Klinik für Nuklearmedizin, Universität Ulm, Ulm 89081, Germany.
Med Phys. 2013 Oct;40(10):102504. doi: 10.1118/1.4820367.
Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error.
The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB.
To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit parameters and their standard error estimated by using SAAM numerical and NUKFIT showed differences of <1%. The differences for the time-integrated activity coefficients were also <1% (standard error between 0.4% and 3%). In general, the application of the software is user-friendly and the results are mathematically correct and reproducible. An application of NUKFIT is presented for three different clinical examples.
The software tool with its underlying methodology can be employed to objectively and reproducibly estimate the time integrated activity coefficient and its standard error for most time activity data in molecular radiotherapy.
计算时间积分活度系数（停留时间）是分子放射治疗剂量学的关键步骤。然而，现有的软件存在缺陷，要么不适合分子放射治疗使用，要么不包括所有必需的估计方法。因此，本工作的目的是开发和编程一种算法，以客观和可重复的方式确定时间积分活度系数及其标准误差。
该算法包括从预定义的指数和的和中选择一组拟合函数，并为所用数据选择误差模型。为了估计可调参数的值，依赖于数据、误差模型的参数、拟合函数（如果需要且可用）和贝叶斯信息的目标函数被最小化。为了提高可重复性和用户友好性，使用曲线剥离和随机搜索的组合自动确定起始值。视觉检查、决定系数、拟合参数的标准误差以及相关矩阵用于评估拟合质量。使用修正的 Akaike 信息准则确定最受数据支持的函数。通过分析积分拟合函数来估计时间积分活度系数。假设高斯误差传播，确定其标准误差。该软件使用 MATLAB 实现。
为了验证目标函数和拟合函数的正确实现，比较了 NUKFIT 和 SAAM 数值的结果，后者是一种商业上可用的软件工具。自动搜索起始值的可重复性测试成功。与 Akaike 信息准则一起应用的质量标准允许选择合适的函数。使用 SAAM 数值和 NUKFIT 估计的函数拟合参数及其标准误差差异小于 1%。时间积分活度系数的差异也小于 1%（标准误差在 0.4%至 3%之间）。一般来说，该软件的应用用户友好，结果在数学上是正确且可重复的。呈现了 NUKFIT 在三个不同临床示例中的应用。
该软件工具及其基础方法可用于客观和可重复地估计分子放射治疗中大多数时间活性数据的时间积分活度系数及其标准误差。
