Few-time-points time-integrated activity coefficients calculation using non-linear mixed-effects modeling: Proof of concept for [¹¹¹In]In-DOTA-TATE in kidneys

Purpose: The purpose of this study is to investigate the accuracy of few-time-points (FTP) time-integrated activity coefficients (TIACs) in peptide-receptor radionuclide therapy (PRRT) using non-linear mixed-effects (NLME) modeling. Methods: Biokinetic data of [¹¹¹In]In-DOTA-TATE in kidneys at T-1 = (2.9 ± 0.6) h, T-2 = (4.6 ± 0.4) h, T-3 = (22.8 ± 1.6) h, T-4 = (46.7 ± 1.7) h, and T-5 = (70.9 ± 1.0) h after injection were obtained from eight patients using planar imaging. The Sum-Of-Exponentials (SOE) function with four parameters was used, which was selected as the best model for the renal biokinetic data of [¹¹¹In]In-DOTA-TATE. The parameters of the SOE function were fitted to the all-time-point data in the NLME framework to derive reference (rTIACs). FTP fits, which consist of all combinations of time points, are done to calculate the estimated TIACs (eTIACs). The accuracy of the FTP-NLME TIACs calculations was assessed by calculating the relative deviations (RDs) and relative root-mean-square errors (RMSEs) between the eTIACs and rTIACs. Results: The lowest (mean ± SD) of RDs for the single-, two-, three-, four-time point FTPs were (0 ± 8) % (T-4), (1 ± 6) % (T-3 and T-4), (3 ± 5) % (T-2, T-3 and T-4), and (0 ± 2) % (T-2, T-3, T-4, and T-5), respectively. The lowest RMSEs for the one-, two-, three-, and four-time point FTPs were 8 % (T-4), 6 % (T-3 and T-4), 5 % (T-2, T-3 and T-4), and 2 % (T-2, T-3, T-4, and T-5), respectively. Conclusion: Our results showed that FTP-NLME in an example of [¹¹¹In]In-DOTA-TATE could lead to a high accuracy of eTIAC across various time points, when incorporating time point T-4 = (46.7 ± 1.7) h.