Design of a Multi-Pinhole Collimator and Its Evaluation for Application to High-Resolution Pre-Clinical SPECT system for Small Animal Imaging

Transcription

1 Design of a Multi-Pinhole Collimator and Its Evaluation for Application to High-Resolution Pre-Clinical SPECT system for Small Animal Imaging Hyun-Ju Ryu The Graduate School Yonsei University Department of Radiological Science

2 Design of a Multi-Pinhole Collimator and Its Evaluation for Application to High-Resolution Pre-Clinical SPECT system for Small Animal Imaging A Master s Thesis Submitted to the Department of Radiological Science and the Graduate School of Yonsei University in partial fulfillment of the requirements for the degree of Master of Science Hyun-Ju Ryu January 2013

3 This certifies that the Masters Thesis of Hyun-Ju Ryu is approved. [s e] Thesis Supervisor : Prof. Hee-Joung Kim [s re] Thesis Committee Member : Prof. Bong-Soo Han [s re] Thesis Committee Member : Prof. Yong-Hyun Chung The Graduate School Yonsei University December 2012

4 Acknowledgements I must first express my gratitude towards my advisor, Prof. Hee-Joung Kim. I deeply appreciate for his support and trust throughout my years of research. Also, I thank him for giving me an opportunity to do this research in Johns Hopkins University. I am fortunate to be educated by Prof. Kim and Prof. Benjamin M.W. Tsui who generously and wholeheartedly shared their knowledge to me. Especially for the work I have done at Johns Hopkins, I deeply appreciate to Dr. Tsui for his care not only academic but also for my life in Baltimore. I am also grateful for Prof. Yong Hyun Chung for his invaluable suggestions to the research, and Prof. Bong Soo Han for his precious lessons for the fundamental theory. I am lucky to have a team like a big family, Medical Physics and Imaging Laboratory. Especially, Chang-Lae Lee, Hye-Sook Park, Dae- Hong Kim, Seung-Wan Lee, Yu-Na Choi, Young-Jin Lee, Yeseul Kim, and SuJin Park. I could feel lots of love and affection from their support. Also, I would like to thank to Hyo-Min Cho, Chul-Pyo Hong and Do-Wan Lee for unstinting support and trust. Additionally, I am fortunate to have been studied with Dr. Jingyan Xu, Andrew rittenbach and Tao Feng who supported me a lot on this research. And I thank to Dr. Taek-Soo Lee for the words of encouragement. I would like to give a special thanks to Dong-Hoon Lee who has inspired me by his constant love and encouragement. Finally and most importantly, I would like to express my greatest appreciation to my family. They have always been my number one supporters and I know that wherever life brings me, I have them. Words will never be enough to express my love for them but I hope that by offering this thesis to them, together with all my achievements in life, I would be able to show how much they mean to me. January 2013 From Hyun-Ju Ryu iii

5 Table of Contents Acknowledgements iii Table of Contents iv List of Figures vi List of Tables vii Abstract in English viii 1 Introduction 1 2 Materials and Methods Geometric configurations of the multi-pinhole imaging system MPH collimator design optimization Evaluation of the MPH collimator design and SPECT system imaging performance using analytic computer simulation 12 3 Results MPH collimator design optimization Sensitivity map and the optimum number of projections 16 iv

6 3.3 Evaluation of the Optimized MPH Collimator with hot-rod resolution phantom 19 4 Discussion 24 5 Conclusion 26 6 References 28 Abstract in Korean 31 Acknowledgements in Korean 33 v

7 List of Figures Figure 1. Geometric configurations of the small animal SPECT Imaging System. 5 Figure 2. Geometric parameters of a pinhole collimator. 6 Figure 3. MPH collimator optimization process. 9 Figure 4. Detection efficiency and the number of pinholes. 11 Figure 5. Eleven detectors in a row to present the projections through MPH collimator. 12 Figure 6. Center slice of a uniform sphere and a hot-rod resolution phantom. 13 Figure 7. Simulated Projection with a full CVOV sphere phantom with different configurations of MPH collimators: 8% overlap (top) and 18% overlap (bottom). 15 Figure 8. Sensitivity map of the backprojected image of a uniform projection. 17 Figure 9. Sensitivity profile from the central profile of the sensitivity map. 17 Figure 10. Simulated MPH projections with 3 rotational stops: 0 (top row), 24 (middle row) and 48 (bottom row). 18 Figure 11. Reconstructed image of the hot-rod resolution phantom with different rotation and iteration numbers. 20 Figure 12. Reconstructed image of the hot-rod resolution phantom with different rotation and iteration numbers. 21 Figure 13. Projection of the hot-rod resolution phantom without noise (top), and with Gaussian noise (bottom). 22 Figure 14. Reconstructed image of the hot-rod resolution phantom without noise (top), and with Gaussian noise (bottom). 22 vi

8 List of Tables Table 1. System parameters of the small animal SPECT system. 4 Table 2. Optimized system parameters of the MPH collimator. 16 vii

9 Abstract Design of a Multi-Pinhole Collimator and Its Evaluation for Application to High-Resolution Pre-Clinical SPECT system for Small Animal Imaging Hyun-Ju Ryu Dept. of Radiological Science The Graduate School Yonsei University A multi-pinhole (MPH) collimator was designed for a pre-clinical SPECT system for small animal imaging to provide maximum detection efficiency and highest image quality given a targeted system spatial resolution and other system constraints. The performance of the collimator was evaluated through simulation and experimental studies. The optimum number of pinhole was calculated based on the geometry of the small animal SPECT system for 24 mm common volume-of-view (CVOV) with the target system resolution of 1 mm. The optimized MPH collimator viii

10 design consisted of 15 pinholes with 0.56 mm effective pinhole diameter and were placed 22.0 mm from the CVOV. In addition, the MPH collimator-detector response (CDR) function was incorporated in the 3D MPH maximum-likelihood expectation-maximization (ML-EL) image reconstruction algorithm. With CDR modeling, even the smallest rods can be differentiated. The reconstructed images of the phantom showed that the MPH SPECT system gives a fine resolution for small animal imaging. Key words: Multi-Pinhole Collimator, Pre-Clinical SPECT, Optimization, High resolution, small animal imaging, Maximum-likelihood expectationmaximization, Collimator-detector response modeling. ix

11 1 Introduction Small animal nuclear medicine imaging techniques allow direct visualization and quantification of three-dimensional (3D) distribution of radiotracers in different organs in static or as a function of time. Pinhole collimators have been widely used for small-animal single photon emission computed tomography (SPECT) systems due to their superior resolution and detection efficiency trade-off as compared to conventional parallel-hole collimators for imaging small objects at close range (Jaszczak et al. 1999, 425, Ogawa et al. 1998, ). High-resolution pinhole SPECT can be very useful in preclinical research where small organs are usually imaged as a target (Ishizu et al. 1995, 2282, Weber et al. 1994, 342). However, single pinhole collimator system provides poor detection efficiency especially at high spatial resolution (Schramm et al. 2003, ). Due to its low sensitivity, high doses of radio-tracers were injected into mice in previous studies to achieve fine image resolution with appropriate counts (Acton et al. 2002, , Habraken et al. 2001, ). The use of a multi-pinhole (MPH) collimator can increase the detection efficiency which may reduce the dose to the small animal while maintaining high resolution. Also, the additional data from MPH - 1 -

12 collimator can reduce the data incompleteness of a single pinhole collimator (Vunckx et al. 2008, 36-46, Rentmeester, Van Der Have, and Beekman 2007, 2567). A MPH collimator can be designed in various ways depends on the objective of an imaging system. In this study, a MPH collimator was designed for a small animal SPECT system to maximize the detection efficiency without degrading the spatial resolution. The performance of the MPH collimator was evaluated through analytic simulation, and it was constructed for a preliminary evaluation study

13 2 Materials and Methods 2.1 Geometric configurations of the multi-pinhole imaging system The small animal SPECT system used in the study was designed to have eleven blocks of detector modules to form a complete polygonal configuration. Each detector module consisted of a mm 2 pixelated CsI(Tl) crystal with 1 mm pixel pitch and 0.1 mm gap. The pixelated CsI crystal was attached to two mm 2 position-sensitive-photomultiplier tubes (PSPMT) (Model H9500, Hamamatsu Photonics K. K, Hamamatsu City, Shizuoka, Japan) with anodes. The distance from the center of the commonvolume-of-view (CVOV) to the face of the detector modules was mm. Currently only eight detector modules were completed for the polygonal SPECT system. Table 1 show the small animal SPECT system design parameters

14 Table 1. System parameters of the small animal SPECT system. pixel pitch crystal pixel thickness size light guide thickness number of detector CVOV to detector distance Photo-multiplier tube 1 mm 4 mm mm2 2 mm 11 (complete ring) 8 (completed) mm Hamamatsu H9500 The pixelated crystal could significantly alter the light distribution compare to a continuous crystal due to the light blockage at the edge of each pixels (Giokaris et al. 2004, ). The PSPMT (Hamamatsu H9500) with anodes and 256 data collection channels combined with the pixelated CsI(Tl) provided a state-of-the-art high-resolution detector module for the small animal SPECT system. Figure 1 illustrates the polygonal SPECT system configuration with the complete eleven detector modules (with eight completed). The detector modules were attached to a rotational gantry. A MPH collimator could be attached to the system and rotated with the gantry for additional angular data sampling to acquire sufficient number of projections for image reconstruction

15 Figure 1. Geometric configurations of the small animal SPECT Imaging System. 2.2 MPH collimator design optimization In this study, the goal of the optimized MPH collimator design is to provide the maximum detection efficiency for a given total system resolution under the constraints imposed by the SPECT system configuration. To design the optimized MPH collimator for the small animal SPECT system described above, first, we specified the target system resolution to be 1.0 mm at the center of the common volume-of-view (CVOV) of the multiple pinholes of the MPH collimator. We then determined the optimum MPH collimator design parameters that provide the highest possible detection efficiency - 5 -

16 given the constraints of the SPECT system geometric parameters including: the size of the CVOV for imaging, the distances between the center of the CVOV to the face of the detector modules, and the total area of the detector. The CVOV was set to 24 mm for imaging mice and the distance between the axis-of-rotation and all pinhole apertures were the same. To achieve this, the multiple pinholes were placed on a cylindrically-shaped collimator sleeve made with high density material and with its central axis coincided with the axis-ofrotation of the small animal SPECT system

17 Figure 2. Geometric parameters of a pinhole collimator. The characteristics of a pinhole collimator with the geometric parameters on Figure 2 were calculated using following equations (Beekman, and van der Have 2007, ). The parameters used in the equations are the distance from the center of the CVOV to a pinhole ( b ), the distance from the pinhole to the detector ( l ), diameter of the pinhole aperture (d), the pinhole aperture angle (α), and the attenuation coefficient of the collimator material (μ). The geometric resolution of a collimator can be calculated by R coll d eff (b + l)/l where the effective pinhole diameter is Equation 1. d eff = d[d + 2μ 1 tan (α/2)] Equation 2. The total system resolution was calculated from the collimator resolution and the system resolution: R sys = [(b/l)r int ] R coll Equation

18 The detection efficiency of a pinhole collimator is g d effcos 3 θ 16b 2 Equation 4. And the geometric efficiency of multiple pinholes is g d eff cos 3 θ/16b 2 Equation 5. Figure 3 illustrates the procedures to optimize the process of MPH collimator optimization. The total system resolution of a MPH SPECT system is a function of the collimator resolution, collimator geometry and the intrinsic resolution of the detector. There are a large numbers of sets of design parameters which can provide a targeted system resolution. Among them, it was our goal to find the design parameters of the MPH apertures and their pattern that provides the highest possible detection efficiency under the constraints of the SPECT system configuration

19 Figure 3. MPH collimator optimization process

20 There are geometric constraints such as the diameter of the CVOV, total detector area, the distance between the center of the CVOV and the detector surface, the intrinsic resolution of the detector, the photon energy, and the collimator material. The optimization of the MPH collimator was processed based on the geometric constraints By changing the distance from the center of the CVOV to the collimator aperture, the cone angle of the collimator and the size of the projection were also affected. The maximum number of projection at each distance from the CVOV to the collimator aperture was calculated using total detector area divided by the area of the projection. Then, the size of the collimator apertures were calculated to provide 1 mm total system resolution. With different collimator distances, the efficiencies of the MPH collimators were calculated with maximum number of projections at each distance. The optimal number of the pinholes was designed based on the constraints of the MPH collimator design as plotted in Figure 4. As shown in the figure, detection efficiency of the pinholes was increased as the number of the pinhole increased to a certain point and started to decrease after that. Therefore, the optimum number of the pinholes could be found near the point with the maximum

21 efficiency. Figure 4. Detection efficiency and the number of pinholes. Once the number of pinholes that provided the highest detection efficiency for the targeted system resolution was determined, the arrangement of the pinhole apertures on the MPH collimator to maximize the use of total detector area by the MPH projections with less than 20% multiplexing were determined. To visualize and present the patterns of the multiple pinhole projections onto the detector surface, the 11-sided polygonal SPECT detector ring was

22 unfolded into a flat surface as shown in Figure 5. Detection efficiency of the MPH collimator can be measured by plotting the projections on the detector using a computer simulation. Figure 5. Eleven detectors in a row to present the projections through MPH collimator. 2.3 Evaluation of the MPH collimator design and SPECT system imaging performance using analytic computer simulation The MPH collimator design and SPECT system imaging performance was evaluated using computer simulations. For the projection simulation, a sphere phantom with a size of full CVOV was used to evaluate the geometry of the MPH collimator. A resolution phantom with different sizes of hot rods was used to evaluate the MPH system performance. The sphere phantom and the hot-rod resolution phantom are shown in Figure 6. The 3D

23 maximum-likelihood expectation-maximization (ML-EM) algorithm was used to reconstruct the phantom projections. Figure 6. Center slice of a uniform sphere and a hot-rod resolution phantom

24 3 Results 3.1 MPH collimator design optimization The optimum number of pinhole was calculated based on the geometry of the small animal SPECT system for 24 mm CVOV with the target resolution 1 mm and other constraints of the geometric configuration of the small animal SPECT system. From the calculations described in Chapter 2, various designs of 15 pinholes were evaluated to pursue the maximum detection efficiency. The pinhole projections were allowed to have less than 20% overlaps of its area to maximize the use of the detector area compare to the non-overlapping arrangements. The efficiency of the MPH collimator design can be compared by measuring the intensity of the projections in the detector area as compared in Figure 7. The integrated intensity of 15 projections on 11 detectors were compared to determine detected efficiency on the detector. The arrangement of pinhole projections at the bottom of Figure 7 shows 18% overlap for each projection, which gives higher total detection efficiency of the MPH collimator compared to the arrangement of pinhole projections with 8% overlap

25 Figure 7. Simulated Projection with a full CVOV sphere phantom with different configurations of MPH collimators: 8% overlap (top) and 18% overlap (bottom). The optimized MPH collimator for 1 mm system resolution with 24 mm CVOV was determined to have 15 pinholes placed at 22.0 mm from the axis-of-rotation and the diameter of each pinhole projection was 65.2 mm on the detector surface. The cone angle of the pinholes was 66.2 mm with 0.56 mm effective aperture diameter. The optimized design parameters of the MPH collimator are shown in Table

26 Table 2. Optimized system parameters of the MPH collimator Target resolution Diameter of the CVOV Distance from CVOV to pinhole Distance from pinhole to the detector Diameter of the projection 1.0 mm 24.0 mm 22.0 mm 59.7 mm 65.2 mm Cone angle of the pinhole 66.2 Optimal number of pinholes 15 Effective pinhole aperture 0.56 mm 3.2 Sensitivity map and the optimum number of projections The reconstructed image field sensitivity map of the CVOV was evaluated by backprojecting the uniform projections through the MPH collimator. It showed the uniformity and the symmetry of the reconstruction image space generated by the MPH collimator. Examples of the reconstructed image field sensitivity maps with different rotational stops are shown in Figure 8. Each rotational stop provides 15 projections from the MPH collimator, and the rotation was performed to generate equiangular views between rotational stops

27 Figure 8. Sensitivity map of the backprojected image of a uniform projection. Figure 9. Sensitivity profile from the central profile of the sensitivity map

28 The reconstructed image field sensitivity profiles along the central line of each sensitivity map, as indicated on the first image of Figure 8, were compared on Figure 9 with different rotational stops. Three and four rotational stops of the 15-pinhole collimator, which generate 45 and 60 projections, respectably, give more uniform sensitivity profiles than those from no or one additional rotational stop of the MPH collimator. Figure 10. Simulated MPH projections with 3 rotational stops: 0 (top row), 24 (middle row) and 48 (bottom row). By using the uniform sphere phantom, Figure 10 shows the projections from the 15-pinhole collimator at three rotational stops

29 were simulated. The projections were obtained by rotating the MPH collimator at equiangular stops of 24 degrees. 3.3 Evaluation of the Optimized MPH Collimator with hotrod resolution phantom An analytical simulation was performed using the hot-rod resolution phantom shown in Figure 6 without noise, and the reconstruction was performed using a 3D MPH ML-EM image reconstruction algorithm. The reconstructed images gave improved resolution as the number of iteration increases in the noise-free case. The hot-rod phantom consists of six groups of rods with higher intensity than the background. The diameters of the rods in each group are the same and are 0.4 mm, 0.6 mm, 0.8 mm, 1.0 mm, 1.2 mm, 1.4 mm from the smallest to the largest. In Figure 11, the reconstructed images with different numbers of rotational stops were compared with the hot-rod phantom to evaluate the performance of the MPH collimator

30 Figure 11. Reconstructed image of the hot-rod resolution phantom with different rotation and iteration numbers. The reconstructed images from one stop to three stops showed significant increases in resolution, but three and four rotational stops showed a marginal difference. The results indicate the 15- pinhole collimator required at least three rotational stops for a total of 45 pinhole projections to achieve the highest possible reconstructed image resolution using the 3D MPH ML-EM algorithm. In addition, the MPH collimator-detector response (CDR)

31 function was incorporated in the 3D MPH ML-EL image reconstruction algorithm. A comparison of the reconstructed images of the hot rod phantom obtained with and without the CDR modeling is shown in Figure 12. With CDR modeling, even the smallest rods can be differentiated. Figure 12. Reconstructed image of the hot-rod resolution phantom with different rotation and iteration numbers. To simulate the noisy projection, Gaussian noise was applied to the projections of hot-rod phantom. The projections of the hot-rod phantom with and without noise were shown in Figure

32 Figure 13. Projection of the hot-rod resolution phantom without noise (top), and with Gaussian noise (bottom). Figure 14. Reconstructed image of the hot-rod resolution phantom without noise (top), and with Gaussian noise (bottom). The noisy projection was also reconstructed using 3D ML-EM, and the CDR function was applied. As shown in Figure 14, 0.6 mm

33 rods can be differentiated from the reconstructed image of the hotrod phantom even with the noisy projections. A Butterworth filter with Order2 and cutoff 0.4 was applied to the reconstructed image from the noisy projections

34 4 Discussion In this study, a MPH collimator was designed based on achieving the highest possible geometric detection efficiency given a target MPH SPECT system resolution, theoretical formula of the imaging characteristics of a MPH collimator as a function of its designed parameters and under various system designed constraints. The efficiency of a MPH collimator tends to increase at first as the number of pinholes increases; however, it decreases with further increase of the number of pinholes. As a result, there is an optimum number of the pinholes for a given MPH SPECT system geometry to achieve the target resolution with the most photon efficiency. Moreover, the pattern of the pinholes was designed to fully utilize the detector area with the projection. Overlapping of the projections could generate artifacts on the reconstructed image. However, if the projection contains relatively less information on the edge compare to the center, the artifact can be reduced by using iterative reconstruction method for limited overlapping of the projections (of less than 20%) and at the same time provide improved design optimization. The minimum number of collimator rotations was determined by

35 comparing the reconstructed image field sensitivity map of the MPH SPECT system, and the reconstructed images of the hot-rod resolution phantom. The results show the 15-pinhole collimator with minimum of three rotational stops generating a total of 45 pinhole projections would achieve the highest possible resolution in the reconstructed images using the 3D MPH ML-EM algorithm. The simulation was performed with and without noise, and the reconstructed images showed improved resolution with CDR modeling

36 5 Conclusion The optimum number of pinholes and the geometry of the MPH collimator was designed to have the highest possible photon detection efficiency for the given targeted system resolution and geometry of a small animal SPECT system. By using analytic simulation methods, MPH projections and the reconstructed image field sensitivity map were generated with the optimized MPH collimator. The reconstructed image of a hot-rod resolution phantom was used to provide quality assessment of the system resolution obtained with the MPH collimator. Image reconstruction was performed using a 3D MPH ML-EM image reconstruction algorithm with a minimum of three rotational stops and a total of 45 simulated pinhole projections can achieve the highest possible reconstructed image resolution. Also, higher resolution can be achieved by incorporating model of the collimator-detector response (CDR) function in the 3D MPH image reconstruction algorithm. As shown in the reconstructed image of the projections of hot-rod phantom with noise, the MPH SPECT system could differentiate 0.6 mm which gives a fine resolution for the small animal imaging. Future studies will include Monte Carlo simulation and

37 experimental studies for further evaluation of the small animal SPECT system fitted with the optimized MPH collimator

38 6 References Acton, P. D., S. R. Choi, K. Plossl and H. F. Kung "Quantification of dopamine transporters in the mouse brain using ultra-high resolution single-photon emission tomography". European journal of nuclear medicine, 29(5): Beekman, F. and F. van der Have "The pinhole: gateway to ultra-high-resolution three-dimensional radionuclide imaging". European journal of nuclear medicine and molecular imaging, 34(2): Giokaris, N., G. Loudos, D. Maintas, A. Karabarbounis, V. Spanoudaki, E. Stiliaris, S. Boukis, A. Gektin, A. Boyarintsev and V. Pedash "Crystal and collimator optimization studies of a high-resolution γ- camera based on a position sensitive photomultiplier". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 527(1): Habraken, J. B. A., K. de Bruin, M. Shehata, J. Booij, R. Bennink, B. L. F. van Eck Smit and E. B. Sokole "Evaluation of high-resolution pinhole SPECT using a small rotating animal". Journal of Nuclear Medicine, 42(12): Ishizu, K., T. Mukai, Y. Yonekura, M. Pagani, T. Fujita, Y. Magata, S

39 Nishizawa, N. Tamaki, H. Shibasaki and J. Konishi "Ultra-high resolution SPECT system using four pinhole collimators for small animal studies". Journal of nuclear medicine: official publication, Society of Nuclear Medicine, 36(12): Jaszczak, R., J. Li, H. Wang, M. Zalutsky and R. Coleman "Pinhole collimation for ultra-high-resolution, small-field-of-view SPECT". Physics in medicine and biology, 39(3): 425. Ogawa, K., T. Kawade, K. Nakamura, A. Kubo and T. Ichihara "Ultra high resolution pinhole SPECT for small animal study". Nuclear Science, IEEE Transactions on, 45(6): Rentmeester, M., F. Van Der Have and F. Beekman "Optimizing multi-pinhole SPECT geometries using an analytical model". Physics in medicine and biology, 52(9): Schramm, N., G. Ebel, U. Engeland, T. Schurrat, M. Behe and T. Behr "High-resolution SPECT using multipinhole collimation". Nuclear Science, IEEE Transactions on, 50(3): Vunckx, K., D. Bequé, M. Defrise and J. Nuyts "Single and multipinhole collimator design evaluation method for small animal SPECT". Medical Imaging, IEEE Transactions on, 27(1): Weber, D., M. Ivanovic, D. Franceschi, S. Strand, K. Erlandsson, M. Franceschi, H. Atkins, J. Coderre, H. Susskind and T. Button

40 "Pinhole SPECT: an approach to in vivo high resolution SPECT imaging in small laboratory animals". Journal of nuclear medicine: official publication, Society of Nuclear Medicine, 35(2):

41 국문요약 단일광자단층촬영장치의공간해상도향상을위한 다중바늘구멍조준기설계및전임상적적용가능성평가 다중바늘구멍조준기는소동물용단일광자단층촬영장치 (SPECT) 에서고해상도의영상얻으면서도검출효율이단일바늘구멍조준기에비하여높은특성을갖는다. 따라서같은 SPECT 장치내에서다중바늘구멍조준기를사용함으로서검출효율과해상도를함께증가시킬수있는장점이있다. 본논문에서는시뮬레이션을이용하여소동물용 SPECT 장치내에서 1 mm 이하의고해상도를가지면서도검출효율이최대가되도록하는다중바늘구멍조준기를설계하였다. SPECT 장치내시야 ( common volume-ofview, CVOV) 는실험용쥐를모델링하여지름 24 mm 의구형태를가지며, 이때전체시스템의해상도가 1 mm 가되도록조준기설계를최적화하였다. 설계된다중바늘구멍조준기는 15 개의바늘구멍을가지는튜브형태의텅스텐으로이루어졌으며, 바늘구멍의유효직경은 0.56 mm 이고중심으로부터바늘구멍까지의거리는 22.0 mm 이다. 다중바늘구멍조준기의 상을이용하여영상을재구성하기위해서 3 차원 maximum-likelihood expectation-maximization (ML-EM) 알고리듬이사용되었으며, collimatordetector response (CDR) 함수를이용한모델링도추가적으로적용되어이를 이용해재구성된영상의해상도향상을확인할수있었다. 영상의노이즈

42 또한시뮬레이션되었으며, 노이즈를포함한상의재구성영상에서도 1 mm 이하의해상도를가짐을확인하였다. 이러한결과를바탕으로본연구에서 설계한다중바늘구멍조준기는소동물용 SPECT 에서전임상적활용 가능성을나타낸다. Key words : 다중바늘구멍조준기, 전임상적 SPECT, 최적화, 고해상도, 소동물영상장치, Maximum-likelihood expectation-maximization, Collimator-detector response modeling

43 감사의글석사논문을마무리하며지금의제가있기까지도움을주신모든분들께감사의뜻을전합니다. 연세대학교방사선학과에서학부를거쳐석사과정을마치는동안다른누구보다도많은경험을할수있도록기회를주신김희중교수님께가장먼저감사를전하고싶습니다. 학생들보다도더욱열정적이신교수님을뵈며학문적인길뿐만아니라삶의자세에대해서도큰배움을얻었습니다. 김희중교수님의배려로기회를얻은존스홉킨스에서의연구과정과 Benjamin M.W. Tsui 교수님을만난것또한저에게는너무나도감사한시간이되었습니다. 두교수님의가르침이있었기에이렇게석사과정을무사히마치게되었습니다. 또한학문에대한열정으로항상저의부족한부분을짚어주시고방향을제시해주신정용현교수님과탄탄한이론정립의중요성을다시한번깨우치게해주신한봉수교수님께깊은감사를드립니다. 대학원생활을하며한가족이된의학물리및영상연구실의모든선후배들께도아낌없는지지와응원에대해고마운마음을전합니다. 특히언제나든든한창래오빠와대홍, 조언을아끼지않고후배들을챙겨주는혜숙언니, 처음부터지금까지함께마음을나누어준승완오빠와유나, 함께고민하고연구해준고마운영진과수진, 연구실을즐겁게만들어주는예슬이에게감사를표합니다. 끊임없는격려와지지를보내주시는박사 1기홍철표, 조효민부부그리고응원의메시지를잊지않는도완에게고마운마음을보내며, 홉킨스에서의연구기간동안다양한시각을가질수있도록도와주신이택수박사님께도감사드립니다. 학위과정동안더욱집중할수있도록사랑으로지원해준동훈에게도고마운마음을전합니다. 멀리서도언제나언니를믿어준동생자영이와오빠처럼누나를돌보아준정현이가있기에힘차게달려올수있었습니다. 삶의방향을일깨워주시는도류스님과청연스님, 함께공부하기에더힘이되는은지언니, 영원한멘토안현준삼촌, 따뜻한위로가되는김순명숙모, 반짝반짝빛이나는안채원과안채린모두가저의든든한지원군입니다. 마지막으로큰사랑과지원으로항상그곳에있어주신부모님께말로다할수없는감사를드립니다 년 1 월 류현주드림