On the implementation of acollinearity in PET Monte Carlo simulations

Objective. Acollinearity of annihilation photons (APA) introduces spatial blur in positron emission tomography (PET) imaging. This phenomenon increases proportionally with the scanner diameter and it has been shown to follow a Gaussian distribution. This last statement can be interpreted in two ways: the magnitude of the acollinearity angle, or the angular deviation of annihilation photons from perfect collinearity. As the former constitutes the partial integral of the latter, a misinterpretation could have significant consequences on the resulting spatial blurring. Previous research investigating the impact of APA in PET imaging has assumed the Gaussian nature of its angular deviation, which is consistent with experimental results. However, a comprehensive analysis of several simulation software packages for PET data acquisition revealed that the magnitude of APA was implemented as a Gaussian distribution. Approach. We quantified the impact of this misinterpretation of APA by comparing simulations obtained with GATE, which is one of these simulation programs, to an in-house modification of GATE that models APA deviation as following a Gaussian distribution. Main results. We show that the APA misinterpretation not only alters the spatial blurring profile in image space, but also considerably underestimates the impact of APA on spatial resolution. For an ideal PET scanner with a diameter of 81 cm, the APA point source response simulated under the first interpretation has a cusp shape with 0.4 mm FWHM. This is significantly different from the expected Gaussian point source response of 2.1 mm FWHM reproduced under the second interpretation. Significance. Although this misinterpretation has been found in several PET simulation tools, it has had a limited impact on the simulated spatial resolution of current PET scanners due to its small magnitude relative to the other factors. However, the inaccuracy it introduces in estimating the overall spatial resolution of PET scanners will increase as the performance of newer devices improves.