Researchers at Yale University are examining a new option: MOLAR (motion-compensation OSEM list-mode algorithm for resolution-recovery reconstruction), an algorithm that uses the original list-mode data rather than creating a sinogram. "List-mode-based reconstruction preserves the original spatial and temporal information of detected coincidence events," explained author Yiqiang Jian. "It is well recognized that list-mode data are substantially useful in motion correction and dynamic PET reconstruction."

Using simulations and phantom studies, Jian and colleagues showed that MOLAR decreases bias to reasonable levels, even for an extremely low number of counts (Phys. Med. Biol. 60 15).

Brain simulations

The Yale team first examined a simulated 3D brain PET image. They modelled the HRRT PET system to simulate list-mode data, and then down-sampled the high-count data list (containing 500 M events) by 10, 100, 500 and 2500 to generate low-count sample lists with noise equivalent count (NEC) levels of 50 M, 5 M, 1 M and 0.2 M. They note that the "ultra-low" 0.2 M count level was lower than seen in any single frame of human brain reconstruction on the HRRT.

Three regions-of-interest (ROIs) were defined in the image: cerebellum (low-activity voxels), thalamus (high-activity voxels) and striatum (high-activity voxels). The researchers applied the ROIs to all reconstructed images and calculated the bias and coefficient of variation (CoV) for each ROI at each count level. They performed two experiments: one using data containing only true coincidence events (Soff); and one with 30% scattered and 10% random events added to the simulated data (Son).

For the Soff experiment, no visual indication of bias was seen in the mean reconstructed images, though the 0.2 M mean image appeared noisier. Results showed that, for a fixed number of effective iterations (iterations x subsets), both bias and variance increased as count levels decreased. Bias values in all three ROIs were small, in the range of –0.5% to –5%, with the largest bias of –4.2% seen in striatum at 0.2 M NEC. They note that the observed bias was always negative, and substantially lower than previously reported for low-count-level HRRT reconstructions.

To investigate the impact of subset number, the researchers reconstructed images using one, five, 10, 15 and 30 subsets. For fair comparison, iterations were increased to maintain a constant number of effective iterations. In the ultra-low-count reconstruction, bias and variance both increased with increasing subset number. The striatum showed the largest underestimation, with bias and CoV of –4.2% and 2.9%, respectively, in the 30-subset reconstruction, reducing to –2.9% and 1.9% in the one- subset reconstruction.

The Son experiment revealed a similar dependency of bias and variability on counts and subsets, but with greater bias. For example, in the 0.2 M NEC reconstruction, bias of between –5% and –8% was observed. The variability of ROI estimates was also 1–4% higher in Son than Soff. Both bias and variability increased with larger subset numbers, with the 30-subset reconstructions introducing an additional 5–10% negative bias compared with the one-subset reconstructions.

Phantom studies

The researchers next performed a low-count evaluation using a NEMA body phantom scanned on a Biograph mCT PET scanner and reconstructed with MOLAR. The phantom was filled with 18F-FDG and had a contrast ratio of 6.2:1 between hot and cold ROIs. Again, the original list-mode data (600 M events obtained in 30 min, including 12% random coincidences and 31% scatter coincidences) were down-sampled by factors of 10, 100 and 1000 to generate low-count datasets with NEC levels of 20 M (180 s), 2 M (18 s) and 0.2 M (1.8 s).

As seen in the simulations, both bias and variability increased as NEC decreased, though bias values were extremely small. For example, 1–2% negative bias was seen at 2 M NEC and 2–3% at 0.2 M NEC, after 21 subsets/six iterations. With an increased number of iterations, negative bias increased slightly in the hot ROI and decreased in the cold ROI.

At a given NEC level, larger numbers of subsets produced more bias. For example, the bias at 0.2 M was –4.2% with three subsets and –5.9% with 21 subsets, after 126 effective iterations. This subset-dependent effect only applied to low-count reconstructions, however, with bias remaining below 1% for all 20 M NEC reconstructions.

The authors conclude that the MOLAR provides substantially lower bias at reasonably low count levels than previously reported and provides an effective image reconstruction platform for dynamic imaging using short time frames. "As the point spread function (PSF) is different between MOLAR and other sinogram-based algorithms, we believed that the PSF in MOLAR may contribute to lower bias, or slower convergence of bias as iterations proceed," explained Jian. The team is now performing further clinical studies to verify their results.

Related articles in PMB
Evaluation of bias and variance in low-count OSEM list mode reconstruction
Y Jian et al Phys. Med. Biol. 60 15
List-mode reconstruction for the Biograph mCT with physics modeling and event-by-event motion correction
Xiao Jin et al Phys. Med. Biol. 58 5567
Cerebral blood flow with [15O]water PET studies using an image-derived input function and MR-defined carotid centerlines
Edward K Fung and Richard E Carson Phys. Med. Biol. 58 1903

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