Uncertainty Propagation From Projections to Region Counts in Tomographic Imaging: Application to Radiopharmaceutical Dosimetry

Radiopharmaceutical therapies (RPTs) pre- sent a major opportunity to improve cancer therapy. Although many current RPTs use the same injected activity for all patients, there is interest in using absorbed dose measurements to enable personalized prescriptions. However, image-based absorbed dose calculations incur uncertainties from calibration factors, partial volume effects and segmentation methods. While previously published dose estimation protocols incorporate these uncertainties, they do not account for uncertainty that originates from Poisson noise in the projection data that gets propagated through reconstruction algorithms. This effect should be accounted for to adequately estimate the total uncertainty in absorbed dose estimates. This paper proposes a computationally practical algorithm that propagates uncertainty from projection data through clinical reconstruction algorithms to obtain uncertainties on the total activity within volumes of interest (VOIs). The algorithm is first validated on ${}^{{177}}$ Lu and ${}^{{225}}$ Ac phantom data by comparing estimated uncertainties from individual SPECT acquisitions to empirical estimates obtained from multiple acquisitions. It is then applied to (i) Monte Carlo and (ii) multi-time point ${}^{{177}}$ Lu-DOTATATE and ${}^{{225}}$ Ac-PSMA-617 patient data for time integrated activity (TIA) uncertainty estimation. The outcomes of this work are two-fold: (i) the proposed uncertainty estimation algorithm is validated, and (ii) the propagation of VOI uncertainties to TIA uncertainty is validated with Monte Carlo data and applied to patient data. The proposed algorithm is made publicly available in the open-source image reconstruction library PyTomography and in the SPECT reconstruction extension of 3D Slicer.