This paper demonstrates through Monte Carlo simulations that a practical
positron emission tomograph with (1) deep scintillators for efficient detection,
(2) double-ended readout for depth-of-interaction information, (3) fixed-level
analog triggering, and (4) accurate calibration and timing data corrections can
achieve a coincidence resolving time (CRT) that is not far above the statistical
lower bound.
One Monte Carlo algorithm simulates a calibration procedure that uses
data from a positron point source. Annihilation events with an interaction near
the entrance surface of one scintillator are selected, and data from the two
photodetectors on the other scintillator provide depth-dependent timing
corrections. Another Monte Carlo algorithm simulates normal operation using
these corrections and determines the CRT. A third Monte Carlo algorithm
determines the CRT statistical lower bound by generating a series of random
interaction depths, and for each interaction a set of random photoelectron times
for each of the two photodetectors. The most likely interaction times are
determined by shifting the depth-dependent probability density function to
maximize the joint likelihood for all the photoelectron times in each set.
Example calculations are tabulated for different numbers of
photoelectrons and photodetector time jitters for three 3 × 3 ×
30 mm3 scintillators: Lu2SiO5:Ce,Ca (LSO),
LaBr3:Ce, and a hypothetical ultra-fast scintillator. To isolate
the factors that depend on the scintillator length and the ability to estimate
the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For
LSO with 4000 photoelectrons and single photoelectron time jitter of the
photodetector J = 0.2 ns (FWHM), the CRT value using
the statistically weighted average of corrected trigger times is 0.098 ns FWHM
and the statistical lower bound is 0.091 ns FWHM. For LaBr3:Ce with
8000 photoelectrons and J = 0.2 ns FWHM, the CRT values
are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with
1 ns decay time, 4000 photoelectrons, and J = 0.2 ns
FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. The examples
also show that calibration and correction for depth-dependent variations in
pulse height and in annihilation and optical photon transit times are necessary
to achieve these CRT values.