Object independent scatter sensitivities for PET, applied to scatter estimation through fast Monte Carlo simulation

TL;DR

This work tackles the quantitative bias caused by scattered coincidences in PET by moving beyond cylinder-only scatter models to include detector physics through a 5D photon detection probability LUT. The LUT is integrated into a fast MC simulator (MCGPU-PET) to generate scatter sinograms that, when multiplied by a scatter sensitivity sinogram, yield object-aware scatter estimates. Across three simulated scenarios and two real Signa PET/MR acquisitions, the approach with a 5D LUT achieves near 1% global bias and robust local bias containment, closely matching vendor tail-fitted SSS in practice. The results demonstrate the feasibility of fast, detector-physics-informed MC scatter estimation, with implications for improved accuracy and noise robustness in clinical PET reconstructions.

Abstract

Scattered coincidences introduce quantitative bias in positron emission tomography (PET) and must be compensated during reconstruction. Conventional scatter estimates typically rely on simplified cylindrical scanner models that omit detector physics. Incorporating detector sensitivities for scatter is challenging because scattered events exhibit less constrained properties, such as incidence angles, compared to true coincidences. We integrated a 5D single-photon detection probability lookup table (LUT) accounting for photon energy, incidence angle, and detector location into the simulator logic. The resulting scatter sinogram is scaled by a precomputed, LUT-specific scatter sensitivity sinogram. Scatter was simulated using MCGPU-PET, a fast Monte Carlo (MC) simulator with a simplified scanner model, and applied to phantom data from a simulated GE Signa PET/MR in GATE. We evaluated three scenarios: (1) high-count MC simulations from a known activity distribution; (2) limited-count simulations; and (3) joint estimation of activity and scatter under low-count conditions. The method was also tested on two real Signa PET/MR acquisitions. In scenario 1, scatter-compensated reconstructions achieved <1% global bias in all active regions. In scenario 2, noisy scatter estimates caused positive bias, but Gaussian smoothing restored accuracy to scenario 1 levels. In scenario 3, joint estimation maintained <1% bias in nearly all regions. For real scans, the MC-based scatter estimate closely matched the vendor-provided scatter estimate. This proof-of-concept demonstrates that scatter sensitivity modeling can enhance simulators by incorporating detector physics. It supports the feasibility of using fast MC simulations for real scans, offering improved accuracy and robustness to acquisition noise in clinical PET reconstruction.

Figures (14)

• Figure 1: This schematic shows the difference in possible photon incidence angles for the same LOR. True coincidences (red) have a very limited distribution, as the two photons always travel along a straight line through the annihilation point. Scattered coincidences (green and blue) can connect the two detectors with a much larger degree of freedom, resulting in a larger possible distribution for the angles of incidence. The shape of this distribution is also correlated with the remaining photon energy.
• Figure 2: Voxelized representations of activity and attenuation for all 3 phantoms used in this study. The outline of the activity images is shown in red on the attenuation images.
• Figure 3: Schematic overview of our approach to scatter simulation. The simulator requires an activity and attenuation image as inputs, and outputs a list of coincidences. These coincidences are unlisted into an output sinogram which takes the photon detection probability LUT into account (LUT scatter), which is multiplied with the corresponding scatter sensitivity sinogram to produce the final scatter estimate (LUT scatter $\times$ sensitivity).
• Figure 4: Crystal definitions for MCGPU-PET and the detection probability LUT. The crystal that a photon is assigned to is selected based on the location of the intersection of the photon with the MCGPU-PET detector cylinder, located at the depth of interaction. Both the axial and transaxial configurations include virtual crystals, one for each side of the gaps between blocks.
• Figure 5: Angular definitions for the detection probability LUT. The (trans)axial angle is defined as the angle that the photon path makes in the (trans)axial plane with the position vector of its intersection with the detector cylinder. The range of both angles is [-90,90] degrees.