Virtual-patient nonlinear mixed-effects modelling for data-driven optimisation of single-time-point dosimetry: a
Yeni Pertiwi1,2, Indra Budiansah3, Jaja Muhamad Jabar1,4
1Nuclear Physics and Biophysics Research Group, Physics Department, Faculty of Mathematics and Science, Institut Teknologi Bandung, Bandung, Indonesia.
Background:
Robust single-time-point (STP) dosimetry critically depends on selecting an imaging time that yields reliable estimates of the time-integrated activity coefficient (TIAC). This study developed and evaluated a virtual-patient nonlinear mixed-effects modelling (NLMEM) framework to optimise STP imaging schedules for renal TIAC estimation, using [¹⁷⁷Lu]Lu-PSMA-617 therapy as a proof of concept.
Methods:
A previously published NLMEM (sum-of-exponentials structure and parameter distributions) describing renal [¹⁷⁷Lu]Lu-PSMA-617 biokinetics in 63 patients served as the generative model [1]. Based on fixed- and random-effects parameters, 500 virtual patients (VPs) were sampled, and reference TIAC values were computed analytically (rTIAC). For each candidate imaging time, renal activity measurements were simulated by applying proportional noise (7.9%). Estimated STP TIAC values (sTIAC) were obtained via leave-one-out cross-validation and compared with rTIAC to quantify population-level error metrics using mean absolute percentage error (MAPE) and root-mean-square error (RMSE). Time-dependent MAPE-time and RMSE-time profiles were modelled using polynomial fits selected by predefined goodness-of-fit criteria to identify time windows with low and stable errors. Individual-level robustness was assessed by quantifying extreme patient-specific relative deviations (RD) using thresholds of 10%, 20%, and 30%.
Results:
MAPE- and RMSE-versus-time profiles were concordant and showed a pronounced minimum around 50 h post-injection. Among the investigated imaging time points, the lowest observed population-level error metrics occurred at 48 h, whereas polynomial modelling predicted an optimum centred at approximately 50 h (about 33-67 h). An additional VP-NLMEM evaluation at 50 h demonstrated comparable population-level performance and the lowest frequency of |RD| >30%, while the minima for the 10% and 20% thresholds occurred at nearby imaging times.
Conclusion:
The proposed virtual-patient NLMEM framework enables data-driven optimisation of STP imaging by identifying robust time windows that minimise both population-level error and extreme individual deviations in renal TIAC estimation for [¹⁷⁷Lu]Lu-PSMA-617 therapy. The approach appears transferable to STP dosimetry optimisation for other radiopharmaceuticals.
