OptiGAN for Crystal Arrays: Physics-Informed Generative Modeling of Optical Photon Transport in PET Detector Arrays

TL;DR

This work extends OptiGAN to a $3 \times 3$ BGO crystal array to model optical photon transport in PET detectors, addressing the computational bottleneck of Monte Carlo simulations. By incorporating Fourier Feature Encoding, a learnable Latent Mapping Network, and a Physics-Informed Loss that enforces momentum conservation, the method achieves high-fidelity, physics-consistent generation of sensor-level optical data while exploiting $D_4$ symmetry to reduce training data. Evaluation across full-array, high-resolution, and pencil-beam scenarios shows agreement with ground-truth GATE10/Geant4 simulations within $3\sigma$, with strong generalization to unseen positions and practical floodmap characteristics. The approach provides a foundation for fast, physics-guided generative modeling of segmented scintillator arrays and supports PET detector development and design exploration across diverse configurations.

Abstract

Monte Carlo simulations of optical photon transport are computationally prohibitive for large-scale optical systems including detector arrays and PET systems, restricting practical use to single-crystal studies. This work presents an enhanced conditional generative adversarial network (optiGAN) replacing optical simulations at the crystal array level, extending our single-crystal approach to a 3x3 BGO array. We enhance the Wasserstein-GAN framework with Fourier feature encoding, a learnable latent mapping network, and a physics-informed loss enforcing momentum conservation. Training data is reduced eight-fold by exploiting symmetry. Evaluation employs three studies: a full array evaluation testing generalization from the fundamental domain to the complete geometry, a high-resolution study probing out-of-distribution generalization to untrained positions, and a pencil beam $γ$-photon study assessing practical applicability for experimental detector characterization. Performance is benchmarked against GATE10/Geant4 ground truth, using intrinsic fluctuations between independent Monte Carlo runs as baseline. OptiGAN achieves sliced Wasserstein similarity within 3$σ$-agreement of the baseline across all conditions, demonstrating successful generalization to the full array. The model transitions from electron-emission training data to realistic $γ$-photon interactions, producing flood maps that reproduce characteristic patterns including photopeak clusters and inter-crystal scatter lines. This proof-of-concept demonstrates that physics-informed generative models can accurately simulate optical photon transport in segmented scintillator arrays. The reproduction of experimentally relevant flood map features validates optiGAN for PET detector development and establishes a foundation for models generalizing across diverse array configurations.

Figures (6)

• Figure 1: Schematic architecture of the enhanced optiGAN model. Rectangles in yellow represent newly introduced modifications for properly modeling the crystal array. Input data is marked as light blue rectangles. The generator and discriminator design have not been changed.
• Figure 2: Simulated crystal array consisting of 3 x3 BGO crystals.
• Figure 3: SWS results for the full array evaluation. The location of each scatter point represents the condition location, while the color visualizes the estimated SWS value. The row and column-wise results are depicted in the side and top plots. The blue point indicates the mean, and the bright and transparent error bars show one and three standard deviations. The dashed red line, with a bright and transparent red band, represents the baseline SWS performance (mean, one standard deviation, three standard deviations) achieved by two independent simulation runs with the same settings. Points with a blue edge color coincide with emission locations that were originally present during the training.
• Figure 4: SWS results for the high-resolution evaluation. The location of each scatter point represents the condition location, while the color corresponds to the estimated SWS value. The row and column profiles are shown in the side and top plots. The blue point indicates the mean, and the bright and transparent error bars show one and three standard deviations. For conditions that are located in a row or column having fewer than four other conditions, the row or column-averaged standard deviation is used. The dashed red line, with a bright and transparent red band, represents the baseline SWS performance (mean, one standard deviation, three standard deviations) achieved by two independent simulation runs with the same settings. Transparent blue crosses ($Z = \qty{1}{\milli \metre}, \qty{5}{\milli \metre}, \qty{9}{\milli \metre}$) mark the emission locations that were originally present during training.
• Figure 5: COG distribution generated by the baseline Monte-Carlo simulation and optiGAN (Left and right, respectively). Photopeak (bright clusters) and inter-scatter (lines) events are clearly visible in both figures. The gray grid represents the crystals of the detector array.