1 Virtual PET Scanner – From Simulation in GATE to a Final Multiring Albira PET / SPECT / CT Camera

Simulation of the Positron Emission Tomography (PET) camera became a useful tool at the level of scanner design. One of the most versatile methods with several packages available is Monte-Carlo method, reviewed in (Rogers 2006). It was applied in GEANT4 code (Agostinelli et al. 2003) used in nuclear physics applications. Other codes used in medical physics and medicine are EGS (for review see (Rogers 2006)), FLUKA (Andersen et al. 2005), MCNP (Forster et al. 2004), PENELOPE (Sempau et al. 2001).


Introduction
Simulation of the Positron Emission Tomography (PET) camera became a useful tool at the level of scanner design.One of the most versatile methods with several packages available is Monte-Carlo method, reviewed in (Rogers 2006).It was applied in GEANT4 code (Agostinelli et al. 2003) used in nuclear physics applications.Other codes used in medical physics and medicine are EGS (for review see (Rogers 2006)), FLUKA (Andersen et al. 2005), MCNP (Forster et al. 2004), PENELOPE (Sempau et al. 2001).
The simulations of PET scanners are done in GATE software (Jan et al. 2004) which extensively uses GEANT4.This versatile package offers the possibility of simulation of radioactive source decays.It allows tracking of the individual γ events resulting after positron-electron annihilation.They can be absorbed by photoelectric event in the detector crystal or scattered in the phantom.It allows also simulation of detector electronics including paralyzed mode of the amplifiers.Coincidences can be monitored if they are true or random.The software is now available in version 6.1.Part of the simulations were performed in version 3.0, part in vGate 1.0 (containing version 6.0 via virtualization software for Linux).GATE was used in simulation of SPECT and CT systems (see papers citing (Jan et al. 2004)).Among PET systems for example Siemens PET/CT Biograph 6 scanner (Gonias et al. 2007), GE Advance/Discovery LS (Schmidtlein et al. 2006), Philips Gemini/Allegro (Lamare et al. 2006), Philips Mosaic small animal PET (Merheb, Petegnief and Talbot 2007) or purely insilicon (van der Laan et al. 2007) were used for simulation or design of new detectors and systems.

Positron Emission Tomography -Current Clinical and Research Aspects 4
After the initial electronic designs of the camera, its geometry and number of detectors, one can successfully simulate the data collection process including a wide variety of radioactive sources.Data can be classified to individual interactions in the detector (photoelectrically absorbed, scattered), at the coincidence level (true coincidences, scattered coincidences or random coincidences).Singles and coincidences are processed in digitizer module which simulates event collection from initial gamma absorption, via photon generation and reflection within the crystal (not implemented in current simulation), electronic pulse formation, amplification with dead times of the amplifiers, forming of singles and coincidences and then reconstructed into an image of the measured source.
We started from simulating an existing PET scanner called Albira with one ring formed by eight detectors and compared with actual measurements of point sources, animal NEMA phantoms and source grids.As the simulations reproduced very well the actual data in terms of coincidence and single rates, and also in terms of image quality, we moved forward to two and three rings scanner composition, which were at this time only in the design phase.As the electronic modules were to be the same it was a perfect case for simulation.
In the development of new electronics, the depth of interaction was to be included and, this implementation was also simulated in GATE prior to preparation of electronics.This data allow us to observe how the image quality is influenced by the particular implementation of such correction.
On the base of PET camera design and simulation, the multiring version of a breast PET tomograph (MAMMI) was also introduced into the simulation.Again, the simulated data were the base of design modifications and allowed to prepare a reconstruction software long before first real data were taken with a prototype.

Methods
We thoroughly modified the simulation of 1-ring Albira scanner prepared by Aurora Gonzalez for her Master thesis on the base of the benchmark of a PET scanner simulation included in Gate release (Gonzalez 2008).
Generally, the simulation of the PET scanner contains the following modules and submodules: 1. Main module, containing calls to submodules. 2. Visualization module, which defines the way the simulation, is presented during run.3. Camera module, which defines tomograph size, crystal dimensions and grouping.4. Phantom module, which defines phantom inserted in the scanner.The phantom can be a geometrical structure or a pixelated phantom, based on 3D image.5. Physics module, which defines the processes to be included in the simulation.6. Digitizer module, which defines how the γ particle detection is processed.It can be very detailed, i.e. storing information on individual interactions in stopping process, then how photons of the scintillation process are reflected in the crystal, how they are detected by the photomultiplier.Then the amplification stage is simulated with energy windows, dead times of the amplifiers, if they are paralysable or not, etc.This leads to detection of a single event, which can also be stored, and then processed in several coincidence processors, with individual energy (or signal height) windows, and delays.7. Sources module, which defines sources in geometrical or point form.Sources may be also masked with the phantoms, which allow more complicated geometries, like Derenzo phantom, animal pixelated phantoms, etc.
The listing of the Gate macro with corresponding submodules is provided in Appendix 1 The Albira camera mounts one to three rings formed by eight detectors, each containing only one single crystal fit to a position sensitive photomultiplier (PSPMT).One can see the details in Fig. 1, Fig. 2 and Fig. 7.Such large crystal coupled to the PSPMT allows one to additionally detect the depth of interaction of the annihilation gamma ray in the crystal (Lerche et al. 2005;Lerche 2006).The position detection resolution in this continuous crystals are 1.9±0.1 mm in plane of the PSPMT (i.e.axial and tangential directions), and about 3.9±1.5 mm in depth direction (i.e.radial).The errors of these values resulted from variation of these values in the crystal space.The largest errors appear in the edges and corners whereas and smallest errors are located in the center of the crystal, as expected.
General characteristics of the simulated Albira camera are as follows:  8 tapered center-pointing trapezoid crystals of 9.8 mm thickness (1-ring scanner), or 12 mm thickness (2-and 3-ring scanner).

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Albira crystals are made of LYSO (Lu 0.95 Y 0.05 ) 2 SiO 5 :Ce  The process and stored area of each detector is 40×40 mm.

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Dead time for singles is 0.4 µs paralysable and then 2 µs in non-paralysable mode, for coincidences is 1.8 µs non-paralysable mode.

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For simulations we used a mouse phantom and a point-like source at the center of the FOV according to NEMA standard.

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The separation of multiple rings is 4.4 mm.Crystal separation (bore) along the scanner diameter is 112 mm.

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For verification of the 1 ring simulation we placed the "real" mouse phantom in the center of the FOV of the actual scanner and loaded the tube with 237 µCi of 18-FDG.For a point source measurement, an eppendorf with a droplet of a few tens of µl (18-FDG) was centered placed.The measurements were performed for about 16 hours to end up at the activities of around 1µCi, as suggested also in NEMA standards. Radioactivity of 176 Lu was not included in the simulations.In the crystals of Albira we estimate the abundance of 176 Lu (2.59% naturally, 3.78×10 10 years half-life) to be 280Bq/ml (Moszynski et al. 2000).
The sketch of 2-ring scanner is shown in Fig. 1 Fig. 1.Sketch of the dimensions of 2-rings camera in a horizontal plane.All dimensions are in mm.For 1-ring scanner the main difference is that the crystals are 9.8 mm thick, instead of 12 mm for 2-and 3-ring scanner.In simulations, 12 mm crystals were used, in actual production they are of 10 mm.

Validation of simulation for a one-ring scanner with the measurement of mouse phantom
We simulated six different activities for a mouse phantom, exactly the ones that were measured with the phantom.A view of scanner with the mouse phantom and source during the simulation is depicted in Fig. 2. The simulations were initially done for 1 s acquisition, while the measurements were taken in 10 s frames, and the values of singles and coincidences were counted with a customized Albira application.The comparison between the simulated and acquired real data is shown in Fig. 3 and Table 1.
One can see from Fig. 3, that coincidence rate is particularly well reproduced almost in the whole activity range down to 1.5 µCi (-10% error) and reduces to about 20% below 1 Ci levels.. Single rates are well reproduced down to 100 µCi, while below this activity the correspondence is quite poor.We would not underestimate the discrepancies for low activities, as this may be the source of artifacts in the images in animals in the areas of low injected activity.
One possible explanation of the effect is the background activity of 176 Lu.The estimate gives the rate of 176 Lu decay events of about 270 cps per ccm, which translates into about 45 kcps in all detectors, and about 2700 cps in one detector at ±30% energy window (see background spectrum of LSO:Ce in Figure 1 of (Moszynski et al. 2000). 1 ring Albira scanner has 33% solid angle coverage (Balcerzyk et al. 2009).0.92 µCi (32 kBq) source generates about 770 singles in a detector.If, as calculated, 176 Lu background is about 2700 cps in a single crystal, we would simulate only about 770 770 + 2700 = 22% ⁄ which corresponds well with 29% shown in Fig. 3. Fig. 3. Comparison between simulated and real coincidences and singles in the 1-ring Albira scanner geometry.Diamonds show the ratio of simulated to real coincidences.Squares show the analogous ratio but for singles.Coincidences are well reproduced (i.e.above 90% agreement) down to 1.5 µCi, while singles agree well for activity values higher than about 50 µCi.Data labels indicate detailed values of these ratios.

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A 5 ns coincidence window should translate into about 1 to 2 cps in coincidences, which is the measured rate in empty scanner.We see in Table 1 that for all very low activities there is about 50 cps coincidence differences between measured and simulated ones.For the same activities, the singles difference is about 15 kcps, which increases to about 70 kcps for high activities.15 kcps difference in singles treated as randoms yields about 2.3 cps in coincidences (from R=2τS 2 relation, R being randoms, S singles rate, τ coincidence window (Balcerzyk et al. 2009)).
With the above in mind, one can tell, that background activity of 176 Lu is rather not responsible for discrepancy between simulation and experiment in coincidences but only for singles.One possible reason may be the singles (and hence coincidences) discarded from the tapered region of the crystals.In simulation, the distinction for the localization is very sharp, as we do not simulate photon transport.In real measurement some of the signal from the tapered area may probably leak into the detected area.
Background activity of 176 Lu is now used in Albira scanner for internal tests of detectors upon initialization of the instrument.The efficiency for low activities stabilizes at about 0.9% regarding measurement and simulates mouse phantom data.Those activities may serve as a reference for saturation and dead time level calculations.For mouse phantom, an activity of 1 µCi may be taken as a reference, especially for saturation estimations.
The simulation result of a cylindrical phantom for ∅10×10mm and 3.7 MBq 18F activity is shown in Fig. 5 for a cross section perpendicular to 1 ring scanner axis.One can see that true scattered and random coincidences contribute little to the image quality, as their total level is about 10% at NEC maximum.In Fig. 6  Fig. 6.Simulated NEMA mouse phantom rates for true unscattered, true scattered, random and total coincidences and noise equivalent counts (NEC) for 1 ring Albira scanner.Scatter fraction is constant and about 9% for the whole activity range.NEC has its maximum at 8.8 MBq of the described mouse phantom.

Three-and two-ring scanner simulation
The 3D renders of the 2-and 3-ring scanner with the mouse phantom inside the camera are shown in Fig. 7.

Efficiency
Fig. 8 shows the efficiencies for coincidences for 30% energy window for 1-, 2-and 3-ring scanner for simulations with closed symbols.1-ring values are the same as in Fig. 4. In this picture one can see the power of a 3-ring scanner, where all coincidences are stored.With a mouse phantom the efficiency reaches 5.3% for low activities.Assuming the proper simulation of 1-ring camera, one can expect the same efficiency for a measured mouse phantom, and for real animal measurements.
With open diamonds we show the efficiency in the projected 3-ring scanner with omission of the coincidences between border rings 0 th and 2 nd .In one of the first projects, such design was considered.It was estimated by analysis of first 50 coincidences from that scanner for the pair of detectors which form the coincidence.Once can generate such ASCII output in a table from Gate.The coincidences between rings 0 th and 2 nd include about 34% of all detected coincidences.The line of response is at small angle towards z-axis of the scanner, so one can expect large parallax errors for this pair of detectors.That effect suggested to include the depth of interaction encoding, which was considered in the final version.

Saturation level
Saturation levels for multiring scanners are shown in Fig. 9.They heavily relay on the choice of the two activities for which the efficiency is constant within 5%, being around 1µCi.However, some simulations there is higher efficiency at 0.5 µCi activity.The difference may be due to fluctuations of small numbers, as the coincidence count for these activities is around a few hundreds.In this only aspect 2-ring scanner is better than 1-and 3-ring scanner.The saturation of 50% for 1-and 3-ring scanner is at the level of about 120 µCi, while for 2-ring scanner it is about 320 µCi.We do not see the reason for 2-ring scanner to behave so well in terms of saturation.It is possible that it is a geometrical effect of having smaller fraction of the phantom within FOV of each ring in this geometry (see Fig. 7).Fig. 9. Saturation levels for multiring scanners.For the 3-ring scanner with omitted 0 th vs. 2 nd ring coincidences, the saturation curve would be the same as for 3-ring geometry, as the efficiency is calculated as a fraction of valid coincidences for all activities.As the number of points for simulation is limited, we added the trend lines (2 nd order polynomials) to look for expected evolution at higher activities.
We drew also prediction lines using simple polynomial 2 curves level.The predictive value of this curve is low, but it shows, that the expected 50% saturation level for 3-ring scanner is higher than for 1-ring scanner.The reader may have already found that we try to encourage the designers to drop the idea of excluding 0 th vs. 2 nd ring coincidences.It would result in the loss of 34% of detected coincidences.In Gate, there is no straightforward way to exclude the mentioned coincidences from the simulation.The only way we perceive it, is to post-hoc exclude them from simulated 3-ring scanner during the creation of list mode files.The problem is that there will be false overestimation of saturation, dead times for coincidences and others during the simulation, so the resulting list mode file will have an artificially lower coincidence level.

Point source
The proper way (NEMA standard) to measure the efficiency is to place a point source of activity corresponding to saturation level of less than 5% in the center of FOV.The simulations were done for exactly 0.95 µCi source, which roughly fulfills the requirement and the results are shown in Fig. 10 in comparison with the real study in 1-ring scanner.The real scanner measurement was done using a droplet of few tens of µl of about 10µCi of 18-FDG placed in the eppendorf tube and at the center of FOV.For the 1-ring scanner the measured value is 2.49%, while simulation returns 3.2% being in reasonable agreement with expected 10% saturation level at 10 µCi.Again, one can see the superiority of 3-ring scanner reaching 9.35% efficiency.This value may be further increased to about 12.9% if the tapered areas of the crystal are used for the coincidence detection.This would require most likely sophisticated point-spread function inclusion in the reconstruction besides other technical challenges regarding position calibration of such impinging events.

Depth of interaction
For the sources or phantom parts far radially from the center of the field of view, the resolution is deteriorating, mainly due to the so-called parallax error.To correct it, if possible, depth of interaction (DOI) of the detection of annihilation 511 keV γ photon needs to be recorded, and not only planar coordinates in plane of the photomultiplier.In the Albira detector, the DOI is estimated from the scintillation light spread into the position sensitive photomultiplier as shown in Fig. 11.In the current Albira 3 ring scanner the DOI is included, but not in the simulations.The DOI is included in the following way: the exact line of response is calculated for each detected coincidence connecting the point corresponding to detected blue arrow in Fig. 11 to the interaction point in second detector.The cross section point with the surface optically coupled to the photomultiplier is then re-calculated.This corresponds to already stored LOR for planar detectors.One can see that this sort of DOI for very oblique angles of LOR may result in cross sections with neighboring detectors.
The simulation did not include DOI corrections.The interaction point on the plane of PMT corresponded to the planar simulated coordinates.

Conclusion
Surprisingly for a point source there is little (from 3% to 4%) increase in efficiency for 2 ring scanner compared to 1-ring (see Fig. 10).The larger difference appears with the inclusion of a third ring and, moreover, if coincidences among all rings are allowed, resulting in a efficiency increase up to 9.35%.Higher values reaching 12.9% efficiency would be expected if the events impinging the tapered parts of the crystals are also used for reconstruction.
Upon the simulations results, some managerial decisions in Oncovision have been made.Namely, for 3 ring scanners, coincidences in between all three rings were included in the final product.Depth of interaction correction was introduced as well.For future versions, inclusion of all coincidences, also from the tapered region of the crystal would be available, as it considerably increases the detector total efficiency.

Fig. 2 .
Fig.2.Simulated 1-ring Albira scanner at a cross section at x=0 plane.XYZ axes are coded as x in red (not seen in the image), y in green and z in blue.The green cylinder in the image represents the location of the tube with radioactive material.In the camera, green structures refer to the crystals.

Fig. 4 .
Fig. 4. Efficiency for a mouse phantom simulated (filled symbol) in 1-ring camera compared with measured data (open symbol).

Fig. 5 .
Fig. 5. Gate simulation of ∅10×10mm phantom with a solution of 3.7 MBq of 18 F in water obtained with the 1 ring Albira scanner.Contribution of each type of coincidences is described on the left and right margins.Gate simulated events were converted to four separate list mode files and reconstructed in Albira reconstruction program.

Fig. 7 .
Fig. 7.The cross section view at around x=0 of the simulated 2-and 3-ring scanner with the mouse phantom inside.The coding of the colors is the same as in Fig.2, disregard extra shapes inside the red mouse phantom.

Fig. 8 .
Fig. 8. Efficiency in 30% energy window of coincidences for 1-, 2-and 3-ring scanner.Blue shows 3-ring scanner, squares 2-rings and triangles 1-ring geometry.Open diamonds show the efficiency for a 3-ring scanner with removed coincidences between 0 th and 2 nd ring (border rings).
www.intechopen.comVirtualPET Scanner -From Simulation in GATE to a Final Multiring Albira PET/SPECT/CT Camera 13

Fig. 10 .
Fig. 10.Efficiency for a real 1-ring scanner and simulated multiring scanners for the low activity (0.95 µCi) point source placed in the center of FOV.

Table 1 .
Detailed comparison between single and coincidence rates for 1-ring scanner, used to calculate the diagram in Fig.3for a mouse phantom.Note that for activites below 1.5µCi there is a slight discrepancy between simulated and registered singles.