Bias reduction in Y-90 PET with reconstruction that relaxes the non-negativity constraint

Objectives: Y-90 PET is complex due to the very low probability positrons in the presence of increased singles events from bremsstrahlung photons and gammas from natural radioactivity in Lu based crystals used in some PET systems. Due to these attributes of Y-90, positive bias in cold regions and underestimation in hot regions of interest are reported in many Y-90 PET papers when using conventional EM reconstruction. This bias is introduced by the current standard PET reconstruction algorithms that enforce a nonnegativity constraint in the image domain. In this work, we evaluate image reconstruction algorithms that relax this constraint, including a method that we recently proposed, for potential reduction of bias in the low count-rate setting clinically realistic in Y-90 PET.

Methods: We used an anthropomorphic liver/lung torso phantom with total activity and distribution that is clinically realistic for imaging following radioembolization with Y-90 microspheres: 5% lung shunt, 1.2 MBq/mL in liver, 3 hepatic lesions (8 and 14 mL spheres, 30 mL ovoid) of 6.5 MBq/mL. The phantom was scanned for 30 minutes on a Siemens Biograph mCT PET/CT on day 0 and day 3 with total activity of 2.0 and 1.0 GBq respectively. Four different reconstruction algorithms were implemented in-house: (1) Standard Expectation Maximization (EM) algorithm used in the clinic, (2) regularized Separable Paraboloidal Surrogates (SPS) algorithm, (3) regularized NEG-ML-Reg algorithm and (4) regularized Alternating Direction Method of Multipliers (ADMM-Reg) algorithm. EM and SPS enforce the non-negativity constraint in the image domain. NEG-ML, where Poisson likelihood function is replaced by Gaussian distribution when the estimated measurement is below the switching parameter, has been proposed for the bias reduction in low-count-rate settings. ADMM(-Reg) is an algorithm that we recently proposed for the reduction of bias in Y-90 PET. The algorithm relaxes the conventional image-domain nonnegativity constraint by instead imposing a positivity constraint on the predicted measurement (projection) mean. The advantage of ADMM(-Reg) over NEG-ML(-Reg) is the absence of parameter tunning. Neither NEG-ML-Reg or ADMM-Reg has been evaluated previously with measured Y-90 PET data. We evaluate each algorithm by calculating the contrast recovery (relative to truth) of the hepatic lesions and the relative standard deviation of the liver background.

Results: We compared 10th iterations of EM to the 100th iterations of regularized methods (SPS-Reg, NEG-ML-Reg, ADMM-Reg) because EM algorithm without regularization needs to stop before convergence to have an acceptable noise level. Between regularized methods (2) - (4), ADMM-Reg achieved highest contrast recovery in both data acquisition points (day 0, day 3). The average of 3 hepatic lesions contrast recovery in day 0 was 81%, 72%, 65% and 61% when the image was reconstructed using ADMM-Reg, NEG-ML-Reg, SPS-Reg and EM respectively. ADMM-Reg also gave the highest relative standard deviation, but this can be controlled by increasing the value of the regularization parameter. We also visually compared the reconstructed images with patient data. ADMM and NEG-ML achieved higher contrast between enhancing and necrotic regions of a lesion.

Conclusions: Quantification of Y-90 PET reconstruction is enhanced by allowing negative values in image domain. Phantom measurements show that our implementation (ADMM-Reg) gave highest contrast recovery at the cost of increased noise, which, however can be controlled by regularization. Research Support: NIH R01EB022075