KU Leuven, University of Leuven, Department of Imaging and Pathology, Nuclear Medicine & Molecular imaging; Medical Imaging Research Center (MIRC), B-3000, Leuven, Belgium.
Department of Nuclear Medicine, Vrije Universiteit Brussel, B-1090, Brussels, Belgium.
Phys Med Biol. 2023 Dec 22;69(1). doi: 10.1088/1361-6560/ad078c.
Measurement of the time-of-flight (TOF) difference of each coincident pair of photons increases the effective sensitivity of positron emission tomography (PET). Many authors have analyzed the benefit of TOF for quantification and hot spot detection in the reconstructed activity images. However, TOF not only improves the effective sensitivity, it also enables the joint reconstruction of the tracer concentration and attenuation images. This can be used to correct for errors in CT- or MR-derived attenuation maps, or to apply attenuation correction without the help of a second modality. This paper presents an analysis of the effect of TOF on the variance of the jointly reconstructed attenuation and (attenuation corrected) tracer concentration images.The analysis is performed for PET systems that have a distribution of possibly non-Gaussian TOF-kernels, and includes the conventional Gaussian TOF-kernel as a special case. Non-Gaussian TOF-kernels are often observed in novel detector designs, which make use of two (or more) different mechanisms to convert the incoming 511 keV photon to optical photons. The analytical result is validated with a simple 2D simulation.We show that if two different TOF-kernels are equivalent for image reconstruction with known attenuation, then they are also equivalent for joint reconstruction of the activity and the attenuation images. The variance increase in the activity, caused by also jointly reconstructing the attenuation image, vanishes when the TOF-resolution approaches perfection.These results are of interest for PET detector development and for the development of stand-alone PET systems.
测量每个符合对光子的飞行时间（TOF）差可提高正电子发射断层扫描（PET）的有效灵敏度。许多作者已经分析了 TOF 对重建活性图像中定量和热点检测的益处。然而，TOF 不仅提高了有效灵敏度，还能够联合重建示踪剂浓度和衰减图像。这可用于校正 CT 或 MR 衍生衰减图中的误差，或在没有第二种模式的帮助下应用衰减校正。本文分析了 TOF 对联合重建衰减和（衰减校正）示踪剂浓度图像方差的影响。分析针对具有可能非高斯 TOF 核分布的 PET 系统进行，包括常规高斯 TOF 核作为特殊情况。在利用两种（或更多）不同机制将入射的 511keV 光子转换为光光子的新型探测器设计中，经常观察到非高斯 TOF 核。通过简单的 2D 模拟验证了分析结果。我们表明，如果两个不同的 TOF 核对于具有已知衰减的图像重建是等效的，那么它们对于活性和衰减图像的联合重建也是等效的。当 TOF 分辨率接近完美时，由于也联合重建衰减图像而导致的活性方差增加会消失。这些结果对于 PET 探测器开发和独立 PET 系统的开发都很重要。
