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Relating β+ radionuclides’ properties by order theory


We studied 27 β+ radionuclides taking into account some of their variants encoding information of their production, such as integral yield, threshold energy and energy of projectiles used to generate them; these radionuclides are of current use in clinical diagnostic imaging by positron emission tomography (PET). The study was conducted based on physical, physico-chemical, nuclear, dosimetric and quantum properties, which characterise the β+ radionuclides selected, with the aim of finding meaningful relationships among them. In order to accomplish this objective the mathematical methodology known as formal concept analysis was employed. We obtained a set of logical assertions (rules) classified as implications and associations, for the set of β+ radionuclides considered. Some of them show that low mass defect is related to high and medium values of maximum β+ energy, and with even parity and low mean lives; all these parameters are associated to the dose received by a patient subjected to a PET analysis.

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  1. An enriched target allows obtaining a high purity radionuclide; however the process is expensive. Even though, for the production of 18F in a cyclotron facility, one of the most widely used β+ radionuclide in PET; it is necessary to use an expensive enriched target (H 182 O, 18O > 95%).

  2. In our study, the maximum energy of projectiles was divided into three ranges: low (E < 14.7 MeV), medium (E = 14.8–59.0 MeV) and high energies (E = 60–110 MeV) (Table 4).

  3. Although the desired property is zero β decay in diagnostic image, 64Cu has proven to be very suitable for combining PET imaging and targeted therapy [17, 32], as it has three decay modes.

  4. Endpoint energy of a β+ decay is the kinetic energy of all positrons emitted through β+ decay. Since the surplus in energy has to be divided between the positron and the neutrino, there is a continuous energy spectrum for the positron up to the maximum energy [16].


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N. Y. Quintero thanks G. A. Aranda-Corral and M. Bal for their support and discussions about the application of FCA. Several scientists belonging to FCA community cited in the references are acknowledged for their enriching comments. G. Restrepo specially thanks the Universidad de Pamplona for the financial support to conduct this research.

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Correspondence to Nancy Y. Quintero.

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Quintero, N.Y., Restrepo, G. & Cohen, I.M. Relating β+ radionuclides’ properties by order theory. J Radioanal Nucl Chem 298, 1937–1946 (2013).

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  • β+ Radionuclides
  • Positron emission tomography
  • Formal concept analysis
  • Statistical data analysis
  • Association rules