Analytical calculation of the lower bound on timing resolution for PET scintillation detectors comprising high-aspect-ratio crystal elements

Abstract

Excellent timing resolution is required to enhance the signal-to-noise ratio (SNR) gain available from the incorporation of time-of-flight (ToF) information in image reconstruction for positron emission tomography (PET). As the detector’s timing resolution improves, so does SNR, reconstructed image quality, and accuracy. This directly impacts the challenging detection and quantification tasks in the clinic. The recognition of these benefits has spurred efforts within the molecular imaging community to determine to what extent the timing resolution of scintillation detectors can be improved and develop near-term solutions for advancing ToF-PET. Presented in this work, is a method for calculating the Cramér-Rao lower bound (CRLB) on timing resolution for scintillation detectors with long crystal elements, where the influence of the variation in optical path length of scintillation light on achievable timing resolution is non-negligible. The presented formalism incorporates an accurate, analytical probability density function (PDF) of optical transit time within the crystal to obtain a purely mathematical expression of the CRLB with high-aspect-ratio (HAR) scintillation detectors. This approach enables the statistical limit on timing resolution performance to be analytically expressed for clinically-relevant PET scintillation detectors without requiring Monte Carlo simulation-generated photon transport time distributions. The analytically calculated optical transport PDF was compared with detailed light transport simulations, and excellent agreement was found between the two. The coincidence timing resolution (CTR) between two 3×3×20 mm3 LYSO:Ce crystals coupled to analogue SiPMs was experimentally measured to be 162±1 ps FWHM, approaching the analytically calculated lower bound within 6.5%.

Evaluation of a clinical TOF-PET detector design that achieves ⩽100 ps coincidence time resolution

“…This model can also include the travel time of 511 keV photons to interaction locations (weighted by a material’s linear attenuation coefficient), scintillation luminescence profile, depth-dependent scintillation photon transit time, and temporal response of the photosensor to calculate the Cramér-Rao Lower Bound (CRLB) on CTR via the Fisher statistic [DeGroot 2012], which represents that statistical limit on achievable timing resolution performance for a scintillation detector. The model builds upon a first formalism to analytically calculate this statistic limit on CTR for scintillation detectors [Seifert et al 2012] by including scintillation light transport for crystal geometries with non-negligible scintillation photon transit time jitter [Cates et al 2015]. …”

“…In this standard configuration, the LCE for 20 mm length crystals is reduced to ~40% compared to ~70% for the 3 mm length crystal [Pauwels et al 2009, Gundacker et al 2013]. The scintillation photon transit time spread is also increased from tens-of-picoseconds to hundreds-of-picoseconds [Cates et al 2015]. This light transit time variance is depth-of-interaction (DOI) dependent, including the travel time of the 511keV photon to a specific DOI in the crystal element of interaction.…”

A promising new mechanism of ionizing radiation detection for positron emission tomography: modulation of optical properties

“…Apart from the intrinsic scintillation process, other influencing factors on the timing properties of scintillation based PET detectors have also been extensively investigated, including the intrinsic light yield, decay time, scintillation light transit time variations (a function of crystal element length and photon interaction depth), surface treatment, the photon detection efficiency and time jitter of the photodetector, and the properties (bandwidth and time jitter) of readout electronics (Spanoudaki and Levin 2011, Derenzo et al 2014, Gundacker et al 2014, Cates et al 2015). These factors determine the limitation for the coincidence time resolution of a realistic scintillation based PET detector.…”

“…These factors determine the limitation for the coincidence time resolution of a realistic scintillation based PET detector. The current performance of “clinically relevant” PET scintillation detectors (with crystal length larger than or equal to 20 mm) is greater than 100 ps (Nemallapudi et al 2015, Cates et al 2015, Cates and Levin 2016). …”

CDL, a Precise, Low-Cost Coincidence Detector Latch

“…It should be clear that the quality of the resulting image directly depends on the available time resolution, which is about 1 ns or below in state-of-the-art time-of-flight PET systems [2,3]. Since these resolutions are still quite challenging for software-based systems, the field of PET systems still enjoys significant activity in the development of hardware-based coincidence detectors.…”