A deep neural network for positioning and inter-crystal scatter identification in multiplexed PET detectors: a simulation study

Objective.High-resolution positron emission tomography (PET) relies on the accurate positioning of annihilation photons impinging the crystal array. However, conventional positioning algorithms in light-sharing PET detectors are often limited due to edge effects and/or the absence of additional information for identifying and correcting scattering within the crystal array (known as inter-crystal scattering). This study explores the feasibility of deep neural network (DNN) techniques for more precise event positioning in finely segmented and highly multiplexed PET detectors with light-sharing.Approach.Initially, a Geant4 Application for Tomographic Emission (GATE) simulation was used to study the spatial and statistical properties of inter-crystal scatter (ICS) events in finely segmented LYSO PET detectors. Next, a DNN for crystal localisation was designed, trained and tested with light distributions of photoelectric (P) and Compton + photoelectric (CP) events simulated using optical GATE and an analytical method to speed up data generation. Using the statistical properties of ICS events, an energy-guided positioning algorithm was then built into the DNN. The positioning algorithm enables selection of the unique or first crystal of interaction in P and CP events, respectively. Performance of the DNN was compared with Anger logic using light distributions from simulated 511 keV point sources placed at different locations around a single PET detector module.Main results. The fraction of events forward and backward scattered in the LYSO detector was 0.54 and 0.46, respectively, whereas naïve application of the Klein-Nishina formulation predicts 70% forward scatter. Despite coarse photodetector data due to signal multiplexing, the DNN demonstrated a crystal classification accuracy of 90% for P events and 82% for CP events. For crystal positioning, the DNN outperformed Anger logic by at least 34% and 14% for P and CP events, respectively. Further improvement is somewhat constrained by the physics-specifically, the ratio of backward to forward scattering of gamma rays within the crystal array being close to 1. This prevents selecting the first crystal of interaction in CP events with a high degree of certainty.Significance.Light sharing and multiplexed PET detectors are common in high-resolution PET, yet their traditional positioning algorithms often underperform due to edge effects and/or the difficulty in correcting ICS events. Our study indicates that DNN-based event positioning has the potential to enhance 2D coincidence event positioning accuracy by nearly a factor of 3 compared to Anger logic. However, further improvements are difficult to foresee without additional information such as event timing.

Simulation study of 1D U-Net-based inter-crystal scatter event recovery of PET detectors

To achieve high spatial resolution of reconstructed images in positron emission tomography (PET), the size of the scintillation crystal element is set small in current PET systems, which greatly increases the inter-crystal scattering (ICS) frequency. The ICS is a type of Compton scattering of the gamma photons from one crystal element to its neighborhood element, which obscures the determination of the first interaction position. In this study, we propose a 1D U-Net convolutional neural network (CNN) to predict the first interaction position which provides a universal way to efficiently solve the ICS recovery problem. The network is trained by using the dataset collected from the GATE Monte Carlo simulation. The 1D U-Net structure is applied due to its capability of synthesizing both low-level and high-level information which shows superiority in solving the ICS recovery problem. After being well trained, the 1D U-Net can generate the prediction accuracy of 78.1%. Compared to the coincidence events only composed by two photoelectric (PE) gamma photons, the sensitivity is improved by 149%. The contrast-to-noise ratio (CNR) of the reconstructed contrast phantom increases from 6.973 to 10.795 for the 16 mm hot sphere. Compared to the take-energy-centroid (TEC) method, the spatial resolution of the reconstructed resolution phantom can obtain the best improvement of 33.46%. Compared with the previous deep learning method based on the fully connected network (FCN), the proposed 1D U-Net can work more stably with much less network parameter amount. The 1D U-Net network model shows good universality when predicting different phantoms and the computation speed is fast.

Resolving inter-crystal scatter in a light-sharing depth-encoding PET detector

Objective.Inter-crystal scattering (ICS) in light-sharing positron emission tomography (PET) detectors leads to ambiguity in positioning the initial interaction, which significantly degrades the contrast, quantitative accuracy, and spatial resolution of the resulting image. Here, we attempt to resolve the positioning ambiguity of ICS in a light-sharing depth-encoding detector by exploiting the confined, deterministic light-sharing enabled by the segmented light guide unique to Prism-PET.Approach.We first considered a test case of ICS between two adjacent crystals using an analytical and a neural network approach. The analytical approach used a Bayesian estimation framework constructed from a scatter absorption model-the prior-and a detector response model-the likelihood. A simple neural network was generated for the same scenario, to provide mutual validation for the findings. Finally, we generalized the solution to three-dimensional event positioning that handles all events in the photopeak using a convolutional neural network with unique architecture that separately predicts the identity and depth-of-interaction (DOI) of the crystal containing the first interaction.Main results.The analytical Bayesian method generated an estimation error of 20.5 keV in energy and 3.1 mm in DOI. Further analysis showed that the detector response model was sufficiently robust to achieve adequate performance via maximum likelihood estimation (MLE), without prior information. We then found convergent results using a simple neural network. In the generalized solution using a convolutional neural network, we found crystal identification accuracy of 83% and DOI estimation error of 3.0 mm across all events. Applying this positioning algorithm to simulated data, we demonstrated significant improvements in image quality over the baseline, centroid-based positioning approach, attaining 38.9% improvement in intrinsic spatial resolution and enhanced clarity in hot spots of diameters 0.8 to 2.5 mm.Significance.The accuracy of our findings exceeds those of previous reports in the literature. The Prism-PET light guide, mediating confined and deterministic light-sharing, plays a key role in ICS recovery, as its mathematical embodiment-the detector response model-was the essential driver of accuracy in our results.