單光子發射斷層造影系統（Single photon emission computed tomography, SPECT）能夠藉由針孔式準直儀達到次毫米等級的空間解析度，然而針孔式準直儀有著昂貴、笨重以及難以製造的缺點。在先前的研究中，為了克服上述問題而提出了利用射束擋塊（Beam stopper, BS）取代針孔準直儀的造影技術，並且使造影系統保有高解析度的特性。對於BS-SPECT而言，造影時需進行兩次的掃瞄：空氣與射束擋塊掃描，將兩次掃描所收集到的投影資料（Sinogram）相減後便能得到與針孔式準直儀等效的投影資訊。在本研究中，為了進行系統最佳化的評估，提出了用於計算BS-SPECT系統之點擴散函數（Point spread function, PSF）的光線追蹤模型（Ray-tracing model），該方法相較於使用蒙地卡羅模擬（Monte Carlo simulation），由於少了重複性的亂數取樣而將更有效率。該模型假設BS-SPECT是由一片平板偵檢器與一個射束擋塊所構成，藉由計算不同系統幾何、擋塊特性所投影出的點擴散函數並分析之，便能夠得到系統的靈敏度與解析度。研究結果中顯示（1）圓形金質的擋塊有著較佳的系統性能；（2）使用較大的擋塊可以得到較高的靈敏度對半高全寬比；（3）盡可能地將擋塊放置於離物體較近的位置能夠有較好的靈敏度與解析度；（4）將偵檢器放置於離物體較遠的位置能夠提高解析度，對於靈敏度則未有影響；（5）兩次掃描的時間比例為1：1時，將有最高的訊雜比。

Single photon emission computed tomography (SPECT) employing pinhole collimators are capable of generating images with sub-millimeter spatial resolution. However, the pinhole collimator is expensive, heavy and difficult to fabricate. In our previous study, beam stopper (BS) device was employed to replace the pinhole collimator for high resolution SPECT imaging. In BS-SPECT system, dual scans with and without the BS are conducted for all directions, and the difference between these two sinograms yields the pinhole equivalent projections. For optimization, a novel ray-tracing model was proposed to evaluate the system performance of BS-SPECT system in this study. By omitting the repeated random sampling, ray-tracing simulations are more efficient than Monte Carol simulations. This model assumes that the BS-SPECT system consists of a flat detector combined with a BS. By calculating the point spread functions (PSF's) of various system geometries and BS designs, the total sensitivities and resolutions can be derived. The results show that (1) circle BS made of gold has the optimal system performance; (2) high sensitivity-to-FWHM ratio can be achieved by using large BS; (3) the BS should be placed as close as possible to the object for optimal sensitivity and resolution; (4) the detector can be placed away from the object to improve the resolution without sensitivity losses; (5) the highest SRN is derived by using 1:1 scan time ratio.

[1] F. Beekman and F. van der Have, "The pinhole: gateway to ultra-high-resolution three-dimensional radionuclide imaging," European journal of nuclear medicine and molecular imaging, vol. 34, pp. 151-161, 2007.
[2] F. J. Beekman and B. Vastenhouw, "Design and simulation of a high-resolution stationary SPECT system for small animals," Physics in medicine and biology, vol. 49, p. 4579, 2004.
[3] R. Jaszczak, 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, vol. 39, p. 425, 1994.
[4] S. R. Meikle, P. Kench, M. Kassiou, and R. B. Banati, "Small animal SPECT and its place in the matrix of molecular imaging technologies," Physics in medicine and biology, vol. 50, p. R45, 2005.
[5] S. Metzler, R. Jaszczak, N. Patil, S. Vemulapalli, G. Akabani, and B. Chin, "Molecular imaging of small animals with a triple-head SPECT system using pinhole collimation," Medical Imaging, IEEE Transactions on, vol. 24, pp. 853-862, 2005.
[6] N. Schramm, G. Ebel, U. Engeland, T. Schurrat, M. Behe, and T. Behr, "High-resolution SPECT using multipinhole collimation," Nuclear Science, IEEE Transactions on, vol. 50, pp. 315-320, 2003.
[7] K.-S. Chuang, J. Wu, M.-L. Jan, S. Chen, and C.-H. Hsu, "Novel scatter correction for three-dimensional positron emission tomography by use of a beam stopper device," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 551, pp. 540-552, 2005.
[8] J. Wu, K.-S. Chuang, C.-H. Hsu, M.-L. Jan, M. Hwang, and T.-J. Chen, "Scatter correction for 3D PET using beam stoppers combined with dual-energy window acquisition: a feasibility study," Physics in medicine and biology, vol. 50, p. 4593, 2005.
[9] C. S. Levin and E. J. Hoffman, "Calculation of positron range and its effect on the fundamental limit of positron emission tomography system spatial resolution," Physics in medicine and biology, vol. 44, p. 781, 1999.
[10] K. Shibuya, E. Yoshida, F. Nishikido, T. Suzuki, T. Tsuda, N. Inadama, et al., "Limit of spatial resolution in FDG-PET due to annihilation photon non-collinearity," in World Congress on Medical Physics and Biomedical Engineering 2006, 2007, pp. 1667-1671.
[11] S. Y. Chun, J. A. Fessler, and Y. K. Dewaraja, "Correction for Collimator-Detector Response in SPECT Using Point Spread Function Template," Medical Imaging, IEEE Transactions on, vol. 32, pp. 295-305, 2013.
[12] J. Palmer and P. Wollmer, "Pinhole emission computed tomography: method and experimental evaluation," Physics in medicine and biology, vol. 35, p. 339, 1990.
[13] K. Ishizu, T. Mukai, Y. Yonekura, M. Pagani, T. Fujita, Y. Magata, et al., "Ultra-high resolution SPECT system using four pinhole collimators for small animal studies," Journal of nuclear medicine: official publication, Society of Nuclear Medicine, vol. 36, p. 2282, 1995.
[14] D. A. Weber and M. Ivanovic, "Ultra-high-resolution imaging of small animals: implications for preclinical and research studies," Journal of Nuclear Cardiology, vol. 6, pp. 332-344, 1999.
[15] F. J. Beekman, F. van der Have, B. Vastenhouw, A. J. van der Linden, P. P. van Rijk, J. P. H. Burbach, et al., "U-SPECT-I: a novel system for submillimeter-resolution tomography with radiolabeled molecules in mice," Journal of Nuclear Medicine, vol. 46, pp. 1194-1200, 2005.
[16] S. R. Cherry and S.-C. Huang, "Effects of scatter on model parameter estimates in 3D PET studies of the human brain," Nuclear Science, IEEE Transactions on, vol. 42, pp. 1174-1179, 1995.
[17] J. M. Ollinger, "Model-based scatter correction for fully 3D PET," Physics in medicine and biology, vol. 41, p. 153, 1996.
[18] C. Watson, D. Newport, M. Casey, R. DeKemp, R. Beanlands, and M. Schmand, "Evaluation of simulation-based scatter correction for 3-D PET cardiac imaging," Nuclear Science, IEEE Transactions on, vol. 44, pp. 90-97, 1997.
[19] M. Rentmeester, F. Van Der Have, and F. Beekman, "Optimizing multi-pinhole SPECT geometries using an analytical model," Physics in medicine and biology, vol. 52, p. 2567, 2007.
[20] M. Goorden, M. Rentmeester, and F. Beekman, "Theoretical analysis of full-ring multi-pinhole brain SPECT," Physics in medicine and biology, vol. 54, p. 6593, 2009.
[21] M. Gieles, H. W. de Jong, and F. J. Beekman, "Monte Carlo simulations of pinhole imaging accelerated by kernel-based forced detection," Physics in medicine and biology, vol. 47, p. 1853, 2002.
[22] H. M. Deloar, H. Watabe, T. Aoi, and H. Iida, "Evaluation of penetration and scattering components in conventional pinhole SPECT: phantom studies using Monte Carlo simulation," Physics in medicine and biology, vol. 48, p. 995, 2003.
[23] F. van der Have and F. J. Beekman, "Photon penetration and scatter in micro-pinhole imaging: a Monte Carlo investigation," Physics in medicine and biology, vol. 49, p. 1369, 2004.
[24] F. van der Have and F. J. Beekman, "Penetration, scatter and sensitivity in channel micro-pinholes for SPECT: a Monte Carlo investigation," Nuclear Science, IEEE Transactions on, vol. 53, pp. 2635-2645, 2006.