Department of Clinical Physiology and Nuclear Medicine, Copenhagen University Hospital - Rigshospitalet, Copenhagen, Denmark; Neurobiology Research Unit, Copenhagen University Hospital - Rigshospitalet, Copenhagen, Denmark.
Phys Med. 2023 Dec;116:103174. doi: 10.1016/j.ejmp.2023.103174. Epub 2023 Nov 25.
In NM-imaging, theoretical curves for the recovery coefficient (RC) of the signal maximum and mean are known for spheres and cubes, if a 3D Gaussian PSF is assumed. The RC of the maximum is also known for cylinders. For these and other shapes empirical equations with one or two fit-parameters have been utilized.
An equation for the RC for large objects of arbitrary shape is derived and generalized into an empirical equation for smaller objects, which is verified by numerical simulations. The proposed equation is compared to published results on SPECT kidney phantom measurements and to PET measurements on the NEMA IEC PET body phantom with six spheres.
The signal loss (1-RC) for large spheres is inversely proportional to the radius, where the slope is proportional to the FWHM of the spatial resolution. For non-spherical shapes the generalized instead of the volume equivalent radius should be utilized. For smaller objects, an equation with one added empirical fit-parameter is presented. It is demonstrated that the EANM-guidelines' two-parameter logistic function results in a poor fit if the theoretical slope and inverse proportionality are forced and it gives a suboptimal fit when both parameters are fitted.
A novel model-based equation for the mean RC-curve is derived. It can be used for arbitrary shapes as long as the sphericity is taken into account and it is accurate down to RC = 10 %. One parameter is directly related to the spatial resolution, while the other is a shape depending fit-parameter.
在 NM 成像中，如果假设 3D 高斯 PSF，则已知球体和立方体的信号最大值和平均值的恢复系数（RC）的理论曲线。圆柱体的最大值 RC 也已知。对于这些形状和其他形状，已经使用了具有一个或两个拟合参数的经验方程。
推导出了任意形状大物体的 RC 方程，并将其推广为较小物体的经验方程，通过数值模拟进行了验证。将提出的方程与 SPECT 肾脏体模测量的已发表结果以及具有六个球体的 NEMA IEC PET 体模的 PET 测量进行了比较。
对于大球体，信号损失（1-RC）与半径成反比，其中斜率与空间分辨率的 FWHM 成正比。对于非球形形状，应使用广义而不是体积等效半径。对于较小的物体，提出了一个具有一个附加经验拟合参数的方程。结果表明，如果强制理论斜率和反比例关系，则 EANM 指南的双参数逻辑函数拟合效果不佳，而当两个参数都拟合时，拟合效果也不是最佳的。
推导出了一种新的基于模型的平均 RC 曲线方程。只要考虑到球形度，它就可以用于任意形状，并且在 RC=10% 时精度很高。一个参数与空间分辨率直接相关，而另一个参数是形状相关的拟合参数。
