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Positron emission tomography (PET) system energy response is typically characterized in singles detection mode, yet there are situations in which the energy spectrum of coincidence events might be different than the spectrum measured in singles mode. Examples include imaging with isotopes that emit a prompt gamma in coincidence with a positron emission, imaging with low activity in a LSO/LYSO-based cameras, in which the intrinsic activity is significant, and in high scatter situations where the two 511 keV photons have different scattering probabilities (i.e. off-center line source). The ability to accurately measure the energy spectrum of coincidence events could be used for validating simulation models, optimizing energy discriminator levels and examining scatter models and corrections. For many PET systems operating in coincidence mode, the only method available for estimating the energy spectrum is to step the lower and upper level discriminators (LLD and ULD). Simple measurement techniques such as using a narrow sliding energy window or stepping only the LLD will not yield a spectrum of coincidence events that is accurate for cases where there are different energy components contributing to the spectrum. In this work we propose a new method of measuring the energy spectrum of coincidence events in PET based on a linear combination of two sets of coincident count measurements: one made by stepping the LLD and one made by stepping the ULD. The method was tested using both Monte Carlo simulations of a Siemens microPET R4 camera and measured data acquired on a Siemens Inveon PET camera. The results show that our energy spectrum calculation method accurately measures the coincident energy spectra for cases including the beta/gamma spectrum of the 176Lu intrinsic activity present in the LSO scintillator crystals, a 68Ge source and an 124I source (in which there are prompt γ-rays emitted together with the positron).
The energy response of a positron emission tomography (PET) system is normally characterized and measured with the system operating in singles mode. Singles mode acquisition of energy spectra is sufficient, and indeed essential, for uses such as characterizing the energy resolution of a PET system and setting up energy discriminator levels. In general, the architecture of PET system electronics is such that when the camera is operating in coincidence detection mode, energy information about each detected event is not explicitly included in the data stream. Thus, the only energy information available for the two singles that created a coincidence event is whether each was above some lower level discriminator (LLD) and below some upper level discriminator (ULD) value. For many reasons, the energy spectrum of coincidence events can be different from the energy spectrum of singles events. One example of this is when low amounts of activity are imaged in a lutetium oxyorthosilicate (LSO)- or lutetium–yttrium oxyorthosilicate (LYSO)-based PET system, which has intrinsic radioactivity in the detector scintillation crystals (Goertzen et al 2007, Yamamoto et al 2005). The decay scheme of 176Lu involves a β− emission (mean energy 420 keV) followed by a prompt gamma cascade with energies of 307 keV (94%), 202 keV (78%) and 88 keV (15%) (Browne and Junde 1998). This decay scheme leads to the creation of a number of true coincidence events originating from the detection of the β− in the crystal in which the 176Lu decay occurred and one of the prompt γ-rays in another detector crystal. We have previously shown that when very low amounts of radioactivity are in the PET system field of view (FOV), the coincident count rate is dominated by the detection of these intrinsic true events (Goertzen et al 2007).
The energy spectrum of these intrinsic coincidence events cannot be measured using the traditional method of a singles-mode acquisition because the spectrum that will be measured will be dominated by the β− emission spectrum due to the high probability of detection. In addition, the method of using a compact scattering source, as suggest by Watson (1997), does not apply because the activity is originating from within the scintillation crystals. Another commonly used option for measuring the coincidence energy spectrum is to set a high value for the ULD and step the LLD, recording the difference in counts between two successive LLD settings. This method will not accurately describe the higher energy β− particle contribution to the coincident energy spectrum because once the LLD is set high enough to exclude the γ-rays at 202 keV and 307 keV, the coincidence count rate will effectively drop to zero. In addition, stepping the LLD will distort the shape and position of the γ-ray photopeaks, since the coincidence spectrum in practice involves two photons rather than just one. The case can be made that current methods are inadequate for evaluating the energy spectrum of coincidence events for any imaging situation in which a coincidence pair is created by two singles that are drawn from different energy spectra. Examples other than the intrinsic radioactivity of LSO could include so-called dirty positron emitters, such as 124I or 76Br, which emit one or more prompt photons in coincidence with a positron, or asymmetrical scatter situations, where an offset source causes one detector to see minimal scatter and another detector to see large amounts of scatter. Finally, the energy spectrum of detected coincident events will always be different from that of the single events when a limited transaxial field of view is imposed when histogramming the coincident events.
In this paper we present a new simple method for estimating the energy spectrum of coincidence events in a PET system. The method uses a combination of two complementary measurements, one acquired by stepping the LLD and the other by stepping the ULD. The spectrum calculation method is derived theoretically and evaluated using both Monte Carlo simulation methods and measured data.
We assume that coincidence events are generated by two events with different energy spectra S1(E) and S2(E). For coincidence events we should know the average of S1(E) and S2(E), Savg(E), where
We normalize S1(E) and S2(E) as
and define the probability P1(E1, E2) that an event in spectrum 1 has an energy between E1 and E2 as (with a similar definition for spectrum 2)
For a defined energy window of E1 = LLD to E2 = ULD, the probability of two events from spectra 1 and 2 being within the window, PC(LLD, ULD) is the product of P1(LLD, ULD) and P2(LLD, ULD):
When we step the LLD up from a level E to E+ΔE with a very high ULD setting, the difference in counts for the two energy windows, ΔCLLD, is
When we step the ULD down from a level of E+ΔE to E with a very low LLD setting, the difference in counts for the two energy windows, ΔCULD, is
If we add ΔCLLD and ΔCULD for a similar step (E, E+ΔE) we get
It can be shown that the rearrangement of equation (7) will give
But from equation (3), as ΔE becomes small we can make the approximation that
with a similar approximation for P2(E, E + ΔE) so that
Then the average spectrum of the coincidence events, Savg(E), is simply given by
In this way, the average energy spectrum of the two events forming the coincidence pair can be measured through a simple linear combination of two measurements, the first acquired by stepping the LLD with a fixed ULD (ULDmax) and the second acquired by stepping the ULD with a fixed LLD (LLDmin).
PET data were simulated using GATE, the Geant4 application for emission tomography (Jan et al 2004). The geometry simulated was that of the Siemens microPET R4 (Knoess et al 2003) (Siemens Preclinical Solutions, Knoxville, TN). Briefly, this system has 96 detector blocks arranged in four rings with a 14.8 cm ring diameter, providing an axial FOV of 7.8 cm and a transaxial FOV of 10.0 cm. Each detector block consists of an 8 × 8 array of 2.1 × 2.1 × 10 mm3 LSO scintillator crystals with a center-to-center spacing of 2.4 mm. Only coincidence events within the 10 cm transaxial FOV were accepted. Simulated activity levels were kept sufficiently low so that neither the effects of system dead time nor random coincidences were considered. A system energy resolution of 15% was used in all simulations. Simulated data were histogrammed into Concorde microPET format sinograms using custom-built histogramming software. Single slice rebinning (SSRB) (Daube-Witherspoon and Muehllehner 1987) was used with a ring difference of 31. Four source distributions were simulated.
For each of the source distributions, two coincidence mode data acquisition runs were simulated. In the first, the ULD was fixed at 850 keV and the LLD was stepped from 50 to 840 keV in 10 keV steps. For each of the first three source distributions, 400 s of data acquisition was simulated per energy window. For the 124I source, 1800 s of data acquisition was simulated per energy window. These times were chosen because it gave a total of approximately 106 coincidence counts for each source distribution (176Lu, 68Ge and 124I) when the energy window was 50–850 keV. For the second simulated data acquisition, the LLD was fixed at 50 keV and the ULD was stepped from 60 to 850 keV in 10 keV steps. Again, for the first three source distributions, 400 s of data acquisition was simulated for each ULD setting and 1800 s was simulated for the 124I source. All simulations were run using the GATE multiples policy of ‘KillAll’, in which no multiple coincidence events (i.e. three or more valid single events in coincidence) are accepted as a valid coincidence. In addition to the coincidence mode simulations, a singles mode acquisition was simulated for each source distribution with the energy window set at 50–850 keV.
For each simulated source distribution, five energy spectra were calculated. After calculation all simulated spectra results were normalized to have 106 total counts. The spectra calculated are as follows.
For each of the spectra that have a 68Ge source, the position and full width at half maximum (FWHM) energy resolution of the 511 keV photopeak were calculated.
Data were collected on a Siemens Inveon dedicated PET system (Bao et al 2009, Visser et al 2009, Kemp et al 2009) (Siemens Preclinical Solutions, Knoxville, TN) located at the UCLA Crump Institute for Molecular Imaging. Briefly, this system has 64 detector blocks arranged in four rings with a 16.1 cm ring diameter, providing an axial FOV of 12.7 cm and a transaxial FOV of 10.0 cm. Each detector block consists of a 20 × 20 array of 1.51 × 1.51 × 10 mm3 LSO scintillator crystals with a center-to-center spacing of 1.59 mm. The geometry of the Inveon system is very similar to that of the microPET R4 model used in the Monte Carlo simulation work, with the key differences being the extended axial FOV and larger detector block size present in the Inveon. An Inveon system was used to acquire the measured data instead of a microPET R4 because the data acquisition software for the Inveon allowed the use of imaging protocols with multiple acquisition steps that could be acquired without user intervention. This is in contrast to the older microPET R4 software, which would have required the user to manually start each of the 150 acquisitions needed for a spectrum measurement. The Monte Carlo simulations were performed using the microPET R4 geometry, as we had previous experience with simulating this system and had the existing custom-built software to histogram the simulation output into sinograms for the microPET R4.
Coincidence mode data were acquired in which the LLDmin was set at 50 keV and the ULDmax was set at 800 keV. A discriminator step size (ΔE) of 10 keV was used for all acquisitions. With the ~14% energy resolution of the Inveon, this would allow approximately seven measurements across the 511 keV photopeak in the energy spectra. With these values for the LLDmin, ULDmax and ΔE, each spectrum measurement consisted of 150 acquisition steps, 75 of which were acquired with the LLD being stepped from 50 to 800 keV in steps of 10 keV with a fixed ULDmax and then a subsequent 75 measurements acquired with the ULD being stepped from 800 to 50 keV in steps of 10 keV with a fixed LLDmin. Acquisition of the measured data was done by setting up an ‘acquisition workflow’ in the Inveon acquisition software so that the entire data acquisition could be performed without manual intervention. On average, between each acquisition step the Inveon system required 15.6 s to change the energy window and setup for the next acquisition so that the total acquisition time required for all 150 measurements was 39 min plus the actual measurement time. Data were histogrammed using the manufacturer’s histogramming software into sinograms with 128 bins × 160 angles × 159 planes using SSRB with a ring difference of 39. A number of histogrammed trues were extracted from the header of each sinogram and used to calculate ΔCLLD(E, E + ΔE) and ΔCULD(E, E + ΔE).
Five data sets were acquired using the method described above for the Siemens Inveon. The sources and acquisition details for the five measurements were as follows.
In addition to the coincidence mode energy spectra measurements, singles mode data were acquired in energy spectrum measurement mode for the first four sources used for the coincidence energy measurements. The singles-mode energy spectrum for each source was extracted for one of the detector modules in the system for comparison with the coincidence energy spectra. Variations in the energy response of each crystal was normalized by using the location of the 511 keV photopeak from the spectra acquired with the 7.7 MBq 68Ge source to scale the energy spectrum for each crystal. The scaled spectra from the 400 crystals were then combined into one summed spectrum for the entire block detector, referred to as the singles-mode energy spectrum.
Figures 1–3 show the five energy spectra for the cases of the 176Lu activity only, 68Ge only and 176Lu plus 68Ge activity, respectively. In all three cases, the Savg spectra calculated using equation (11) most accurately recovers the true spectrum shape represented by the coincidence spectrum line. It is believed that discrepancies observed between Savg and the coincidence spectrum plot at lower energies are due to cases where a single γ-ray creates a coincidence event by scattering in one detector and then being detected in a second detector. These types of events are enhanced in the simulations due to the small bore geometry of the microPET R4 that is simulated and the fact that no shielding materials are simulated to attenuate these photons. Further, the multiples policy of ‘KillAll’ has the effect of actually increasing the number of valid coincidences within a given energy window relative to what would be expected from the 50 to 850 keV window because as the LLD is raised, some of the low energy scatter events will be excluded from the singles, thus reducing the number of multiples coincidences and increasing the number of valid coincidences.
For cases containing the intrinsic 176Lu activity, the singles spectrum has a much larger β− emission spectrum component as compared to the coincidence spectrum. This result is expected since the true coincident events can only occur for a detection of a β− plus γ-ray emission in coincidence. In the spectra with 176Lu activity it can be seen that measurements made by simply stepping the LLD completely miss the presence of the higher energy β− events. Similarly, measurements made by stepping the ULD underestimate the γ-ray components of the spectra.
Table 1 gives the location and FWHM resolution of the 511 keV photopeak for the simulations that include a 68Ge source. As expected, for the simulation with only a 68Ge source, the 511 keV photopeak location and the 15% FWHM energy resolution were accurately recovered with the singles spectrum. It can be seen that the 511 keV photopeak location is underestimated when only the Δ CLLD method of stepping the LLD is used to create the energy spectrum and the location is correspondingly overestimated for the Δ CULD method of stepping only the ULD. In addition, the FWHM energy resolution was underestimated for both cases. In both source distributions that have a 68Ge source, the spectrum given by the calculation of Savg according to equation (11) gives the accurate 511 keV photopeak location and FWHM energy resolutions.
Figure 4 shows the five energy spectra for the 124I source. In the decay of 124I, approximately 50% of positron emissions are accompanied by a 603 keV γ ray emission, and overall, the number of emissions of this γ-ray energy is very similar to the number of 511 keV annihilation photons created. This is reflected in the singles emission spectrum, in which the 511 keV and 603 keV photopeaks are of comparable magnitude. The coincidence energy spectrum is distinctly different from the singles spectrum, with a far larger amount of counts in the 511 keV as compared to the 603 keV photopeak. Again for this case the Savg energy spectrum accurately recovers the true coincidence energy spectrum. As described above for the other coincidence spectra, there are some discrepancies at lower energies, which we attribute to back-scattered photons creating multiple coincidence events.
Figure 5 shows the singles mode energy spectra for the 7.7 MBq 68Ge source with and without the 6.8 MBq 133Ba source present. As is expected, the energy spectrum for the two sources clearly shows the contributions of the multiple prominent γ-ray emission lines 161, 276, 302, 356 and 384 keV of the 133Cs daughter of the 133Ba decay (Rab 1995). Figure 6 shows the energy spectra for the 176Lu activity present in the LSO scintillator crystals with and without a 35 kBq 68Ge source. The contribution of the 68Ge source to the spectrum is very subtle compared to the large contribution of the background scintillator activity. The 176Lu spectrum clearly shows a summing peak above 600 keV due to the sum of β− emission plus γ-ray detection in the same scintillator crystal.
Figure 7 shows the coincidence mode energy spectra for the 68Ge source with and without the 133Ba source present in the camera. It can clearly be seen that the two spectra have nearly perfect agreement, indicating that the 133Ba photons are not contributing to the coincidence counts in the camera. It should be pointed out that no scaling was applied to the two spectra to normalize for total counts. The agreement between the measurements with and without the 133Ba source being present is distinctly different from the situation of the singles spectra in figure 4 in which the emissions from the 133Cs decay product are clearly seen between 200 and 400 keV. Figure 8 shows the coincidence mode energy spectra for the 176Lu intrinsic activity with and without the 35 kBq 68Ge source present in the camera. Again, no scaling for total counts was applied to the spectra. Differences in acquisition time were accounted for by dividing the total counts in the sinogram by the acquisition time. The β− plus γ-ray nature of the intrinsic coincidence events can be clearly seen in the spectra and the summing peak about 600 keV that is present in the singles spectra in figure 5 is not seen in the coincidence spectra. The 511 keV peak from the 68Ge source is clearly seen in the spectrum with the 68Ge source and is much more prominent than in the singles spectrum. In every coincidence mode energy spectrum measured with the Inveon system, the measured location of the photopeak was between 2 and 5% lower than the nominal γ-ray energy for that photopeak. In discussions with Siemens, we believe that this discrepancy is most likely explained by variations in gantry temperature, which cause the signal energy to decrease approximately 1.5% °C−1 rise in temperature. These effects were not seen in the singles mode spectra, as the 511 keV energy was defined for each detector by the location of the 511 keV photopeak in the 68Ge spectrum measurements.
Figure 9 shows the energy spectra for the low scatter compact 68Ge source and the high scatter 10 cm diameter 68Ge cylinder source. The two spectra have been scaled to have the same number of total counts for clarity. It can be clearly seen that for the cylinder source, there are considerably more counts in the energy region below the photopeak due to the increased scatter.
In this work we propose a simple method to allow the calculation of the energy spectrum of coincidence events in a PET system using a linear combination of two measurements, one acquired by stepping the LLD and the other acquired by stepping the ULD. This proposed method is tested using Monte Carlo simulation techniques, which showed that the energy spectrum of the coincidence events could be accurately recovered even when the two singles events creating the coincidence event had different emission spectra as is the case of the 176Lu intrinsic activity. For the 176Lu coincidence events, the method we propose accurately shows the β− emission spectrum at energies above the 511 keV photopeak normally seen in PET from β+ annihilation photons. For simulations that included a β+ emitter in the FOV, the 511 keV photopeak location and FWHM energy resolution were both accurately described with this spectrum calculation method. Finally, this method accurately measures the energy spectrum of coincidence events for 124I, which emits prompt γ-rays in coincidence with the positron emission.
In all of the simulation cases, the new coincidence energy spectrum calculation method most accurately matched the energy spectrum of coincidence events calculated directly from the list-mode simulation data. Simple methods of stepping the LLD and ULD incorrectly identified the photopeak location, energy resolutions and general shape of the coincidence energy spectra.
The energy spectrum measurement method was performed on a Siemens Inveon camera for source configurations that ranged from the intrinsic 176Lu only to a combination of strong 68Ge and 133Ba sources. In the measurements of the 176Lu intrinsic activity and 68Ge sources, the coincidence energy spectra closely match the shape of the simulated results. For the case of a mix of β+ emitter (68Ge) together with a single photon emitter (133Ba), the measured coincidence energy spectrum demonstrates that only the 68Ge β+ emissions are significantly contributing to coincidence events despite the singles mode energy spectrum showing that approximately 50% of detected photons are from 133Ba emissions. For a reasonable source strength, the measured acquisitions could be acquired in as little as 90 min using 15 s acquisition frames. This relatively short acquisition protocol means that 18F could possibly be used for the measurements, provided a correction was employed for the decay of the source throughout the measurement.
We believe that there are many applications that can make use of this simple technique for measuring the energy spectrum of coincidence events, especially given the ease with which this measurement could be acquired on an actual PET system. An obvious example, as shown in our simulation work, is for imaging studies that make use of so-called dirty positron emitters such as 124I, which emit prompt γ-rays in coincidence with the β+ emission. Image reconstruction methods for these isotopes must account for the contamination in the sinograms from the prompt γ-rays. Our energy spectrum measurement technique allows a simple and rapid way to measure the energy spectrum of coincidence events from these dirty positron emitters that will simplify the benchmarking of simulations and reconstruction algorithms as well as the optimization of energy windows. Another potential application of this technique is in validating the modeling of scatter in the PET system. If the imaging case contains an asymmetric activity distribution and scattering environment, it is very likely that detectors on opposite sides of the detector ring will be exposed to different input energy spectra, containing both scattered and unscattered photons. Our technique could easily be extended to evaluate the coincidence energy spectrum on a per detector basis by evaluating only certain regions on the sinogram, thus allowing the validation of energy spectrum models of scatter on all sides of an object being imaged. Finally, for imaging situations where a LSO-based camera is used to image weak emission sources, an estimate of the extent of the contribution of the intrinsic radioactivity to the counts in the sinogram can be made by measuring the energy spectrum of the coincident events.
One limitation of our method is that it cannot provide real-time information about the energy spectrum of the coincidence events. This means that it cannot easily be used for energy-dependent techniques for scatter estimation and image reconstruction such as those proposed by Popescu et al (2006). These techniques depend on real-time acquisition of complete energy information, which our method is not capable of, and require a PET system that includes information about the energy of each event in the list-mode data. PET systems that are capable of acquiring energy information about events in the list-mode coincidence can directly measure the energy spectrum of the coincidence events and thus do not have use of our new method. For these reasons, our approach is useful only for PET systems that are not capable of acquiring coincidence data with energy information included.
In summary, a new method for evaluating the energy spectrum of coincidence events in PET is proposed and evaluated with both Monte Carlo simulation and measured results. The new method accurately calculates the energy spectra of the coincidence events using a combination of stepping the LLD and ULD independently. The Monte Carlo simulation results demonstrate that this new method accurately recovers the energy spectrum of coincidence events even for the case of coincidence events being generated from two single events with different emission energy spectra, such as is the case for the intrinsic radioactivity present in lutetium-based scintillators due to the presence of 176Lu or for dirty positron emitters such as 124I. The measurement method was successfully performed on a Siemens Inveon camera, allowing measurements of the coincidence energy spectrum to be acquired in as little as 90 min with a 15 s per acquisition time frame.
This work was supported by the Natural Science and Engineering Research Council of Canada under Discovery Grant 341628. We wish to thank Qinan Bao of the Crump Institute for Molecular Imaging at UCLA for her help with the singles mode energy spectrum measurements and Stefan Siegel of Siemens Preclinical Solutions for helpful discussions about the Inveon system data acquisition software. The Western Canada Research Grid high performance computing resource was used for the Monte Carlo simulation work.
Some figures in this article are in colour only in the electronic version