Rethinking Timing Residuals: Advancing PET Detectors with Explicit TOF Corrections

Stephan Naunheim ^1,2* Luis Lopes de Paiva ^1,2 Vanessa Nadig ² Yannick Kuhl ^1,2 Stefan Gundacker ^2,3 Florian Mueller ² Volkmar Schulz ^1,4,5,6*

• ¹ RWTH Aachen University, Institute of Imaging and Computer Vision, Aachen, Germany
• ² University Hospital RWTH Aachen, Aachen, Germany
• ³ Institute of High Energy Physics, Austrian Academy of Sciences, Vienna, Austria
• ⁴ Hyperion Hybrid Imaging Systems GmbH, Aachen, Germany
• ⁵ Fraunhofer Institute for Digital Medicine (MEVIS), Aachen, Germany
• ⁶ III. Physics Institute B, RWTH Aachen University, Aachen, Germany

PET is a functional imaging method that can visualize metabolic processes and relies on the coincidence detection of emitted annihilation quanta. From the signals recorded by coincident detectors, TOF information can be derived, usually represented as the difference in detection timestamps. Incorporating the TOF information into the reconstruction can enhance the image's SNR. Typically, PET detectors are assessed based on the coincidence time resolution (CTR) they can achieve. However, the detection process is affected by factors that degrade the timing performance of PET detectors. Research on timing calibrations develops and evaluates concepts aimed at mitigating these degradations to restore the unaffected timing information. While many calibration methods rely on analytical approaches, machine learning techniques have recently gained interest due to their flexibility. We developed a residual physicsbased calibration approach, which combines prior domain knowledge with the flexibility and power of machine learning models. This concept revolves around an initial analytical calibration step addressing first-order skews. In the subsequent step, any deviation from a defined expectation is regarded as a residual effect, which we leverage to train machine learning models to eliminate higher-order skews. The main advantage of this idea is that the experimenter can guide the learning process through the definition of the 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). We demonstrate that the explicit correction approach allows for a massive simplification of the data acquisition procedure, offers exceptionally high linearity, and provides corrections able to improve the timing performance from (371±6)ps to (281±5)ps for coincidences from 430keV to 590keV. Furthermore, the novel definition makes it possible to exponentially reduce the models in size, making it suitable for applications with high data throughput, such as PET scanners. All experiments are performed with two detector stacks comprised of 4×4 LYSO:Ce,Ca crystals (each 3.8mm × 3.8mm × 20mm), which are coupled to 4×4 Broadcom NUV-MT SiPMs and digitized with the TOFPET2 ASIC.