Monte Carlo calculations of PET coincidence timing: single and double-ended readout

Abstract

We present Monte Carlo computational methods for estimating the coincidence resolving time (CRT) of scintillator detector pairs in positron emission tomography (PET) and present results for Lu2SiO5 : Ce (LSO), LaBr3 : Ce, and a hypothetical ultra-fast scintillator with a 1 ns decay time. The calculations were applied to both single-ended and double-ended photodetector readout with constant-fraction triggering. They explicitly include (1) the intrinsic scintillator properties (luminosity, rise time, decay time, and index of refraction), (2) the exponentially distributed depths of interaction, (3) the optical photon transport efficiency, delay, and time dispersion, (4) the photodetector properties (fill factor, quantum efficiency, transit time jitter, and single electron response), and (5) the determination of the constant fraction trigger level that minimizes the CRT. The calculations for single-ended readout include the delayed photons from the opposite reflective surface. The calculations for double-ended readout include (1) the simple average of the two photodetector trigger times, (2) more accurate estimators of the annihilation photon entrance time using the pulse height ratio to estimate the depth of interaction and correct for annihilation photon, optical photon, and trigger delays, and (3) the statistical lower bound for interactions at the center of the crystal. For time-of-flight (TOF) PET we combine stopping power and TOF information in a figure of merit equal to the sensitivity gain relative to whole-body non-TOF PET using LSO. For LSO crystals 3 mm × 3 mm × 30 mm, a decay time of 37 ns, a total photoelectron count of 4000, and a photodetector with 0.2 ns full-width at half-maximum (fwhm) timing jitter, single-ended readout has a CRT of 0.16 ns fwhm and double-ended readout has a CRT of 0.111 ns fwhm. For LaBr3 : Ce crystals 3 mm × 3 mm × 30 mm, a rise time of 0.2 ns, a decay time of 18 ns, and a total of 7600 photoelectrons the CRT numbers are 0.14 ns and 0.072 ns fwhm, respectively. For a hypothetical ultra-fast scintillator 3 mm × 3 mm × 30 mm, a decay time of 1 ns, and a total of 4000 photoelectrons, the CRT numbers are 0.070 and 0.020 ns fwhm, respectively. Over a range of examples, values for double-ended readout are about 10% larger than the statistical lower bound.

Bismuth germanate coupled to near ultraviolet silicon photomultipliers for time-of-flight PET

“…This agrees well with the pattern of the ratio of FWTM to FWHM in figure 4(c). Although the timing derived from the scintillation photons can also show small differences between the H2H and B2B configurations (Derenzo et al 2015), due to the different propagation velocities of scintillation light versus 511 keV photons inside the crystal, the timing differences between the H2H and B2B configurations are too large to be explained by this effect. Consequently, it appears that the coincidence timing resolution of BGO is considerably improved by detection of Cerenkov photons.…”

“…This phenomenon has been observed in both experimental (Davisson and Evans 1952, Hedgran and Hultberg 1954) and simulation studies (Brunner et al 2014, Somlai-Schweiger and Ziegler 2015). Although the timing derived from the scintillation photons can show small differences between the H2H and B2B configurations (Derenzo et al 2015), Cerenkov photons should contribute more to the coincidence timing resolution in H2H measurements than in B2B measurements.…”

Modelling the transport of optical photons in scintillation detectors for diagnostic and radiotherapy imaging

“…More recent examples of optical MC research on nuclear imaging using gamma cameras include compact gamma cameras based on avalanche photodiodes (Després et al , 2007), dedicated brain SPECT model (Hirano et al , 2012) and faster MC computation (Hunter et al , 2013). A larger number of papers were published on PET including work on monolithic scintillation crystals (van der Laan et al , 2010b; Vinke and Levin, 2014), crystal surface characterization (Roncali and Cherry, 2013b; Yang et al , 2013), and temporal resolution for time-of-flight (TOF) PET (Berg et al , 2015; Derenzo et al , 2014, 2015; Moses et al , 2014; Roncali et al , 2014). …”

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

“…(Derenzo et al 2015) presented Monte Carlo calculations of the optical photon time dispersion as a function of Z in a polished 3 mm × 3 mm × 30 mm LSO crystal with an external Teflon reflector. For the photodetectors on the surfaces X = A and B, the optical photon intensity I X ( T ) for T > λ X ( Z ) was described by I X ( T ) = I X λ X ( Z )exp[−( T – λ X ( Z ))/ D X ( Z )], and the time dispersion parameters D X ( Z ) were fitted as functions of Z by…”

“…In Derenzo et al (2015) fixed-fraction triggering was used for estimating the CRT in PET, and a calibration procedure was necessary to correct for time slewing due to depth-dependent variations in optical photon dispersion. This paper shows that in PET the variations in pulse height over the DOI range are sufficiently small that a similar calibration procedure can also correct for fixed-level time slewing, and the resulting CRT values are essentially the same.…”