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

Efthimiou, Nikos; Thielemans, Kris; Emond, Elise; Cawthorne, Chris; Archibald, Stephen J.; Tsoumpas, Charalampos


Nikos Efthimiou

Kris Thielemans

Elise Emond

Chris Cawthorne

Charalampos Tsoumpas


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-coincidence γ-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

Journal Article Type Article
Publication Date Jun 19, 2020
Journal EJNMMI Physics
Publisher SpringerOpen
Peer Reviewed Peer Reviewed
Volume 7
Issue 1
Article Number 42
APA6 Citation Efthimiou, N., Thielemans, K., Emond, E., Cawthorne, C., Archibald, S. J., & Tsoumpas, C. (2020). Use of non-Gaussian time-of-flight kernels for image reconstruction of Monte Carlo simulated data of ultra-fast PET scanners. EJNMMI Physics, 7(1),
Keywords Monte Carlo; Positron emission tomography; Photon travel spread; Depth of interaction; Fast timing
Publisher URL
Additional Information Received: 27 August 2019; Accepted: 20 May 2020; First Online: 19 June 2020; : Not applicable.; : Not applicable.; : The authors declare that they have no competing interests.


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