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Positron range in PET imaging: an alternative approach for assessing and correcting the blurring

Abstract : Positron range impairs resolution in PET imaging, especially for high-energy emitters and for small-animal PET. De-blurring in image reconstruction is possible if the blurring distribution is known. Furthermore, the percentage of annihilation events within a given distance from the point of positron emission is relevant for assessing statistical noise. This paper aims to determine the positron range distribution relevant for blurring for seven medically relevant PET isotopes, $^{18}$F, $^{11}$C, $^{13}$N, $^{15}$O, $^{68}$Ga, $^{62}$Cu and $^{82}$Rb, and derive empirical formulas for the distributions. This paper focuses on allowed-decay isotopes. It is argued that blurring at the detection level should not be described by the positron range $r$, but instead the 2D projected distance $\delta$ (equal to the closest distance between decay and line of response). To determine these 2D distributions, results from a dedicated positron track-structure Monte Carlo code, Electron and POsitron TRANsport (EPOTRAN), were used. Materials other than water were studied with PENELOPE. The radial cumulative probability distribution G$_{2D}$($\delta$) and the radial probability density distribution $g_{2D}$($\delta$) were determined. G$_{2D}$($\delta$) could be approximated by the empirical function 1 - exp(-$A \delta^2$ - $B \delta$), where A = 0.0266 ($E_{mean}$)$^{-1.716}$ and B = 0.1119 ($E_{mean}$)$^{-1.934}$, with $E_{mean}$ being the mean positron energy in MeV and $\delta$ in mm. The radial density distribution $g_{2D}$($\delta$) could be approximated by differentiation of G$_{2D}$($\delta$). Distributions in other media were very similar to water. The positron range is important for improved resolution in PET imaging. Relevant distributions for the positron range have been derived for seven isotopes. Distributions for other allowed-decay isotopes may be estimated with the above formulas.
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L Jødal, C. Le Loirec, C. Champion. Positron range in PET imaging: an alternative approach for assessing and correcting the blurring. Physics in Medicine and Biology, IOP Publishing, 2012, 57 (12), pp.3931-3943. ⟨10.1088/0031-9155/57/12/3931⟩. ⟨cea-02134410⟩

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