Rethinking Timing Residuals: Advancing PET Detectors with Explicit TOF Corrections

TL;DR

This work tackles the challenge of timing residuals in TOF-PET by introducing a residual physics-based calibration framework with an explicit correction formulation. By defining residuals as correction values $l_i = r_i(\Delta t_{m,i}, z_i) = \frac{\Delta t_{m,i} - \Delta t_{\mathbb{E}}(z_i)}{2}$, the approach enables direct prediction of timing corrections and is robust to limited spatial sampling due to translational symmetry. Experiments with 4×4 LYSO:Ce,Ca crystal stacks and TOFPET2 readout demonstrate that explicit corrections reduce timing errors from $371 \pm 6$ ps to $281 \pm 5$ ps (430–590 keV), while reducing model size and maintaining or improving CTR across energy windows. The findings show explicit corrections offer stronger robustness to training data sparsity and are well-suited for high-throughput, in-system PET calibration, with future work focusing on cross-detector generalization and calibrated phantoms for streamlined implementation.

Abstract

PET is a functional imaging method that visualizes metabolic processes. TOF information can be derived from coincident detector signals and incorporated into image reconstruction to enhance the SNR. PET detectors are typically assessed by their CTR, but timing performance is degraded by various factors. Research on timing calibration seeks to mitigate these degradations and restore accurate timing information. While many calibration methods use analytical approaches, machine learning techniques have recently gained attention due to their flexibility. We developed a residual physics-based calibration approach that combines prior domain knowledge with the power of machine learning models. This approach begins with an initial analytical calibration addressing first-order skews. The remaining deviations, regarded as residual effects, are used to train machine learning models to eliminate higher-order skews. The key advantage is that the experimenter guides the learning process through the definition of timing residuals. In earlier studies, we developed models that directly predicted the expected time difference, which offered corrections only implicitly (implicit correction models). In this study, we introduce a new definition for timing residuals, enabling us to train models that directly predict correction values (explicit correction models). The explicit correction approach significantly simplifies data acquisition, improves linearity, and enhances timing performance from $371 \pm 6$ ps to $281 \pm 5$ ps for coincidences from 430 keV to 590 keV. Additionally, the new definition reduces model size, making it suitable for high-throughput applications like PET scanners. Experiments were conducted using two detector stacks composed of $4 \times 4$ LYSO:Ce,Ca crystals ($3.8\times 3.8\times 20$ mm$^{3}$) coupled to $4 \times 4$ Broadcom NUV-MT SiPMs and digitized with the TOFPET2 ASIC.

Figures (15)

• Figure 1: Visualization of the label distributions of the implicit (green) and explicit (blue) correction approach. The radiation source positions are displayed as red cubes.
• Figure 2: Visualization of the source distribution for a part of the transaxial study.
• Figure 3: Examples of the prediction distribution of implicit and explicit correction models. While the explicit correction model preserves the Gaussian time difference shape, the implicit correction model is strongly affected by edge effects leading to non-Gaussian distributions. In this example, the implicit model IM$_{10,12}$ and the explicit model EM$_{10,4}$ is used.
• Figure 4: In-plane source distributions. The red dots represent the position of a source, while the gray background displays the detector.
• Figure 5: MAE progression of the correction models trained on a dataset using a step width of 10, and tested on unseen data with a step width of 10. The blue axis and histogram display the label distribution of the training dataset. The MAE progression IM$_{10, 20}$ cannot be seen in plot (a), since it resulted in a very high MAE of about 1000, being far outside the displayed range.