- Email: [email protected]
Compact hybrid gamma camera with a coded aperture for investigation of nuclear materials
Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Compact hybrid gamma camera with a coded aperture for investigation of nuclear materials Taewoong Lee, Wonho Lee n Department of Bio-convergence Engineering, Korea University, Seoul 136-103, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 6 March 2014 Received in revised form 27 June 2014 Accepted 17 July 2014 Available online 21 August 2014
Mechanical collimation commonly uses the photoelectric effect to reconstruct radiation images. Electronic collimation (i.e. Compton camera) using Compton scattering has been developed to reconstruct radiation images without utilizing mechanical collimators. Generally, for radiation imaging, electronic and mechanical collimation methods are used individually. In order to increase the quality of imaging and the efficiency of radiation detection, we combined both collimation methods in a single system. Our compact hybrid gamma camera comprised a modified uniformly redundant array (MURA) and a Compton camera, and the information from each modality was obtained simultaneously. The entire system formed a radial shape with detector modules which comprising CsI(Na) scintillators coupled with position-sensitive photomultiplier tubes (PSPMTs) whose anodes were connected to custom-made circuits. For various energy sources, the reconstructed images produced using this hybrid method were obtained and compared with reconstructed images from the two aforementioned methods. The maximum likelihood expectation maximization (MLEM) algorithm was applied for the reconstruction method. Compared with individual imagers at intermediate energies, the hybrid imager showed equal or better performance. & 2014 Elsevier B.V. All rights reserved.
Keywords: MURA (mechanical collimation) Compton camera (electronic collimation) MLEM Hybrid
1. Introduction Gamma-ray imaging has been applied in nuclear medicine, astrophysics, homeland security, and various industries. In most low-energy applications (o200 keV), conventional mechanical collimation using a pinhole or a coded aperture comprising a high density material is employed to form the gamma-ray shadow on a position-sensitive detector [1–3]. Other systems employ electronic collimation using sequential gamma-ray interactions in a single detector or multiple detectors for intermediate and high energies (800–2000 keV) [4–6]. Mechanical collimation is effective at low energies, while electronic collimation shows high performance at high energies. At intermediate energies (200–800 keV), two particular interactions – the photoelectric effect and Compton scattering – compete with each other. Researchers have developed advanced equipment using both collimation methods to the advantage of each modality. Gormley attempted to combine the modalities of different collimation methods. The resulting combined image, which applied a penalized weighted least-square algorithm, showed equal or
n
Corresponding author. E-mail address: [email protected] (W. Lee).
http://dx.doi.org/10.1016/j.nima.2014.07.031 0168-9002/& 2014 Elsevier B.V. All rights reserved.
better performance than the best individual system, but the modalities operated in separate systems [7]. In order to increase signal-to-noise ratio (SNR), Uritani added parallel plates to an electronically collimated camera, but detection efficiency and field of view (FOV) were severely decreased [8]. For higher detection efficiency and a larger field of view, a coded aperture replaced the parallel plate in 2009. At intermediate energies, the modified system demonstrated better performance than both mechanical collimation and the electronic collimation [9]. Lee proposed and built the URA coded mask with an attached Compton camera using LaCl3(Ce) scintillators. This device represented the single system using both photoelectric events and Compton scattering simultaneously [10–12]. Because the system utilized lanthanide scintillators, its angular resolution and timing resolution were high compared with other scintillator-based gamma cameras. However, because of the bulky position-sensitive photomultiplier tube (PSPMT) and the small number of detectors, both the portability and the detection efficiency of this system were significantly limited. In this study, a portable hybrid gamma-ray imaging system was manufactured using pixelated scintillators coupled with very compact PSPMTs. In order to increase detection efficiency, multiple secondary detectors were back-positioned in a radial shape. Consequently, the detection efficiency of the system was much
6
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
higher than the previous system, and its portability was significantly improved.
2. Materials and methods Fig. 1(a) shows a schematic diagram of a compact hybrid gamma camera consisting of a modified uniformly redundant array (MURA) mask [1] and CsI(Na) planar detectors. At the rear of the first detector, the secondary detection modules form a radial shape directed toward the first detector (cf. Fig. 1(b)). As shown in Fig. 2, the first and second detectors were CsI(Na) arrays [13] coupled with a PSPMTs [14]. The non-uniformity of the multianode PSPMTs response to incident light was corrected using a readout circuit [15,16]. The scintillator consisted of 20 20 voxels, and each voxel had a dimension of 2 2 5 mm3. The size of the PSPMT with readout boards was 50 50 60 mm3, which was approximately 11 times smaller than the previous PSPMT [12]. Comprised of tungsten, the entire MURA mask was 73 73 5 mm3 in size, while each pixel was 2 2 5 mm3. MURA had an approximately 50% opening area to pass radiations for gamma ray imaging. The activities of all sources (57Co, 133Ba, 137 Cs, and 22Na) for the experiment were 10 μCi. The visible light from the CsI(Na) was converted to electric signals in PSPMTs and was then transmitted to a custom-made circuit in which the signals’ timing and amplitude information was measured. The timing information was sent to a field-programmable gate array (FPGA), which triggered a data acquisition board (DAQ). Owing to this procedure, only effective interactions resulting from photoelectric events and Compton scattering were selected in the DAQ, and their information was sent to a computer, in which the source distribution was reconstructed. In a previous simulation study, the optimized condition for a hybrid system combining both a mechanical and an electronic collimator was calculated. The angle between the second detectors
and the system axis was set at 451, and the distance between the first detector and the second detectors was 100 mm in the hybrid system [17]. The radiation source was located at a distance of 200 mm from the first detector. The hybrid system was based on the combination of the mechanical collimation imager (MURA imager) and the electronic collimation imager (Compton imager). In the first modality, the incident radiation passed through the 11 11 MURA mask and deposited its energy on the first detector (mechanical collimation imager). In the second modality, the incident radiation underwent scattering in the first detector and was absorbed in the second detectors (electronic collimation imager). Fig. 3 shows the timing resolution of the coincident events. To evaluate the timing resolution, the digitized timing output of the
Fig. 3. Timing histogram of coincidence events.
Fig. 1. A compact hybrid gamma camera. (a) Schematic diagram and (b) photograph.
Fig. 2. Components of a compact hybrid gamma camera. (a) One detector module, (b) the CsI(Na) scintillator, and (c) the mosaic of a basic 11 11 MURA coded mask.
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
first detector was connected to the start input of the time-toamplitude converter (TAC), while the timing output of the second detector was connected to the delay circuit. The signal was converted to an amplitude in the TAC, and the TAC and the amplitude was measured by a multichannel analyzer. The timing resolution (FWHM) of the hybrid system for coincident events was approximately 14.6 ns.
7
In order to combine the mechanical and the electronic collimation, the hybrid update maximum likelihood-expectation maximization (MLEM) algorithm was applied, as shown in Eq. (1) [18]. The superscript n represented the iteration number of the MLEM algorithm and each iteration uses the result of the previous iteration. λj represents the source intensity of pixel j. The superscripts M and C represented mechanical collimation and electronic
Fig. 4. Reconstructed images using MURA array and MLEM method for a 122-keV point source: (a) 1st iteration, (b) 10th iteration, and (c) 50th iteration.
Fig. 5. Reconstructed images using MURA array and MLEM method for a 356-keV point source. TOP, Middle, and bottom rows represent mechanical, electronic, and hybrid collimation, respectively. Left, middle, and right columns represent 1st, 10th, and 50th iterations, respectively.
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T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
collimation, respectively. C M ij denotes the elements of the system matrix for the MURA mask consisting of tungsten and air. The matrix C Cij , included the attenuation in the MURA mask and the Compton cross-section, approximated using the Klein–Nishina C formula. Y M i was the shadowgram of the MURA mask and Y i is unity because the total number of photons detected was significantly smaller than the number of possible combinations of the information (such as the position and energy). λnj þ 1 ¼ λnj
M C C M C n n ∑i ðC M ij Y i =∑k C ik λk Þ þ ∑i ðC ij Y i =∑k C ik λk Þ C ∑i C M ij þ ∑i C ij
ð1Þ
Receiver operator characteristic (ROC) curves are used for nuclear medical images [19,20]. In order to quantify performance, ROC curves were used for comparison between the performance of conventional imagers and the performance of hybrid imagers. For this evaluation method, one hundred images in positive (source with background) and negative (background only) conditions were reconstructed using the MLEM method, and then the maximum pixel values of reconstructed images at the 50th iteration were compared at varying thresholds. The ROC curve was obtained by plotting the true positive fraction (TPF) against the false positive fraction (FPF). In the ROC curve, the x- and y-axes represented the FPF and the TPF, respectively. As shown in Eqs.
(2)–(4), the TPF was defined by the sensitivity, that is, the probability that a result was positive when the radiation source was present. The FPF was 1-specificity, where the specificity was defined as the probability that a result would be negative when the radiation source was not present [20]. In positive cases, if the maximum pixel value was higher than the threshold, this result was classified as true positive (TP), and if the value was lower than the threshold, this result was classified as false negative (FN). In negative cases, if the maximum pixel value was higher than the threshold, this result was classified as false positive (FP), and if the value was lower than the threshold, this result was classified as true negative (TN). Sensitivity ¼ TPF ¼ TP=ðTP þFNÞ
ð2Þ
Specificity ¼ TN=ðFP þ TNÞ
ð3Þ
1 Specificity ¼ FPF ¼ FP=ðFP þ TNÞ
ð4Þ
3. Results The imaging performance of a compact hybrid gamma camera system was evaluated using point sources with various energies. In order to neglect the events adding background noise to the
Fig. 6. Reconstructed images using MURA array and MLEM method for a 662-keV point source. TOP, Middle, and bottom rows represent mechanical, electronic, and hybrid collimation, respectively. Left, middle, and right columns represent 1st, 10th, and 50th iterations, respectively.
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
reconstructed image, energy windows around a photoelectric peak were applied. In addition, all mechanical collimation images were obtained by using a mask which was anti-symmetric for 901 rotation to reduce background noise. The measurements time was 14 h. At 122 keV, the photoelectric effect was dominant, and most radiation was absorbed in the first detector; hence only a mechanical collimation image was acquired in the experiment (cf. Fig. 4). As the number of iterations increased, the resolution of the mechanical collimation images improved as expected. Fig. 5 shows the images reconstructed by using mechanical, electronic, and hybrid collimation for a 356-keV point source. The hybrid images were similar to the mechanical collimation images in a lower number of iterations and showed much better performance than the electronic collimation images. The hybrid images had slightly smaller noise than mechanical for a higher number of iterations. The images reconstructed using mechanical, electronic and hybrid collimation for a 662-keV point source were shown in Fig. 6. As the incident radiation energy increased, the resolution of the electronic and hybrid collimation images improved while the noise of mechanical images remained. As a result, there was similar between the electronic collimation imager and the hybrid collimation imager for the all iterations. At 1275 keV, Compton scattering was dominant, and a large portion of the radiation
9
penetrated or was scattered at the MURA mask; hence, the mechanical collimation images were severely degraded as shown in Fig. 7. The performance of the electronic collimation imagers at 1275 keV was improved compared with that at lower energies since energy uncertainty, inversely proportional to the energy of incident radiations, is related with angular uncertainty [17]. In summary, the performance of hybrid collimation showed the optimized performance at the widest range of energies (356, 662, and 1275 keV). Fig. 8 shows a quantitative evaluation of the images using a resolution–variance curve (RV). The resolution was represented by the full width half maximum (FWHM) of the point images, and the variance was estimated using the relative standard deviation (RSTD). As the number of iterations increased, resolution improved, but noise increased for all images; hence, the RV curve was chosen for a quantitative evaluation. In order to calculate the RSTD, the data for each point image were divided into ten subsets, and images were reconstructed for all subsets. The maximum pixel value in each subset was measured, and the RSTD of the maximum number of pixels was calculated and used for evaluation. Smaller FWHM and RSTD values indicate better images, and hence, a curve closer to the origin indicates better performance. As shown in Fig. 8, the performance of hybrid collimation was superior to the performance of conventional methods, and electronic collimation showed the lowest performance. Comparing the performance of
Fig. 7. Reconstructed images using MURA array and MLEM method for a 1275-keV point source. TOP, Middle, and bottom rows represent mechanical, electronic, and hybrid collimation, respectively. Left, middle, and right columns represent 1st, 10th, and 50th iterations, respectively.
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T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
Fig. 8. Resolution-variance graphs for a point source reconstructed by the MLEM method. (a) 356 keV, (b) 662 keV, and (c) 1275 keV.
Table 1 Peak of the source to the RMS of the background in imager.
Table 2 Performance of compact hybrid gamma camera using point sources with various radiation energies.
Energy (keV)
Collimation method
Maximum value to RMS
356
Mechanical Electronic Hybrid Mechanical Electronic Hybrid Mechanical Electronic Hybrid
6.90 5.86 7.14 4.47 5.62 6.14 2.12 3.08 4.19
662
1275
Energy (keV)
122
electronic collimation, in contrast with performance at 356 keV, the performance of electronic collimation for 662 and 1275 keV was improved because energy resolution improved with increased radiation energy. Table 1 shows the maximum peak of the source compared with the root mean square (RMS) of the background for the reconstructed images at the 50th iteration. The hybrid collimation imager shows the highest ratio and thereby demonstrates the best performance. Detection efficiency, angular resolution and ratio of sensitivity for various radiation energies were shown in Table 2. The angular resolution of mechanical collimation was independent of the incident radiation energy because the angular resolution was related to the geometric parameters only. The theoretically calculated result based on Eq. (5) was 3.811, which was almost same to that measured in experiments. As previous estimation, the angular resolution of electronic collimation improved as the radiation energy increased [17]. The detection efficiency of mechanical and electronic collimation was the ratio of the number of effective events used for image reconstruction to the total number of gamma rays incident on the surface of the first detector. The ratio of sensitivity decreased with the radiation energy which proved the effectiveness of electronic collimation at high energy compared with mechanical collimation. Δθ ¼ tan 1 ðc=2dÞ
ð5Þ
d: distance between a MURA mask and a planar detector, c: width of a MURA element Figs. 9–12 showed a quantitative evaluation of the images for intermediate and high energies at the 50th iteration. The measurement time was 10 min. Fig. 9 showed histograms of maximum pixel values for reconstructed images in both positive (source with background) and negative (background only), conditions using
356 662 1275
Detection efficiency
Angular resolution at 50th iteration (1)
Mechanical Electronic
Mechanical Electronic
Ratio of sensitivity (photoelectric events to Compton scattering events)
1.06 10 2 Not relevant 2.50 10 3 1.99 10 4 4 5.54 10 9.67 10 5 1.21 10 4 3.11 10 5
4.121
Not relevant
3.821 3.791 3.711
Not relevant 8.21 7.01 3.71
12.6:1 4.8:1 3.9:1
mechanical, electronic, and hybrid collimation methods for a 356keV point source. Only small differences were observed between the performance of the hybrid collimation imager and the performance of the mechanical collimation imager (cf. Fig. 9(a) and (c)), which outperformed the electronic collimation imager (cf. Fig. 9 (b)). Figs. 10 and 11 showed histograms of maximum pixel values for reconstructed images for a 662- and 1275-keV point source, respectively. At high energy, Compton scattering is the dominant interaction, and increased radiation penetration largely degraded the performance of mechanical collimation. Hence, the overlap area under the positive and negative graphs was largest for the mechanical collimation imager (cf. Fig. 10(a) and Fig. 11(a)). As the incident radiation energy increased, the performance of the electronic collimation imager improved (cf. Fig. 10(b) and Fig. 11 (b)). The performance of the hybrid collimation imager was slightly superior to the performance of the electronic collimation imager cf. Fig. 11(b), and (c), Fig. 12(b), and (c)). Fig. 12 shows ROC curves related to the histograms of the maximum pixel values in the reconstructed images. As shown in the histograms for the hybrid collimation images (cf. Fig. 9(c), Fig. 10(c) and Fig. 11(c)), the overlaid area under the negative and positive plot was smallest. Therefore, the ROC curves of the hybrid imagers were closest to the y-axes (0, 1), and the areas under the curves (AUC) were largest for all energies (cf. Fig. 12(a)–(c)). This finding is ascribed to the fact that both collimation methods contributed effectively to the hybrid images. Fig. 13 showed a reconstructed image of a 662-keV multiple point sources with source off axis in the field of view. The measurements time was 14 h. The three multiple sources were positioned on a plane which was 200 mm away from the first detector. Three sources were located at (50, 0, 200), ( 50, 0, 200)
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
11
Fig. 9. Histograms of maximum pixel values in reconstructed images for a 356-keV point source. (a) Mechanical (b) electronic, and (c) hybrid.
Fig. 10. Histograms of maximum pixel values in reconstructed images for a 662-keV point source. (a) Mechanical (b) electronic, and (c) hybrid.
Fig. 11. Histograms of maximum pixel values in reconstructed images for a 1275-keV point source. (a) Mechanical (b) electronic, and (c) hybrid.
and (0, 100, 200) when the center of the first detector was positioned at (0, 0, 0) in millimeter dimension. As can be seen, the multiple point sources with natural background radiation could be reconstructed clearly by our system. Moreover, the results showed that the performance of hybrid collimation method was better than those obtained by either a mechanical or an electronic collimation only. The performance of the compact hybrid gamma camera was compared with that of a previously developed system consisting of only a pair of detectors [12] (cf. Table 3). The energy resolution of a single unit in our camera for the a 662-keV radiation was 15% in average while that in a previous developed system consisting of
LaCl3(Ce) scintillator was approximately 5%, which significantly affected the angular resolution of the cameras. The angular resolution is also related to the finite spatial resolution of detectors; hence, if the size of the scintillator element can be smaller or finer positional estimation in a single crystal can be obtained, the angular resolution of the electronic collimation improves as much [17]. The angular resolution of mechanical collimation was almost same as before since the angular resolution depends on geometrical parameters only. However, the detection efficiency of compact hybrid gamma camera was 43 times higher than that of a previously developed system. It is because the number of secondary detector was increased from one to four and the distance
12
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
Fig. 12. ROC curve using MLEM method (50th iteration): (a) 356 keV, (b) 662 keV, and (c) 1275 keV.
Fig. 13. Reconstructed images using MURA array and MLEM method for a 662-keV multiple point sources (50th iteration): (a) mechanical, (b) electronic, and (c) hybrid.
Table 3 Comparison of the performance for the two detection systems. Performance
Compact hybrid gamma camera
Paired detectors [12] 5.991 (13 11 URA array consist of 3.5 mm elements) 91 2.27 10 6
Angular resolution (1)
Mechanical collimation (1st iteration, 356 keV) Electronic collimation (1st iteration, 356 keV)
5.591 (11 11 MURA array consist of 2 mm elements) 161
Detection efficiency
Electronic collimation (662 keV)
9.67 10 5
between 1st and 2nd detector was reduced from 20 cm to 10 cm. Moreover, the atomic numbers and density of CsI(Na) scintillator is higher than those of LaCl3(Ce) scintillator. The minimum time of radiation detection to show point images of 10 μCi 57Co (122 keV), 133 Ba(356 keV), 137Cs(662 keV), 22Na(1275 keV) at 20 cm distance were 1, 30, 50, and 90 s, respectively.
662, and 1275 keV). Three quantitative evaluations – the RV curve, the ROC curve, and signal-to-background ratio – proved that the performance of the hybrid collimation method exceed the performance of the conventional collimation methods. In addition, the hybrid collimation imager covered a very broad range of radiation energies originating from various radioactive isotopes such as nuclear materials and wastes in nuclear power plants and reservoirs, or in residences or borders of countries.
4. Conclusion Combining conventional collimation methods, a compact hybrid collimation imager with full secondary detectors was developed, and its performance was compared with the performance achieved by conventional methods. The hybrid imager employed a coded mask (MURA) and radially positioned CsI(Na) scintillators coupled with compact PSPMTs. For ideal performance, optimized parameters of the hybrid system were applied. The MLEM method was used to reconstruct both the conventional and the hybrid images. The performances of the imagers were validated experimentally with various radiation energies (122, 356,
Acknowledgments This work was supported by National Research Foundation of Korea (NRF) grants (2012-0006399, 2012M2AA401092) and BK21 Plus (21A20132212094), funded by the Korean government.
References [1] S.R. Gotesman, E.E. Fenimore, Applied Optics 28 (1978) 4344.
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[2] S.V. Guru, Z. He, D.K. Wehe, G.G. Knoll, R.H. Redus, M.R. Squillante, Nuclear Instruments and Methods A 378 (1996) 612. [3] P.T. Durrant, M. Dallimore, I.D. Jupp, D. Ramsen, Nuclear Instruments and Methods A 422 (1999) 667. [4] M Singh, D Doria, Medical Physics 10 (1983) 421. [5] M Singh, D Doria, Medical Physics 10 (1983) 428. [6] C.E. Lehner, Ph.D. Dissertation, University of Michigan, 1997. [7] J. Gormley, Ph.D. Dissertation, University of Michigan, 1997. [8] A. Uritani, N.H. Clinthorne, J.E. Gormley, J.W. LeBlanc, IEEE Transactions on Nuclear Science NS44 (3) (1997) 94. [9] L.E. Smith, C. Chen, D.K. Wehe, Z. He, Nuclear Instruments and Methods A 462 (2001) 576. [10] W. Lee, D.K. Wehe, in: IEEE Nucl. Sci. Sym. Con. Rec, San Juan, Puerto Rico (2005). [11] W. Lee, Ph.D. Dissertation, University of Michigan, 2007.
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[12] W. Lee, D.K. Wehe, M. Jeong, P. Barton, J. Berry, IEEE Transactions on Nuclear Science NS56 (1) (2009) 308. [13] Online. Available: 〈http://www.hamamatsu.com/jp/en/product/category/3100/ 3002/H8500C/index.html〉. [14] Online. Available: 〈http://www.hilger-crystals.co.uk/arrays.asp〉. [15] P.D. Olcott, J.A. Talcott, C.S. Levin, Habte, IEEE Transactions on Nuclear Science NS52 (1) (2005) 27. [16] V. Popov, S. Majewski, B. L, Welch, Nuclear Instruments and Methods A 567 (2006) 319. [17] W Lee, Journal of the Korean Physical Society 54 (4) (2009) 1427. [18] C.E. Metz, B.A. Herman, G.H. Shen, Statistics in Medicine 17 (1998) 1033. [19] D.R. Gilland, B.M. Tsui, C.E. Metz, R.J. Jaszczk, J.R. Perry, Journal of Nuclear Medicine 33 (1992) 451. [20] V. Premachandran, R. Kakarala, IEEE Transactions on Nuclear Science NS56 (4) (2010) 2511.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Compact hybrid gamma camera with a coded aperture for investigation of nuclear materials Taewoong Lee, Wonho Lee n Department of Bio-convergence Engineering, Korea University, Seoul 136-103, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 6 March 2014 Received in revised form 27 June 2014 Accepted 17 July 2014 Available online 21 August 2014
Mechanical collimation commonly uses the photoelectric effect to reconstruct radiation images. Electronic collimation (i.e. Compton camera) using Compton scattering has been developed to reconstruct radiation images without utilizing mechanical collimators. Generally, for radiation imaging, electronic and mechanical collimation methods are used individually. In order to increase the quality of imaging and the efficiency of radiation detection, we combined both collimation methods in a single system. Our compact hybrid gamma camera comprised a modified uniformly redundant array (MURA) and a Compton camera, and the information from each modality was obtained simultaneously. The entire system formed a radial shape with detector modules which comprising CsI(Na) scintillators coupled with position-sensitive photomultiplier tubes (PSPMTs) whose anodes were connected to custom-made circuits. For various energy sources, the reconstructed images produced using this hybrid method were obtained and compared with reconstructed images from the two aforementioned methods. The maximum likelihood expectation maximization (MLEM) algorithm was applied for the reconstruction method. Compared with individual imagers at intermediate energies, the hybrid imager showed equal or better performance. & 2014 Elsevier B.V. All rights reserved.
Keywords: MURA (mechanical collimation) Compton camera (electronic collimation) MLEM Hybrid
1. Introduction Gamma-ray imaging has been applied in nuclear medicine, astrophysics, homeland security, and various industries. In most low-energy applications (o200 keV), conventional mechanical collimation using a pinhole or a coded aperture comprising a high density material is employed to form the gamma-ray shadow on a position-sensitive detector [1–3]. Other systems employ electronic collimation using sequential gamma-ray interactions in a single detector or multiple detectors for intermediate and high energies (800–2000 keV) [4–6]. Mechanical collimation is effective at low energies, while electronic collimation shows high performance at high energies. At intermediate energies (200–800 keV), two particular interactions – the photoelectric effect and Compton scattering – compete with each other. Researchers have developed advanced equipment using both collimation methods to the advantage of each modality. Gormley attempted to combine the modalities of different collimation methods. The resulting combined image, which applied a penalized weighted least-square algorithm, showed equal or
n
Corresponding author. E-mail address: [email protected] (W. Lee).
http://dx.doi.org/10.1016/j.nima.2014.07.031 0168-9002/& 2014 Elsevier B.V. All rights reserved.
better performance than the best individual system, but the modalities operated in separate systems [7]. In order to increase signal-to-noise ratio (SNR), Uritani added parallel plates to an electronically collimated camera, but detection efficiency and field of view (FOV) were severely decreased [8]. For higher detection efficiency and a larger field of view, a coded aperture replaced the parallel plate in 2009. At intermediate energies, the modified system demonstrated better performance than both mechanical collimation and the electronic collimation [9]. Lee proposed and built the URA coded mask with an attached Compton camera using LaCl3(Ce) scintillators. This device represented the single system using both photoelectric events and Compton scattering simultaneously [10–12]. Because the system utilized lanthanide scintillators, its angular resolution and timing resolution were high compared with other scintillator-based gamma cameras. However, because of the bulky position-sensitive photomultiplier tube (PSPMT) and the small number of detectors, both the portability and the detection efficiency of this system were significantly limited. In this study, a portable hybrid gamma-ray imaging system was manufactured using pixelated scintillators coupled with very compact PSPMTs. In order to increase detection efficiency, multiple secondary detectors were back-positioned in a radial shape. Consequently, the detection efficiency of the system was much
6
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
higher than the previous system, and its portability was significantly improved.
2. Materials and methods Fig. 1(a) shows a schematic diagram of a compact hybrid gamma camera consisting of a modified uniformly redundant array (MURA) mask [1] and CsI(Na) planar detectors. At the rear of the first detector, the secondary detection modules form a radial shape directed toward the first detector (cf. Fig. 1(b)). As shown in Fig. 2, the first and second detectors were CsI(Na) arrays [13] coupled with a PSPMTs [14]. The non-uniformity of the multianode PSPMTs response to incident light was corrected using a readout circuit [15,16]. The scintillator consisted of 20 20 voxels, and each voxel had a dimension of 2 2 5 mm3. The size of the PSPMT with readout boards was 50 50 60 mm3, which was approximately 11 times smaller than the previous PSPMT [12]. Comprised of tungsten, the entire MURA mask was 73 73 5 mm3 in size, while each pixel was 2 2 5 mm3. MURA had an approximately 50% opening area to pass radiations for gamma ray imaging. The activities of all sources (57Co, 133Ba, 137 Cs, and 22Na) for the experiment were 10 μCi. The visible light from the CsI(Na) was converted to electric signals in PSPMTs and was then transmitted to a custom-made circuit in which the signals’ timing and amplitude information was measured. The timing information was sent to a field-programmable gate array (FPGA), which triggered a data acquisition board (DAQ). Owing to this procedure, only effective interactions resulting from photoelectric events and Compton scattering were selected in the DAQ, and their information was sent to a computer, in which the source distribution was reconstructed. In a previous simulation study, the optimized condition for a hybrid system combining both a mechanical and an electronic collimator was calculated. The angle between the second detectors
and the system axis was set at 451, and the distance between the first detector and the second detectors was 100 mm in the hybrid system [17]. The radiation source was located at a distance of 200 mm from the first detector. The hybrid system was based on the combination of the mechanical collimation imager (MURA imager) and the electronic collimation imager (Compton imager). In the first modality, the incident radiation passed through the 11 11 MURA mask and deposited its energy on the first detector (mechanical collimation imager). In the second modality, the incident radiation underwent scattering in the first detector and was absorbed in the second detectors (electronic collimation imager). Fig. 3 shows the timing resolution of the coincident events. To evaluate the timing resolution, the digitized timing output of the
Fig. 3. Timing histogram of coincidence events.
Fig. 1. A compact hybrid gamma camera. (a) Schematic diagram and (b) photograph.
Fig. 2. Components of a compact hybrid gamma camera. (a) One detector module, (b) the CsI(Na) scintillator, and (c) the mosaic of a basic 11 11 MURA coded mask.
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
first detector was connected to the start input of the time-toamplitude converter (TAC), while the timing output of the second detector was connected to the delay circuit. The signal was converted to an amplitude in the TAC, and the TAC and the amplitude was measured by a multichannel analyzer. The timing resolution (FWHM) of the hybrid system for coincident events was approximately 14.6 ns.
7
In order to combine the mechanical and the electronic collimation, the hybrid update maximum likelihood-expectation maximization (MLEM) algorithm was applied, as shown in Eq. (1) [18]. The superscript n represented the iteration number of the MLEM algorithm and each iteration uses the result of the previous iteration. λj represents the source intensity of pixel j. The superscripts M and C represented mechanical collimation and electronic
Fig. 4. Reconstructed images using MURA array and MLEM method for a 122-keV point source: (a) 1st iteration, (b) 10th iteration, and (c) 50th iteration.
Fig. 5. Reconstructed images using MURA array and MLEM method for a 356-keV point source. TOP, Middle, and bottom rows represent mechanical, electronic, and hybrid collimation, respectively. Left, middle, and right columns represent 1st, 10th, and 50th iterations, respectively.
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T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
collimation, respectively. C M ij denotes the elements of the system matrix for the MURA mask consisting of tungsten and air. The matrix C Cij , included the attenuation in the MURA mask and the Compton cross-section, approximated using the Klein–Nishina C formula. Y M i was the shadowgram of the MURA mask and Y i is unity because the total number of photons detected was significantly smaller than the number of possible combinations of the information (such as the position and energy). λnj þ 1 ¼ λnj
M C C M C n n ∑i ðC M ij Y i =∑k C ik λk Þ þ ∑i ðC ij Y i =∑k C ik λk Þ C ∑i C M ij þ ∑i C ij
ð1Þ
Receiver operator characteristic (ROC) curves are used for nuclear medical images [19,20]. In order to quantify performance, ROC curves were used for comparison between the performance of conventional imagers and the performance of hybrid imagers. For this evaluation method, one hundred images in positive (source with background) and negative (background only) conditions were reconstructed using the MLEM method, and then the maximum pixel values of reconstructed images at the 50th iteration were compared at varying thresholds. The ROC curve was obtained by plotting the true positive fraction (TPF) against the false positive fraction (FPF). In the ROC curve, the x- and y-axes represented the FPF and the TPF, respectively. As shown in Eqs.
(2)–(4), the TPF was defined by the sensitivity, that is, the probability that a result was positive when the radiation source was present. The FPF was 1-specificity, where the specificity was defined as the probability that a result would be negative when the radiation source was not present [20]. In positive cases, if the maximum pixel value was higher than the threshold, this result was classified as true positive (TP), and if the value was lower than the threshold, this result was classified as false negative (FN). In negative cases, if the maximum pixel value was higher than the threshold, this result was classified as false positive (FP), and if the value was lower than the threshold, this result was classified as true negative (TN). Sensitivity ¼ TPF ¼ TP=ðTP þFNÞ
ð2Þ
Specificity ¼ TN=ðFP þ TNÞ
ð3Þ
1 Specificity ¼ FPF ¼ FP=ðFP þ TNÞ
ð4Þ
3. Results The imaging performance of a compact hybrid gamma camera system was evaluated using point sources with various energies. In order to neglect the events adding background noise to the
Fig. 6. Reconstructed images using MURA array and MLEM method for a 662-keV point source. TOP, Middle, and bottom rows represent mechanical, electronic, and hybrid collimation, respectively. Left, middle, and right columns represent 1st, 10th, and 50th iterations, respectively.
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
reconstructed image, energy windows around a photoelectric peak were applied. In addition, all mechanical collimation images were obtained by using a mask which was anti-symmetric for 901 rotation to reduce background noise. The measurements time was 14 h. At 122 keV, the photoelectric effect was dominant, and most radiation was absorbed in the first detector; hence only a mechanical collimation image was acquired in the experiment (cf. Fig. 4). As the number of iterations increased, the resolution of the mechanical collimation images improved as expected. Fig. 5 shows the images reconstructed by using mechanical, electronic, and hybrid collimation for a 356-keV point source. The hybrid images were similar to the mechanical collimation images in a lower number of iterations and showed much better performance than the electronic collimation images. The hybrid images had slightly smaller noise than mechanical for a higher number of iterations. The images reconstructed using mechanical, electronic and hybrid collimation for a 662-keV point source were shown in Fig. 6. As the incident radiation energy increased, the resolution of the electronic and hybrid collimation images improved while the noise of mechanical images remained. As a result, there was similar between the electronic collimation imager and the hybrid collimation imager for the all iterations. At 1275 keV, Compton scattering was dominant, and a large portion of the radiation
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penetrated or was scattered at the MURA mask; hence, the mechanical collimation images were severely degraded as shown in Fig. 7. The performance of the electronic collimation imagers at 1275 keV was improved compared with that at lower energies since energy uncertainty, inversely proportional to the energy of incident radiations, is related with angular uncertainty [17]. In summary, the performance of hybrid collimation showed the optimized performance at the widest range of energies (356, 662, and 1275 keV). Fig. 8 shows a quantitative evaluation of the images using a resolution–variance curve (RV). The resolution was represented by the full width half maximum (FWHM) of the point images, and the variance was estimated using the relative standard deviation (RSTD). As the number of iterations increased, resolution improved, but noise increased for all images; hence, the RV curve was chosen for a quantitative evaluation. In order to calculate the RSTD, the data for each point image were divided into ten subsets, and images were reconstructed for all subsets. The maximum pixel value in each subset was measured, and the RSTD of the maximum number of pixels was calculated and used for evaluation. Smaller FWHM and RSTD values indicate better images, and hence, a curve closer to the origin indicates better performance. As shown in Fig. 8, the performance of hybrid collimation was superior to the performance of conventional methods, and electronic collimation showed the lowest performance. Comparing the performance of
Fig. 7. Reconstructed images using MURA array and MLEM method for a 1275-keV point source. TOP, Middle, and bottom rows represent mechanical, electronic, and hybrid collimation, respectively. Left, middle, and right columns represent 1st, 10th, and 50th iterations, respectively.
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Fig. 8. Resolution-variance graphs for a point source reconstructed by the MLEM method. (a) 356 keV, (b) 662 keV, and (c) 1275 keV.
Table 1 Peak of the source to the RMS of the background in imager.
Table 2 Performance of compact hybrid gamma camera using point sources with various radiation energies.
Energy (keV)
Collimation method
Maximum value to RMS
356
Mechanical Electronic Hybrid Mechanical Electronic Hybrid Mechanical Electronic Hybrid
6.90 5.86 7.14 4.47 5.62 6.14 2.12 3.08 4.19
662
1275
Energy (keV)
122
electronic collimation, in contrast with performance at 356 keV, the performance of electronic collimation for 662 and 1275 keV was improved because energy resolution improved with increased radiation energy. Table 1 shows the maximum peak of the source compared with the root mean square (RMS) of the background for the reconstructed images at the 50th iteration. The hybrid collimation imager shows the highest ratio and thereby demonstrates the best performance. Detection efficiency, angular resolution and ratio of sensitivity for various radiation energies were shown in Table 2. The angular resolution of mechanical collimation was independent of the incident radiation energy because the angular resolution was related to the geometric parameters only. The theoretically calculated result based on Eq. (5) was 3.811, which was almost same to that measured in experiments. As previous estimation, the angular resolution of electronic collimation improved as the radiation energy increased [17]. The detection efficiency of mechanical and electronic collimation was the ratio of the number of effective events used for image reconstruction to the total number of gamma rays incident on the surface of the first detector. The ratio of sensitivity decreased with the radiation energy which proved the effectiveness of electronic collimation at high energy compared with mechanical collimation. Δθ ¼ tan 1 ðc=2dÞ
ð5Þ
d: distance between a MURA mask and a planar detector, c: width of a MURA element Figs. 9–12 showed a quantitative evaluation of the images for intermediate and high energies at the 50th iteration. The measurement time was 10 min. Fig. 9 showed histograms of maximum pixel values for reconstructed images in both positive (source with background) and negative (background only), conditions using
356 662 1275
Detection efficiency
Angular resolution at 50th iteration (1)
Mechanical Electronic
Mechanical Electronic
Ratio of sensitivity (photoelectric events to Compton scattering events)
1.06 10 2 Not relevant 2.50 10 3 1.99 10 4 4 5.54 10 9.67 10 5 1.21 10 4 3.11 10 5
4.121
Not relevant
3.821 3.791 3.711
Not relevant 8.21 7.01 3.71
12.6:1 4.8:1 3.9:1
mechanical, electronic, and hybrid collimation methods for a 356keV point source. Only small differences were observed between the performance of the hybrid collimation imager and the performance of the mechanical collimation imager (cf. Fig. 9(a) and (c)), which outperformed the electronic collimation imager (cf. Fig. 9 (b)). Figs. 10 and 11 showed histograms of maximum pixel values for reconstructed images for a 662- and 1275-keV point source, respectively. At high energy, Compton scattering is the dominant interaction, and increased radiation penetration largely degraded the performance of mechanical collimation. Hence, the overlap area under the positive and negative graphs was largest for the mechanical collimation imager (cf. Fig. 10(a) and Fig. 11(a)). As the incident radiation energy increased, the performance of the electronic collimation imager improved (cf. Fig. 10(b) and Fig. 11 (b)). The performance of the hybrid collimation imager was slightly superior to the performance of the electronic collimation imager cf. Fig. 11(b), and (c), Fig. 12(b), and (c)). Fig. 12 shows ROC curves related to the histograms of the maximum pixel values in the reconstructed images. As shown in the histograms for the hybrid collimation images (cf. Fig. 9(c), Fig. 10(c) and Fig. 11(c)), the overlaid area under the negative and positive plot was smallest. Therefore, the ROC curves of the hybrid imagers were closest to the y-axes (0, 1), and the areas under the curves (AUC) were largest for all energies (cf. Fig. 12(a)–(c)). This finding is ascribed to the fact that both collimation methods contributed effectively to the hybrid images. Fig. 13 showed a reconstructed image of a 662-keV multiple point sources with source off axis in the field of view. The measurements time was 14 h. The three multiple sources were positioned on a plane which was 200 mm away from the first detector. Three sources were located at (50, 0, 200), ( 50, 0, 200)
T. Lee, W. Lee / Nuclear Instruments and Methods in Physics Research A 767 (2014) 5–13
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Fig. 9. Histograms of maximum pixel values in reconstructed images for a 356-keV point source. (a) Mechanical (b) electronic, and (c) hybrid.
Fig. 10. Histograms of maximum pixel values in reconstructed images for a 662-keV point source. (a) Mechanical (b) electronic, and (c) hybrid.
Fig. 11. Histograms of maximum pixel values in reconstructed images for a 1275-keV point source. (a) Mechanical (b) electronic, and (c) hybrid.
and (0, 100, 200) when the center of the first detector was positioned at (0, 0, 0) in millimeter dimension. As can be seen, the multiple point sources with natural background radiation could be reconstructed clearly by our system. Moreover, the results showed that the performance of hybrid collimation method was better than those obtained by either a mechanical or an electronic collimation only. The performance of the compact hybrid gamma camera was compared with that of a previously developed system consisting of only a pair of detectors [12] (cf. Table 3). The energy resolution of a single unit in our camera for the a 662-keV radiation was 15% in average while that in a previous developed system consisting of
LaCl3(Ce) scintillator was approximately 5%, which significantly affected the angular resolution of the cameras. The angular resolution is also related to the finite spatial resolution of detectors; hence, if the size of the scintillator element can be smaller or finer positional estimation in a single crystal can be obtained, the angular resolution of the electronic collimation improves as much [17]. The angular resolution of mechanical collimation was almost same as before since the angular resolution depends on geometrical parameters only. However, the detection efficiency of compact hybrid gamma camera was 43 times higher than that of a previously developed system. It is because the number of secondary detector was increased from one to four and the distance
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Fig. 12. ROC curve using MLEM method (50th iteration): (a) 356 keV, (b) 662 keV, and (c) 1275 keV.
Fig. 13. Reconstructed images using MURA array and MLEM method for a 662-keV multiple point sources (50th iteration): (a) mechanical, (b) electronic, and (c) hybrid.
Table 3 Comparison of the performance for the two detection systems. Performance
Compact hybrid gamma camera
Paired detectors [12] 5.991 (13 11 URA array consist of 3.5 mm elements) 91 2.27 10 6
Angular resolution (1)
Mechanical collimation (1st iteration, 356 keV) Electronic collimation (1st iteration, 356 keV)
5.591 (11 11 MURA array consist of 2 mm elements) 161
Detection efficiency
Electronic collimation (662 keV)
9.67 10 5
between 1st and 2nd detector was reduced from 20 cm to 10 cm. Moreover, the atomic numbers and density of CsI(Na) scintillator is higher than those of LaCl3(Ce) scintillator. The minimum time of radiation detection to show point images of 10 μCi 57Co (122 keV), 133 Ba(356 keV), 137Cs(662 keV), 22Na(1275 keV) at 20 cm distance were 1, 30, 50, and 90 s, respectively.
662, and 1275 keV). Three quantitative evaluations – the RV curve, the ROC curve, and signal-to-background ratio – proved that the performance of the hybrid collimation method exceed the performance of the conventional collimation methods. In addition, the hybrid collimation imager covered a very broad range of radiation energies originating from various radioactive isotopes such as nuclear materials and wastes in nuclear power plants and reservoirs, or in residences or borders of countries.
4. Conclusion Combining conventional collimation methods, a compact hybrid collimation imager with full secondary detectors was developed, and its performance was compared with the performance achieved by conventional methods. The hybrid imager employed a coded mask (MURA) and radially positioned CsI(Na) scintillators coupled with compact PSPMTs. For ideal performance, optimized parameters of the hybrid system were applied. The MLEM method was used to reconstruct both the conventional and the hybrid images. The performances of the imagers were validated experimentally with various radiation energies (122, 356,
Acknowledgments This work was supported by National Research Foundation of Korea (NRF) grants (2012-0006399, 2012M2AA401092) and BK21 Plus (21A20132212094), funded by the Korean government.
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