Physics of Medical Scans
Radiotracers and Cyclotrons
To fully understand the explanations here, please first read the PET – advanced webpage.
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PET Radiotracers
Through time, many different radiotracers have been used in PET scanning. Fluorine-18 is the most widely used today, injected into patients in the form of the compound fluorodeoxyglucose (FDG). This radiotracer has a half-life of 110 minutes, which is long enough for activity to remain considerable while scans are taken but short enough for activity to decrease to negligible levels in a patient in a reasonable timescale. The emitted positron from the decay of FDG has a tissue range (the mean distance travelled by the positron before it decays) of 2.3mm. This yields high resolution scans with minimised radiation doses for the patient. [1]
Unlike carbon, nitrogen, and oxygen, which are key elements in biological systems with a natural positron-emitting radioisotope, fluorine does not normally occur in biological systems. Fluorine can, however, replace hydrogen atoms or organic groups containing hydrogen in organic molecules. The half-life of its positron emitting radioisotope is more suitable for PET scanning than the other elements, whose shorter half-lives require unrealistic production and delivery times. It is for this reason, combined with its relative ease of production, that fluorine-18 is so widely used as a radiotracer in modern medicine. [3]
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Production of Radiotracers: Cyclotrons
The short half-life of the radiotracers means that they are normally produced by hospitals on-site. Hospitals with PET scanners usually have on-site cyclotrons for this process. Cyclotrons are particle accelerators that accelerate charged particles to high speeds before directing them onto targets that (in a nuclear reaction) produce a radioisotope. When accelerated to high energies, these charged particles are made to collide with the nuclei of other elements. The electrical repulsion between the particles is overcome by the high energy of the inbound particle. After overcoming these forces, the nucleons can interact and form new, radioactive isotopes.
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A cyclotron accelerates particles through the use of an electric field. The limited strength of an electric field means that cyclotrons use the repeated crossing of the gaps between electrodes to accelerate particles. Within electrodes, there is no electric field, so the voltage can change polarity but has no effect on the beam. This polarity switch happens whilst the beam is travelling through an electrode, so that it can again experience an accelerating field when it crosses the electrode gap. [5]
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The centripetal force needed to produce a circular orbit, with radius r, of a particle with mass m, speed v, and charge q, in a magnetic field B, is given by
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(1)
The time, T, that a particle needs to make a full revolution is given by
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(2)
Therefore, the revolution frequency (the inverse of time) is not dependent on the radius of the beam orbit, nor the energy of the beam. As the electric field must switch in phase with these revolutions, it is also independent of the radius and energy of the beam. From Eq. (2) it follows that, for a given particle mass and charge, the revolution frequency only depends on the magnetic field. This is the basic principle of the cyclotron operation. [5]
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The kinetic energy, ,of a particle accelerated by a cyclotron is given by [6]:
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(3)
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A cyclotron consists of two large permanent dipole magnets (‘dees’ – see fig. 1), producing a permanent, downward-facing, semi-circular magnetic field. These magnets are placed back-to-back, with a small gap between them. An alternating magnetic field is produced between the two dees, and it is this that accelerates the particles as they repeatedly cross it on their outward spiral path. The field switches polarity with the angular frequency of the beam.
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Most commonly, medical cyclotrons for PET radioisotopes have a beam energy of between 15 and 25MeV. Unlike higher energy cyclotrons (which are used in the production of photon emitting radioisotopes, like Iodine-131 for SPECT scanning), which require a large infrastructure and have high costs, these accelerators are compact, cost-effective and easily installed in a hospital facility. [5]
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Synthesising FDG
The most common method for producing fluorine-18 is by bombarding oxygen-18 (a stable, naturally occurring isotope of oxygen) with high energy protons. Upon interaction of the high energy proton with the oxygen nucleus, a neutron is emitted, leaving fluorine-18. Normally, oxygen-18 enriched water is used for this process. [3]
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To synthesise FDG from flourine-18, the fluorine-18 must be recovered from the target water. A small amount of potassium carbonate is normally dissolved into the water, so the fluorine-18 reacts to form potassium fluoride, which can be more easily recovered. Chemical reactions including basic hydrolysis, and reaction with tetra acetyl mannose (a type of sugar) produces the required optical isomer of FDG.
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In hospital laboratories, the process in automated in a computer- controlled system. Irradiation of the oxygen-18 and synthesis of FDG can all be remotely controlled, reducing radiation exposure and increasing reproducibility. [3]
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References:
[1] Basu, S. et al. (2011). Fundamentals of PET and PET-CT scanning, New York: New York Academy of Sciences. pp. 8-11.
[2] Schippers, J. M. (no date). Cyclotrons for Particle Therapy. Switzerland: Paul Scherrer Institut.
[3] Jadvah, H and Parker, J. A. (2005). Clinical PET and PET CT. New York: Springer. pp. 45-67
[4] Ionization. Available at: https://www.britannica.com/science/ionization[Accessed 22/02/19].
[5] Braccini, F. (2016). Compact medical cyclotrons and their use for radioisotope production and multi-disciplinary research.Laboratory for High Energy Physics, University of Bern, Switzerland. pp. 229-232.
[6] Dewan, L. (2007). Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV.Massachusetts Institute of Technology. p.6.
[7] Half-Life. Available at: https://www.britannica.com/science/half-life-radioactivity [Accessed 22/02/19].
What is half-life?
Radioactive half-life is the time required for one half of the radioactive nuclei in a sample to decay (or equivalently, it is the time required for the radioactive activity to decrease to half its initial value. [2]
Figure 1: Diagram of a simple cyclotron being used to accelerate protons. The proton beam follows the dotted track shown.
(Image source: Hemantmore)
