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Purpose: 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., Methods: 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., Results: 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., Conclusions: 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.

Purpose: In targeted radionuclide therapy, patient-specific dosimetry based on voxel S values (VSVs) is preferable to dosimetry based on mathematical phantoms. Monte-Carlo (MC) simulations are necessary to deduce VSVs for those voxel sizes required by quantitative imaging. The aim of this study is, starting from a single set of high-resolution VSVs obtained by MC simulations for a small voxel size along one single axis perpendicular to the source voxel, to present a suitable method to accurately calculate VSVs for larger voxel sizes., Methods: Accurate sets of VSVs for target voxel to source voxel distances up to 10 cm were obtained for high-resolution voxel sizes (0.5 mm for electrons and 1.0 mm for photons) from MC simulations for Y-90, Lu-177, and I-131 using the radiation transport code MCNPX v.2.7a. To make these values suitable to any larger voxel size, different analytical methods (based on resamplings, interpolations, and fits) were tested and compared to values obtained by direct MC simulations. As a result, an optimal calculation procedure is proposed. This procedure consisted of: (1) MC simulation for obtaining of a starting set of VSVs along a single line of voxels for a small voxel size for each radionuclide and type of radiation; (2) interpolation within the values obtained in point (1) for obtaining the VSVs for voxels within a spherical volume; (3) resampling of the data obtained in (1) and (2) for obtaining VSVs for voxels sizes larger than the one used for the MC calculation for integer voxel ratios (voxel ratio=new voxel size∕voxel size MC simulation); (4) interpolation on within the data obtained in (3) for integer voxel ratios. The results were also compared to results from other authors., Results: The results obtained with the method proposed in this work show deviations relative to the source voxel below 1% for I-131 and Lu-177 and below 1.5% for Y-90 as compared with values obtained by direct MC simulations for voxel sizes ranging between 1.0 and 10.0 cm. The results obtained in this work show differences between the scored deposited energy and the emitted energy lower than 2% for electron radiation. Higher differences, attributable to the short considered radius of 10 cm in comparison with their penetration, can be found for photons. The authors' results agree well with previously published data obtained by other authors using different methods., Conclusions: A reliable and fast approach for obtaining accurate VSVs for voxel sizes larger than the voxel size used for the MC calculation of the starting set of high-resolution VSVs was developed and successfully tested for three different radionuclides of interest for targeted radiotherapy: one pure beta (Y-90) and 2 beta-gamma emitters (Lu-177 und I-131). Applying the method of this work allows any interested reader to repeat the calculations for arbitrary radionuclides of interest and∕or smaller high-resolution voxel sizes, provided the means for running MC simulations are available.