Semi-empirical Monte Carlo optical-gain modelling of Nuclear Imaging scintillators
Semi-empirical Monte Carlo optical-gainmodelling of Nuclear Imaging scintillators E. M. Vlamakis, X. A. Argyriou, T. J. Sevvos, A. A. Fotopoulos, N. N. Chatzisavvas, P. H. Yannakopoulos, N. Kalyvas, I. Valais, I. Kandarakis, D. Nikolopoulos
AimDevelop a theoretical model of the optical gain of single-crystal scintillators, via Monte Carlo methods. Comparetheoretical results to experimental data for photon energies of140keV and 364keV. The presented results could be useful indesigning nuclear medicine imaging systems.
IntroductionScintillation detector applications Conventional and digital x-rayradiography, x-ray computed tomography, single-photon emissiontomography (SPECT) positron emission tomography(PET)
Introduction + The emission of light of granular and non-granularscintillators has been investigated through analyticalmodelling [9-14]. These models take into account scintillator thickness as themain influencing parameter, while the other dimensions (e.garea or lateral thickness) are assumed to be infinite. For theapplication of scintillators in nuclear medicine systems, theanalytical models [9-15] are insufficient in scoring gammaradiation deposited energy. The stochastic processes of radiation transport have beenstudied efficiently through Monte Carlo simulation [16-28].Several general Monte Carlo packages are available (e.g.TART, PENELOPE, MCNP, GEANT4, GATE, EGSnrcMP) [16,17, 22, 23, 25].
Introduction ++ Recent reports have employed general Monte Carlopackages in studying radiation and optical photon transport inmedical imaging scintillators [26-27]. The combination however of analytical optical modelling andsimulation of radiation transport with general Monte Carlocodes has not been attempted for single crystal scintillators. In such an attempt, the present study employs a hybridsemi-empirical method for the estimation of the optical outputof scintillator crystals in terms of Detector-Optical-Gain(DOG). The method uses specially developed Monte-CarloEGSnrc codes for scoring the gamma ray photon and energyredistribution within certain crystal scintillators.
Introduction +++ The EGS (Electron–Gamma–Shower) platform is a generalpurpose package for the Monte Carlo simulation. The newenhanced version of EGS is called EGSnrc. The outputs of the EGSnrc simulations are utilised as inputsinto a semi-empirical analytical model which predicts DOG. Semi-empirical model adjustments are based on scintillatormeasurements in the energy range of Nuclear Medicine. The model is used for the estimation of the effective opticalphoton loss per mm. The latter parameter is employed in theestimation of an optimum scintillator thickness, between 5mmand 25mm, per incident gamma ray energy for theGd2SiO5:Ce (GSO:Ce), Lu2SiO5:Ce (LSO:Ce) andYAlO3:Ce (YAP:Ce) scintillators.
Materials & Methods +Single-crystal scintillatordivided in N layers a fraction was absorbed toeach layer Optical photons propagateeither in the forward or inthe backward direction per crystal layer only afraction, hereafter called k,was propagated to the nextlayer
Materials & Methods ++ Qn(E) is calculated via the EGS4rnc Monte Carlo code. Theabsorbed X-ray energy is transformed into optical photon energy inthe scintillator. The number of the produced optical photons in thenth layer, Ln can be calculated as: E Ln ( E ) = Qn ( E )nC (1) Eλwhere nC is the intrinsic conversion efficiency and Ελ is the opticalphoton energy , . It is assumed that half of the produced opticalphotons are propagating forward and half backwards. To the next layer,n+1, only a fraction, k, of the produced optical photons arrives. That is: Lnn + 1 ( E ) = Ln ( E )k (2)
Materials & Methods +++ The optical photons in Forward direction are calculated as: 1 Lnf ( E ) = (1 − R) Ln ( E )k N− n (3) 1− k R 2N 2 The optical photons in Backward direction are calculated as: 1 k 2N R 2Lm ( E ) = Lnf ( E ) + Lnb ( E ) = (1 − R) Ln ( E )k N − n + (1 − R) Ln ( E ) Rk n k N 1 − k 2N R 2 1 − k 2N R 2 (4)
Materials & Methods +++ If all the layers as well as equation (1) are considered then the total number ofoptical photons produced per absorbed gamma ray (i.e. DOG) equals to: N E k N− n k 2N R 2 DOG ( E ) = ∑ Qn ( E )nC (1 − R ) + Rk n + N 2 1− k R 1− k R 2N 2 2N n= 1 Eλwhere the values of Qn(E) is calculated by EGSnrc. (5)The value of the reflectance, R, when a light ray propagates from a medium withindex of refraction n1, to a medium of index of refraction n2 (equals to 1 for air),depends upon the polarization of the incident ray.The total reflectance can becalculated as R(θ i ) = Rs (θ i ) + Rp (θ i ) and the mean reflectance used in the 2estimation of equation 5 was found as: θ crit ∑ R (θ ) R= θ =0 noawhere noa is the number of angles used in the summation and θcrit is the criticalangle above which total reflection occur. In the calculation of R it was assumedthat the input and exit surfaces of the crystal were perfect planes and anyexisted surface anomalies  were not considered.
Results & DiscussionQn(E) values for gamma ray energies of 140keV and 364keV for LSO:Ce, GSO:Ce andYAP:Ce. The curves represent exponential fits at the 99% confidence interval. The errors arebelow 0.5%. The legend presents the dimensions of the modeled scintillator block
Results & Discussion + Crystal Energy (keV) DOG k DOG DOG experimental theoretical k - 1% LSO:Ce 140 323±16 0.80 248 227 364 644±45 790 753 GSO:Ce 140 150±8 0.86 146 133 364 275±19 291 275 YAP:Ce 140 57±3 0.74 50 48 364 95±7 111 107Experimental and semi-empirical method predicted DOG values. In the last two columns thesensitivity of the method in k values is demonstrated
Results & Discussion ++DOG values for different scintillator total thickness (T) and gamma ray energies of140keV, 364keV and 512keV for (a) GSO:Ce, (b) LSO:Ce and (c) YAP:Ce
Results & Discussion +++Predicted DOG values of GSO:Ce, LSO:Ce and YAP:Ce for gamma ray energy of 140keV.
Conclusion A semi-empirical theoretical model, describing light transportin single crystals was developed. The model was used in conjunction with a Monte Carlogenerated gamma ray absorption data to describe theDetector Optical Gain (DOG) of single crystal scintillatormaterials excited by gamma rays. The model was checked against experimental results andthe fraction of the optical photons propagating through crystallayers (named k) was determined. The model was used to find an optimum crystal thicknessper gamma ray energy application. It was found that theoptimum thickness is a function of the scintillator material andthe gamma ray energy
References O Mineev et al., Scintillator detectors with long WLS fibers and mulit-pixel photodiodes, JINST 6 (2011) P012004. A. Vandenbroucke et al., Performance characterization of a new high resolution PET scintillation detector, Phys. Med. Biol. 56(2011) 4135. B.K. Cha et al., Design and image-quality performance of high resolution CMOS-based X-ray imaging detectors for digital mammography,JINST 7 (2012) C012004. A. Nassalski, Comparative study of scintillators for PET/CT detectors, IEEE T. Nucl. Sci. 54 (2007) 3. M Nikl, Scintillation detectors for X-rays, Meas. Sci. Technol. 17 (2006) R37. I.G. Valais et al., Luminescence efficiency of Gd2SiO5 : Ce scintillator under X-ray excitation, IEEE T. Nucl. Sci. 52 (2005) 1830. I.G. Valais et al., Luminescence properties of (Lu;Y)2SiO5 : Ce and Gd2SiO5 : Ce single crystal scintillators under X-ray excitationfor use in medical imaging systems, IEEE T. Nucl. Sci. 54 (2007) 11.. I.G. Valais, Systematic study of the light emission efficiency and the corresponding intrinsic physical characteristics of single crystalscintillators, doped with the trivalent cerium (Ce3+) activator, in wide energy range (from 20kV-18MV) for medical applications, Doctorate Thesis,Patras 2008, http://nemertes.lis.upatras.gr/jspui/bitstream/10889/997/1/Thesis_Valais_sec.pdf G.E. Giakoumakis et al., Light angular distribution of non-granular fluorescent screens excited by X-rays, Phys. Med. Biol. 30(1985) 993. G.E. Giakoumakis et al., Light angular distribution of fluorescent screens excited by X-rays, Phys.Med. Biol. 30 (1985) 21. G.E. Giakoumakis et al., Absolute efficiency of Gd2O2S:Tb screens under fluoroscopic conditions, Phys. Med. Biol. 34 (1989)673. G.E. Giakoumakis et al., Absolute efficiency of rare earth oxysulphide screens in reflection mode observation, Phys. Med. Biol. 35(1990) 1017. I. Kandarakis et al., A theoretical model evaluating the angular distribution of luminescence emission in X-ray scintillating screens,Appl. Radiat. Isotopes 64 (2005) 508. C. Carrier and R. Lecomte, Theoretical modeling of light transport in rectangular parallelepidedic scintillators, Nucl. Instr. and Meth A 292(1990) 685. A. Petropoulou et al., A theoretical model describing the light emission efficiency of single-crystal scintillators in the diagnosticenergy range, JINST 4 (2009) P06016. www.opengatecollaboration.org
References S. Jan et al., GATE: a simulation toolkit for PET and SPECT. Phys. Med. Biol. 49 (2004) 4543. N. Ghazanfari et al., Quantitative assessment of crystal material and size on the performance of rotating dual head small animalPET scanners using Monte Carlo modeling. Hell J. Nucl. Med. 15 (2012) 33. P. Gonias et al., Validation of a GATE model for the simulation of the Siemens PET/CT biograph 6 scanner. Nucl. Instr. Meth.Phys. Res. A 571 (2007) 263. N Karakatsanis et al., Comparative evaluation of two commercial PET scanners, ECAT EXACT HR+ and Biograph 2, usingGATE. Nucl. Instr. Meth. Phys. Res. A 571 (2006) 368. YH Chung et al., Optimization of dual layer phoswich detector consisting of LSO and LuYAP for small animal PET. IEEE Trans.Nucl. Sci. 52 (2005) 217. D. Nikolopoulos et al., Investigation of radiation absorption and X-ray fluorescence properties of medical imaging scintillators byMonte Carlo methods, Nucl. Instr. Meth. Phys. Res. A 565 (2006) 821. D. Nikolopoulos et al., Monte Carlo validation in the diagnostic radiology range, Nucl. Instr. Meth. Phys. Res. A 571 (2007) 267. B A Faddegon, J Perl and M Asai, Monte Carlo simulation of large electron fields, Phys. Med. Biol, 53 (2008) 1497. http://irs.inms.nrc.ca/software/egsnrc D.J. (Jan) van der Laan et al., Optical simulation of monolithic scintillator detectors using GATE/GEANT4, Phys. Med. Biol. 55(2010) 1659.´F. Ciocia et al, GEANT4 studies on the propagation and detection of scintillation light in long thin YAP crystals, Nucl. Instr. Meth.Phys. Res. A 600 (2009) 506. P.F. Liaparinos et al., Modeling granular phosphor screens by Monte Carlo methods, Med. Phys. 33 (2006) 4502. C.W.E Van Eijk, Inorganic scintillators in medical imaging Phys. Med. Biol. 47 (2002) R85. C.W.E.Van Eijk, Radiation detector developments in medical applications: inorganic scintillators in positron emission tomography,Rad. Prot. Dosim. 129(1-3) (2008) 13. S. Zelakiewich and J. Shaw, Modeling MTF and DQE for arbitrary scintillator thickness, IEEE Nuclear Science SymposiumConference Record M11-170 (2006), 2551. D. Hugh Young, University physics. Extended version with modern physics, 8th, Addison-Wesley Publishing Company Inc., U.S.A.(1995), ISBN 960-02-1088-8.