A projection-domain low-count quantitative SPECT method for alpha-particle emitting radiopharmaceutical therapy

Single-photon emission computed tomography (SPECT) provides a mechanism to estimate regional isotope uptake in lesions and at-risk organs after administration of {\alpha}-particle-emitting radiopharmaceutical therapies ({\alpha}-RPTs). However, this estimation task is challenging due to the complex emission spectra, the very low number of detected counts, the impact of stray-radiation-related noise at these low counts, and the multiple image-degrading processes in SPECT. The conventional reconstruction-based quantification methods are observed to be erroneous for {\alpha}-RPT SPECT. To address these challenges, we developed a low-count quantitative SPECT (LC-QSPECT) method that directly estimates the regional activity uptake from the projection data, compensates for stray-radiation-related noise, and for the radioisotope and SPECT physics. The method was validated in the context of three-dimensional SPECT with 223 Ra. Validation was performed using both realistic simulation studies, including a virtual clinical trial, and synthetic and anthropomorphic physical-phantom studies. Across all studies, the LC-QSPECT method yielded reliable regional-uptake estimates and outperformed the conventional ordered subset expectation maximization (OSEM)-based reconstruction and geometric transfer matrix (GTM)-based post-reconstruction partial-volume compensation methods. Further, the method yielded reliable uptake across different lesion sizes, contrasts, and different levels of intra-lesion heterogeneity. Additionally, the variance of the estimated uptake approached the Cram\'e-Rao bound-defined theoretical limit.