Keywords
Digital phantom - Geant4 Application for Tomographic Emission - Monte Carlo simulation
- positron emission tomography scanner - validation
Introduction
Medical imaging modalities such as computed tomography (CT) and magnetic resonance
imaging provide accurate anatomical information of the body by providing high spatial
resolution and contrast. However, PET imaging, which is based on the body metabolism
rate, does not offer a good spatial resolution despite its high sensitivity.[1],[2] Given the constraints of each imaging system, multimodality systems such as PET/CT
have been embraced and employed as a standard method for oncological staging and diagnosis.[3],[4],[5] Such systems can simultaneously provide anatomical and functional information of
the body and high-resolution and high-sensitivity images, in particular for therapeutic
goals and precise determination of tumor volume.[6],[7] The limitation of PET in terms of spatial resolution affects the image quality.[8] Therefore, several studies have focused on factors affecting PET image quality and
spatial resolution, including photon noncollinearity, off-axis detector penetration,
detector size and response, positron range, photon scatter, and patient motion, as
well as the impact of each on improving the image quality.[9],[10] Following these types of study in recent years, PET hardware and software have witnessed
technological advancements, which have led to the ever-increasing enhancement of this
scanner's performance.[10]
Several studies have used Monte Carlo methods to evaluate the parameters affecting
image quality in nuclear medicine.[11] These methods are time-consuming, however, which have been relatively overcome with
the advances in computer science and the advent of high-speed supercomputers, leading
to their ever-increasing application particularly in PET and single photon emission
computed tomography (SPECT) imaging.[12],[13] Numerous Monte Carlo simulation codes have so far been developed, which are widely
used in PET and SPECT imaging applications such as scanner design, image reconstruction,
scatter correction, and imaging protocol enhancement.[14] SimSET, EGS4, MCNP,[15] and Geant4[16] are a number of such codes, which are precise and versatile and have been developed
for physics with diagnostic and therapeutic energy.[17]
The Geant4 Application for Tomographic Emission (GATE) is a simulation code based
on GEANT4 libraries and is a modular, versatile, and scripted toolkit specifically
designed for nuclear medicine applications. This simulation code, developed by the
International openGATE collaboration, allows defining time-dependent phenomena such
as source decay time and source or patient movements.[5]
With the increased application of Monte Carlo simulations in research, validation
studies are carried out to obtain accurate scanner models to be used in studies aiming
at improving image quality and performance of imaging systems. Therefore, numerous
validation studies have been conducted to determine the ability of various simulation
codes, including the GATE, to model various scanners such as PET, neuroPET, small
animal PET, and SPECT. Validation studies for PET scanners include the simulation
of PET Allegro and GEMINI,[18] Advance/Discovery LS,[9] Biograph 2,[19] ECAT EXAT HR+,[20] Sedecal Argus preclinical PET,[21] FLEX Triumph™ preclinical PET/CT,[22] and rodent-research PET[8] scanners for small animals. Similar studies have been carried out on SPECT scanners.[23],[24],[25] Such studies have been occasionally conducted on multimodality scanners including
PET/magnetic resonance[26] and PET/SPECT/CT.[27]
In the present study, the GATE simulation code was used for performance assessment
and validation of the GE Discovery PET/CT 690 VCT scanner. This study aimed to provide
an accurate and reliable model for this scanner and to evaluate its performance by
a Monte Carlo simulator. This study aimed to design an accurate and reliable model
of this scanner for the evaluation of performance parameters using GATE Monte Carlo
simulation. Various validation studies were performed for numerous PET scanners. However,
as per our knowledge, there are no such studies performed for the GE Discovery 690
scanner. However, the GE Discovery 690 scanner has not been validated so far, and
the current study validates the simulation results of this scanner for the first time.
In order to perform the simulation, the geometry, physics, and electronics of the
device were defined by GATE. In addition to simulation, the scanner was used for imaging
to achieve the gold standard required for validation. After performing the simulation
and modification of its model, the experimental results from the scanner were compared
with the simulation results in order to validate the designed model. The final analysis
was limited to the comparison of the spatial resolution, sensitivity, and contrast
of the simulation and experimental images. In addition, the image quality was evaluated.
The results can be used in future studies for designing new PET scanners, optimization
of acquisition protocols, development of reconstruction algorithms, and implementation
of correction techniques to improve image quantification.
Materials and Methods
Simulation
In this study, the GATE simulation package which is based on the Geant4 Monte Carlo
simulation toolkit was used to simulate the PET scanner. This simulation code uses
the Geant4 libraries and has a scripting mechanism. GATE has various modules, each
assigned with the task of simulating a part of the scanner. These modules simulate
the behavior of the system geometry, radioactive source, physics of interactions,
scanner detectors, and signal processing chain to obtain a precise model of the desired
system.
In this study, in order to simulate the PET/CT imaging system, the system geometry,
physics processes, and signal flow, called the “digitizer” in GATE, were defined for
the PET scanner in the simulation code and will be explained in detail:
Geometry
In GATE, simple geometries such as cylinder, box, and sphere can be defined. These
geometries can be used and combined to produce any other kind of geometry, even complex
geometries. In this study, the geometry of the PET scanner detectors and its shields
were defined in detail.
The GE Discovery 690 VCT PET scanner system has 13,824 LYSO crystals with dimensions
of 4.2 mm × 6.3 mm × 25 mm, arranged in 24 ring detectors. The detection unit of this
scanner is composed of blocks consisting of 9 × 6 crystals, each containing a total
of 64 blocks per ring. The geometry branch was used to model ring detectors consisting
of blocks and crystals. In addition, the shields surrounding the scanner rings and
the light guides around the crystals were also defined to incorporate the photon scattering
media into the model [Figure 1].
Figure 1 Schematic representation of the Discovery 690 positron emission tomography scanner
model with its ring shields simulated using Geant4 Application for Tomographic Emission
(a), including oblique view of a block (b) and a crystal (c)
Physics
Physics in GATE is based on GEANT4 libraries, which include physical models of all
interactions for particles and photon with different energies. In this simulation,
the standard model was defined for photonic interactions (photoelectric, compton,
ionization, and bremsstrahlung) and the PENELOPE model for the Rayleigh interactions;[27] the energy cutoff of photons and electrons was considered 1 cm for LYSO crystals
and 10 cm for the phantom.
Signal processing
Digitizer, which simulates the behavior of the electronic components and the signal
processing of the scanner, is one of the most vital parts of the GATE simulation for
achieving a real, reasonable, and comparable output. Digitizer has different modules
that mimic each part of the signal processing chain, and the presence, absence, or
change in each module can lead to a fundamental change in the final output. Therefore,
defining this part is so important in imaging scanners. The defined layout of the
digitizer in this study is shown in [Figure 2].
Figure 2 Flowchart display of digitizer module of Discovery 690 positron emission tomography
scanner
A sequence of modules was used to model the digitizer. The Geant4 hits module, which
imitates the production of photons due to the interaction of gamma rays with detector
crystals, is the first step in defining the signal-processing chain. Subsequently,
the Adder module was placed. The Adder collects the energy deposited by hits and stores
time information with respect to the last recorded interaction and site by weighing
the energy deposited by particles. The readout module was then defined, which collects
the previous module information at a larger level from the detector, i.e., the blocks,
and generates the pulse. Energy blurring is the next module, which simulates the readout
of the produced pulse energy spectrum blur. The scanner crystal is made of LYSO. In
some studies, a constant energy resolution for this type of crystal has been defined.[18],[28] In fact, the energy resolution of all crystals is not the same; therefore, the energy
resolution of the crystals was determined using the crystal blurring module in a nonuniform
range of 10% and 20%. The detection efficiency factor, equal to 90%, was also applied
to the readout output.[29],[30] In addition, the time blurring module was applied to the recorded singles with a
temporal resolution of 3 ns. The resolution value was defined according to the value
considered by Stortz et al.,[31] who used a similar detector to what was used in the present study (LYSO). Simulation
of the dead-time effect on the detection of events was performed using the dead-time
module. Since Eriksson et al.[32] showed that two paralyzable dead-time (one at the level of the singles and the other
at the coincidence level) is enough to emulate the count rate performance in the PET
scanner, the effect of dead-time was also considered in this simulation at the stage
of recording singles in scintillation detectors and at the stage of recording coincident
event in electronic circuits. The dead-time module of 300 ns was applied at block
levels and 60 ns at the coincidence recording stage. In order to reduce the scattering
effect, the energy window in the range of 425–650 keV was then determined in accordance
with the vendor's recommendation for a standard device function. This section was
applied to the dead-time output singles by the thresholder and upholder modules. In
the next step, the singles were investigated in terms of coincident events. Coincidence
occurs when two singles are recorded with a relatively similar energy at a range of
511 keV in a time window in two detectors apart from each other. To define this part
in the GATE, a coincidence module with a 4.9 ns time window was defined, and a 4.9
ns delay time window with a 500 ns offset was used for the estimation of the random
events. The coincidence dead-time mentioned above was included in this section. Crystal
crosstalk effects and pileup rejection were not considered in this simulation as the
information needed to model these two effects is not readily available. Ignoring these
effects in simulation may influence the simulation results and lead to different simulation
and experimental results. The parameters defined for simulating the scanner signal
processing chain, including energy resolution, energy window, coincidence time window,
and delay time windows for collection of random events, were extracted from the datasheet
published by the manufacturer and from the study of Bettinardi et al.[10]
Assessment strategy
Model verification
After simulating the scanner, four line sources, with a diameter of 1.1 mm and a length
of 75 mm which were, respectively, placed at the center, and 1, 10, and 20 cm tangentially
from the center of field of view (FOV), were used to evaluate the simulated scanner
model. [Figure 3] depicts the position of the simulated line sources. The Full width at half maximum
(FWHM) of the line spread function was then calculated in simulation and experimental
images by interpolation between adjacent pixels. In addition, the sensitivity of the
center of FOV was calculated in all slices, and the sensitivity diagram was plotted
as a function of the image slice number in order to examine the model correctness.
Finally, based on the comparison results, the simulation parameters were modified
to allow the simulation results to approach the experimental results, offering a precise
model of the scanner.
Figure 3 Illustration of simulated line sources placed at the center of field of view and
1, 10, and 20 cm tangentially from the center of field of view showed in the A Medical
Image Data Examiner
Model validation
Voxelized phantom – A polymethyl methacrylate-made phantom with a height of 30 cm
and a diameter of 19 cm was used for the experimental part of validation. In this
phantom, eight cylinders of 8, 11, 16, and 21 mm in eight different positions in the
active FOV were placed and filled uniformly with water and F18. The activity level
used for the background was 3.54 Bq/cc. Each source had two different activity concentrations,
i.e., two times and eight times of the background activity, in two different positions.
[Figure 4] shows the cylindrical phantom used in this study.
Figure 4 Graphical illustration of cylindrical validation phantom. Top (a) and oblique (b)
views
The experimental measurements were carried out at the Tehran MassihDaneshvari Hospital
using the GE Discovery 690 VCT PET/CT scanner. The voxelized phantom module of the
GATE was used to simulate the phantom. To this end, a 256 × 256 × 12 matrix was assigned
to the phantom, and a phantom with similar dimensions to the experimental phantom
was designed therein. The activity concentration and tissue attenuation per pixel
corresponding to the clinic were then defined in two ASCII files, i.e., activity and
attenuation. Instead of defining the positron emitter source, the back-to-back gamma
source was defined during simulation. The GATE code was validated by comparing the
measured and the simulated images in terms of the three parameters of spatial resolution,
sensitivity, and contrast.
The simulation output data were reconstructed using Software for Tomographic Image
Reconstruction (STIR),[33] and ECAT7 output was used to reconstruct the image with STIR. The implemented reconstruction
algorithm was OSEM. Images with a 256 × 256 × 12 matrix were reconstructed. The output
data were not corrected in terms of attenuation, normalization, and noncollinearity.
Spatial resolution
In this study, the spatial resolution was calculated for four sources with an activity
eight times that of the background with different dimensions and positions. These
sources were placed in four different positions from the center (radially and tangentially
7 cm apart from the center of FOV).
The spatial resolution of all sources was obtained in two axial positions, i.e., the
central and ¼ axial FOV slice, by determining FWHM for point spread function, through
interpolation between the adjacent pixels in the radial and tangential profiles.
Sensitivity
At this stage, the region of interest (ROI) was plotted in the source range and in
a similar-sized range in the background. The accumulated counts were then calculated
in these ROIs. To calculate the count rate, the count values were divided by the imaging
time. The sensitivity was then calculated using the count rates of sources and the
corresponding backgrounds, as well as the activity of each source, according to the
following formula:
Where Rs is the source count rate, RBG is the background count rate, and AS is the
source activity.
Contrast
In order to evaluate the image contrast, several ROIs were plotted on the sources
and on the image uniform regions, as the background in the central slice. The contrast
was then calculated according to the following equation:
Where CS is the mean source count and CBG is the mean background count.
Image quality
The CRC was used to evaluate the image quality. This parameter was measured in two
source-to-background ratios of 2:1 and 8:1 for a slice at the center in four different
positions. First, the source and background counts were calculated by drawing several
ROIs for the sources and the background. Then, using the source-to-background ratio
and the calculated count, the CRC was calculated as follows:
Where NS and NBG are the mean source and background counts, respectively, and AS and
ABG are the source and background activity concentrations, respectively.
Results
Model verification
[Table 1] presents the results of FWHM for evaluation of the simulation accuracy and optimization
of simulation parameters in the measured and simulated images for four line sources
in millimeters.
Table 1 Measured FWHM for sources in different positions tangentially from the center: Simulated
and experimental results
In [Figure 5], the FWHM diagram of the line sources is represented as a function of the spatial
position. According to the diagram, the image FWHM increases by increasing the distance
from the FOV center in two simulated and measured images. The process of FWHM changes
is similar in two simulated and clinical images.
Figure 5 The full width at half maximum as a function of tangential placement of sources.
Results for central slice of simulated and measured images
[Figure 6] qualitatively examines the trend of sensitivity changes in two simulated and experimental
images. This diagram shows the sensitivity at the center of FOV, which is the location
of a line source. The diagram demonstrates that the sensitivity is high in the line
source range and tends to zero outside the line source where there is no activity.
The qualitative examination of this diagram shows that simulation and experimental
results have similar trends.
Figure 6 Sensitivity as a function axial slice number at the center of field of view. Results
for simulated and measured images
Model validation
Spatial resolution
The images for the quantification of the spatial resolution were reconstructed using
the STIR and OSMAPOSLcode without normalization correction. FWHM calculations were
performed on both clinical and simulated images. The spatial resolution was calculated
radially and tangentially in millimeters in each of the four positions related to
cylindrical sources in the central and ¼ axial FOV slice; the results are reported
in [Table 2] and [Table 3]. The differences between simulated and measured values are also specified in the
last column. Based on the findings, the results of the simulation spatial resolution
had a mean difference, with the measured values, of <6.5% in the tangential direction
and <5.5% in the radial direction.
Table 2 Tangential simulated and measured FWHM for sources in different positions in central
and 1/4 axial field of view slice
Table 3 Radial simulated and measured FWHM for sources in different position in central and
1/4 axial field of view slice
[Figure 7] depicts the FWHM changes in terms of source dimensions. Based on this chart, the
spatial resolution decreases by increasing the source diameter. This trend was observed
in both simulation and experimental images for both central and ¼ axial FOV slices.
Figure 7 Simulated and measured tangential FWHM as a function of source diameter in central
(a) and 1/4 axial field of views (b)
Sensitivity
[Table 4] compares the sensitivity values in four different positions for the scanner and
simulated images in two central and ¼ axial FOV slices. The sensitivity values are
in cps.kBq−1. According to the results reported in this table, the mean sensitivity
difference in the simulation image was <7% compared to the experimental results.
Table 4 Simulated and measured sensitivity for sources in different positions in central
and 1/4 axial field of view slice
Contrast
In [Table 5], the contrast results are reported for sources with different dimensions and different
positions in the two source-to-background ratios. As expected, the sources' contrast
in the 2:1 source-to-background ratio was less than the 8:1 source-to-background ratio,
which was observed in both the simulated and measured images.
Table 5 Comparison between simulated and experimental values obtained for the contrast of
four sources with different size in two different source-to-background ratios
[Figure 8a] and [Figure 8b] illustrates the sources' contrast as a function of the source diameter for the source-to-background
ratio of 2:1 and 8:1. As shown in these diagrams, the contrast is increased by increasing
the source size in both simulated and clinical images.
Figure 8 Contrast of four sources with 2:1 (a) 8:1 (b) source-to-background ratios. The plots
refer to simulated and measured images
Figure 9 Contrast recovery coefficient calculated over region of interests in central slice
encompassing the four sources in cylindrical phantom as a function of source diameter.
The plots refer to images with source-to-background ratio 2:1 (a) and 8:1 (b)
Image quality
The simulation output was reconstructed using STIR and the OSMAPOSL code in order
to evaluate the quality of simulated images. Then, the CRC was calculated for both
clinical and simulated images. The results of these calculations are reported in [Table 6], according to which, the mean difference of the simulation image recovery coefficient
was below 8%.
Table 6 Comparison between simulated and experimental values obtained for the contrast recovery
coefficient of four sources with different size in two different source-to-background
ratios
The two diagrams of [Figure 9] show the CRC percent for the simulated and measured data, and diagrams a and b represent
CRC for the 2:1 and 8:1 source-to-background ratios, respectively. These diagrams
compare the image contrast for the sources with four different sizes. As can be seen,
there is a good agreement between the simulated and measured values in each of the
four sizes. According to the diagrams, in both source-to-background ratios, CRC increases
with the increase in the sources' diameter, which is evident in both simulated and
experimental images.
Discussion
The present study aimed to develop an accurate model of the GE Discovery 690 PET scanner
and evaluate its performance using the GATE Monte Carlo simulation. The validity of
the proposed model was also evaluated against experimental data.
In the first stage, the scanner was simulated. To this end, its geometry was designed
in the GATE simulation code based on the information from the scanner geometry. The
physics of interactions was then defined. The digitizer, which mimicked the scanner
signal flow, was simulated based on the specifications of the scanner and information
from the device provided by the manufacturer. After system simulation, the accuracy
of the developed model was evaluated using the line sources and comparing the scanner
images with the simulated images. The results of simulation and measured data were
approached through modification of the digitizer module parameters, and a model with
an acceptable correctness was presented. In order to validate the developed model,
the voxelized phantom was used by performing the validation with an emphasis on the
sensitivity, spatial resolution, and contrast of the images. The CRC parameter was
compared in two images in order to evaluate the simulated image quality.
The spatial resolution of the line sources in [Figure 5] indicates that the spatial resolution decreases with an increase in the source distance
from the center, which is consistent with the results reported by Grogg et al.[34] This decrease in spatial resolution can be influenced by the detector geometric
factors, such as depth of interaction, that can be observed both in simulation and
measured data. The similar trend of FWHM variations in this diagram in both simulation
and experimental modes confirms the correctness of the proposed model. The observed
difference between simulation and experimental results is due to a number of phenomena
that basically occur during the radiation detection and image formation processes.
However, they were not considered in the current simulation due to lack of access
to the exact information required for their simulation. Therefore, in future studies,
a scale factor can be obtained and applied to the simulation results to improve the
accuracy of the proposed model and reduce the impact of these phenomena.
Quantitative evaluation of the image sensitivity, as a function of the slice number
[Figure 6], indicates that the sensitivity variation trend was correct with respect to the
presence of a line source in the study area in both the simulated and measured images,
and a sensitivity peak existed in the system center, precisely in the region of the
line sources. This sensitivity was sharply reduced in the area outside the line source
length. Nonuniform variations of the sensitivity in the original image can be due
to the fact that the central line source was not at a flat and stable position during
imaging, affecting the sensitivity results as the count accumulated from each area
as per the activity concentration. However, the similar trend to the results confirms
the correctness of the simulation and the proposed model.
[Table 2] and [Table 3] show a good agreement between the simulated and experimental spatial resolution
results in both radial and tangential directions. The simulated radial and tangential
FWHM values had a mean difference of <6.5% compared to the experimental values. This
means that the spatial resolution of simulated images was better than the measured
images. This underestimation for FWHM can be attributed to nonsimulation of a number
of phenomena in the GATE. For example, light shielding between and inside block detectors
as well as the inherent limitation of photo multiplier tube (PMTs) and optical scattering
occurring in crystals was not considered. In addition, the light sharing between PMTs
can also be specified as a reason,[35] which was not considered in this simulation. Simulation of the crosstalk phenomenon
between crystals can also reduce the difference between results. The evaluation of
spatial resolution in [Figure 7] illustrates the relationship between the source size and FWHM, meaning that the
spatial resolution decreases by increasing source dimensions. This problem can be
similarly observed in both the simulated and experimental images.
The mean overall difference between the simulated and measured sensitivity results
was <7%, which is acceptable. This difference can be attributed to the factors described
for the spatial resolution. The definition of a global quantum efficiency in this
study has an impressive effect on reducing the difference between results. However,
considering a uniform quantum efficiency is consistent with the reality. Therefore,
taking into account a variable quantum efficiency can greatly reduce these disparities.
According to [Table 5], the simulated image contrast for the two source-to-background ratios of 2:1 and
8:1 had a mean divergence of 1.5% and 6%, respectively. The results show a good agreement
in the contrast between the simulated and measured images. As expected, with increasing
the source diameter, the image contrast increases. The contrast in the source-to-background
ratio of 8:1 was more than 2:1, which was observed in both simulated and experimental
images [Figure 8].
Based on what is reported in [Table 6], the CRC results show a good agreement between the simulated and clinical images,
and the mean difference in results for the source-to-background ratio of 2:1 and 8:1
was <6.5% and 9%, respectively. Comparison of the CRC results for evaluation of image
quality indicated that the divergence of results was higher for sources with smaller
diameter. This conclusion was also reported in the Zagni et al.'s study.[18]
[Figure 9] shows that in both source-to-background ratios of 2:1 and 8:1, the higher the diameter
of the source, the higher will be the CRC; this is consistent with the data published
in other studies.
In general, the observed differences in the results were in an acceptable range, and
these under- and over-estimations can be related to the effects of the actual detection
process mentioned earlier and to the inaccessibility to precise information for their
definition in GATE. In addition, the model proposed in this study was simulated based
on finite geometric information of scanner geometry, and hence was approximate.
Conclusion
In this study, the performance parameters of the GE Discovery 690 PET scanner were
evaluated using GATE MC simulation and validated with the results obtained from clinical
images. The spatial resolution, sensitivity, contrast, and image quality evaluated
for the scanner in this study are well validated. Furthermore, the results indicate
that the designed model has potential to become a reliable tool for imaging protocol
optimization, design of new scanners, and performance evaluation under different imaging
conditions.
