A general framework to study positron range distributions

The positron range, that is, the distance from the positron emission point to the annihilation one in β⁺ decay, limits the spatial resolution of PET images. Thus, any realistic simulation of PET acquisitions must include this effect as accurately as possible. Positron range distributions have been computed and compared in the literature. Not all authors present it in the same way. For instance, accumulated range distributions, 1D projection of the positrons annihilation coordinates, or angular integrated 3D radial distributions, have been used. Any of these presentations may emphasize a different physical property. Thus it is difficult to perform a meaningful comparison of the results obtained by different authors. The aim of this work is to present a general framework to compare positron range distributions. We use a genetic algorithm to fit the radial, angle integrated, g^3D(r) distribution of the annihilation points to any positron annihilation distribution chosen as reference. Therefore, given a positron range distribution presented in a certain way, we can obtain the distributions, first fitting g^3D and then using the relations between distributions. Using this procedure, positron range distributions available in the literature are compared with the ones computed with the simulation package PeneloPET.