Berthot, J.

Breton, Vincent

Brette, P.

Giokaris, N.

Lazaro, Delphine

Maublant, J.

Meritet, L.

HAL Clermont Université

Monte-Carlo simulation of gamma-cameras usingGEANTJ. Berthot, Vincent Breton, P. Brette, N. Giokaris, Delphine Lazaro, J.Maublant, L. MeritetTo cite this version:J. Berthot, Vincent Breton, P. Brette, N. Giokaris, Delphine Lazaro, et al.. Monte-Carlosimulation of gamma-cameras using GEANT. IEEE Nuclear Science Symposium and MedicalImaging Conference 20, Oct 2000, Lyon, France. pp.210-213, 2000. <in2p3-00013760>HAL Id: in2p3-00013760http://hal.in2p3.fr/in2p3-00013760Submitted on 11 Jun 2003HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Monte−Carlo simulation of gamma−cameras using GEANTJ. Berthot 2, V. Breton2 , P. Brette3 , N. Giokaris4, D. Lazaro2 , J. Maublant5 ,L. Méritet22LPC, Campus des Cézeaux, 63177 Aubière cedex, France3Clérad, 16 Avenue de l’agriculture, 63000 Clermont−Ferrand, France4 Institute of Accelerating Systems and Applications, Athens, Hellas5 Service de Médecine Nucléaire, Centre Jean Perrin, 63000 Clermont−Ferrand, FranceAbstractThere is a growing interest among nuclear and particlephysicists for the application of the detection techniquesused in subatomic physics to medical imaging. As well, thecode used to simulate the response of these detectors toionizing particles, named GEANT, can be applied to simulatemedical imaging devices. GEANT allows a completeMonte−Carlo treatment of the attenuation by body parts andof the generation and tracking of optical photons fromscintillation inside the crystal. We used GEANT to simulatea high resolution gamma camera for small animal imaging.Our study shows a significant correlation between the depthof a source in the body and the energy spectrum of thephotons detected in the gamma−camera. I.  INTRODUCTIONA reliable Monte−Carlo simulation is of utmostimportance to evaluate the performances of the gammacameras and search for compromises between resolution andsensitivity. Usually, the research teams working on their owngamma−camera prototype have been developing their ownsimulation code which implies an increased risk of bugs anda reduced transportability. For more than 2 decades, the subatomic physicscommunity around the world has been using the Monte−Carlo code GEANT to describe the interaction of ionizingparticles with matter. The GEANT code was developed atCERN to deal with the increasing scale and complexity ofthe high energy physics experiments. Simulation studiesbecame essential to design and optimize the detectorsdevelop and test the reconstruction and analysis programsand interpret the experimental data.The interest of using GEANT to simulate gamma−cameras is threefold :All the physics processes involved from theemission of the radioisotope to the creation of the image inthe gamma−camera are described in GEANT or can beadded. The code is highly reliable because it is usedextensively around the world.The code is a standard in high energy physics andtherefore there is abundant documentation and many experts.The first version of GEANT was written in 1974 as a bareframework which initially emphasized tracking of a fewparticles per event through relatively simple detectors. Thesystem has been developed continuously over the yearsthanks to the devoted and constant collaboration of physicistsaround the world. There are today two versions :GEANT version 3 [1] was written in Fortran by a team atCERN as a complete update from previous versions.Concerning medical imaging applications, electromagneticprocesses are simulated down to 10 keV.GEANT version 4 is a completely new code developedwithin an international collaboration of about 100 scientistsparticipating in more than 10 experiments in Europe, Russia,Japan, Canada and the United States. To extend its usetoward medical physics and space physics, very low energyprocesses down to tens of electron−volts are included.Written in object−oriented language, the GEANT4 sourcecode is freely available [2].This paper presents the results we have obtained usingGEANT321, the last version of GEANT in fortran, forimaging low energy gamma rays from 99mTc. We studied thereliability of the simulation to reproduce the performance(spatial resolution, sensitivity) of a camera which is presentlyunder development for small animal imaging [5]. Once thesimulation was validated, we studied the correlation betweenthe depth of the source inside the body and the shape of theenergy spectrum of photons detected in the camera. II. STRUCTURE OF THE SIMULATION CODEWe are going to describe the different parts of thesimulation code. Figure 1 shows the different elements of thegeometry: source(s), body, collimator, crystal andphotomultipliers. A.  SourcesThe sources are located inside the body. Their number,size, shape and position are parameters adjustable atexecution time. We considered only 99mTc isotropic sourcesemitting 140  keV photons. Page     (Do NOT include page numbers!)Figure 1: The different elements of the geometry.B.  Body The camera we simulate is designed for small animalimaging. However, our focus is mammography. Therefore,body was simulated by a trapezoid of variable thickness.Breast tissue atomic composition was taken from NIST website [2]. In the body, photons emitted from the sourcesundergo Compton scattering and photoelectric effect.Rayleigh scattering was neglected. C.  CollimatorAmong the gamma cameras on the market, many optionsfor the geometry of the collimators are considered dependingupon the specific needs. For the purpose of validating thesimulation, we considered 2 widely used configurations :parallel hole and pin−hole geometry. For parallel holecollimators, we considered hexagonal cells separated by thinfoils. Among the heavy materials used for collimators, wechose lead. The size of the holes and the septa, the thickness of thecollimator as well as its material are free parameters of thesimulation.D.  CrystalOne of the hardest issues for the Monte−Carlo simulationof gamma cameras concerns the treatment of optical photonsgenerated by scintillation in the doped NaI(Tl) crystal.Indeed, about 40000 optical photons per MeV of energy aregenerated. Each photon must be followed in its travel insidethe crystal to the photomultipliers entrance window.GEANT321 allows a reliable description of optical photonstransport, reflection and refraction. It has however notreatment of scintillation. We therefore added our owngeneration of optical photons : when GEANT stops trackingphotons and electrons inside the crystal because they fellbelow the energy threshold (≈ 10 keV), 3eV optical photonsare generated isotropically at stopping point : 40000 opticalphotons per MeV incident energy are then tracked byGEANT.   E.  Light collectionLight collection is probably the weakest point of oursimulation because we did not enter into the details ofdescribing the electronic shower in the photomultipliers. Inthis work, the number of photons collected by the PM’s wasadjusted varying the quantum efficiency. Photomultipliersoutput was calibrated on the photoelectric peak.  III. VALIDATION OF THE SIMULATIONWe first checked the validity of the simulation bycomparing the collimator performances to the analyticalformulas. The energy resolution of the camera was tuned byvarying the crystal thickness and the quantum efficiency ofthe photomultipliers. A.  Collimators intrinsic resolution and sensitivityWe studied two types of collimators. This section presentsour results compared to the analytical formulas concerningthe intrinsic resolution and the sensitivity of the simulatedcollimators. The intrinsic resolution of a collimator is definedas the FWHM of the spatial distribution of photons passingthrough the collimator. Three parameters characterize thegeometry of a parallel hole collimator : the holes diameter,the septa diameter and the collimator height (see figure 1).For 500000 photons generated at the source located 10 cm infront of the collimator, the simulation results are in excellentagreement with analytical formulas as shown in table 1. Thesame results are obtained for the pin−hole collimator.Table 1Collimator resolution :  analytical formula  vs. simulationCollimator Parallel hole Pin holeHole diameter(mm)1,9 4,0Septum diameter(mm)0,5Height (cm) 3,0 3,0Simulatedresolution(mm)6,5 5,0Analyticalresolution(mm)6,5 5,2The sensitivity is the ratio of the number of incidentphotons emitted by the 99mTc source and transmitted by thecollimator, to the number of photons emitted by the 99mTcsource. The simulation conditions are the same as previously.We compare again simulated and analytical sensitivities for500000 photons generated.Page     (Do NOT include page numbers!)distanceheight tcrystaltglassdseptumdholetbodyhuman bodymylar PM  s glassPMcollimatorNaI(Tl) crystalTable 2 Collimator sensitivity : analytical formula  vs. simulationCollimator Parallel hole Pin holeSimulatedsensitivity (%)0,011 0,013Analyticalsensitivity (%)0,013 0,010 Table 2 shows the good agreement between simulated andanalytical values for the parallel hole and the pin−holegeometry.B. Energy resolutionMost of the photons entering the crystal are stopped in thecrystal through a photoelectric effect. For those photons thatdid not scatter inside the body, energy deposit in the crystalis therefore 140keV. This energy is converted in opticalphotons. The output signal from the photomultipliers isproportional to the number of optical photons collected. For a given collimator, energy resolution characterizesthe chain crystal − photomultipliers. To take out the impactof the collimator, we considered a gamma camera with apin−hole collimator and a 99mTc source at 10 cm in front of itemitting photons along the camera axis. Figure 2 shows theenergy spectrum of the photons entering the crystal (in black)and reconstructed from PM’s output (in white) for 2 differentquantum efficiencies : 10% and 20%. Figure 2 : Figure 2 : energy spectra of the photons entering the crystal (inblack) and reconstructed from PM’s output (in white) for 2different quantum efficiencies : 10% and 20%.The energy resolution is the FWHM of the distribution ofthe number of optical photons for the events in thephotoelectric peak. We find an energy resolution of 13,6%for a PM’s quantum efficiency of 10%, and an energyresolution of 10,9% for a PM’s quantum efficiency of 20%.We studied the energy resolution for various thicknessesof crystal and a 10% quantum efficiency. The results arepresented in Table 3.Table 3Energy resolution vs. crystal thicknessCrystal thickness (mm) Energy resolution (%)2 10,44 12,06 13,68 14,610 15,9 The energy resolution obtained by simulation iscompatible with the experimental values usually observedand  increases with the crystal thickness. All these results contribute to say that GEANT321 is avalid simulation tool to evaluate gamma camerasperformances. We chose to study with GEANT theinformation the Compton peak could bring on the depth ofthe source inside the body.  IV. ATTENUATION RATIO  The standard procedure to reconstruct the image of abody part from the output of a gamma camera is to select theevents in the photoelectric peak. These photons arecharacterized by the fact they did not undergo Comptonscattering in the body. We call Pi the probability for a photonto enter the crystal after scattering i times in the body. It iseasy to see that the probability for a photon to have scatteredat least once before entering the crystal is :By definition of Pi, the probability not to have interactedbefore entering the crystal is:We define the ratio R of the number of events in thephotoelectric peak to the number of events in the Comptonpeak. If the energy resolution of the detector is good enoughto separate the two peaks, arguments developed abovesuggest that R is proportional to Pi , probability for a photon to have undergone Comptonscattering i times before leaving the body and entering thecrystal, depends on the Compton scattering cross section andthe body thickness tbody. It can be written as  Page     (Do NOT include page numbers!)PM conversionefficiency : 20%PM conversionefficiency : 10%∑=ni iP1∑=−ni iP11∑∑==−ni ini iPP111ibodyii tP α=where the coefficient αi contains the information pertainingto the Compton cross section integrated on the scatteringangle. The ratio R is therefore proportional toIn the limit bodyt → 0, R should behave as 1/ bodyt andtherefore depend strongly on bodyt  . We have simulated the variation of the ratio R with thedepth of the source inside the body. We have definedwindows of energies for the 2 energy spectra available : trueenergy of photons entering the crystal and reconstructedenergy from PM’s output. Results are shown on figure 3. The1/ bodyt  dependence is well reproduced by the simulation. Figure 3: Evolution of the ratio R in the NaI(Tl) crystal and in thePM vs. source depth.This result has to be compared to an experimentalobservation of the same effect [6]. V.  CONCLUSIONAccording to the very good agreement betweensimulation results and theoretical values, we can sayGEANT321 constitutes a promising simulation tool forgamma−cameras. The results obtained concerning collimatorresolution and sensitivity allow to validate the simulation,although certain parts of it still deserve to be developed. Sowe have at our disposal a complete and reliable simulationcode.With GEANT321, we focussed on the possibility to usethe Compton peak information to determine the source depth.Our simulation stresses the fact that the ratio R of the numberof events in the photoelectric peak to the number of events inthe Compton peak goes with the inverse of the source depthin the body. Provided events in the Compton peak could becollected together with the events in the photoelectric peak,the information on the source depth could be obtainedwithout additional exposure of the patient.VI.  REFERENCES[1] GEANT3, Detector description and simulation tool,Application Software Group, CERN Geneva,Switzerland, 1993[2] GEANT4 web site :wwwinfo.cern.ch/asd/geant4/geant4.html[3] NIST web site: www.physics.nist.gov/PhysRefData[4] Development of a High Resolution Spect GammaCamera for Small Animals Imaging, S.C.Archimandritis et al, IEEE 2000[5] Small Gamma−Ray Imager Based on a PositionSensitive Photomultiplier Tube, A. Lebedev, S.Majewski, D. Steinbach and A. Weisenberg, submittedto Nuclear Instruments and Methods in PhysicsResearch. [6] M.A. Gambaro et al, contribution to EuropeanAssociation of Nuclear Medicine Congress, Paris 2000Page     (Do NOT include page numbers!)∑∑αα−ibodyiibodyItt10 20 40 60 80 1000123456789R (cristal)R (PM)source depth (mm)Ratio R

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