Maximum likelihood estimation yields accurate line-of-response assignment for positron + prompt gamma ray events in multiplexed PET (mPET)

For accurate disease characterization using positron emission tomography (PET), it is desirable to image multiple radiotracers in a single scan. Conventional PET methods cannot do this due to the indistinguishable annihilation photons produced by different radiotracers. One approach is to label one radiotracer with a positron+prompt-gamma (β⁺\!\!-\!\!γ) isotope producing triple coincidences, and another with a pure positron-emitting (β⁺) isotope producing double coincidences. However, β⁺\!\!-\!\!γ emitters present challenges in correctly identifying the two annihilation photons, or equivalently, assigning the correct line-of-response (LOR) to triple-photon coincidence events. Here, we propose a maximum likelihood estimation (MLE) framework leveraging spatial, timing, and energy information to determine the most probable LOR. Simulation studies validated the method: simulations showed over 96% and 94% accuracy for LOR assignment of β⁺\!\!-\!\!γ emitters ²²Na and ¹²⁴I point sources, respectively. Furthermore, simulated phantom imaging of ²²Na or ¹²⁴I distributions alongside a β⁺ emitter demonstrated that MLE LOR assignment achieved comparable image quality-measured by contrast recovery coefficient (CRC) and cross-talk ratio (XR)-to benchmark methods, where the prompt gamma was identified using an energy threshold (≥ 650 keV) for ²²Na and as the highest-energy photon for ¹²⁴I.