Nuclear Medicine

1. Basic Physics

Radioactive decay is the stochastic process by which an unstable atomic nucleus loses energy by radiation.

Nuclei are unstable if:

• Very large number of nucleons (max. 83 protons, A > 209 are intrinsically
  unstable)
• N/Z is too high
• Odd number of protons and/or neutrons

1.1. Activity

Activity (A) is the quantity of radioactive atoms undergoing nuclear transformation per unit time (t), measured as becquerels (Bq) where 1 Bq is 1 disintegration per second. It is equivalent to the change (dN) in the total number of radioactive atoms (N) in a given period of time (dt). The minus sign indicates that the number of radioactive atoms decreases with time.

A = - dNdt

1.2. Radioactive decay

Radioactive decay is a stochastic (random) process, where number of atoms decaying over time is proportional to the number of unstable atoms present. The unit of radioactive decay is the becquerel (Bq).

dNdt ∝N

This proportional relationship can be expressed as an equality by using a decay constant λ, which is characteristic of each radio nuclide. N(t) is the number of atoms at time (t).

N(t) = N(0)e-λt

• The radioactivity decay of a radionuclide decreases by equal fractions (%) in equal intervals of time (exponential law)
• The rate of decay (activity of the radioactive material) is proportional to the count rate i.e. the higher the rate of decay, the higher the number of gamma and beta particles produced.
• The number of radioactive atoms in a sample is proportional to the rate of decay.
• The degree of radioactivity depends on the quantity of radioactive material at any given moment.
• The activity of a radionuclide decreases exponentially and hence never reaches zero.

1.3. Physical, biological & effective half-life

Physical half-life

The physical half-life is the time it takes for half of a given sample of a radionuclide to have undergone radioactive decay. The process follows exponential decay.

• A short half-life generally indicates a less stable radionuclide.
• The physical half-life is a fixed characteristic of the radiopharmaceutical and is unaffected by factors such as heat and chemical reactions.
• It is used to calculate how much radiopharmaceutical agent to prepare depending on .its time of use

Biological half-life

• Biological half-life is dependent on the rate of elimination of the radiopharmaceutical from the body.
• A radiopharmaceutical is eliminated from the body by organ-dependent processes such as metabolism (liver) and excretion (kidneys), hence it may increase as a result of organ failure.
• The biological half-life is dependent on the pharmaceutical agent used, as well as patient factors (e.g. disease process, renal failure) and therefore differs among individuals.

Effective Half-Life

The effective half-life is calculated fromboth the biological and physical half-lives.

1/effective half-life = 1/physical half-life + 1/biological half-life.

• The effective half-life is shorter than the biological or physical half-life.
• The dose received by an organ is proportional to the effective half-life.
• It differs among individuals for a given radiopharmaceutical according to disease state and physiological factor

1.2 Types of particles

• α-particle:
  • heavy: 2 neutrons & 2 protons
• β^– particle:
  • electron
• β⁺ particle:
  • anti-matter equivalent of an electron
  • same mass but positive charge
• ν (neutrino)
  • practically massless and chargeless
  • moves at speed of light, virtually never interacting with matter
  • difficult to detect

2. Types of Decay

2.1. Alpha decay

Occurs when the nucleus spontaneously ejects an alpha particle (identical to a helium nucleus).

ZAX → A-2A-4’X + 24α2+ + transition energy

• Typically occurs with heavy nuclides (A > 150 or Z > 83), often followed by gamma and characteristic x-ray emission.
• Heaviest and least penetration form of radiation.
• Not used in medical imaging due to short range and high linear energy transfer.

2.2. Beta-minus decay

A neutron is converted to a proton, an electron and an antineutrino.

• Occurs in a radionuclide with excess of neutrons
• The atomic number (Z) increases by 1
• Results in a daughter nucleus with a higher energy state, hence the nucleus undergoes de-excitation emitting a γ ray or a cascade of emissions

2.3. Beta-plus decay

A proton is converted to a positron (anti-matter equivalent of an electron with positive charge), a neutron and a neutrino.

• Occurs in proton-rich (or neutron-deficit) nuclides and where the parent isotope has at least 1022 keV in excess energy
• The atomic number (Z) decreases by 1
• The atomic mass remains the same (proton conversion to a neutron conserves mass)

2.4. Electron capture

A nucleus captures an orbiting electron (K shell), causing a proton to convert into a neutron. The vacancy in the inner shell is then filled by outer shell electrons, with the emission of a characteristic x-ray or Auger electron being emitted.

• Occurs in neutron-deficit radionuclides

e.g. A radionuclide with a neutron deficit may increase its number of neutrons by capturing an electron from the K-shell, which combines with a proton to form a neutron.

2.5. Gamma decay

Occurs when a radioactive nucleus first decays by the emission of an α or β particle. The daughter nucleus that results is usually left in an excited state and it can decay to a lower energy state by emitting a gamma ray photon.

More info on beta radiation

• It is emitted with a continuous spectrum of energy
• The maximum energy of the electron is dependent on the radionuclide material
• The distance travelled by a beta particle is inversely proportional to the density of the material through which it is travelling
• Like other secondary electrons, beta rays follow a random path in matter
• As these secondary electrons travel through tissue, some of their kinetic energy is transformed to heat energy.

Radiopharmaceuticals

• The half-life should ideally be a few hours, roughly equal to the time from injection to scanning. The biological half-life should be suited to the duration of the test but should not be unduly long in order to reduce the dose to the patient.
• It decays to a stable daughter in order to minimize the dose to the patient. 
• It should only accumulate in the target tissue.
• radionuclide should have a high specific activity, i.e. high activity per unit volume.
• The energy of the photon should be more than 100 keV Below 100 keV, scatter and attenuation within the patient become problematic, e.g. Tl-201.
• monoenergetic gamma rays are preferable as the pulse height analyser filters out scatter by accepting gamma rays that fall within a small energy window
• High-energy gamma rays are difficult to collimate and a proportion will also pass straight through the crystal of the gamma camera without being detected. Conversely low-energy gamma rays are absorbed by the patient and do not reach the gamma camera.
• Emission of pure gamma rays – gamma rays result in the formation of the image, whereas the beta particles
  deposit an unnecessary dose in the patient

Tc-99m

• 6 hour half-life
• The parent compound of Tc-99m is Mo-99, but it is produced following the emission of a negative beta particle. Tc-99m subsequently emits pure gamma rays to form its isomer Tc-99.
• Tc-99m emits gamma rays with 140 keV, which are suitable for imaging.