Paper presented at IEEE, Nuclear Science Symposium. Anaheim, November 2{4 Oct Simulating the Performances of an LSO Based

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1 Paper presented at IEEE, Nuclear Science Symposium TRI{PP{96{58 Anaheim, November 2{4 Oct 1996 Simulating the Performances of an LSO Based Position Encoding Detector for PET C. Moisan, D. Vozza and M. Loope y TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., CANADA V6T 2A3 y CTI PET Systems, 810 Innovation Drive, Knoxville, TN Abstract We investigated the impact of replacing BGO by lutetium oxyorthosilicate (LSO) in the fabrication of the EXACT HR PLUS position encoding detector for PET. A detailed Monte Carlo simulation was used to track the interactions of energetic photons in the volume of the block as well as to treat the generation and propagation of scintillation light through its geometry. The simulation also accounts for LSO's non-proportional scintillation response, the bulk attenuation to its own scintillation and the noise contribution from the amplication of photoelectrons in the readout units. The model predicts that the increased photostatistics available in LSO compared to BGO leads to improvements by up to a factor ve in the peak-to-valley ratios of the position response of the block to a uniform ood of 511 kev photons. For the crystals located along the diagonal, the position encoding accuracy is found to vary from 50% to 78% representing a gain of up to 7% compared to its BGO parent. With peak photoelectron counts of 678 to 2024, the energy resolution of the same crystals is found to vary from 14% to 9%. I. Introduction Recent advances in the techniques for growing lutetium oxyorthosilicate in large quantities at competitive cost, announce the development of photon detectors based on this ecient, bright and fast inorganic scintillator. Here, we present a Monte Carlo model of an LSO based position encoding block detector for positron emission tomography (PET). A detailed Monte Carlo simulation was used to track the interactions of 511 kev photons in the volume of the block as well as to treat the generation and propagation of scintillation light through the multicrystal detector. The simulation is based on DETECT [1] and was previously described in Ref. [2]. The block geometry adopted is that of the EXACT HR PLUS block manufactured by Siemens-CTI. Constraining the model to this state-of-theart detector allows for a comparison of the performances predicted for the LSO block to those already established for its BGO parent. In the next section, we rst discuss the input parameters used to model scintillation light production and propagation in LSO. The section also presents simple treatments of the non-proportional scintillation response of LSO and of the noise associated with the amplication of photoelectrons by the photomultiplier tubes, (PMTs), reading out the block. The model is then used to predict the position and energy responses of the LSO HR PLUS to a uniform ood of 511 kev photons. Position encoding accuracies and energy resolutions achieved in selected crystals of the LSO block are then presented and compared to those of its BGO parent. The last section nally discusses the impact of LSO's natural background on the predicted performances and treats the possibility of increasing the transverse segmentation of the block. II. A. LSO Model Inputs LSO Block Model The HR PLUS detector is made of a BGO crystal with dimensions of mm, segmented in an 88 crystal matrix, and is read out by an array of four circular PMTs that are 19 mm in diameter. A realistic model of this block was presented in Ref. [2]. For the present study, we borrowed directly from that previous work all the geometrical specications of the HR PLUS model. Table 1 presents the input parameters of the HR PLUS model aected by replacing BGO for LSO. Parameter LSO BGO refraction index light yield (ph./mev) quantum eciency absorption length (mm) scattering length (mm) nish GROUND GROUND reection coecient Table 1: Comparison of the input parameters to the HR PLUS block model aected by replacing BGO for LSO. Our model rst assumes that LSO has a constant in-

2 dex of refraction of 1.82 borrowed from the literature [3]. Although still subject to signicant variations associated with crystal growth processes, the model also assumes that LSO yields scintillation photons/mev as was recently reported by the Delft group in its discussion of conventional and new inorganic scintillators [4]. An average value was calculated for the quantum eciency of the phototubes to account for the impact of the wavelength distribution of LSO's scintillation upon the collected photostatistics in the block. An eciency of 22.5% was obtained by weighting the spectral response of Hamamatsu bialkali photocathodes by the emission spectrum of LSO [5]. The number of scintillation photons reaching the photodetectors also depends upon their interactions with the crystal's bulk and surface coat. In DETECT, bulk attenuation of scintillation photons is split into two components to account for scattering processes, which change their direction, and for absorption which terminates them. The strength of each process is specied by independent values for the scattering and absorption lengths, s and a respectively. Similarly, DETECT provides two surface nish models, GROUND and POLISH [1], to treat the interactions of scintillation photons at the interface between a dielectric surface and a diuse reective coat. The options are named after the angular distribution of the normal vector to an element of the crystal surface. In both options, a reection coecient, RC, species the surface coat's reectivity. A realistic set for s, a, the surface nish, and RC could be found from the following measurements taken on small LSO samples. Firstly, the transmittance of LSO provides information on bulk attenuation in this crystal. From measurements taken on a 10 mm thick, well polished LSO crystal [5], the total attenuation length, t, of LSO takes a value of 138 mm at its peak emission wavelength. This result gives a useful constrain on s and a through the relationship: 1= t = 1= s + 1= a. Secondly, the longitudinal variation of the photopeak in pencil-like crystals results from the combined eect of bulk attenuation, surface nish and coat reectivity, and can be used to constrain these parameters. This variation was therefore measured in two LSO crystals by stepping a collimated fan beam of 511 kev photons along their long axis. The crystals had respective dimensions of mm and mm, were mechanically polished, and covered with a highly reective white coat. The full points in Figure 1 presents the results. The program DETECT was used to reproduce the response of these crystals. The POLISH and GROUND options were both considered as potential models for their surface nish. The relative values of s, a, and of RC were then varied systematically until the variation of the light yield predicted by the simulation matched that of the photopeak observed in both LSO crystals simultaneously. Relative values of s and a were kept constrained to a total attenuation length of 138 mm. The best match was obtained using the GROUND n- Figure 1: Variation of the photopeak pulse height in two LSO crystals as a function of the longitudinal or depth position of a collimated fan beam of 511 kev photons. ish with a RC value of 97 to 98% along with a = 1 and s =138 mm. The predictions of the simulation for this set of parameters are compared against the experimental data shown in Figure 1. It is interesting to note that setting s = t =138 mm indicates that the diusion of scintillation photons is dominant in LSO. B. Non-Proportional Scintillation of LSO For the purpose of this study, the cross sections for the photoelectric and Compton interactions in LSO for photons of energies ranging from 10 to 511 kev were derived using GEANT from the CERN libraries. Following the method described in Ref. [2], the number of scintillation photons generated at each interaction was derived from the product of the energy lost at the interaction vertex and of the light yield of LSO from Table 1. The scintillation response of LSO displays a signicant dependence upon the energy of incident photons. From the recent compilation available in Ref. [4], the scintillation yield of this crystal eectively doubles as incident photon energies increase from 10 to 100 kev. Above 100 kev it reaches a nominal plateau of scintillation photons/mev which extends at least up to 1 MeV. Implementing this eect in our model only requires a simple correction to the number of scintillation photons associated with each interaction vertex of an energetic photon tracked in the block. This correction factor was taken directly from the experimental scintillation response curve of LSO available in Ref. [4]. Page 2

3 C. Photoelectron Amplication Noise In the HR PLUS block, the scintillation light is converted to pulses by an assembly of four 19 mm diameter PMTs, optically coupled to the back face of the block. For each incident photon, estimators for the energy, E, and incident transverse coordinates, (X ; Y ), are then obtained from: E = A + B + C + D ; (1) (B + D) X? (A + C) = A + B + C + D ; (2) (A + B) Y? (C + D) = A + B + C + D ; (3) where A, B, C and D, are the respective digital conversions of the analog pulses integrated by each phototube. Statistical noise associated with the amplication of the photoelectrons from the photocathode through the dynode chain is signicant and was modeled by adding to the number of photoelectrons collected in each phototube a random gaussian component of standard deviation given by [4]: X = p X (1 + v(m)) ; (4) where X can be A, B, C or D, and where v(m) is the variance in the amplication of photoelectrons through the dynode chain of the phototube. For v(m) a value of 0.07 was calculated, as prescribed in Ref. [4]. This value is representative of a tube with 10 dynodes and a mean multiplication factor of 15 at each stage. In recent work [6], the addition of this source of noise was shown to lead to a prediction of crystal dependent energy resolutions observed in the BGO version of the HR PLUS block with an average accuracy of 1%. III. A. Position Response Results The top panel of Figure 2 presents in the (X, Y ) plane, the simulated position response of one quadrant of an LSO made HR PLUS block. The response was obtained for a uniform ood of photons with an energy of 511 kev. It is compared, in the bottom panel, to that derived for its BGO parent under the same conditions and using the inputs of Table 1. Both simulated responses include corrections for the non-proportional scintillation and noise associated with photoelectron amplication in the PMTs. Both response distributions are normalized independently to unity. Comparing the 2D ood responses obtained for the HR PLUS geometry using LSO and BGO respectively indicates that the additional photostatistics of LSO leads to an obvious increase in the peak-to-valley ratios of the 2D ood response. This is particularly signicant for the crystals belonging to the edge row and column for which a much better separation is achieved in the LSO block with Figure 2: Simulated ood position responses for a quadrant of an LSO (top) and a BGO (bottom) HR PLUS block. a peak-to-valley ratio that is a factor 3 to 5 better that that observed in the BGO block. Table 2 compares the probabilities, predicted by the simulation, to correctly identify the entrance crystal of events normally incident on the LSO and BGO blocks. Results are presented for the diagonal crystals only. These are labelled after their row and column numbers with crystal (1,1) and (4,4) dening the center and the corner of the block respectively. The identication probabilities are rst given exclusively for events that had a prompt photoelectric interaction (P), one or more Compton diusion followed by a nal photoelectric interaction (C+P), and for those that only had Compton interactions and escaped (C). The last column gives the probabilities obtained considering all events inclusively. The Monte Carlo history of each photon was used to obtain the address of its crystal of incidence. Simple rectangular regions-of-interest (ROIs), in the (X, Y ) signal plane, were then used to identify the crystal address encoded after the interaction of the event in the block. The ROIs' boundaries were found along X and Y by requiring that each row and column includes four local maxima of the 2D position response. This was done independently for the LSO and BGO blocks. Considering the exclusive probabilities shows, for all classes of events, a systematic increase of the encoding accuracy in the inner crystals of the block. While not being a surprize for events interacting through the prompt photoelectric channel, this indicates for Compton scattered events, that the additional photostatistics of LSO improves the sensitivity of the block to the point of rst interaction of the events. The only exception to this is for Compton events in crystal (4,4) at the corner of the block. However, combining all interaction channels together indicates Page 3

4 LSO Block (row,col.) P (%) C+P (%) C (%) All (%) (1,1) (2,2) (3,3) (4,4) BGO Block (row,col.) P (%) C+P (%) C (%) All (%) (1,1) (2,2) (3,3) (4,4) Table 2: Comparison of the position encoding probabilities predicted by the LSO and BGO HR PLUS block models. an increase of at most 7% in the encoding accuracy of the diagonal crystals of the block. This is explained by the larger fraction of Compton scattered events in LSO compared to BGO which cancels part of the gain from the extra photostatistics. Crystal (1,1) at the center of the block provides a good example of the competing eects. While in BGO, events incident on that crystal interact in the ratios P:C+P:C of 42:42:16 with respective encoding accuracies of 89%:62%:45%; in LSO the proportions become 32:46:22 with accuracies of 98%:72%:62%. The drop in the fraction of prompt photoelectric interactions at the benet of Compton events limits the net gain in the encoding accuracy of that crystal to 7%. B. Energy Response Table 3 presents the predicted peak number of photoelectrons and the FWHM resolution obtained by tting to a gaussian the E distribution formed by events incident on the diagonal crystals of the LSO HR PLUS block. Systematic uncertainties on the gaussian t are also given for the energy resolutions. The identication of the crystal of interaction of each event was performed using the ROIs discussed in the previous paragraph. The results are presented at three dierent stages of the simulation. The rst column gives the prediction of the model assuming a constant scintillation light yield of photons/mev, (CSLY). The next two columns show the evolution of the energy response of the block when corrections are successively made for the non-proportional scintillation response of LSO, (NPSR Corr.), and for the photoelectron amplication noise, (PAN Corr.). The simulation results rst show that taking into account the non-proportional scintillation of LSO brings down the peak photoelectron counts by only 5%. Further correcting for the PMT amplication noise has no signicant impact on the photoelectron statistics. The nal peak photoelectron counts vary from 678 for the corner crystal to a maximum of 2024 in crystal (3,3). As discussed previously in Ref. [2], this range is associated to variations in the coupling eciencies between the individual crystals and the PMT array in the HR PLUS block geometry. The correction for LSO's non-proportional response doesn't have a signicant impact on the energy resolutions. The situation is quite dierent when correcting for the amplication noise. Accounting for that source of noise increases the predicted energy resolutions by a quadratic contribution of 7 to 8%. The additional noise is larger than could be expected from the total photoelectron counts due to the sharing of the photostatistics between four PMTs. The nal energy resolutions are found to vary from 9 to 14%. This is roughly a factor 2 higher than what could naively be expected from the available photoelectrons using Poisson statistics. These resolutions still advantageously compare to those of 21 to 33% observed for the same crystals in the BGO version of the block [2]. IV. Discussion and Conclusions In this work we investigated the impact of using LSO instead of BGO in the design of the EXACT HR PLUS block, a state-of-the-art high resolution position and energy encoding detector for PET. Under the constrained inputs listed in Table 1, the model predicts that the increased photostatistics available in LSO compared to BGO leads to improvements by up to a factor ve in the peak-to-valley ratios of the 2D ood response map of the block. The corresponding benet to the position encoding accuracy of the diagonal crystals of the LSO block was however shown to be limited to 7%. This limit was explained by the larger fraction of Compton scattered events in LSO compared to BGO which cancels part of the gain from the extra photostatistics. Taking into account the non-proportional scintillation response of LSO was shown to have only a small eect on the block response. This correction was found to typically lower the peak photoelectron counts in the diagonal crystals of the block by 5%, leading to photoelectron counts varying from 678 to 2024 depending on the crystal of interaction. The noise contribution associated with the amplication of the photoelectrons proved to have a large impact on the energy resolutions observed in the block. Its eect is enhanced by the sharing of the net photoelectron counts among the four PMTs and leads to FWHM resolutions that vary from 9% to 14%. This remains a signicant improvement over the energy resolution of the BGO block. One could expect a steady rate of 12 khz from the natural activity of 176 Lu contained in the volume of a single block. Provided the biasing circuit of the PMTs is designed to prevent gain drifts at that rate, this is not expected to have a signicant impact on the predicted performances of the LSO HR PLUS. The natural background will produce a 2D position response very similar to that of Figure 2 due to its uniform distribution throughout the volume of the block. However, in routine operation, this contribution will be highly suppressed by the time coincidence requirement of PET. Assuming a conservative coincidence window Page 4

5 crystal id. CSLY NPSR Corr. PAN Corr. (row,col.) Peak (phe) FWHM (%) Peak (phe) FWHM (%) Peak (phe) FWHM (%) (1,1) (2,2) (3,3) (4,4) Table 3: Peak number of photoelectrons and the FWHM resolution predicted for the diagonal crystals of the LSO HR PLUS. width of 12 nsec, leads to an acceptance of only 2 random counts per second from that source, which can be further reduced by energy thresholding. From the results of this study, one concludes that replacing BGO by LSO in the design of the present generation of multicrystal detectors for PET would be of immediate benet to their energy resolution. The increased photoelectron counts should also lead to an improved timing resolution. However, our study indicates that the extra scintillation yield of LSO brings only marginal gain to the position resolution achieved by this design. Segmenting the block into a ner crystal matrix may appear as an attractive option to improve the position resolution of the block. Figure 3 presents the simulated 2D ood response of an LSO HR PLUS block cut in a 1010 crystal matrix and clearly shows that a ner transverse segmentation is possible. With values distributed from 9% to 15%, the energy resolution is little aected by the ner segmentation. However, this scenario deserves more careful consideration. A detailed analysis indeed shows that the position encoding accuracies for events incident on these smaller crystals is signicantly lower, with values of 44% to 65%. This loss of accuracy can be attributed to cross-talk from Compton scattered events and an enhanced non-linearity of the block position response. Added to the noise contribution from the phototubes, these seem to effectively limit the segmentation of the crystal matrix to Despite the high photoelectron counts still available, all attempts to simulate a 1212 HR PLUS block lead to ood position responses that did not resolve all crystals. Figure 3: Simulated ood position response of an LSO HR PLUS block segmented in a 1010 crystal matrix. Finally, one should remember that several aspects of the present study are bound to remain speculative until an HR PLUS block is cut out of a LSO boule. Despite the care taken in choosing the model's inputs, the values assumed for LSO's scintillation yield as well as for its total bulk attenuation may well turn out to be pessimistic, given the rapid advances of the growing techniques. The surface nish that will be practically achieved in the full block is also likely to be dierent from that used to constrain the model and may similarly impact on the accuracy of our predictions. Whether the performances predicted in this study will be met in practice now needs to be addressed by experiment. V. Acknowledgments At TRIUMF the authors are thankful to Ken R. Buckley and J. G. Rogers for helpful discussions while working on this project. Daniela Vozza's stay at TRIUMF is made possible by a fellowship of the University of Bari, Italy. Christian Moisan is thankful to the province of Quebec's \Fonds pour la Formation des Chercheurs et l'assistance a la Recherche" for its support through a postdoctoral fellowship. VI. References [1] G. F. Knoll et al., IEEE Trans. Nucl. Sci., NS (1988). [2] G. Tsang, C. Moisan and J. G. Rogers, \A Simulation to Model Position Encoding Multicrystal PET Detectors", IEEE Trans. Nucl. Sci., NS (1995). [3] C. L. Melcher and J. S. Schweitzer, \Cerium-doped Lutetium Oxyorthosilicate: A fast, ecient new scintillator", IEEE Trans. Nucl. Sci., 39, No. 4, 502 (1992). [4] P. Dorenbos et al., IEEE Trans. Nucl. Sci., NS (1995). [5] C. L. Melcher, Schlumberger-Doll Research, private communication. [6] D. Vozza, C. Moisan and S. Paquet, \An Improved Model for the Energy Resolution of Multicrystal Encoding Detectors for PET", submitted to IEEE Trans. Nucl. Sc. Page 5