Monte-Carlo Modeling of Scintillator Crystal Performance for Stratified PET Detectors with DETECT2000

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1 Monte-Carlo Modeling of Scintillator Crystal Performance for Stratified PET Detectors with DETECT2 Francois Cayouette, Member, IEEE, Christian Moisan, Nan Zhang, Member, IEEE and Christopher J. Thompson, Member, IEEE a Abstract In order to determine the theoretical performance of the multi-layer BGO scintillation block used in small PET scanners, we have used the DETECT2 Monte-Carlo simulation of the light transport in scintillation crystals software. The scintillation block is made of two arrays of individual crystals and they are held together by an interconnecting layer. The results given by this software demonstrate that some of the individual crystals in the block could not be distinguished even under the best circumstances. Also, we have found that it would be difficult to correctly distinguish an important fraction of the individual crystals under bad conditions. The simulations determined that the layer connecting the different crystals is the most important factor of degradation of the performance of the scintillation block. Simulations of different width of interconnecting layer suggest that much better identification could be obtained by reducing the width of this layer. I I. INTRODUCTION N high resolution Position Emission Tomography (PET), it is very important to determine the point of interaction of a γ-ray in a scintillator crystal. Many schemes have been devised in order to collect the light photons in a way that would give as much information as possible about the point of interaction of the γ-ray. The most common scheme is to cut the crystal into a matrix of multiple quasi-independent crystals as it is done in many PET scanners like the ECAT Exact HR+[1]. By looking at the distribution of the detected light photons, it is possible to determine from which crystal the light came from. The main drawback of this method is that the depth of interaction cannot be computed. The use of a lossy reflective material can give some depth information but F. Cayouette work is supported by a Natural Science and Engineering Research Council of Canada (NSERC Grant no. PGS A ) C. J. Thompson work is supported by a Natural Science and Engineering Research Council of Canada (NSERC Grant no. OPG662) F. Cayouette is with McGill University, Biomedical Engineering Departement, Montreal, QC, HA 2B4 Canada. (Tel: , fcayouet@gel.ulaval.ca). C. Moisan is with Laval University, St-Francois d Assise Hospital and Radiology Department, Quebec, QC, G1L L5 Canada. (Tel: x921 Christian.moisan@rad.ulaval.ca). C. J. Thompson is with McGill University, Montreal Neurological Institute, and Biomedical Engineering Department, Montreal, QC, HA 2B4 Canada. (Tel chris@med.mcgill.ca). it can reduce the number of detected light photons by an appreciable amount[2]. We have modeled the stratified detectors used in the high-resolution mammography system PEM-1[] and the animal PET system ANIPET[4]. The BGO scintillator has three distinct layers. The closest layer to the photo-multiplier tubes (PMT), the proximal layer, is cut in a 1x1 matrix of crystals. The height of this layer is 11.5mm. The layer of the scintillator that is the farthest from the PMT, the distal layer, is cut in an 18x18 matrix of crystals and has a height of 6.5mm. In between these two layers, there is a full layer of BGO that interconnects the layers. This layer has width of 2mm. Since, the distal and proximal layers are offset by one half of a crystal in both lateral directions, the centroid of the detected light photons for an interaction in the distal layer should fall between the centroid of the γ-ray interactions in the proximal layer. Because of the offset, the crystals on the edge of the scintillation block in the distal layer are only half as wide. Each crystal is optically isolated from its neighbors in the same layer by a mixture of clear epoxy and an epoxy based white paste containing titanium dioxide. In ANIPET and PEM-1, four scintillation blocks are coupled to a position sensitive PMT and Anger logic is used to determine the location of the centroid of detected light photons[5]. II. MATERIAL AND METHODS A. Features of DETECT2 To do the theoretical simulations of the scintillation block, we used DETECT2. DETECT2 is a Monte-Carlo simulation software that generates one light photon at a time and traces it in the crystal. The final fate of each light photon is then recorded along with the flight time, number of surfaces encountered and the length of the flight path. DETECT2 is the successor DETECT9, a version that was developed at TRIUMF that is one of the successor of the DETECT software that was originally developed at the University of Michigan[6]. DETECT is known to predict the position and energy response of PET detectors realistically[]-[8]. DETECT2 was translated from the DETECT9 s C language to the object-oriented language C++. The translation process was done in such a way that a simulation file that ran

2 under DETECT9 would also run under DETECT2 with similar results. A list of new features follow. 1. Exciton decay time and the detection surface response time can be generated from a user-defined distribution. DETECT2 accepts three different methods in order to define the time distributions. One other improvement is the wavelength dependent coefficients of surface and material properties. These features can be used for any relevant coefficient in the model. 2. Statistical counting method. By using the inverse of the last quantum efficiency of the detection surface, the number of actually simulated light photons can be drastically diminished, increasing the speed of the simulation without significantly decreasing the simulation precision.. Position sensitive detection surfaces. At the end of a simulation involving a position sensitive surface, the centroid of the detected light photons will be written with all the other simulation data. Also it is possible to create 2D histograms of where the light photons hit the detecting surfaces. This is needed to predict the light pattern incident on a position sensitive PMT. 4. New random number generator: the L Ecuyer generator with Bays-Durham shuffle[9]. This generator has a very long period, about 2x 18 numbers. The change of random number generator means that a simulation run under DETECT9 would give different results than DETECT2. However, the changes should not be statistically significant. 5. Streamlined code resulting in an increase of about to 15% in the simulation speed. This is further increased by the new photon generation methods. This additional increase cannot be quantified because it is dependent on the size of the simulation model and on the type of simulation that are performed on the model. 6. More thorough model file checker. It can detect errors such as a lack of interface between two different types of material. This kind of error was going unnoticed in DETECT9.. All limitations on the size of the model and the number of output files have also been removed. DETECT2 can now support any size of model, the only limiting factor being the physical memory of the system DETECT2 is being run on. B. Creation and Simulation of the Scintillator In order to create the scintillator crystal model, BUILDER[], a program in the DETECT2 suite is used. BUILDER can create scintillator model by processing a definition file. Since BUILDER is not able to create a two layers scintillation crystal, each layer of the scintillation crystal was created independently. The two resulting simulation files were then merged using a custom program. The resulting file was later merged to a.1mm glass plate that has at the bottom a perfectly detecting surface. The interface between the crystal and the glass plate is assumed to be perfectly flat without any air gap. For the simulations, we are using two different kinds of surface finish. The first one is a perfectly flat surface and every time there is a light photon interaction, a specular, mirror, reflection occurs. The second surface finish used is a very rough surface and there is a Lambertian, random angle, reflection at every surface interaction. To reduce the simulation time and to avoid the complete simulation of internally trapped photons, the surfaces have a reflection coefficient of 99%. This means that at every light photon interaction with a surface there is a 1% percent chance that the light photon is absorbed by the surface. The specular surface finish can be considered the best-case scenario for the scintillation crystal. In the ideal case, the cutting and etching procedures during the crystal machining process leaves a perfectly smooth surface and the titanium dioxide reflection is in such a way that there is a specular reflection every time. The Lambertian surface, however, can be considered the worst-case scenario for the scintillator. The cutting and etching could leave a roughened surface on each individual crystal and the reflecting surface could be such that there is an equivalent to a Lambertian reflection every time. The simulations were done using axial traversal of the scintillator block starting from the top of the crystal and going toward the position sensitive PMT by increment of.mm. For each simulation point, light photons were simulated in order to have a good approximation of were the centroid of detected light photons would fall. The axial dotted lines where chosen in such a way that they did not fall in a gap in between individual crystals in a given layer as shown in figure 1. The simulations occurred in the center of the scintillator element and only in one half of the crystal because it is symmetric in width and depth. The γ-rays are assumed to have a photo-electric interaction with that point in the scintillator so all the light photons are generated from this point with random orientations. Ideally, we would hope that the centroid of detected light photons would fall at the center of the crystal in which the interaction occurred as shown in figure 2. For simplicity, we ignore γ-ray interactions in the middle layer but in the real case, we should expect the centroid of detected light photons be near to the center of the nearest crystal. This kind of simulation is very CPU intensive. Depending on the type of crystal surface, the simulation of all the γ-ray interactions takes between 5 and 8 hours on a Pentium III MHz computer. For light photons, the average simulation time is about 2 seconds. C. Variations to Simulated Scintillator Geometry After the first run of simulations, we decided to remove the half-crystals found on the edge of the distal layer because they are undistinguishable from the crystals in the proximal layer. Each of the half-crystals was deleted from the simulation file and the interface with the middle layer was replaced by a reflector of the appropriate type. Since the removal of these crystals did not change the overall performance of the scintillator block, we decided to reduce the width of the middle layer in order to see what middle layer width would allow peak performance for a Lambertian surface. In order to do so, we have increased the depth of the simulated saw cut in both the distal and proximal layers in the simulation file until

3 good results were obtained. We have done simulations for crystals that have a 1.5mm, 1mm,.5mm,.25mm and.1mm middle layer. Since there is almost no change in the best-case specular reflector, the results of these simulations are not presented. In the worst-case scenario Lambertian reflector, the results are not very different from one to another so only the 1mm and the.1mm simulations are presented. A. Simulation of the Crystal III. RESULTS Figure shows the results of the simulations done on a scintillator that have specular reflecting surfaces. We are able to see that all the individual crystals can be easily identified with one exception. The γ-ray interactions occurring in the half-crystals in the distal layer have a centroid of detected light photons at about the same place as the crystal just below in the proximal layer. This can be explained by the fact that the light photons generated in these crystals will have to travel in the proximal crystal in order to be detected by the PMT. Since the light photons will most likely interact with the proximal crystal surfaces, the centroid of detected light photons will be the same for both crystals. We can also see that the centroids of detected light photons are always about the center of each crystal except for edge crystal. At the edge, the lines of where the centroids of detected photons occurs, the line of response, are slightly shifted toward the center of the scintillator. This can be explained by the fact that the light photons is reflected by the edge of the scintillation block and are reflected toward the center of the block. In the simulations nearer to the edge of the scintillator, there is one point that goes closer to the center of the scintillator than the others. This simulation point is very near to the edge of the saw cut in the proximal layer and this could explain why there is a big shift in the position of the centroid of detected for that particular simulation point. Figure 4 shows the results of the simulations done on the scintillator with a Lambertian reflecting surface. We can see that there are only a few crystals that would be correctly identified if this kind of surface finish was used in the actual scintillator. If this were the actual case, only % of all the crystals could be correctly differentiated. The other crystals would have centroids of detected light photons of one or more crystals in their line of response. With this kind of surface finish, very few crystals have their line of response on or near center of the crystal. One of the most noteworthy effects of this surface finish is the importance of the middle layer. The crystals in the distal layer tend to be shifted toward the center of the block. Since all the scintillation photons coming from that layer have to cross the middle layer, the Lambertian reflections scatter light photons across the crystal. Since they reflect on the edge of the scintillation block, they are more likely to continue in the centermost proximal crystals in order to be detected. This kind of behavior also happens for the γ-ray interactions occurring in the proximal layer, but in that case, the effect is a function of the distance to the PMT and the distance to the center of the crystal. At the edge of the crystal, this effect causes the outermost crystals in the proximal layer to have centroids of detected light photons at about the same place as the third outermost crystal. This kind of behavior would greatly impact on the spatial resolution of the scintillator because we would have too great an uncertainty on where the γ-ray interaction would have really occurred. B. Simulation of the Modified Scintillator Models Figure 5 shows the results of the simulations done on the modified scintillation block model that have a middle layer that is only 1mm thick with Lambertian surface finish. This time, the distal half-crystals have been removed and there are no simulation results in that part of the scintillation block. With that kind of model, we are able to see a noticeable improvement in theoretical performance over the normal model that has a 2mm middle layer. The centroids of detected light photons tend to be less attracted toward the center than before. The effect is strong enough to mix the line of response starting from the fourth outermost proximal crystal. As a whole, this kind of scintillator block has the possibility of distinguishing 49% of all the individual crystals. Also, we are able to see that the lines of response of the outermost proximal crystals only mix with the lines of response of their neighboring proximal crystals. This represents an important improvement over the normal scintillation block. Figure 6 shows the same model, but with a middle layer of.1mm. This time, we are able to see that the scintillator, even though it has Lambertian reflectors on all of its individual crystal surfaces, has nearly perfect behavior. Almost all crystals produce lines of response that fall exactly on the ideal line of response. The only exceptions are the ones on the edge of the block. In addition, all the crystals can be distinguished solely on the base of the centroid of detected light photons. The only factor that could degrade the performance of this kind of crystal is the γ-ray interactions occurring near the middle layer. The centroid of detected light photons is influenced by the other crystals but it does not have a tendency to move toward the center of the block. The only negative point is the line of response of the outermost proximal layer that still has a tendency to go toward the middle of the block. IV. DISCUSSION AND CONCLUSION Using DETECT2, we have been able to determine some flaws in the scintillator geometry. The first flaw is that the half-crystals in the distal layer at the edge of the block has lines of response that fall almost at the same place as the crystal just beneath it. We have decided to remove them from the simulation model and from further scintillation block machining. We have simulated that this removal did not impact on the overall performance of the scintillation crystal.

4 We have also seen that if the surfaces of the individual crystals are an ideal specular reflector, we are able to have a very good crystal differentiation. However, with a Lambertian reflector, the results are very bad and very few crystals can be correctly distinguished with the current scintillator block design. Since we are still unsure of the true scintillator surface, we have decided to simulate blocks that have smaller middle layers. We have found that halving the middle layer width had a big effect on the performance but still a large portion of the individual crystals could not be differentiated. The complete differentiation occurs with a block geometry that has a middle layer width of.1mm. The technique developed in our lab to cut BGO blocks uses multiple passes of a multi-blade diamond saw. It was felt that making the center layer less than 2mm would make the scintillator too fragile to survive the cutting as it is held in a vice which compresses this layer. Currently we are exploring new crystal geometries that would give perfect crystal recognition while being easy to cut. One such new research direction is a scintillation block that will be cut in two in order to remove the middle layer and then glued back together with optical glue. Preliminary simulations tend to give good results for that kind of crystal. Another research path is the actual determination of the surfaces of the crystals. By taking broken crystals that went through the entire machining process it will be possible to measure the actual roughness of the crystal surface. V. REFERENCES [1] S. R. Cherry, M. P. Tornai, C. S. Levin, S. Siegel, E. J. Hoffman, M. S. Andreaco and C. W. Williams, A comparison of PET detector modules employing rectangular and round photomultiplier tubes, IEEE Trans. Nucl. Sci. vol. 42, p. 64, [2] J. G. Rogers, C. Moisan, E. M. Hoskinson, M. S. Andreaco, C. W. Williams and R. Nutt, A practical block detector for a depth-encoding PET camera, IEEE Trans. Nucl. Sci. vol. 4. pp , 1996 [] J. L. Robar, C. J. Thompson, K. Murthy, R. Clancy, A. M. Bergman, Construction and calibration of detectors for high resolution metabolic breast cancer imaging, Nucl. Inst. And Meth. In Phys. Res. A92, p.42-6,199. [4] C. J. Thompson, P. Sciassa and al. ANIPET, a versatile PET scanner for imaging small animals, Paper # M6- Proceedings of the 1998 IEEE Medical Imaging Conference, Toronto, [5] N. Zhang, C. J. Thompson, C. L. Thompson, K. Nguyen, Improving the performance of small planar detectors for dedicated PET. IEEE Nucl. Sci. Symp. Conference Record, vol., pp 1_51-1_5, 2. [6] G. F. Knoll, T. F. Knoll and T. M. Henderson. Light collection scintillation detector composites for neutron detection, IEEE Trans. Nucl. Sci. NS-95, p. 82, [] G. Tsang, C. Moisan and J. G. Rogers, A simulation to model postion encoding multicrystal PET detectors, IEEE Trans. Nucl. Sci. vol. 42, pp , [8] G. Tsang, A simulation for the design of position encoding detectors for positron emission tomography, M.Sc. thesis Univ. of British Columbia, 1995 [9] P. L Ecuyer, Communications of the ACM, vol. 1, 1988, pp 42-4 [] E. Hoskinson, A. Levine and C. Moisan, BUILDER, a high level language interface to DETECT for the design of scintillation detectors, Version., TRI-DN-96-28, Subject PMT Fig. 1 This is half of a slice of the scintillation block. The crystals at the top are the distal crystal and those at the bottom are the proximal crystals. The dashed lines show the axial lines where the simulations were actually done. The center of the crystal is in the proximal crystal at the right of the figure. Subject PMT Fig. 2 This is half of a slice of the scintillation block. The crystals at the top are the distal crystal and those at the bottom are the proximal crystals. The dashed lines show where the centroid of detected light photons are expected for each crystal, in the center of each crystal.

5 Fig. Results of the simulation done on the scintillation crystal using specular reflecting surfaces. The solid vertical lines are drawn at the centerline of all crystal elements. The line of the half-crystals in the distal layer has been omitted. Each dot represents the position of the centroid of detected light photons for a simulation at a given depth. The actual position of the simulations follows the lines of figure 1. 2 Fig. 6 Results of the simulation on the modified scintillator that has a middle layer of only.1mm. The crystal surface finish is a Lambertian reflector. 1 1 Fig. 4 Results of the simulations on the scintillation crystal that has a Lambertian crystal surfaces Fig. 5 These are the results of the simulations done on the modified scintillation block. The crystal no longer has the distal half-crystals and its middle layer has only 1mm width instead of 2mm. The crystal surface is a Lambertian reflector.