2012 IEEE Nuclear Science Symposiwn and Medical Imaging Conference Record (NSS/MIC)
N28-2
Ray Tracing Simulations In Scintillators: a Comparison Between SLitrani and Geant4
Marco Pizzichemi, Etiennette Auffray, Remi Chipaux, Giacomo Cucciati, Nicolas Di Vara, Alessio Ghezzi, Riccardo Iaconelli, Paul Lecoq, Marco Toliman Lucchini, Arno Knapitsch, Marco Paganoni, Kristof Pauwels
Abstract-The extensive use of scintillating crystals in medical imaging field is generating a growing interest in Monte Carlo simulation of light transportation and photon collection inside inorganic materials. The critical parameters under study which affect the performance of medical devices are the number of pho tons collected per unit of energy deposited (light yield), the energy resolution, the effect of dimensions and surface state and the time profiles of the scintillation process. Moreover, most of the crystals used in Positron Emission Tomography (PET) applications, such as lutetium orthosilicate (LSO), are anisotropic, potentially influ encing the performances. In particular the recent development of time of flight PET scanners requires a detailed knowledge of timing profiles of the crystals in terms of time of arrival of single photons, scintillation rise and decay times. Furthermore the effort towards innovative endoscopic probe for PET examination requires an extensive analysis of the effect of the dimensions of small crystals on the parameters mentioned. Different simulation tools are employed nowadays for detailed studies of interaction of particles in inorganic materials and tracing of the scintillating photons produced. In particular our attention is focused on SLitrani and Geant4. SLitrani is a general purpose Monte-Carlo program simulating light propagation, developed for high energy experiments, in particular in the frame of the CMS experiment
modeling the optic behavior of heavy inorganic scintillating crystals. Different simulation programs are used nowadays in medical physics community, and we decided to concentrate on Geant4 [1] and SLitrani [2]. In order to correctly assess the influence that every parameter under study has on simulation performances, we focus on a modular approach, first assessing the difference in the simulation of photon interactions, and then analyzing the effect of the overall characteristics on a model detector. A first part of this study is therefore dedicated to energy deposition in the crystal bulk, mechanisms of production of optical photons, photon tracing and time profiles. Subsequently, we investigate the effect of such differences on the overall characteristics of the simulation of a bulk crystal, with particular attention to photon extraction efficiency. In Geant4 we used the package emstandard_opt3, designed for any application requiring higher accuracy in electron, hadron and ion tracking without magnetic field, and there fore suitable for low energy processes, in particular medical physics.
at LHC. Its most advanced characteristics is the ability to handle anisotropic materials, thus retaining a quite general application.
II.
Geant4 is a general purpose Monte Carlo toolkit widely used in high energy physics, astroparticle physics and nuclear physics, which includes an optical physics process category to simulate the production and propagation of light. In the frame of the Crystal Clear Collaboration, we have been developing and testing innovative scintillation technologies for medical applications, and with this respect Monte Carlo techniques are powerful tools for investigating the performances of our setups. In order to validate and accurately describe the inorganic crystals developed we have been comparing the performances of the SLitrani and Geant4 frameworks, and started a preliminary comparison with experimental results obtained in our laboratories.
Index Terms-SLitrani, Geant4, Scintillators, Ray-tracing.
M
I.
INTRODUCTION
ONTE Carlo simulation tools play an important role in the development of high performance PET scanners. It is therefore desirable to improve their performance in Manuscript received November 16. 2012. M. Pizzichemi. G. Cucciati, R. Iaconelli, M. Paganoni and A. Ghezzi are with the Department of Physics, University of Milano-Bicocca, Milano, Italy e-mail:
[email protected]. E. Auffray, P. Lecoq, A. Knapitsch and K. Pauwels are with CERN - CH1211 Geneve 23 Switzerland. R. Chipaux is with DECEA/DSM/IRFU, CE-Saclay - Gif sur Yvette cedex, France. N. Di Vara and M. T. Lucchini are with the Department of Physics, University of Milano-Bicocca, Milano, Italy as well as CERN - CH-1211 Geneve 23 Switzerland.
978-1-4673-2030-6/12/$31.00 ©2012 IEEE
ENERGY DE POSITION AND TIMING PROFILES
With the aim of focusing on the domain of medical ap plications, we investigated the energy deposition of 511 keV gamma inside a LSO scintillating crystal of 2x2x20 mm3. A collimated beam of incident photons was generated 5 mm far from the crystal back face, directed as the main crystal axis. Scintillation was modeled with a rise time of 100 ps and an intrinsic light yield of 50000 PhotonslMeV. The main difference between the two software lies in the possibility of tracking secondary particles. For what con cerns SLitrani scintillation occurs as soon as the gamma deposits energy with a Compton or photoelectric interaction. In Geant4, instead, a gamma photon is able to produce secondary electrons that, ionizing the medium while they travel, are able to produce optical photons with Cerenkov interaction or scintillation. This results in a higher spatial spread in energy deposition for Geant4 as compared to SLitrani, like shown for example along the longitudinal axis in Fig. 1 and 2. Secondary electrons, however, are generated with very low energy and therefore rapidly fall below Cerenkov threshold, minimizing the impact of this difference to a small amount of photons that do not affect the overall light output of the crystal. A significant difference can instead be found when deal ing with timing applications. Cerenkov photons, in fact, are produced promptly and then propagated and extracted from the crystal, as shown in Fig. 3. This means that in a timing
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Fig. 1. Longitudinal energy deposition map simulated in Geant4 for an LSO crystal irradiated by a collimated beam of 511 keY gamma.
spectrum. This means that a part of the photon produced would be reabsorbed and emitted via the scintillation mechanism. As of this moment, this behavior has still to be implemented. Photons collected in the first 100 ps
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Fig. 2. Longitudinal energy deposition map simulated in SLitrani for an LSO crystal irradiated by a collimated beam of 511 keY gamma.
window similar to the rise time of the crystal scintillation, the amount of Cerenkov photons extracted is comparable to the amount of scintillation photons extracted (see Fig. 4). The total number of Cerenkov photons collected, anyway, depends on the efficiency window of the photodetectors, and, being the emission a continuum in energy, the total number of photons detected will be lower. Moreover, Geant4 does not take into account any excitation spectrum, which, for a certain interval of energy, could be superimposed to the Cerenkov energy
OPTICAL PHOTONS INTERACTIONS
When optical photons are generated inside a crystal, their possibility to be extracted from one side of the scintillator depends on the probability to be absorbed by the crystal itself and on the interactions with the crystal surfaces. These events were individually tested, to point out possible differences be tween the two software. When a material is defined in Geant4 and SLitrani, an energy dependent absorption length labs must be specified. This parameter was tested in both software recording the number of photons absorbed as a function of the distance traveled. Photons were generated by a monochromatic source in the center of a very extended (dimensions > > labs) crystal. The reflection and refraction coefficients, instead, were measured by firing a monochromatic beam of photons, generated inside a crystal, towards an interface with air, and
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Fig. 7. Ratio between results provided by SLitrani and Geant4 on the photon absorption rate on a completely specular coating as a function of the incidence angle.
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recording the number of transmitted and reflected photons as a function of the incidence angle. The ratio of results obtained in SLitrani and Geant4, for an LSO crystal (n 1.82) with ,\ 420 nm, are shown in Fig. 5 and 6, and demonstrate perfect agreement between the two Monte Carlo software. In order to reduce photon losses, scintillating crystals are often wrapped or coated with specular or diffusive materials, such as, among the others, Aluminum and Teflon. Both toolkit provide methods to simulate these experimental conditions, but they partially differ on the approach used to describe the photon-wrapping or photon-coating interaction. The absorp tion of photons at boundary interface was tested by firing a monochromatic beam of photons, generated inside the crys tal, towards the crystal-wrapping or crystal-coating boundary, and varying the incidence angle. Comparison of simulated absorption rates for two relevant configurations (a completely specular coating and a completely diffusive wrapping) are shown in Fig. 7 and 8. A significant difference is found for diffusive wrappings, with SLitrani showing an higher absorption rate for high incidence angles. Depolishing of lateral crystal surfaces is sometimes used =
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Fig. 8. Ratio between results provided by SLitrani and Geant4 on the photon absorption rate on a completely diffusive wrapping as a function of the incidence angle.
in experimental setups, with the aim of improving depth of interaction spatial resolution [3] or to suppress light yield non uniformity, for example in CMS tapered crystals [4]. Both SLitrani and Geant4 can model this interface condition by randomly tilting the crystal surface when they calculate the interaction coefficients for each optical photon. Generation of random tilting is performed using different distributions, leading to different results, for example in terms of overall photon collection. However, in both Monte Carlo software, depolishing leads to an increase of photon collection, in contrast with experimental experience. IV.
PHOTON E XTR ACTION EFFICIENCY
A. Simulation
In order to evaluate the photon extraction efficiency in a realistic setup, we simulated a single LSO crystal with an internal optical isotropic photon source (,\ 420 nm). Photons moving inside the crystals are collected by a glass sensor placed at few microns from one of the small faces. We kept the crystal length fixed at 20 irun, while varying transverse
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Fig. 9. Ratio between results provided by SLitrani and Geant4 on the photon extraction efficiency in LSO crystals wrapped with a completely diffusive material, as a function of the transverse width.
wrapped with Teflon, simulated as a completely diffusive material, are shown. A relevant difference in photon extraction efficiency is found for small crystals, consistent with results shown in Fig. 8. In fact, the smaller the crystal section, the higher is the number of bounces on later surfaces that each photon experiences before having a chance to be extracted from the exit surface. For each bounce SLitrani calculates a higher absorption probability on the wrapping, as compared to Geant4, and this leads to the discrepancy we measured. B. Comparison with experimental data
As a preliminary comparison with experimental data, we used extraction efficiency values obtained in [5]. We chose to focus on the gains in photon extraction that can be obtained by coupling the crystal to a PMT with optical grease and by wrapping it with Teflon.
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Almost all scintillators used in medical imaging applications show some degree of anisotropy in crystal structure, with the noteworthy exception of BGO. This can have strong consequences on the optical properties of scintillators, intro ducing variations of surface reflections due to birefringence, or sensitivity of bulk light absorption to light polarization direction [6]. Only SLitrani can simulate anisotropy, and we tested the potential impact of this structural property on photon extraction efficiency for a PbW04 crystal, using the same set of dimensions described in section IV. Comparison
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The experimental gain delivered by optical grease can be reproduced by both SLitrani and Geant4 (see Fig. 10), with a systematic difference probably due to poor knowledge of optical grease index of refraction. Gain due to the use of Teflon wrapping, instead, is significantly different between experimental data and Monte Carlo simulations, as shown in Fig. 1 1.
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Fig. 10. Simulated and measured photon extraction gain obtained by the use of optical grease in LSO crystals, as a function of the transverse width.
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Fig. 12. Ratio between photon extraction efficiency for anisotropic and isotropic PbW04 crystals, as a function of the transverse width. The choice of optical axis x and y is determined by Ox = 0°,
