Simultaneous Multi-Isotope PET: A Computational Framework for Line of Response (LOR) Identification

PET imaging using non-pure positron emitters as radiotracers can be used to simultaneously image distributions of different molecules. We study the use of radionuclides that emit a high energy gamma in conjunction with positrons, producing triple coincidences. A given triple coincidence could be a true coincidence corresponding to two annihilation photons and a high energy gamma emitted from the same source, or it could be a random triple coincidence arising from different sources. We develop an algorithm to identify true triple coincidences and the correct line of response (LOR) within these coincidences. We employ a probabilistic approach to the identification problem through synthesizing geometric, spatial, energy, and temporal information. These criteria are used to create a joint MLE representing the probability that a given set of particles is a true triple coincidence and contains a valid LOR. This approach allows for more accurate identification of true triple coincidences as opposed to only using a high energy threshold. For proof of concept image reconstruction, we use GATE Monte Carlo simulations. With a simple phantom composed of three spheres, we correctly identified 99% of true triple coincidences and 97% of true double coincidences for image reconstruction. Further correction factors should be implemented to obtain more accurate images.