolic products of bacteria, yeasts, and fungi. Demonstrating that a sample achieves the required level of sterility is not a guarantee of apyrogenicity.

Technetium-99m Generator As has previously been mentioned, 99Tcm is obtained from a radionuclide generator containing 99Mo. This decays to 99Tcm with a half-life of 2.8 days (67.2 hours) by beta decay, as seen in Fig. 1.27. The optimal working life of a generator is around seven to ten days. Although some activity can be extracted beyond this time, it is unlikely to be sufficient for a full day’s activity in a busy nuclear medicine department. Generators are generally referenced by the activity they will produce on a given date, which will typically be tens of gigabecquerels. The generator can be used before this date, but this will reduce the activity available later in its working lifespan. Many departments will get their generators delivered at the weekend or early on a Monday morning to allow optimal production capacity at the beginning of the working week.

The activity of 99Tcm available for extraction from the generator increases as more 99Mo nuclei decay. The process of extraction is known as the elution of the generator and involves the washing of a solution of sterile saline over the ceramic column to which the 99Mo is adhered. Fig. 1.28 shows a simple schematic of the components of the generator. Immediately after each elution, the activity of 99Tcm remaining in the generator is reduced to zero, as shown in Fig. 1.29. By a happy coincidence, the half-lives of the parent and daughter in the technetium generator mean that the maximum activity of 99Tcm is achieved approximately 24 hours after the last elution, which fits in very well with the working day. Over several days, the maximum available activity of 99Tcm decreases with the decay of the parent 99Mo.

For this reason, larger departments may get a second delivery of a smaller generator in the middle of the week to maintain the supply level in the second half of the week. The alternative is to front-load the week with the studies requiring higher activity levels, but this reduces flexibility and can be logistically very difficult.

Mechanisms of Radiopharmaceutical Localisation The vast majority of radiopharmaceuticals in routine use in nuclear medicine are labelled with 99Tcm due to its superior imaging characteristics and ready availability. The number of non-technetium radiopharmaceuticals in use has decreased in recent years as manufacturers have developed technetium-labelled replacements to make use of these advantages. However, a number of nontechnetium radiopharmaceuticals remain due to their

specific characteristics and methods by which they function physiologically. The biochemical and physiological methods by which radiopharmaceuticals reach their target organs are fundamental to the success of nuclear medicine as an imaging technique, and a number of these will now be described in detail.

Facilitated Diffusion Physiological factors of the pharmaceutical, such as lipophilicity, favour passive transport through a lipid membrane. The primary example of this in nuclear medicine is the imaging of cerebral blood flow by use of 99Tcm hexamethylpropyleneamineoxime. This is lipophilic, so it passes through the blood/brain barrier, but once in the brain and subject to a different biochemical environment, it converts to a hydrophilic compound that is essentially ‘locked in’ and cannot pass back through the membrane.

Active Transport

Mechanisms These are methods of uptake where energy is consumed during the transport process. The energy consumption can allow transport across a concentration gradient. One example is during the uptake of 201Tl by the myocardium. The thallous ions are taken up by the transport mechanism for potassium via the sodium-potassium pump with the energy provided by adenosine triphosphate. This has the advantage that uptake of the

radiopharmaceutical by the myocytes directly reflects myocardial blood flow.

However, the poor characteristics of 201Tl (long halflife, low-energy gamma emissions, etc.) result in a high radiation dose to the patient. It has generally been superseded by 99Tcm labelled isonitrile compounds such as sestamibi and tetrofosmin. Uptake of these does not linearly relate to blood flow, but the imaging and radiation dose advantages greatly outweigh this.

Capillary Trapping This method relies on the physical trapping of the molecules of the radiopharmaceutical within small blood vessels by nature of their physical size. Intravenous injection of a particulate suspension with particles of diameter >10–15 μm results in the trapping of these particles in the pulmonary capillary bed. The most common example of this is technetium-99m macroaggregated albumin lung perfusion studies, where 1 mg of human albumin in the form of microspheres 60–90 μm in diameter blocks a maximum of 0.3% of available pulmonary vessels in a normal subject. This allows sufficient activity to obtain diagnostic images in a short time frame whilst posing no significant risk to most patients.

Receptor Binding

The utilisation of receptor sites on molecules offers the possibility for highly specific radiotracers. For example, the neuropeptide somatostatin can be radiolabelled with 111In pentetreotide and used to image tumours with somatostatin receptors, such as carcinoids, pancreatic endocrine tumours, neuroblastomas, and paragangliomas. This has been replaced to some extent by 99Tcm labelled Tektrotyd, which binds to a very similar subset of receptor sites and has the advantages of being technetium labelled.

Another common example is imaging the transport of dopamine through the brain using 123I-FPCIT, known as DaTscan. This demonstrates the dopamine transporter sites within the synapse and is very useful for distinguishing between idiopathic Parkinson’s disease and associated syndromes such as essential tremor.

Compartmental Localisation and Leakage Compartmental localisation refers to the introduction of the radiopharmaceutical into a well-defined anatomic compartment, such as 81Krm gas inhalation into the lung.

Compartmental leakage is used to identify an abnormal opening in an otherwise closed compartment, such as the

use of 99Tcm labelled red blood cells to detect gastrointestinal bleeding.

Physiochemical Adsorption The most common example of this method is the use of diphosphonate compounds, where localisation occurs primarily by adsorption into the mineral structure of the bone. The diphosphonate concentrations are significantly higher in amorphous calcium than in mature hydroxyapatite crystalline structures, which helps to explain their concentration in areas of increased osteogenic activity. This produces an image containing ‘hotspots’ that are more easily detected by the human visual system than ‘cold spots’ produced by purely lytic processes.

Methylene diphosphonate and hydroxyl diphosphonate are the most widely available pharmaceuticals for bone imaging and perform similarly, although with slightly different clearance rates from soft tissue.

Phagocytosis

Uptake by phagocytosis occurs when particles of 25 Å to 10 μm diameter are engulfed by phagocytic cells such as the Kupffer cells of the liver or the macrophages of the spleen and bone marrow. This is brought about by the recognition of the particle by receptors on the cell surface. One example is the use of 99Tcm tin and sulphur colloids for liver scanning.

Metabolic Incorporation As mentioned earlier, radionuclides of specific elements follow identical metabolic pathways to non-radioactive nuclides. Therefore, 123I can be used for thyroid imaging as much of the iodine taken up into the body is concentrated in the thyroid.

The positron emitter fluorine-18 in the chemical form of fluorodeoxyglucose (FDG) is a glucose analogue, and its uptake into cells correlates with their glucose metabolism. This is extremely important for oncology imaging as cancer cells have elevated levels of glucose metabolism.

Chemotaxis Chemotaxis describes the movement of a cell, such as a leukocyte, in response to a chemical stimulus. Therefore, 99Tcm labelled leucocytes (white cells) respond to products formed in immunologic reactions by migrating and accumulating at the site of the reaction as part of an overall inflammatory response. This allows imaging of infective and inflammatory processes such as graft infection, prosthetic joint infection, or inflammatory bowel diseases.

Sequestration

The main use of this method is where autologous platelet cells labelled with 111In are injected, and the site of removal (i.e. sequestration) is evaluated. In patients with idiopathic thrombocytopaenia (ITP), the ratio between splenic and liver sequestration at 5 days determines whether splenectomy is a valid treatment option.

Further Reading

Aufbau principle, Double slit experiment, Jablonski diagram,

Triplet state.

References

1. Medicines and Healthcare Products Regulatory Agency and

Department of Health and Social Care. Good Manufacturing Practice and Good Distribution Practice; 2020 [Online]. Available at: https://www.gov.uk/guidance/good-manufacturingpractice-and-good-distribution-practice#overview (Accessed: 05 May 2022). 2. UK Statutory Instruments. The Human Medicines Regula-

tions; 2012 [Online]. Available at: https://www.legislation.gov. uk/uksi/2012/1916/contents/made (Accessed: 05 May 2022). 3. UK Statutory Instruments. The Ionising Radiations Regula-

tions; 2017 [Online]. Available at: https://www.legislation.gov. uk/uksi/2017/1075/contents/made (Accessed: 05 May 2022).