Calculation of positron range and its effect on the fundamental limit of positron emission tomography system spatial resolution

Developments in positron emission tomography (PET) technology have resulted in systems with finer detector elements designed to further improve spatial resolution. However, there is a limit to what extent reducing detector element size will improve spatial resolution in PET. The spatial resolution of PET imaging is limited by several other factors, such as annihilation photon noncollinearity, positron range, off-axis detector penetration, detector Compton scatter, undersampling of the signal in the linear or angular directions for the image reconstruction process, and patient motion. The overall spatial resolution of the systems is a convolution of these components. Of these other factors that contribute to resolution broadening, perhaps the most uncertain, poorly understood, and, for certain isotopes, the most dominant effect is from positron range. To study this latter effect we have developed a Monte Carlo simulation code that models positron trajectories and calculates the distribution of the end point coordinates in water for the most common PET isotopes used: F-18, N-13, C-11 and O-15. In this work we present some results from these positron trajectory studies and calculate what effect positron range has on the overall PET system spatial resolution, and how this influences the choice of PET system design parameters such as detector element size and system diameter. We found that the fundamental PET system spatial resolution limit set from detector size, photon non-collinearity and positron range alone varied from nearly 1 mm FWHM (2 mm FWTM) for a 10-20 cm diameter system typical for animal studies with F-18 to roughly 4 mm FWHM (7 mm FWTM) for an 80 cm diameter system typical for human imaging using O-15.