Limits...
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.


The total and Ps-formation cross-sections for positrons in water vapour.The full details of the cross-section used are detailed in2122232425.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4526868&req=5

f2: The total and Ps-formation cross-sections for positrons in water vapour.The full details of the cross-section used are detailed in2122232425.

Mentions: To this point, the formalism is quite general, the only restriction being non-relativistic kinetic theory is employed. In order to proceed with the calculation of the range numerical solution of the eigenvalue problem (12) is required. Cross-sections for the various positron scattering processes in the medium are required, in order to evaluate the collision terms in the collision operator (4) appearing in (12). In the case of a liquid water medium, sufficient cross-sections for a meaningful calculation are known only accurately below 100 eV, and this is the regime of focus for what follows. The best available sets have been detailed in2122232425 and references therein, and the important elastic and Ps-formation cross-sections used in the current study are presented in Fig. 2. Note, no attempt is made to compare our results to relevant parameters from PET measurements in the current study. A comprehensive, more accurate analysis of positron transport over the entire energy range relevant to PET (i.e. from keV to thermal energies) would require all the open channel scattering cross-sections from thermal energies to 500 keV to be known, and such cross-section data is currently not available. When a kinematically complete set of cross-sections does become available, simulations of PET like conditions and associated comparisons will be addressed.


Positron kinetics in an idealized PET environment.

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

The total and Ps-formation cross-sections for positrons in water vapour.The full details of the cross-section used are detailed in2122232425.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: The total and Ps-formation cross-sections for positrons in water vapour.The full details of the cross-section used are detailed in2122232425.
Mentions: To this point, the formalism is quite general, the only restriction being non-relativistic kinetic theory is employed. In order to proceed with the calculation of the range numerical solution of the eigenvalue problem (12) is required. Cross-sections for the various positron scattering processes in the medium are required, in order to evaluate the collision terms in the collision operator (4) appearing in (12). In the case of a liquid water medium, sufficient cross-sections for a meaningful calculation are known only accurately below 100 eV, and this is the regime of focus for what follows. The best available sets have been detailed in2122232425 and references therein, and the important elastic and Ps-formation cross-sections used in the current study are presented in Fig. 2. Note, no attempt is made to compare our results to relevant parameters from PET measurements in the current study. A comprehensive, more accurate analysis of positron transport over the entire energy range relevant to PET (i.e. from keV to thermal energies) would require all the open channel scattering cross-sections from thermal energies to 500 keV to be known, and such cross-section data is currently not available. When a kinematically complete set of cross-sections does become available, simulations of PET like conditions and associated comparisons will be addressed.

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.