Vandervoort Eric, Sossi Vesna
Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1 BC Canada.
IEEE Trans Med Imaging. 2008 Mar;27(3):402-12. doi: 10.1109/TMI.2007.909851.
We present an analytical scatter correction, based upon the Klein-Nishina formula, for singles-mode transmission data in positron emission tomography (PET) and its implementation as part of an iterative image reconstruction algorithm. We compared our analytically-calculated scatter sinogram data with previously validated simulation data for a small animal PET scanner with 68 Ge (a positron emitter) and 57 Co (approximately 122-keV photon emitter) transmission sources using four different phantom configurations (three uniform water cylinders with radii of 25, 30, and 45 mm and a nonuniform phantom consisting of water, Teflon, and air). Our scatter calculation correctly predicts the contribution from single-scattered (one incoherent scatter interaction) photons to the simulated sinogram data and provides good agreement for the percent scatter fraction (SF) per sinogram for all phantoms and both transmission sources. We then applied our scatter correction as part of an iterative reconstruction algorithm for PET transmission data for simulated and experimental data using uniform and nonuniform phantoms. For both simulated and experimental data, the reconstructed linear attenuation coefficients (mu-values-values) agreed with expected values to within 4% when scatter corrections were applied, for both the 68 Ge and 57 Co transmission sources. We also tested our reconstruction and scatter correction procedure for two experimental rodent studies (a mouse and rat). For the rodent studies, we found that the average mu-values for soft-tissue regions of interest agreed with expected values to within 4%. Using a 2.2-GHz processor, each scatter correction iteration required between 6-27 min of CPU time (without any code optimization) depending on the phantom size and source used. This extra calculation time does not seem unreasonable considering that, without scatter corrections, errors in the reconstructed mu-values were between 18%-45% depending on the phantom size and transmission source used.
我们提出了一种基于克莱因-仁科公式的解析散射校正方法，用于正电子发射断层扫描（PET）中的单模传输数据，并将其作为迭代图像重建算法的一部分进行实现。我们将通过分析计算得到的散射正弦图数据与先前针对配备68 Ge（一种正电子发射体）和57 Co（约122 keV光子发射体）传输源的小动物PET扫描仪使用四种不同体模配置（三个半径分别为25、30和45 mm的均匀水缸以及一个由水、聚四氟乙烯和空气组成的非均匀体模）所验证的模拟数据进行了比较。我们的散射计算正确地预测了单次散射（一次非相干散射相互作用）光子对模拟正弦图数据的贡献，并且对于所有体模和两种传输源的每个正弦图的散射分数百分比（SF）都提供了良好的一致性。然后，我们将散射校正作为PET传输数据迭代重建算法的一部分，应用于使用均匀和非均匀体模的模拟数据和实验数据。对于模拟数据和实验数据，当应用散射校正时，对于68 Ge和57 Co传输源，重建的线性衰减系数（μ值）与预期值的偏差在4%以内。我们还对两项实验性啮齿动物研究（一只小鼠和一只大鼠）测试了我们的重建和散射校正程序。对于啮齿动物研究，我们发现感兴趣的软组织区域的平均μ值与预期值的偏差在4%以内。使用2.2 GHz处理器时，根据体模大小和使用的源不同，每次散射校正迭代需要6 - 27分钟的CPU时间（未进行任何代码优化）。考虑到如果不进行散射校正，根据体模大小和使用的传输源不同，重建的μ值误差在18% - 45%之间，这种额外的计算时间似乎并非不合理。
