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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.


Schematic for the idealised PET model. A spherical source of radius r′ emits positrons isotropically with a range of speeds v′ at a steady state into a medium of temperature T.
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f1: Schematic for the idealised PET model. A spherical source of radius r′ emits positrons isotropically with a range of speeds v′ at a steady state into a medium of temperature T.

Mentions: To simplify the analysis and elucidate the essential physics, we take an idealized, spherically symmetric situation in which high energy positrons of mass m and charge e are emitted isotropically at a steady rate from a spherical source into an infinite, spatially homogeneous soft matter medium at temperature T (see Fig. 1). The model also assumes that a steady state has been attained whereby there is a balance between the rate at which positrons are produced at the source and the rate at which they are lost (by direct annihilation and Ps formation) in the medium.


Positron kinetics in an idealized PET environment.

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

Schematic for the idealised PET model. A spherical source of radius r′ emits positrons isotropically with a range of speeds v′ at a steady state into a medium of temperature T.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Schematic for the idealised PET model. A spherical source of radius r′ emits positrons isotropically with a range of speeds v′ at a steady state into a medium of temperature T.
Mentions: To simplify the analysis and elucidate the essential physics, we take an idealized, spherically symmetric situation in which high energy positrons of mass m and charge e are emitted isotropically at a steady rate from a spherical source into an infinite, spatially homogeneous soft matter medium at temperature T (see Fig. 1). The model also assumes that a steady state has been attained whereby there is a balance between the rate at which positrons are produced at the source and the rate at which they are lost (by direct annihilation and Ps formation) in the medium.

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.