For therapeutic applications of several isotopes (e.g., 131I, 153Sm, 177Lu) in nuclear medicine, the high activities typically applied require accurate dead time correction in early time point imaging. We present a novel, straightforward dead time correction method using the Lambert W function, which is in principle exact for the paralyzable detector model with a single parameter τ (i.e., dead time). As a proof of concept, the method is validated with a simple model: a commonly used isotope, 99mTc, with a single photopeak. We measured count rates of a gamma camera both intrinsically and extrinsically (i.e., with collimators) with point sources in air and in a scatter phantom (extrinsic only). τ was estimated for both open window (τOW) and a 99mTc photopeak window (τTc), using a “graphical” method for fitting the count rate of decaying sources. These values for τ were subsequently used for dead time correction. τ varied significantly between the different geometries for both energy windows, but τOW was more reproducible than τTc, particularly for the scatter phantom measurements. τOW measured from the phantom measurements was approximately 30% lower than τOW from the intrinsic measurement but corresponded within 15% with the extrinsic point source measurements. Accordingly, using the intrinsic τOW led to an overcorrection of 8% at high count rates; τOW from the extrinsic point source measurements corrected the phantom measurement to within 2%. However, significant differences were observed between τTc values. All measured τTc values underestimated dead time losses in a second independent phantom measurement, with even τTc from the first phantom measurement underestimating activity with 5–10% at the highest count rates. Based on measurements of the effect of energy window settings and geometry, we tentatively attribute the added dead time losses to pulse pile-up. Analytic dead time correction based on the Lambert W function is accurate for the range in which gamma detectors behave as paralyzable systems. However, further investigation indicated measured τ values to be variable with geometry as well as window fraction. We propose that dead time correction should be based on the open window value, τOW, corrected for window fraction.

中文翻译：

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使用Lambert W功能的伽马探测器死区时间校正。

对于核医学中几种同位素（例如131I，153Sm，177Lu）的治疗应用，通常应用的高活性要求在早期时间点成像中进行精确的死区校正。我们提出一种使用Lambert W函数的新颖，简单的停滞时间校正方法，该方法在原理上对于具有单个参数τ（即停滞时间）的可瘫痪探测器模型是精确的。作为概念证明，该方法已通过简单的模型验证：常用的同位素99mTc和单个光峰。我们用空气和散射体模（仅外部）中的点源在内部和外部（即使用准直仪）测量了伽马相机的计数率。对于开窗（τOW）和99mTc光电峰窗口（τTc），都使用“图形”方法拟合衰减源的计数率来估计τ。这些τ的值随后用于停滞时间校正。对于两个能量窗口，在不同的几何形状之间τ都有显着变化，但是τOW比τTc重现性更高，特别是对于散射体模测量。从幻像测量值测得的τOW比从本征测量值测得的τOW大约低30％，但与非本征点源测量值的差距在15％以内。因此，使用固有的τOW在高计数率下会导致8％的过校正；来自外部点光源测量的τOW将幻像测量值校正到2％以内。但是，在τTc值之间观察到显着差异。在第二次独立幻像测量中，所有测得的τTc值均低估了死区时间损失，即使是第一次幻象测量中的τTc，也要以最高计数率低估5-10％的活动。基于对能量窗口设置和几何形状影响的测量，我们暂时将增加的死区时间损耗归因于脉冲堆积。基于Lambert W函数的分析死区时间校正对于伽马探测器表现为可瘫痪系统的范围是准确的。但是，进一步的研究表明测得的τ值随几何以及窗口分数是可变的。我们建议空载时间校正应基于针对窗口分数校正的开窗值τOW。基于Lambert W函数的分析死区时间校正对于伽马探测器表现为可瘫痪系统的范围是准确的。但是，进一步的研究表明测得的τ值随几何以及窗口分数是可变的。我们建议空载时间校正应基于针对窗口分数校正的开窗值τOW。基于Lambert W函数的分析死区时间校正对于伽马探测器表现为可瘫痪系统的范围是准确的。但是，进一步的研究表明测得的τ值随几何以及窗口分数是可变的。我们建议空载时间校正应基于针对窗口分数校正的开窗值τOW。