SPLIT: Statistical Positronium Lifetime Image Reconstruction via Time-Thresholding

Abstract

Positron emission tomography (PET) is a widely utilized medical imaging modality that uses positron-emitting radiotracers to visualize biochemical processes in a living body. The spatiotemporal distribution of a radiotracer is estimated by detecting the coincidence photon pairs generated through positron annihilations. In human tissue, about 40% of the positrons form positroniums prior to the annihilation. The lifetime of these positroniums is influenced by the microenvironment in the tissue and could provide valuable information for better understanding of disease progression and treatment response. Currently, there are few methods available for reconstructing high-resolution lifetime images in practical applications. This paper presents an efficient statistical image reconstruction method for positronium lifetime imaging (PLI). We also analyze the random triple-coincidence events in PLI and propose a correction method for random events, which is essential for real applications. Both simulation and experimental studies demonstrate that the proposed method can produce lifetime images with high numerical accuracy, low variance, and resolution comparable to that of the activity images generated by a PET scanner with currently available time-of-flight resolution.

Fig. 1.

The prompt and delayed time windows. The prompt window is comprised of one 511-keV time window and one prompt-gamma time window. All the boundary values of the time windows displayed are with respect to the time point of the reference 511-keV event. The second 511-keV photon is searched in a range no further than T₅₁₁ into the future; the prompt gamma is searched in a range across the reference time point spanned by Ta and T_b, representing a past and a future time point respectively. Ta and T_b should satisfy $-T_a>T_c^M$ and $-T_b<T_1$, respectively. The prompt time window yields true events as well as all the three types of random events. The delayed windows consist of at least one shifted 511-keV or prompt-gamma time window. Each of the delayed time window yields one or two types of random events.

Fig. 2.

General workflow of the SPLIT method with random events correction.

Fig. 3.

The ground truth lifetime image and the mean and s.d. images of the lifetime images reconstructed by the list-mode ML and the SPLIT methods.

Fig. 4.

The lifetime-measurement histograms of the trues, prompts, estimated randoms, and estimated trues (prompts – randoms) in the simulation study. The true events were obtained by examining the eventID output by GATE.

Fig. 5.

Left: the simulated activity distribution and the activity image of the PLI events reconstructed by standard TOF system matrix. The contrast is not well recovered in the activity image because ⁴⁴Sc has a long positron range. Right: the lifetime images reconstructed by the direct TOF-BP and SPLIT methods. The SPLIT method was tested with the (e) true and (f) pre-estimated short lifetime values. The direct TOF-BP method used the true short lifetimes.

Fig. 6.

(a) The spatial histogram of the events localized by the direct TOF-BP (dTOF-BP, top row) and activity image reconstructed by OSEM (bottom row) at the original and the virtually shrunk (scale of 1/30) source separations. (b) Reconstructed lifetime images of the four sources by the direct TOF-BP (top row) and SPLIT (bottom row) at different source separations.

Fig. 7.

Energy spectra of a source emitting 511-keV photon pairs and a source emitting 1157-keV (energy of the prompt gamma of Sc-44) photons.