Improving the accuracy of the time-integrated activity using non-linear mixed-effects modeling and population-based model selection in molecular radiotherapy

Introduction: An individualized determination of time-integrated activities (TIAs) is highly desirable in molecular radiotherapy (MRT). The aim of this study was to develop a method based on non-linear mixed-effects modeling and population-based model selection (NLME-PBMS) for an accurate determination of TIAs. The technique is demonstrated using the example of kidney dosimetry in 177Lu-PSMA therapy.

Methods: Biokinetic data for the % administered activity of 177Lu-PSMA I&T RLT in kidneys were obtained from thirteen patients with prostate cancer. The patient's age and body surface area were (70±6) years and (2.0±0.1) m2, respectively. The injected dose was (91±5) nmol PSMA I&T labeled with (7.3±0.3) GBq of 177Lu. Planar whole-body scintigraphies were performed at three time points, i.e. (1.1±0.7) h, (20.7±2.3) h, and (163.8±2.0) h post radiopharmaceutical administration. Three patients had two extra time points at (45.9±1.6) h and (68.7±1.7) h, and one had one extra time point at 66.1 h after administration. Eleven sum-of-exponentials (SOE) functions with different parameterizations were used for the analysis. The physical decay with a half-life of 177Lu of 6.6443 days was included as a factor in all SOE functions. The parameters (fixed effect and random effect) of the SOE functions were fitted to the biokinetic data in the NLME framework. The SOE function most supported by the data was selected based on the goodness-of-fit test and the Akaike weight of the population. The goodness-of-fit test was done based on the visual inspection of the fitted curves and the coefficient of variation of the fitted parameters CV<50%. Model averaging was performed with all SOE functions passing the goodness-of-fit test and corresponding Akaike weights. Model averaging was used as the reference for calculating the TIA's Root-Mean-Square Error (RMSE) obtained from the best model of the NLME-MS method. The performance of the NLME-MS method was compared to the performance of the individual-based model selection (IBMS) and a shared-parameter population-based model selection (SP-PBMS).

Results: The SOE function A1 e-(&lambda;1+&lambda;phys)t + A2 e-(&lambda;phys)t with three adjustable parameters was selected as the function most supported by the data based on the goodness-of-fit test and an Akaike weight of (54±11) % (range 38% to 74%). Visual inspection of the fitted curves was acceptable and the maximum CV of the fitted parameters was 20%. The estimated fixed effect (population mean) values of parameters A1, &lambda;1 and A2 were 1.56%, , and 0.26%, respectively. The CV of the estimated inter-individual variability (random effect) of parameters A1, &lambda;1 and A2 was 7.7%, 26.0%, and 28.1%, respectively. The relative deviation of the calculated TIAs from function A1 e-(&lambda;1+&lambda;phys)t + A2 e-(&lambda;phys)t to the TIAs from model averaging was (-2±2)%. The NLME-MS method showed a better or equivalent performance than the IBMS and SP-PBMS methods based on the visual inspection of the fitted curves and the RMSE values. The TIA's RMSEs of the NLME-PBMS, SP-PBMS and IBMS methods were 2.4%, 8.8%, and 7.4%, respectively.

Conclusions: A model selection method was developed to determine the best fit function for calculating TIAs in MRT for a given radiopharmaceutical, organ, and set of biokinetic data. The technique was found to have superior performance than the published IBMS and SP-PBMS methods. The application of this method also helps to improve the reproducibility of fit function selection between different observers.