An Algorithm for Maximum-Likelihood Estimation of the Timing Resolution in TOF-PET


An Algorithm for Maximum-Likelihood Estimation of the Timing Resolution in TOF-PET

Nikulin, P.; Lougovski, A.; Hofheinz, F.; Maus, J.; van den Hoff, J.

INTRODUCTION
As is well known, utilization of time-of-flight (TOF) information can reduce noise and improve convergence rate in PET image reconstruction since it allows to incorporate the (Gaussian) probability density function (the ”TOF-kernel”) of the annihilation event position along the respective LOR into the image reconstruction process. In doing so, it is crucial to use the best possible estimate of the actually given timing resolution in order to achieve a realistic contrast recovery and minimize noise, see [1]. Moreover, it was recently recognized that using the correct timing resolution is necessary to avoid artifacts in Maximum-Likelihood reconstruction of Attenuation and Activity (MLAA), which is in agreement with our own experience. In this context, it is relevant to recognize that the timing resolution of a time-of-flight PET system is count rate dependent, see e.g. [2]. However, count rate dependent TOF-resolution calibration is usually not provided by the vendors. We, therefore, developed a procedure which is compatible with clinical routine and is also applicable retrospectively to existing data.

METHODS
We propose a novel Maximum-Likelihood Timing Resolution Estimation (MLTRE) algorithm that maximizes likelihood by updating activity image and TOF-kernel width alternately. For activity update, TOF-MLEM was used and quadratic surrogate based maximization of the likelihood was performed
to timing resolution update. The listmode version of the algorithm was used to exclude a possible influence of the TOF-binning procedure on the timing resolution estimation process. Ordered subsets optimization was applied in order to reduce computation time. The algorithm was integrated into our
previously developed Tube of response High resolution OSEM Reconstruction (THOR) [3]. THOR incorporates normalization, attenuation, dead-time, randoms corrections, as well as different options for TOF scatter correction including TOF-Single Scatter Simulation algorithm (TOF-SSS), see [4], and
two accelerated in-house algorithms. MLTRE was evaluated using phantom and patient studies covering a large range of count rates that were acquired with a Philips Ingenuity TF PET/MR scanner. Studies were grouped by imaging protocol (”brain” and ”whole-body”, covering different transaxial fields
of view). The iteration scheme of five timing resolution updates per single MLEM update was chosen to achieve convergence of the algorithm in all studies. Iteration was initialized with a timing resolution estimate of 700 ps. Performance of the algorithm was also investigated in the extreme high contrast
conditions that are typical for pelvis region investigations. A dedicated phantom was used for this purpose. Global convergence of MLTRE is not guaranteed. Therefore it is recommended to use a reasonable TOF-kernel width as the start value for the algorithm. In order to assess the stability of the algorithm regarding this start value, MLTRE reconstructions of the same phantom study with varying initial values for the TOF-kernel width in the range [500 − 1000] ps were performed.

RESULTS
Our evaluation yields a linear dependency of timing resolution on count rate which is in correspondence with the reports by other groups, see [2]. According to our results the scanner reaches 551 ps timing resolution at “zero” count rate. Resolution degrades by 146 ps for each ten millions of singles counts per second. Timing resolution degradation can exceed 150 ps ( 25% of initial TOF-kernel width) for clinical relevant count rates. No difference in estimated timing resolution between brain and whole-body protocal was encountered. However, scatter and attenuation correction errors can adversely affect timing resolution estimation. Therefore, using patient data for calibration purposes in PET/MR is not optimal. Dedicated phantom measurements are preferable. However, the procedure is still suitable for retrospective application to existing clinical data if TOF-scatter and attenuation correction
are reliable. Although global convergence of MLTRE algorithm is not guaranteed, no significant influence of the chosen start value for TOF-kernel width on estimated timing resolution was encountered in our data. The results are deviating from the mean by ∼ 4 ps (≈ 0.5%) at maximum whilst the initial values were varied between 500 and 1000 ps.

CONCLUSION
Our preliminary results indicate that the proposed algorithm is capable of realistic timing resolution estimation, while being convenient and easy to use in clinics. To the best of our knowledge, the dependency of timing resolution on singles rate of the Philips Ingenuity TF PET/MR scanner was never published before. According to our findings, the timing resolution of this scanner degrades rapidly with increasing count rate. This fact should be accounted for during image reconstruction.

REFERENCES
[1] S. Vandenberghe, S. Matej, M. E. Daube-Witherspoon, M. Guerchaft, J. Verhaeghe, A. Bol, L. Van Elmbt, I. Lemahieu, and J. S. Karp, “Determining timing resolution from TOF-PET emission data,” IEEE Nuclear Science Symposium Conference Record, vol. 4, pp. 2727–2731, 2007.
[2] S. Surti, A. Kuhn, M. E. Werner, A. E. Perkins, J. Kolthammer, and J. S. Karp, “Performance of Philips Gemini TF PET/CT scanner with special consideration for its time-of-flight imaging capabilities.” Journal of nuclear medicine : official publication, Society of Nuclear Medicine, vol. 48, no. 3, pp. 471–480, 2007.
[3] A. Lougovski, F. Hofheinz, J. Maus, G. Schramm, E. Will, J. van den Hoff, and J. van den Hoff, “A volume of intersection approach for on-the-fly system matrix calculation in 3D PET image reconstruction,” Physics in Medicine and Biology, vol. 59, no. 3, pp. 561–577, feb 2014.
[4] C. C. Watson, “Extension of Single Scatter Simulation to Scatter Correction of Time-of-Flight PET,” IEEE Transations on Nuclear Science, vol. 54, no. 5, pp. 1679–1686, 2007.

Keywords: PET; PET/MR; TOF; time resolution; calibration

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