  Thorium-227-based alpha-particle radiopharmaceutical therapies (alpha-RPTs) are currently being investigated in several clinical and pre-clinical studies. After administration, Thorium-227 decays to Radium-223, another alpha-particle-emitting isotope, which redistributes within the patient. Reliable dose quantification of both Thorium-227 and Radium-223 is clinically important, and SPECT can perform this quantification as these isotopes also emit gamma-ray photons. However, reliable quantification is challenging for several reasons: the orders-of-magnitude lower activity compared to conventional SPECT, resulting in a very low number of detected counts, the presence of multiple photopeaks and substantial overlap in the emission spectra of these isotopes. To address these issues, we propose a multiple-energy-window projection-domain quantification (MEW-PDQ) method that jointly estimates the regional activity uptake of both Thorium-227 and Radium-223 directly using the SPECT projection data from multiple energy windows. We evaluated the method with realistic simulation studies conducted with anthropomorphic digital phantoms, including a virtual imaging trial in the context of imaging patients with bone metastases of prostate cancer who were treated with Thorium-227-based alpha-RPTs. The proposed method yielded reliable regional uptake estimates of both isotopes and outperformed state-of-art methods across different lesion sizes, contrasts, and varying levels of intra-lesion heterogeneity. This superior performance was also observed in the virtual imaging trial. Additionally, the variance of the estimated uptake approached the Cram\'er-Rao lower bound-defined theoretical limit. These results provide strong evidence in support of this method for reliable uptake quantification in Thorium-227-based alpha-RPTs. 
Joint regional uptake quantification of Thorium-227 and Radium-223 using   a multiple-energy-window projection-domain quantitative SPECT method