Mixed model time-activity fitting to reduce SPECT/CT imaging time points for dosimetry in Lu-177 peptide receptor radionuclide therapy (PRRT)

Objectives: When imaging time points are limited, a statistical mixed model (MM) fit using time-activity data from multiple subjects simultaneously has the potential to more reliably predict time-integrated activity (TIA) for dosimetry compared with conventional individual model fitting. The goal was to implement and evaluate MM fits to one and two time-point data to reduce the imaging burden associated with patient-specific kidney dosimetry in Lu-177 PRRT of neuroendocrine tumors.

Methods: Nonlinear monoexponential MMs were fit to kidney time-activity data using one, two, and four time points, and respective TIAs were estimated for 6 patients, each imaged with quantitative SPECT/CT at four times between days 0 and 7 after PRRT (cycle 1). In the MM, fit parameters for each subject were estimated as the sum of a population value (fixed effect) and a value associated with that subject’s kidney (random effect), thereby borrowing information across patients while also incorporating patient-specific deviations. For comparison, TIAs were also estimated using four-time point individual fits and a previously proposed single-time point method (Madsen et al, Med Phys 45(5), 2018) that requires prior knowledge of the population mean fit parameters. To further assess the MM approach, we conducted a simulation study in which virtual patient data were generated using parameter values obtained from analysis of the clinical cohort. A total of 100 simulated data sets, each consisting of time-activity data from 25 patients (50 kidneys) measured at 2h, 24h, 96h, and 144h, were simulated with a similar level of noise as observed in the clinical data (2% relative SD) and under additional settings with greater noise (5% and 10% relative SD). MM TIAs using one and two time points and Madsen single-time point TIAs were compared to true TIAs using mean percentage bias (%B), proportion of simulations with |bias| > 25% (B25), and root mean squared error of prediction (RMSEP).

Results: In analysis of real patient data, both single time point methods exhibited good agreement with four-time point TIAs when the single activity measurement was between 25h and 102h. Average differences were 7% (range [-20,12]) and 3% (range [-22,20]) for Madsen and MM, respectively, with concordance correlation > 0.96 and R² > 0.94 for both methods. In the simulation study, the best single time point results for both the MM and Madsen methods were achieved using the 96h time point, with %B, B25, and RMSEP < 8.3, 11.2, and 0.3, respectively. The corresponding values simulating up to 10% noise were < 13.2, 13.1, and 0.5. Two-time point MMs substantially improved performance with %B, B25, and RMSEP < 0.6, 2.7, and 0.1 in all simulation settings and all possible combinations of two time points, with the best results achieved when using [24h, 96h] or [96h, 144h] imaging points. The computation times for MM fits using SAS 9.4 were <30 seconds and <60 seconds for sample sizes of 50 (one time point) and 100 (two time points), respectively.

Conclusions: While the MM and Madsen single-time point method both performed well, MM fitting with two time points substantially improved performance. The superior performance of the two-time point MM, even when one of the sampling times was at 2h post-therapy, is clinically relevant as only one return visit is needed to reliably estimate patient-specific kidney absorbed doses. These promising results were limited to a small clinical cohort and simulations with parameters that mimicked these patients, thus they need validation in a larger patient study. Implementing biexponential MMs for lesion time-activity fitting is ongoing.