Speaker
Description
Conventional PET employs various techniques to reject scattered data as it creates noise in the reconstructed image. Instead of discarding 30-60% of the coincidence events belonging to single-scattered (SS) category, we propose a novel algorithm that utilizes such events to generate a Scattered Activity Map (SAM). This SAM serves as an initial estimate for MLEM reconstruction, demonstrating an improvement in Contrast-to-Noise Ratio (CNR) in early iterations. While previous studies have explored SS imaging using both Time-of-Flight (TOF) and energy information, our approach extends this capability to plastic scintillators with only TOF information [1]. It is particularly beneficial for low-count plastic PETs with very good timing resolution.
We simulated a generic Cylindrical PET system in GATE [2], incorporating LSO (Lutetium Oxyorthosilicate) and BGO (Bismuth Germanate) crystals, for ideal time resolution. The energy information from these materials were not incorporated in the analysis carried out for validation purposes. The scanner consists of 8 radial sectors each measuring 8 cm in width, 32 cm in height, and 40 cm in length. The LSO and BGO crystals of dimension 3 mm$\times$3.8 mm$\times$15 mm were arranged back-to-back, with a shared radius ranging from 46 cm to 49 cm. We attached a cylindrical phantom of radius 12 cm and height 30 cm, filled with water of uniform attenuation, at the center of the geometry. The studies are performed on a simplified Jaszczak phantom of 3 hot rods of radii 20 mm, 17 mm and 11 mm placed in the cylindrical phantom. The total activity was 4 MBq with hot to background activity ratio of 40:1.
The list-mode data from simulation were processed to classify SS coincidence events within a 3 ns time window without incorporating energy information. There were approximately $10^7$ true-coincidence events and $4\times10^6$ SS events generated from the ROOT output data file for runtime of 10 seconds. We generated SAMs by our algorithm, which models the scattering locus as a circular arc in 2D [3]. Only 1% of the scattered data was enough for the generation of SAMs, which also shows computational benefits. An extension to 3D, our model yields prolate spheroid and spindle torus for scattering locus and annihilation locus, respectively. However, due to the unknown direction of the scattered photon, we incorporate all possible scattering angles constrained by the phantom size, resulting in a combined annihilation distribution.
The SAMs generated by our algorithm are degraded by inherent statistical noise from scattering. We performed Lucy-Richardson (LR) deconvolution on these images using the knowledge of point-spread function to mitigate the background noise. Among all the iterate images generated through LR deconvolution, the $9^{th}$ was chosen as best sharpened and free from systematic error (see Fig. 1). Iterations beyond this point tend to overfit random fluctuations, leading to the introduction of artifacts. We used this deconvoluted image as an initial estimate for the MLEM reconstruction in CASTOR [4]. The reconstructed images are corrected for attenuation, scatter and random coincidences. We also compared our results using SAMs and LR images as initial estimates in MLEM reconstruction, with those using uniform images.
We used the sum squared error, calculated with respect to the original Jaszczak type activity distribution as stopping criteria in MLEM reconstruction. The sum squared errors was used to determine the optimal number of iterations, beyond which the error values begin to saturate. The CRC (Contrast Recovery Coefficient), CoV (Coefficient of variation) and CNR values for the hot rods were calculated using the NEMA standard as defined below.
\begin{aligned}
CRC = \frac{\left( \frac{C_{hot}}{C_{bkg}} - 1 \right)}{A - 1}
\qquad
COV = \frac{\sigma_{bkg}}{C_{bkg}}
\qquad
CNR = \frac{C_{hot} - C_{bkg}}{\sigma_{bkg}}
\end{aligned}
where:
$C_{hot}$ is measured average counts in the region of interest (ROI).
$C_{bkg}$ is corresponding average background counts.
$A$ is the true hot to background Ratio.
$\sigma_{bkg}$ is standard deviation of the background ROI counts.
The reconstructed images reached minima of sum squared error earlier when SS data was used as the initial estimate, compared to using a uniform image as the initial estimate. Fig. 2(a) and Fig. 2(b) shows the improvement of CRC v/s COV and CNR respectively, for different rods at $8^{th}$ iteration, labeled in black box, when compared with uniform initial estimate. The results suggest that the proposed methodology can improve the image quality in low-count PET scans and has scope in implementation for future scanners with better TOF resolution. Other results from S. Ghosh and P. Das [5] depicted the similar trends but they have used energy and TOF information for the generation of SAMs. We are purely working with Single scattered data with only timing information for the purpose of imaging with plastic scintillators. We can confidently say that using the scattered data as initial estimate helps in stopping at earlier iteration number as well as improves the CRC and CNR. We will further investigate how time resolution affects the reconstruction performance for future and state-of-art scanners.
References:
[1] Das P, Verma R, Prasad K, “Exploring PET imaging with scattered photons and polarization characteristics,” Bio-Algorithms and Med-Systems vol. 20, special issue, pp. 10-16, 2024, DOI:10.5604/01.3001.0054.8576
[2] Jan S, Santin G, Strul D, et al., "GATE: a simulation toolkit for PET and SPECT." Phys Med Biol. 2004;49(19):4543-4561. DOI:10.1088/0031-9155/49/19/007
[3] R. Verma, P. Das, “Feasibility Study of PET Imaging Using Single-scattered Events with TOF,” Acta Phys. Pol. B Proc. Suppl. 17, 7-A11 (2024), DOI:10.5506/APhysPolBSupp.17.7-A11
[4] Thibaut Merlin et.al. “CASToR: a generic data organization and processing code framework for multi-modal and multi-dimensional tomographic reconstruction”, Physics in Medicine & Biology, 63 (18)5505, 2018
[5] Satyajit Ghosh and Pragya Das,” Improvement of CNR in low-count PET scans using tissue-scattered data as initial estimate in non-TOF MLEM reconstruction” ,2023 Biomed. Phys. Eng. Express 9 035023
| Workshop topics | Applications |
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