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Positron kinetics in an idealized PET environment.

Robson RE, Brunger MJ, Buckman SJ, Garcia G, Petrović ZLj, White RD - Sci Rep (2015)

Bottom Line: Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue.Comparisons are made with the 'gas-phase' assumption used in current models in which coherent scattering is suppressed.Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.

View Article: PubMed Central - PubMed

Affiliation: College of Science, Technology and Engineering, James Cook University, Townsville QLD 4810, Australia.

ABSTRACT
The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the 'gas-phase' assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.

No MeSH data available.


Impact of coherent scattering effects on the elastic momentum transfer cross-section for positron-water scattering.The static structure factor for water used in presented in Fig. 426.
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f3: Impact of coherent scattering effects on the elastic momentum transfer cross-section for positron-water scattering.The static structure factor for water used in presented in Fig. 426.

Mentions: In Fig. 3, we highlight the modification to the scattering cross-section induced by coherent scattering effects, where we have used the static structure of Badyal et al.26 (see Fig. 4) for the calculation. The effect of coherent scattering is to significantly reduce the momentum transfer cross-section in the low energy range less than 20 eV. Above that energy, the de Broglie wavelength is sufficiently small that coherent scattering effects are significantly reduced, and the cross-section approaches that for binary scattering. Note, there can be modifications to the scattering potential, but that is not considered in this study.


Positron kinetics in an idealized PET environment.

Robson RE, Brunger MJ, Buckman SJ, Garcia G, Petrović ZLj, White RD - Sci Rep (2015)

Impact of coherent scattering effects on the elastic momentum transfer cross-section for positron-water scattering.The static structure factor for water used in presented in Fig. 426.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4526868&req=5

f3: Impact of coherent scattering effects on the elastic momentum transfer cross-section for positron-water scattering.The static structure factor for water used in presented in Fig. 426.
Mentions: In Fig. 3, we highlight the modification to the scattering cross-section induced by coherent scattering effects, where we have used the static structure of Badyal et al.26 (see Fig. 4) for the calculation. The effect of coherent scattering is to significantly reduce the momentum transfer cross-section in the low energy range less than 20 eV. Above that energy, the de Broglie wavelength is sufficiently small that coherent scattering effects are significantly reduced, and the cross-section approaches that for binary scattering. Note, there can be modifications to the scattering potential, but that is not considered in this study.

Bottom Line: Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue.Comparisons are made with the 'gas-phase' assumption used in current models in which coherent scattering is suppressed.Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.

View Article: PubMed Central - PubMed

Affiliation: College of Science, Technology and Engineering, James Cook University, Townsville QLD 4810, Australia.

ABSTRACT
The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the 'gas-phase' assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.

No MeSH data available.