Li Xiaoli, Hunter William C J, Lewellen Tom K, Miyaoka Robert S
University of Washington Department of Physics, Seattle, WA USA 98105.
IEEE Trans Nucl Sci. 2012;59(1):3-12. doi: 10.1109/TNS.2011.2165968.
We have previously reported on continuous miniature crystal element (cMiCE) PET detectors that provide depth of interaction (DOI) positioning capability. A key component of the design is the use of a statistics-based positioning (SBP) method for 3D event positioning. The Cramer-Rao lower bound (CRLB) expresses limits on the estimate variances for a set of deterministic parameters. We examine the CRLB as a useful metric to evaluate the performance of our SBP algorithm and to quickly compare the best possible resolution when investigating new detector designs.In this work, the CRLB is first reported based upon experimental results from a cMiCE detector using a 50×50×15-mm(3) LYSO crystal readout by a 64-channel PMT (Hamamatsu H8500) on the exit surface of the crystal. The X/Y resolution is relatively close to the CRLB, while the DOI resolution is more than double the CRLB even after correcting for beam diameter and finite X (i.e., reference DOI position) resolution of the detector. The positioning performance of the cMiCE detector with the same design was also evaluated through simulation. Similar with the experimental results, the difference between the CRLB and measured spatial resolution is bigger in DOI direction than in X/Y direction.Another simulation study was conducted to investigate what causes the difference between the measured spatial resolution and the CRLB. The cMiCE detector with novel sensor-on-entrance-surface (SES) design was modeled as a 49.2×49.2×15-mm(3) LYSO crystal readout by a 12×12 array of 3.8×3.8-mm(2) silicon photomultiplier (SiPM) elements with 4.1-mm center-to-center spacing on the entrance surface of the crystal. The results show that there are two main causes to account for the differences between the spatial resolution and the CRLB. First, Compton scatter in the crystal degrades the spatial resolution. The DOI resolution is degraded more than the X/Y resolution since small angle scatter is preferred. Second, our maximum likelihood (ML) clustering algorithm also has limitations when developing 3D look up tables during detector calibration.
我们之前报道过提供相互作用深度（DOI）定位能力的连续微型晶体元件（cMiCE）PET探测器。该设计的一个关键组件是使用基于统计的定位（SBP）方法进行三维事件定位。克拉美 - 罗下界（CRLB）表示一组确定性参数估计方差的限制。我们将CRLB视为评估SBP算法性能以及在研究新探测器设计时快速比较最佳可能分辨率的有用指标。在这项工作中，首次基于使用50×50×15 mm³LYSO晶体的cMiCE探测器的实验结果报告了CRLB，该晶体在晶体出射面由64通道光电倍增管（滨松H8500）读出。X/Y分辨率相对接近CRLB，而即使在校正了探测器的束直径和有限的X（即参考DOI位置）分辨率之后，DOI分辨率仍比CRLB大一倍多。具有相同设计的cMiCE探测器的定位性能也通过模拟进行了评估。与实验结果类似，CRLB与测量的空间分辨率之间的差异在DOI方向上比在X/Y方向上更大。还进行了另一项模拟研究，以探究测量的空间分辨率与CRLB之间差异的原因。具有新型入射面传感器（SES）设计的cMiCE探测器被建模为一个49.2×49.2×15 mm³的LYSO晶体，在晶体入射面由12×12阵列的3.8×3.8 mm²硅光电倍增管（SiPM）元件读出，元件中心间距为4.1 mm。结果表明，有两个主要原因导致空间分辨率与CRLB之间存在差异。首先，晶体中的康普顿散射会降低空间分辨率。由于小角度散射更易发生，DOI分辨率比X/Y分辨率下降得更多。其次，我们的最大似然（ML）聚类算法在探测器校准期间开发三维查找表时也存在局限性。
