Positron range modeling for statistical PET image reconstruction

Positron range is one of the factors that fundamentally limits the spatial resolution of PET images. With the higher resolution of small animal imaging systems and increased interest in using higher energy positron emitters, it is important to consider range effects when designing image reconstruction methods. The positron range distribution can be measured experimentally or calculated using approximate analytic formulae or Monte Carlo simulations. We investigate the use of this distribution within a MAP image reconstruction framework. Positron range is modeled as a blurring kernel and included as part of the forward projection matrix. We describe the use of a 3D isotropic shift-invariant blur kernel, which assumes that positrons are propagating in a homogeneous medium and is computed by Monte Carlo simulation using EGS4. We also propose a new shift-variant blurring model for positron range that accounts for spatial inhomogeneities in the positron scatter properties of the medium. Monte Carlo simulations, phantom, and animal studies with the isotopes Cu-60 and Cu-64 are presented.