Analytic derivation of pinhole collimation sensitivity for a general source model using spherical harmonics.
Analytic derivation of pinhole collimation sensitivity for a general source model using spherical harmonics.
复制标题
使用球谐函数对一般源模型的针孔准直灵敏度进行解析推导。
DOI：
10.1088/0031-9155/55/9/020
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发表时间：
2010
影响因子：
3.5
通讯作者：
Chang,Wei
中科院分区：
文献类型：
--
作者：
Li,Yu-Sheng;Oldendick,JamesE;Chang,Wei
针孔准直器广泛用于小器官和动物的单光子发射计算机断层扫描（SPECT）成像。此外，人们对使用针孔阵列进行临床心脏SPECT成像以获得高灵敏度和完整的数据采样也重新产生了兴趣。针孔阵列的整体灵敏度是决定系统性能的关键。传统的方法是采用点源模型来评价系统的灵敏度和优化系统设计。这个模型很简单，但远不现实。这项工作解决了使用更现实的源模型来评估针孔准直的灵敏度性能。利用球面谐波导出了一般源分布模型下针孔准直灵敏度的解析公式。作为一般模型的特例，给出了线源、盘源和球源的针孔灵敏度公式。这些结果表明，点源模型只是其他源模型的零阶近似。与更现实的模型相比，点源模型高估或低估了灵敏度。当不考虑衰减时，球源模型产生的灵敏度与位于球中心的点源相同。在衰减存在的情况下，发射的伽马射线的平均路径长度为球体源半径的3/4。在简单情况下，基于这些公式计算的灵敏度与单独的蒙特卡罗模拟结果吻合较好。本文推导的一般和特殊灵敏度公式可用于针孔准直器SPECT系统的设计和优化。
Pinhole collimators are widely used for single photon emission computed tomography (SPECT) imaging of small organs and animals. There has also been renewed interest in using pinhole arrays for clinical cardiac SPECT imaging to achieve high sensitivity and complete data sampling. Overall sensitivity of a pinhole array is critical in determining a system's performance. Conventionally, a point source model has been used to evaluate the sensitivity and optimize the system design. This model is simple but far from realistic. This work addresses the use of more realistic source models to assess the sensitivity performance of pinhole collimation. We have derived an analytical formula for pinhole collimation sensitivity with a general source distribution model using spherical harmonics. As special cases of this general model, we provided the pinhole sensitivity formulae for line, disk and sphere sources. These results show that the point source model is just the zeroth-order approximation of the other source models. The point source model overestimates or underestimates the sensitivity relative to the more realistic model. The sphere source model yields the same sensitivity as a point source located at the center of the sphere when attenuation is not taken into account. In the presence of attenuation, the average path length of emitted gamma rays is 3/4 of the radius of the sphere source. The calculated sensitivities based on these formulae show good agreement with separate Monte Carlo simulations in simple cases. The general and special sensitivity formulae derived here can be useful for the design and optimization of SPECT systems that utilize pinhole collimators.