Single photon emission computed tomography (SPECT) can enable the quantification of activity uptake in lesions and at-risk organs in α-particle-emitting radiopharmaceutical therapies (α-RPTs). However, this quantification is challenged by the extremely low detected photon counts, complicated isotope physics, and the image-degrading effects in α-RPT SPECT. Thus, strategies to optimize the SPECT system and protocol designs for the task of regional uptake quantification are much needed. Objectively performing this task-based optimization requires a reliable (accurate and precise) regional uptake quantification method. Conventional reconstruction-based quantification (RBQ) methods have been observed to be erroneous for α-RPT SPECT. Projection-domain quantification methods, which estimate regional uptake directly from SPECT projections, have demonstrated potential in providing reliable regional uptake estimates, but these methods assume constant uptake within the regions, an assumption that may not hold. To address these challenges, we propose Wiener INtegration Projection-Domain Quantification (WIN-PDQ), a Wiener-estimator-based projection-domain quantitative SPECT method. The method accounts for the heterogeneity within the regions of interest while estimating mean uptake. An early-stage evaluation of the method was conducted using 3D Monte Carlo-simulated SPECT of anthropomorphic phantoms with 223Ra uptake and lumpy-model-based intra-regional uptake heterogeneity. In this evaluation with phantoms of varying mean regional uptake and intra-regional uptake heterogeneity, the WIN-PDQ method yielded ensemble unbiased estimates and significantly outperformed both reconstruction-based and previously proposed projection-domain quantification methods in terms of normalized root ensemble mean squared error. In conclusion, based on these preliminary findings, the proposed WIN-PDQ method is showing potential for estimating mean regional uptake in α-RPTs and towards enabling the objective task-based optimization of SPECT system and protocol designs.
Objective evaluation of quantitative imaging (QI) methods with patient data is highly desirable, but is hindered by the lack or unreliability of an available gold standard. To address this issue, techniques that can evaluate QI methods without access to a gold standard are being actively developed. These techniques assume that the true and measured values are linearly related by a slope, bias, and Gaussian-distributed noise term, where the noise between measurements made by different methods is independent of each other. However, this noise arises in the process of measuring the same quantitative value, and thus can be correlated. To address this limitation, we propose a no-gold-standard evaluation (NGSE) technique that models this correlated noise by a multi-variate Gaussian distribution parameterized by a covariance matrix. We derive a maximum-likelihood-based approach to estimate the parameters that describe the relationship between the true and measured values, without any knowledge of the true values. We then use the estimated slopes and diagonal elements of the covariance matrix to compute the noise-to-slope ratio (NSR) to rank the QI methods on the basis of precision. The proposed NGSE technique was evaluated with multiple numerical experiments. Our results showed that the technique reliably estimated the NSR values and yielded accurate rankings of the considered methods for 83% of 160 trials. In particular, the technique correctly identified the most precise method for ∼ 97% of the trials. Overall, this study demonstrates the efficacy of the NGSE technique to accurately rank different QI methods when the correlated noise is present, and without access to any knowledge of the ground truth. The results motivate further validation of this technique with realistic simulation studies and patient data.
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