Applied Radiation and Isotopes 75 (2013) 105–114

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Applied Radiation and Isotopes

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Accurate modeling of a DOI capable small animal PET scannerusing GATE

F. Zagni a,n, D. D’Ambrosio a,1, AE. Spinelli a,2, G. Cicoria a, S. Fanti b, M. Marengo a

a Medical Physics Department, University Hospital ‘‘S. Orsola-Malpighi’’, Bologna, Italyb Nuclear Medicine Department, University Hospital ‘‘S. Orsola-Malpighi’’, Bologna, Italy

H I G H L I G H T S

c We developed an MC model of the Argus (Sedecal) small-animal PET scanner using GATE.c Validation was performed through comparison between simulated and experimental data.c Spatial resolution, sensitivity and scatter fraction showed agreement within 7%.c NEC was in excellent agreement at activities up to 50 MBq in the field of view.c Image quality was also compared through the NEMA NU-4 phantom.

a r t i c l e i n f o

Article history:

Received 28 June 2012

Received in revised form

10 December 2012

Accepted 3 February 2013Available online 14 February 2013

Keywords:

GATE

Monte Carlo

Simulations

Small-animal

PET

DOI

43/$ - see front matter & 2013 Elsevier Ltd. A

x.doi.org/10.1016/j.apradiso.2013.02.003

esponding author. Tel.: þ39 51 636 3183.

ail addresses: fedez83@gmail.com, federico.za

ow at: Medical Physics Department, IRCCS S.

aly.

ow at: Medical Physics Department, IRCCS Sa

Italy.

a b s t r a c t

In this work we developed a Monte Carlo (MC) model of the Sedecal Argus pre-clinical PET scanner,

using GATE (Geant4 Application for Tomographic Emission). This is a dual-ring scanner which features

DOI compensation by means of two layers of detector crystals (LYSO and GSO). Geometry of detectors

and sources, pulses readout and selection of coincidence events were modeled with GATE, while a

separate code was developed in order to emulate the processing of digitized data (for example,

customized time windows and data flow saturation), the final binning of the lines of response and to

reproduce the data output format of the scanner’s acquisition software.

Validation of the model was performed by modeling several phantoms used in experimental

measurements, in order to compare the results of the simulations. Spatial resolution, sensitivity, scatter

fraction, count rates and NECR were tested. Moreover, the NEMA NU-4 phantom was modeled in order

to check for the image quality yielded by the model. Noise, contrast of cold and hot regions and

recovery coefficient were calculated and compared using images of the NEMA phantom acquired with

our scanner. The energy spectrum of coincidence events due to the small amount of 176Lu in LYSO

crystals, which was suitably included in our model, was also compared with experimental measure-

ments.

Spatial resolution, sensitivity and scatter fraction showed an agreement within 7%. Comparison of

the count rates curves resulted satisfactory, being the values within the uncertainties, in the range of

activities practically used in research scans. Analysis of the NEMA phantom images also showed a good

agreement between simulated and acquired data, within 9% for all the tested parameters.

This work shows that basic MC modeling of this kind of system is possible using GATE as a base

platform; extension through suitably written customized code allows for an adequate level of accuracy

in the results. Our careful validation against experimental data confirms that the developed simulation

setup is a useful tool for a wide range of research applications.

& 2013 Elsevier Ltd. All rights reserved.

ll rights reserved.

gni@aosp.bo.it (F. Zagni).

Maugeri Scientific Institute,

n Raffaele Scientific Institute,

1. Introduction

Monte Carlo (MC) simulations are increasingly being employedin a wide variety of research fields, not limited to the high energyphysics, such as nuclear medicine, also thanks to the increasingcomputing power available with the latest workstations. Applica-tion of MC simulations in positron emission tomography (PET)provides a powerful tool which often plays a key role in designingnew devices, optimizing existing reconstruction algorithms by

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114106

developing correction techniques to improve image quality, and inassessing the performance of a scanner under specific conditions(Zaidi, 1999). Pre-clinical PET scanners feature high spatial resolu-tion and high sensitivity, enabling basic research on small animals,such as in vivo studies of biochemical and metabolic processes.

A variety of general purpose MC codes are available, suchas Geant4 (Agostinelli et al., 2003; Allison et al., 2006), whichprovides high flexibility and validation from a wide community.However, their application to emission tomography systems oftenresults difficult and inefficient due to their high complexity. Thus,MC software dedicated to medical physics field were developed,such as GATE (Geant4 Application for Tomographic Emission),which was applied to develop the model of our small-animal PETscanner. The advantage of this software is that it allows to modelthe main features of most common medical imaging instrumen-tation by means of a straightforward scripting language, while itexploits the well validated Geant4 libraries for the basic physicalinteractions (Jan et al., 2004). Data flow may also be included inthe simulations, as GATE also provides a set of tools to model thepulses processing such as coincidences selection and dead times(Kerhoas-Cavata and Guez, 2006). This toolkit is seeing increasingpopularity as it has been constantly updated in the last years andseveral imaging systems were validated and reported in theliterature (Assie et al., 2004; Buvat and Lazaro, 2006; Santinet al., 2007; Jan et al., 2011).

The aim of this work was to model the Sedecal Argus pre-clinicalPET scanner installed at our institution. Detectors geometry and thefirst stages of the pulses processing were successfully modeled withGATE, while more specific aspects of our system such as data lossesand CPU saturation were more accurately modeled by writing adedicated code which processes the simulation output. Modelvalidation was performed mainly, but not limited to, evaluatingand comparing simulated and experimental data of the four mainparameters commonly used to assess PET scanners performances:spatial resolution, sensitivity, scatter fraction and count rates.Comparison of simulated and experimentally acquired images ofthe NEMA NU-4 test phantom was used to make qualitative andquantitative analysis on reconstructed images.

2. Materials and methods

2.1. The Argus scanner

The Argus (Sedecal) is a preclinical PET scanner dedicated to smallanimal imaging. It features a dual ring detector, each ring consistingof 18 detector blocks, 11.8 cm in diameter. Each detector blockconsists of 169 phoswich sensitive elements (1.45�1.45�15 mm)arranged in a 13�13 matrix (Fig. 1), while a thin layer of PTFEseparates each individual crystal element. The double layer designallows to store depth-of-interaction (DOI) information leading tobetter and uniform radial spatial resolution in the reconstructedimage (Wang et al., 2006). The front layer crystal is cerium-dopedLutetium-Yttrium Orthosilicate (LYSO, 7 mm long), which is opticallycoupled to the 8-mm-long Gadolinium Orthosilicate (GSO) back layer

Fig. 1. Schematic representation of the detector modules of the Argus scanner.

crystal. The presence of the naturally occurring radioactive isotope176Lu in LYSO, a b�(100%) and gamma emitter (202 keV, 86% and307 keV, 94%), results in a background rate, which is roughly 5 �102

coincidence events per second. For each detector block, scintillationphotons are detected by a position sensitive photomultiplier (PS-PMT) coupled to the GSO layer (Hamamatsu, 2004). Data are there-fore digitized by the corresponding ADC and sent to a computer forfurther processing. Each detector block is set in time coincidence(20 ns) with the 14 opposite blocks (7 for each ring), resulting inabout 28.8 �106 lines of response (LORs) and to a transaxial and anaxial fields of view (FOV) equal to 6.8 cm and 4.7 cm, respectively.Narrow coincidence windows are applied to the digitized data by theacquisition software. The proprietary software allows scans usingthree energy windows (100–700, 250–700, 400–700 keV); theacquired data are normalized to take into account possible differencesof the detectors efficiency and stored into a 3D data set. Thus, rawdata can be reconstructed using 3D OSEM algorithm or 2D algorithms(OSEM or FBP) after Fourier Rebinning (FORE) (Hudson and Larkin,1994; Defrise et al., 1997).

2.2. Modeling the system with GATE

To model the Argus scanner, GATE version 6.1 (Jan et al., 2011)was used. This version makes use of the recent Geant4 libraries andmodels (version 9.4) to simulate the physical processes involved in aPET acquisition, such as positron scattering, annihilation, Comptonscattering, photoelectric absorption (Agostinelli et al., 2003; Allisonet al., 2006). More precisely, the standard libraries for electromag-netic interactions were used, which are effective for energies downto 1 keV. Besides the detector rings described above, such as theDelrin cover of the gantry, lead shields and the carbon-fiber bedwere also included in the model (Fig. 2). The simulated physicalinteractions (hits) occurring within the modeled detector crystals aregrouped into pulses for each detector block. LYSO and GSO crystalswere assigned to different sensitive detectors in GATE in order tostore DOI information. A layer ID is assigned to each event and usedin the subsequent algorithm which creates the final output data set.Thus, the model can take into account the four possible layer

Fig. 2. Graphical visualization of the modeled geometry showed in the OpenGL

window created by GATE. Gantry cover, bed and back shield can be noted.

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114 107

combinations during the identification and counting of LORs. Inorder to model the finite energy resolution, the energy values of thepulses were, thus, blurred using a Gaussian function (FWHM equalto 26% for LYSO, 33% for GSO, referenced to 511 keV). A low-energythreshold (50 keV) and a paralyzable dead-time (220 ns) were alsoapplied to the singles processing chain at this stage of the acquisi-tion. The flow chart of the singles processing chain was shown inFig. 3. The background counts due to the presence of 176Lu withinLYSO crystals were also included in the model. Such coincidenceevents arise when a 176Lu decay occurs in one detector, a subse-quent photon escapes and, after crossing the field of view, isdetected within the time coincidence window. The module providedby GATE to mimic background appeared not well suited to correctlyinclude this effect, since it just generates random events to beintroduced in the pulse-processing chain. A source which modelsthe full decay chain of 176Lu was then placed inside the modeledLYSO crystals. To do that, a source as large as the entire rings wascreated and then restricted to the detector crystals thanks to thededicated command (‘‘confine’’) provided by Geant4, and also avail-able in GATE. The activity of the source was adjusted in order tomatch the prompt count rate recorded by the scanner.

In order to simulate the hardware coincidence trigger of oursystem the coincidenceSorter GATE module was used. More pre-cisely, takeAllGoods criterion was chosen to manage multiplecoincidences. The minSectorDifference parameter was set to 6 tomimic the hardware system matrix of allowed coincidences pre-sent in our scanner. The events acquired at this stage were takenand stored in a ROOT file (Brun and Rademakers, 1997).

In order to better customize electronics and pulse processingsimulation, a dedicated software was developed in Cþþ, whichanalyzes and processes this file. Roughly, the list of the eventsstored in the ROOT file is loaded by this code into an array andprocessed as a data stream coming from the detectors. Detailsabout the developed software are provided in Appendix A.

After these processing steps, valid coincidence events (promptcoincidences) are stored. List-mode prompt coincidences may beanalyzed selecting true, scatter and random events, since thehistory of each detected event has been stored. In our processingchain, list-mode data are binned so that LOR counts are organizedin the same format of the Argus raw data files. Data could, thus, bereconstructed using the algorithms of the Argus scanner. Thenormalization factors, which take into account slight differencesin detectors response and gain, were customized with uniformfactors, since the simulated detectors are all identical. In order tocreate a normalization file which can be used by the proprietarysoftware, a dedicated 68Ge/68Ga annulus source was modeledwith GATE and approximately 1010 prompt counts were collectedfollowing the same procedure as for the real scanner.

Fig. 3. Flow chart of the simula

2.3. Validation

Validation of Argus model was performed by comparing experi-mental measurements and simulated data. Four well establishedparameters for PET performance evaluation were compared, suchas spatial resolution, sensitivity, scatter fraction, prompt and NECrates. Moreover, background coincidences and image quality wereanalyzed.

2.3.1. Spatial resolution

To evaluate radial spatial resolution, point sources were obtainedby soaking a small piece of zeolite (diameter equal to 0.3 mm)in a solution of 18F, (approximately 1 MBq total) and acquired atdifferent radial offsets starting from the center of the FOV (Baileyet al., 2004). Using the GATE model, a source having the samedimensions was simulated at the same offsets, in order to collect atleast 106 prompt counts for each acquisition. Acquisitions andsimulations were performed for the three energy windows (100–700, 250–700, 400–700 keV) and also using a 11C solution contain-ing the activity approximately equal to 1 MBq (Spinelli et al., 2006).Acquired and simulated data were rebinned using FORE algorithmand reconstructed by mean of 2D FBP algorithm. A line-profile inboth the radial and axial direction was drawn across the central sliceof the reconstructed images and fitted by a Gaussian function, inorder to estimate the spatial resolution as FWHM of the gaussian fit.Spatial resolution was evaluated both for 18F and 11C data.

2.3.2. Absolute sensitivity

In order to evaluate the absolute central sensitivity, a 18F pointsource (1 mm in diameter) was acquired and about 105 promptcounts were collected using the three energy windows. Sourceactivity, measured by means of a radionuclide activity metercalibrated using a NIST traceable standard source (Zimmermanand Cessna, 2010), was equal to 1.270.1 MBq. The sensitivity wascalculated as the ratio between the total coincidence rate and thepoint source activity (expressed in Bq). Total coincidences werecounted directly from the scanner’s acquisition software and fromthe list-mode output obtained from the modeled system.

2.3.3. Count rates and scatter fraction

To measure prompt rate, Noise Equivalent Count (NEC) rate andScatter Fraction (SF), procedures suggested by the National ElectricalManufacturers Association (National Electrical ManufacturersAssociation (NEMA), 2008) were followed. Two polyethylene cylind-rical phantoms were made to mimic mouse and rat, which are70 mm long and 25 mm in diameter, 150 mm long and 50 mm indiameter respectively. An off-center cylindrical hole (3.2 mm

ted signal processing chain.

Table 1Comparison between simulated and experimental values (expressed in mm)

obtained for the radial spatial resolution obtained using 18F.

EW Radial offsets

0 5 10 15 20

Spatial resolution (simulations)

100–700 keV 1.25 1.55 1.62 1.85 2.02

250–700 keV 1.23 1.55 1.60 1.76 1.95

400–700 keV 1.22 1.53 1.63 1.74 1.93

Spatial resolution (measurements)

100–700 keV 1.51 1.59 1.75 2.00 2.19

250–700 keV 1.47 1.48 1.65 1.94 2.11

400–700 keV 1.43 1.49 1.54 1.85 2.05

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114108

diameter) was drilled parallel to the central axis at a radial distance of10 mm and 17.5 mm for mouse-and rat-phantom, respectively. Inorder to sample the count rate curves, for the three energy windows,a flexible tube was filled with a uniform high activity concentrationsolution of 18F–FDG and placed within the phantom’s hole. In order toidentify the linearity region and the peak rate value of the NEC curve,acquisitions at fixed time intervals were performed and count rateswere plotted against phantom activity concentration. Each point ofthe NEC curve was, thus, calculated as follows:

NEC ¼T2

TþSþkR¼ðP�RÞ2ð1�SFÞ2

P�RþkR

where P, T, S and R are the prompt, true, scatter and random rates,SF¼S/(SþT) is the scatter fraction and k is the ratio of the transaxialFOV occupied by the phantom. While in simulations these values canbe retrieved directly, since the history of each event is known, inexperimental measures random and scatter events must be esti-mated. To estimate the random counts rate, a variation of the delayedwindow method was developed, since the latter is not implementedin Argus scanner. Events detected as coincidences within the hard-ware time window (20 ns) and rejected by the narrower windowapplied at software level (5 ns) were considered, since almost all thetrue coincidences lied inside this window. Time difference betweentwo events of rejected coincidences was plotted. An approximatelyconstant trend was observed and, thus, the number of the randomcoincidences accepted by the narrow time window could be calcu-lated as a rectangular area. This method was also evaluated by Torres-Espallardo et al., 2006. In simulations, this estimation method wasapplied in order to compare the obtained random counts rate to thedirect count of the randoms based on the history of each event.

An acquisition at very low activity concentration was usedfor SF calculation, so that randoms contribution could beneglected. SF was estimated from sinogram, following themethod described in the NEMA report.

Fig. 4. Plot of the radial spatial resolution values relative to 18F

Fig. 5. Plot of the radial spatial resolution values relative to 11C

Mouse- and rat-phantoms were modeled with GATE, assimple polyethylene cylinders along with the inserted tubing.Simulations were run setting different activity concentrationsof the 18F solution located inside the phantom, in order tocompare the count rates against the experimental results.

2.3.4. Background 176Lu energy spectrum

Measurements of the background prompt counts rate areroutinely performed as stability check within our QA procedures.The presence of 176Lu results in our scanner in 52574 promptcounts per second when acquiring with no sources and no bedwithin the gantry. The activity of the 176Lu source in simulationswas adjusted to match the same value when acquiring 105 counts.

Moreover, an energy spectrum of the coincidence promptcounts was acquired both using the scanner and the GATEmodel. Since the system does not store the energy detected forall the single events, the spectrum was built performingacquisitions applying 10 keV-width energy windows, starting

point source acquisition with 250–700 keV energy window.

point source acquisition with 250–700 keV energy window.

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114 109

from 50 keV, up to 500 keV. Although this spectrum did notinclude all the single events, nor all the coincidence eventsacquired using wider energy windows (i.e. as in normal scans),this method provided an useful tool to assess the simulatedsystem.

Table 2Comparison between simulated and experimental values obtained for the absolute

central sensitivity.

EW Sensitivity (%)

simulations measurements

100–700 keV 5.7470.02 5.970.5

250–700 keV 3.7370.02 3.970.3

400–700 keV 2.2370.02 2.270.2

2.3.5. NEMA phantom

The purpose of the NEMA NU-4 image quality phantom is toproduce images simulating those obtained during an imagingstudy on small rodents, which may contain hot and coldregions. The phantom is a cylinder with diameter 30 mm andheight 50 mm, whose the upper 30 mm section is empty, whilethe remaining 20 mm are solid (plastic) with five fillable rods,with diameters 1, 2, 3, 4, 5 mm, respectively. In theupper section two other cylindrical chambers (diameter8 mm, height 15 mm) may be inserted and used as coldregions or filled with a radioactive solution. It is, therefore,an useful tool to assess the performance of the imagingsystem, for example spatial resolution or signal to noise ratio,as well as scatter correction techniques. The phantom wasmodeled with the main section filled with a 18F solution(activity concentration of the order of 100 kBq/cc), while oneof the two independent chambers was used as cold region

Fig. 6. Comparison of prompt count rates for mouse (a) and rat (b) phanto

(water with no activity) and the other one was filled with anactivity concentration of approximatley 500 kBq/cc, yielding a5:1 ratio with respect to the background region. Images ofNEMA phantom were, thus, acquired collecting about 108

prompt counts. Both acquired and simulated data were recon-structed using 2D OSEM (16 subsets, 2 iterations) after FORE,without any further processing. Matrix of reconstructedimages is 175�175�61 voxels and the voxel size is0.3875�0.3875�0.775 mm. In order to evaluate the perfor-mance of the GATE model with respect to the image quality,several regions of interest (ROIs) were drawn across acquiredand simulated images. Noise was estimated by means ofcoefficient of variation measured in a uniform ROI. Contrast

ms for the three energy windows (100–700, 250–700, 400–700 keV).

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114110

of hot and cold cylinders was calculated as

C ¼RC

RU

where RC is the average value of the ROI on the cylinders andRU is the average value of the ROI on the uniform region.Recovery coefficients were calculated for all the five rods, inorder to plot and compare the obtained values, against the roddiameter, for both acquisitions and simulations.

3. Results

3.1. Spatial resolution

FWHM values calculated from both simulated data using GATEand from experimental data were shown in Figs. 4 and 5. Theplots were related to the 18F and 11C point sources located atdifferent offsets and acquired in the 250–700 keV energy window.An uncertainty of 70.10 mm is associated with the measures,based primarily on the pixel size. In Table 1 were reported theresults related to the 18F source. FWHM values calculated in theaxial direction were 1.78 mm and 1.72 mm for measured andsimulated data, respectively. Spatial resolution estimated valuesfrom simulations appeared to be in good agreement with experi-mental data, being the largest discrepancy of about 7% for all thethree energy window, except for the zero offset point. The largerdiscrepancy observed at zero offset, being better the simulated

Fig. 7. Comparison of NEC rates for mouse (a) and rat (b) phantoms f

resolution, may be attributed to the positioning of the source inthe experiments, that may result slightly off-center, which ismore significant at the central point rather than at larger radialoffsets. On the other hand, the slight general tendency to be betterthe resolution in simulations may be attributed to the modelingof the PS-PMTs resolution. Standard values referred to a standardenvironment, based on the datasheet of the manufacturer, wereused to model PS-PMTs resolution. Therefore, small variationswere possible, anyway giving a minor contribution.

These results are also in agreement with data reported inliterature (Wang et al., 2006; Goertzen et al., 2012). Moreover,the difference in resolution between 18F and 11C is conserved,showing the good reliability of the GATE and Geant4 physicslibraries.

3.2. Sensitivity

Absolute sensitivity values from simulated and experimentaldata were summarized in Table 2. The comparison betweensensitivity values showed excellent agreement, within the uncer-tainties. While uncertainties reported for the simulations werepurely random statistic deviations, those associated with theexperimental measurements included also non systematic devia-tions in the calibration of the radionuclide activity meter, thataffect the determination of the source activity. Lower sensitivityvalues for thinner energy windows were obtained, as expected,since many coincidences were discarded.

or the three energy windows (100–700, 250–700, 400–700 keV).

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114 111

3.3. Count rates and scatter fraction

Prompt count rates were plotted in Fig. 6 for both mouse-likeand rat-like phantoms and for the three energy windows applied.NEC rate curves were shown in Fig. 7. Simulated and measuredcurves were in good agreement for a wide range of activities,particularly within the first linear region, being the discrepancyless than 5% for all the three energy windows and for bothphantoms. At high activities, above the NEC peak, agreementresulted slightly worse. In this case, a better modeling of theelectronics would be required to take into account all the data

Table 3Scatter Fraction values in %, for different energy windows, obtained simulating the

mouse-sized and rat-sized phantoms (left column). In the right column are

reported the experimental results.

EW simulations measurements

Scatter Fraction (Mouse Phantom)

100–700 keV 33.170.3 3372

250–700 keV 28.070.3 2971

400–700 keV 15.170.2 1871

Scatter Fraction (Rat Phantom)

100–700 keV 48.170.3 4972

250–700 keV 38.170.3 3771

400–700 keV 23.370.2 2271

Fig. 8. Comparison of simulated and measured background counts. The peaks match

Fig. 9. Real acquisition of the NEMA phantom filled with 1

losses, dead times and pileup, which become more significant atvery high count rates. However, in practice, most if not allresearch scans are acquired with less than 50 MBq inside thescanner FOV, in the range of count rates for which the results ofour simulations are satisfactory.

Scatter Fraction values, used to evaluate the NEC rates,were reported in Table 3. Good SF values were obtained as themain geometrical elements were included in the model. Inparticular, the lead shielding appeared to give a major con-tribution (Badawi et al., 1999) and also resulted in a slightlyhigher count rate on the most external crystals in bothexperimental and simulated data. As shown in Fig. 7, thelarger discrepancies were observed at high count rates. Theuncertainty of prompts and scatter coincidences have to beconsidered. More precisely, random coincidences, which givea significant contribution to the NEC value at very high countrates, might be not accurately estimated using the methoddescribed in the previous section. In fact an underestimationof measured randoms of about 25% (with low variationsbetween the energy windows) were found with respect tothe value obtained in simulations considering the history ofeach detected photon. As stated above, the estimation methodwas also applied to the simulated data, giving a systematicunderestimation of the random count rate of 10% as a max-imum value, anyway even in this case a more accuratemodeling would require a deeper knowledge of the electronicchain, which, on the other hand, has fewer practicalapplications.

the two main peaks of the 176Lu (307 keV and 202 keV) present in LYSO crystals.

8F solution. Transverse slice (a) and coronal slice (b).

Fig. 10. Simulated transverse (a) and coronal (b) slices of the NEMA phantom with 18F source.

Fig. 11. Recovery coefficient calculated over region of interests encompassing the five rods of the NEMA phantom. The plot refers to images acquired using the

100–700 keV energy window.

Table 4Comparison between simulated and experimental values obtained for the recov-

ery coefficient calculated using the acquired images of the NEMA phantom. An

uncertainty of 5% is associated with the values.

EW Rod diameter (mm)

1 2 3 4 5

Recovery coefficients (simulations)

100–700 keV 0.125 0.383 0.560 0.637 0.684

250–700 keV 0.155 0.411 0.598 0.668 0.731

400–700 keV 0.132 0.445 0.643 0.714 0.771

Recovery coefficients (measurements)

100–700 keV 0.133 0.387 0.558 0.667 0.704

250-700 keV 0.165 0.434 0.614 0.699 0.730

400-700 keV 0.141 0.468 0.657 0.732 0.777

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114112

3.4. Background 176Lu spectrum

In Fig. 8 the comparison between data acquired with Argusscanner and GATE simulations was shown. The simulated back-ground 176Lu source provided results in good agreement withexperimental data. The observed peaks matched the two mainpeaks of 176Lu (307 keV and 202 keV) present in LYSO crystals. Anuncertainty of 5 keV (half bin width) has been set, to take into

account possible differences in energy resolution and calibrationthroughout the energy spectrum.

This comparison allowed us to check, other than the modeledsource itself, important features of the first blocks of the modeledpulse processing chain, such as the correct choice of the criterionin the selection of valid coincidences and multiple coincidences,and their correct location in the whole processing chain (Fig. 3).Such inaccuracies, present in our model at the first stages ofdevelopment, when only the background noise function includedin GATE was used, resulted also in slight discrepancies in theother validation tests, particularly for the prompt counts at bothlow and high rates. However, the correlation between the betaparticle and the two photons emitted from 176Lu nuclei, madethese inaccuracies much more evident in such energy spectrum.The incorrect detection (or rejection) of one of the two pulses dueto wrong coincidence identification, led in fact to both differentratios between the two peaks and to wrong total counts per bin.Simulation of the 176Lu decay accurately solves these issues andthe model now accounts for all these aspect.

3.5. NEMA phantom

In Fig. 9 the reconstructed image of the phantom acquiredusing the Argus scanner was reported. More precisely, transaxialand coronal views were shown. The same views, in Fig. 10, of thesimulated phantom made possible a qualitative comparison of theimage quality yielded by the model.

Table 5Quantitative comparison of simulated and acquired images. Noise was calculated

on the uniform region of the NEMA phantom, while contrast was calculated as the

ratio between hot/cold inserts and the uniform region.

EW simulations measurements

Noise (c.v.%)

100–700 keV 6.4 6.5

250–700 keV 7.2 7.7

400–700 keV 11.5 10.5

Cold region to background100–700 keV 0.21070.019 0.20370.020

250–700 keV 0.19770.018 0.18170.018

400–700 keV 0.18070.016 0.17170.017

Hot region to background100–700 keV 4.3570.31 4.0370.32

250–700 keV 4.2670.34 3.9870.35

400–700 keV 4.3870.48 4.0470.42

F. Zagni et al. / Applied Radiation and Isotopes 75 (2013) 105–114 113

In Fig. 11 were plotted the recovery coefficients calculated fromsimulated and acquired images for the five phantom’s rods withdifferent diameters. The plot is relative to the 100–700 keV energywindow. Data relative to all the energy windows were reported inTable 4. Differences were bigger for the narrower rods and for thenarrower energy windows. In particular, the 1 mm ones, which werebarely resolved by our system, showed a maximum deviation of 6%.Noise and contrast of the two inserts over the uniform region werereported in Table 5. Since the values obtained for the three energywindows were relative to acquisitions of the same duration, anincreasing of the noise was observed for thinner windows due tofewer counts recorded. All the average values were in good agree-ment within their experimental uncertainties. Simulations give ingeneral slight higher contrast and lower noise, being anyway thebigger difference about 9%.

4. Conclusion

The objective of this work was to develop the Monte Carlo modelof the Sedecal Argus PET scanner. To this aim, GATE was used tomodel the scanner geometry and selection of coincidences, while aseparate code was developed to model dead time, processingcapability and PS-PMT resolution. The validation was mainly focusedon PET performance parameters such as system sensitivity, spatialresolution, count rates and scatter fraction. Spatial resolution andsensitivity were reproduced well, being the results in agreementwithin the uncertainties. The model performed well also for scatterfraction when the effect of the lead shielding and the main elementsinside the field of view were included. About the count rates and NEC,an accurate modeling of the electronic processing chain was critical,in particular with regard to the data transmission speed and proces-sing capability, which cause saturation at high count rates. A bettermodeling of the processing chain may further improve the responseof the model at such high count rates; nevertheless, in the range ofactivities practically used in pre-clinical research, our simulationsetup produces results in satisfactory agreement with experimentaldata. This was confirmed also by the comparison of image quality,through the NEMA phantom: contrast and noise of the images yieldedby the model, accurately reproduced experimental results.

The developed model is accurate enough to be usefully applied ina wide range of applications (Quarta et al., 2012; Giussani et al.,2012). It can be used to obtain information that cannot be measuredexperimentally, such as scatter and true coincidences distribution andannihilation positions map. It enables to assess the imaging perfor-mance of experimental PET tracers and to map the system PSF foreach voxel of the field of view, in order to introduce compensations

for the partial volume effect in iterative reconstruction algorithms(D’Ambrosio et al., 2010). Moreover, since GATE allows voxelization ofthe source, more complex phantoms may be developed, such as theMOBY phantom, to reproduce more realistic imaging conditions.

Acknowledgments

The authors thank Juan Manuel Arco and Alberto Romero(Sedecal S.A., Madrid, Spain) for the support and for sharingdetails on the Argus scanner.

Appendix A

In this section details on the pulse-processing steps modeledthrough the dedicated code were reported. More precisely, thedeveloped software loads and processes the GATE output.

The spatial resolution of the PS-PMTs was included in ourmodel by blurring the position of the events within each detectorblock, so that they may be assigned to an adjacent crystal with acertain probability. The probability was calculated by sampling a2D Gaussian function, whose FWHM value (4 mm) was derivedfrom the data sheet of the PMT’s manufacturer (Hamamatsu,2004), using the Geant4 libraries for random numbers generation.The layer identification accuracy (95%) was modeled in a similarway, i.e. the identified layer (LYSO or GSO) was swapped with a5% probability, calculated by sampling a uniform random vari-able. The ADC dead-time (1.4 ms) was modeled by comparing thetimestamp of an event with the last digitized one of the corre-sponding detector block. In case the time difference was found tobe less than the dead-time, the event was not inserted in thesubsequent data stream and, thus, it was discarded. The transmis-sion capacity of the digitized events from the ADCs to the controlcomputer was found to reach a maximum value in our system athigh count rates. To mimic this in our model, a threshold for thenumber of digitized events that can be accepted per unit time wasset, while the exceeding ones were discarded. The threshold wasadjusted to match the maximum prompt count rate obtained fromexperimental data for the rat-phantom using the 100–700 keVwindow. Further processing is performed by the scanner’s controlcomputer, such as the energy selection (according to the selectedwindow) and narrower time coincidence windows. The obtainedevents must also be checked to belong to the allowed matrix, sincesome of them may have overlapped during digitization, resulting ininvalid coincidences. These steps were implemented in the modelsimply as filters which discard the coincidence event which do notmeet all the requested conditions. A second threshold was set afterthe energy selection to mimic the maximum processing capabilityof the CPU, which causes a loss of linearity observed below thepeak of the NEC curves, as can be noticed in Fig. 6. Even in this case,the threshold was selected in order to match the observed slope inthe non-linearity region of the experimental rat-phantom promptcount rate curve, for the 100–700 keV energy window.

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