Single-time-point renal TIA estimation, sparse SPECT/CT data, and nonlinear mixed-effects modelling in [177Lu]Lu-PSMA-617 therapy.

Abstract

Purpose: This study evaluates the feasibility of Single-Time-Point (STP) renal Time-Integrated Activity (TIA) estimation using Population-Based Model Selection (PBMS) and Nonlinear Mixed-Effects Modelling (NLMEM) with sparse time-activity data in [¹⁷⁷Lu]Lu-PSMA-617 therapy.

Methods: Kidney biokinetics of [1⁷⁷Lu]Lu-PSMA-617 from 64 metastatic castration-resistant prostate cancer (mCRPC) patients were collected at TP1=(4.8±0.9h)(n=62),TP2=(24.5±1.5 h)(n=6),TP3=(94.0±6.6h)(n=16),and TP4=(128.5±12.7h)(n=47) post-injection with 1-4 data per patient. Six sum-of-exponentials functions (4-7 adjustable parameters) were fitted to all-time-point (ATP) data using NLMEM, evaluating combinations of fixed effects, inter-individual, and residual variability. The best-supported PBMS-NLMEM model was used to derive the ATP-based internal comparator TIA. Agreement between STP-derived TIAs and ATP-based internal comparator TIAs was quantified using relative deviation (RD), mean absolute percentage error (MAPE), and root-mean-square error (RMSE).

Results: Based on PBMS-NLMEM analysis, function [Formula: see text] with a fixed-effect value of λ₃=7.19×10^-2/h, residual variability of 0.079, and inter-individual variabilities of A₃=0.38 and λ₃=0.52 assigned from the literature was selected as the best function for TIA estimation. STP TIA estimation with NLMEM showed better agreement than Hänscheid's method across all investigated TPs. Moreover, NLMEM-based STP estimation was technically feasible at each TP, with maximum RMSE and MAPE values of 25.2% and 16.5%, respectively. However, findings should be interpreted cautiously because patient subsets differed across TPs, particularly at TP2(n=6).

Conclusion: In this retrospective sparse-data cohort, PBMS-NLMEM-based STP renal TIA estimation was technically feasible at the investigated TPs and showed agreement with an ATP-based internal comparator, with MAPE below 16.5%. Prospective validation in balanced cohorts is required before recommending a specific STP imaging window or clinical implementation.