In this paper, we describe the implementation of support for time-of-flight (TOF) positron emission tomography (PET) for both listmode and sinogram data in the open source software for tomographic image reconstruction (STIR). We provide validation and performance characterization using simulated data from the open source GATE Monte Carlo toolbox, with TOF configurations spanning from 81.2 to 209.6 ps. The coincidence detector resolution was corrected for the timing resolution deterioration due to the contribution of the crystal length. Comparison between the reconstruction of listmode and sinogram data demonstrated good agreement in both TOF and non-TOF cases in terms of relative absolute error. To reduce the reconstruction time, we assessed the truncation of the TOF kernel along lines-of-response (LOR). Rejection of LOR elements beyond four times the TOF standard deviation provides significant acceleration of without compromising the image quality. Further narrowing of the kernel can provide extra time reduction but with the gradual introduction of error in the reconstructed images. As expected, TOF reconstruction performs better than non-TOF in terms of both contrast-recovery-coefficient (CRC) and signal-to-noise ratio (SNR). CRC achieves convergence faster with TOF, at lower noise levels. SNR with TOF was superior for early iterations, but with quick deterioration. Higher timing resolution further improved reconstruction performance, while TOF bin mashing was shown to have only a small impact on reconstructed images.

The combination of positron emission tomography (PET) with magnetic resonance (MR) imaging opens the way to more accurate diagnosis and improved patient management. At present, the data acquired by PET and MR scanners are essentially processed separately, and the search for ways to improve accuracy of the tomographic reconstruction via synergy of the two imaging techniques is an active area of research. The aim of the collaborative computational project on PET and MR (CCP-PETMR), supported by the UK engineering and physical sciences research council (EPSRC), is to accelerate research in synergistic PET-MR image reconstruction by providing an open access software platform for efficient implementation and validation of novel reconstruction algorithms.

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.

Estimation of attenuation from PET data only is of interest for PET-MR and systems where CT is not available or recommended. However, when using data from a single energy window, emission-based non-TOF PET attenuation correction (AC) methods suffer from 'cross-talk' artefacts. Based on earlier work, this manuscript explores the hypothesis that cross-talk can be reduced by using more than one energy window. We propose an algorithm for the simultaneous estimation of both activity and attenuation images as well as the scatter component of the measured data from a PET acquisition, using multiple energy windows. The model for the measurements is 3D and accounts for the finite energy resolution of PET detectors; it is restricted to single scatter. The proposed MLAA-EB-S algorithm is compared with simultaneous estimation from a single energy window (MLAA-S). The evaluation is based on simulations using the characteristics of the Siemens mMR scanner. Phantoms of different complexity were investigated. In particular, a 3D XCAT torso phantom was used to assess the inpainting of attenuation values within the lung region. Results show that the crosstalk present in non-TOF MLAA reconstructions is significantly reduced when using multiple energy windows and indicate that the proposed approach warrants further investigation.

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