An analytic approach to orthopositronium lifetime estimation in positronium lifetime imaging

The localization of hypoxic tumor regions is an important issue in medical imaging as hypoxic tumors worsen patient prognoses. A novel modality which may help to address this is Positronium Lifetime Imaging (PLI) which is an augmentation to Positron Emission Tomography (PET). Positronium (Ps) is the bound state between an electron and a positron and is abundantly formed during a normal PET scan. There are two types of Ps, orthopositronium (o-Ps) and parapositronium (p-Ps). The o-Ps lifetime is long enough that it can interact with its local environment before decaying into the familiar two 511 keV photons used in PET. When o-Ps interacts with an unpaired electron, it quickly decays, shortening its lifetime. Unpaired electrons are readily found in molecular oxygen, meaning the o-Ps lifetime may be a metric for oxygen concentration. Presented here is a novel method for o-Ps lifetime estimation in PLI. This method is analytic and is therefore faster than previous methods. The method was tested in simulated PET systems with timing resolutions of 200 ps and 600 ps, and total event counts of 1 × 10⁵ and 1 × 10⁶. Phantoms with various o-Ps lifetimes were generated and the lifetimes were estimated. The Root Mean Square Error (RMSE) was used for comparison to ground truth, and it was found that the best-case scenario occurred for a timing resolution of 200 ps and 1 × 10⁶ counts, where the minimum RMSE was 0.022±0.003 at the second ordered-subsets expectation-maximization iteration. The method contains tunable parameters which will be optimized in future work. The suppression of noise and increase of contrast will also be investigated. This method has potential to be a fast, monotonic estimation of the o-Ps lifetime.