Use of non-Gaussian time-of-flight kernels for image reconstruction of Monte Carlo simulated data of ultra-fast PET scanners

Abstract

Introduction Time-of-flight (TOF) positron emission tomography (PET) scanners can provide significant benefits by improving the noise properties of reconstructed images. In order to achieve this, the timing response of the scanner needs to be modelled as part of the reconstruction process. This is currently achieved using Gaussian TOF kernels. However, the timing measurements do not necessarily follow a Gaussian distribution. In ultra-fast timing resolutions, the depth of interaction of the γ-photon and the photon travel spread (PTS) in the crystal volume become increasingly significant factors for the timing performance. The PTS of a single photon can be approximated better by a truncated exponential distribution. Therefore, we computed the corresponding TOF kernel as a modified Laplace distribution for long crystals. The obtained (CTR) kernels could be more appropriate to model the joint probability of the two in-coincidenceγ-photons. In this paper, we investigate the impact of using a CTR kernel vs. Gaussian kernels in TOF reconstruction using Monte Carlo generated data. Materials and methods The geometry and physics of a PET scanner with two timing configurations, (a) idealised timing resolution, in which only the PTS contributed in the CTR, and (b) with a range of ultra-fast timings, were simulated. In order to assess the role of the crystal thickness, different crystal lengths were considered. The evaluation took place in terms of Kullback–Leibler (K-L) distance between the proposed model and the simulated timing response, contrast recovery (CRC) and spatial resolution. The reconstructions were performed using STIR image reconstruction toolbox. Results Results for the idealised scanner showed that the CTR kernel was in excellent agreement with the simulated time differences. In terms of K-L distance outperformed the a fitted normal distribution for all tested crystal sizes. In the case of the ultra-fast configurations, a convolution kernel between the CTR and a Gaussian showed the best agreement with the simulated data below 40 ps timing resolution. In terms of CRC, the CTR kernel demonstrated improvements, with values that ranged up to 3.8% better CRC for the thickest crystal. In terms of spatial resolution, evaluated at the 60th iteration, the use of CTR kernel showed a modest improvement of the peek-to-valley ratios up to 1% for the 10-mm crystal, while for larger crystals, a clear trend was not observed. In addition, we showed that edge artefacts can appear in the reconstructed images when the timing kernel used for the reconstruction is not carefully optimised. Further iterations, can help improve the edge artefacts.

Exploring Cherenkov Emission of BGO for TOF-PET

“…For the BGO data the impact of the tails is well visible as it requires a larger coincidence time window until the majority of events are inside. The shape of the distribution completely changes The implementation of non-Gaussian time-of-flight kernels in reconstruction was demonstrated in [32] and reconstruction results comparing BGO timing kernels [17] with a 213 ps FWHM LSO model point towards similar contrast and, due to the higher sensitivity, about 25% better signal-to-noise ratio for the BGO model [33].…”

Fully digital PET is unaffected by any deterioration in TOF resolution and TOF image quality in the wide range of routine PET count rates

“…It may be mentioned that not only the width but also the shape of the TOF distribution needs to be modeled accurately. This distribution is commonly considered as Gaussian, although a Laplace distribution could be more appropriate for very high timing resolutions (< 50 ps) [41].…”

Time of Flight in Perspective: Instrumental and Computational Aspects of Time Resolution in Positron Emission Tomography

“…The same may be the case for detectors based on metamaterials [43,220], where different events can have a very different timing resolution. For those PET systems, the reconstruction model will have to account either for the average non-Gaussian uncertainty or for the timing uncertainty associated with each event, if such information is available [218,219]. Improvement of system TOF resolution is not the only factor that is expected to enable better image quality in future PET systems.…”