A population-based method to determine the time-integrated activity in molecular radiotherapy

Uncertainty Analysis of Time-Integrated Activity Coefficient in Single-Time-Point Dosimetry Using Bayesian Fitting Method

Purpose

Calculation of the uncertainty of the individual time-integrated activity coefficient (TIACs) is desirable in molecular radiotherapy. However, the calculation of TIAC's uncertainty in single-time-point (STP) method has never been reported in the literature. This study presents a method based on the Bayesian fitting (BF) to calculate the standard deviation (SD) of individual TIACs in the STP dosimetry.

Methods

Biokinetic data of 177Lu-DOTATATE in kidneys were obtained from PMID33443063. BF methods with extended objective function, which optimize the fitting using prior knowledge of the function's parameters, were used. Reference TIACs (rTIACs) were calculated by fitting a mono-exponential function to the all-time-point data. The goodness of fit was checked based on the visual inspection and the coefficient of variations (CV) of the fitted parameters < 0.5. BF with relative (BFr) and absolute-based (BFa) variance methods were used to obtain the calculated TIACs (cTIACs) from the STP dosimetry. Performance of the STP method was obtained by calculating the relative deviation (RD) between cTIACs and rTIACs.

Results

Visual inspection showed a good fit for all patients with CV of fitted parameters less than 50%. The mean ± SD of cTIAC's %RD were 7.0 ± 25.2 for BFr and 2.6 ± 8.9 for BFa. The range of %CV of the individual cTIAC's SD for BFr and BFa methods was 36-78% and 22-33%, respectively, while the %CV of the rTIAC SD was 0.8-49%.

Conclusion

We introduce the BF method to calculate the SD of individual TIACs in STP dosimetry. The presented method might be used as an alternative method for uncertainty analysis in STP dosimetry.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13139-024-00851-8.

Single-Time-Point Renal Dosimetry Using Nonlinear Mixed-Effects Modeling and Population-Based Model Selection in [177Lu]Lu-PSMA-617 Therapy

The aim of this study was to investigate the accuracy of single-time-point (STP) renal dosimetry imaging using SPECT/CT data, a nonlinear mixed-effects (NLME) model, and a population-based model selection (PBMS) in a large population for 177Lu-labeled prostate-specific membrane antigen therapy. Methods: Biokinetic data (mean ± SD) of [177Lu]Lu-PSMA-617 in kidneys at time points 1 (1.8 ± 0.8 h), 2 (18.7 ± 0.9 h), 3 (42.6 ± 1.0 h), 4 (66.3 ± 0.9 h), and 5 (160.3 ± 24.2 h) after injection were obtained from 63 patients with metastatic castration-resistant prostate cancer using SPECT/CT. Thirteen functions were derived from various parameterizations of 1- to 5-exponential functions. The function's parameters were fitted in the NLME framework to the all-time-point (ATP) data. The PBMS NLME method was performed using the goodness-of-fit test and Akaike weight to select the best function fitting the data. The best function from ATP fitting was used to calculate the reference time-integrated activity and absorbed doses. In STP dosimetry, the parameters of a particular patient with STP data were fitted simultaneously to the STP data at different time points of that patient with ATP data of all other patients. The parameters from STP fitting were used to calculate the STP time-integrated activity and absorbed doses. Relative deviations (RDs) and root-mean-square errors (RMSEs) were used to analyze the accuracy of the calculated STP absorbed dose compared with the reference absorbed dose obtained from the best-fit ATP function. The performance of STP dosimetry using PBMS NLME modeling was compared with the Hänscheid and Madsen methods. Results: The function [Formula: see text] was selected as the best-fit ATP function, with an Akaike weight of 100%. For STP dosimetry, the STP measurement by SPECT/CT at time point 3 (42.6 ± 1.0 h) showed a relatively low mean RD of -4.4% ± 9.4% and median RD of -0.7%. Time point 3 had the lowest RMSE value compared with those at the other 4 time points. The RMSEs of the absorbed dose RDs for time points 1-5 were 23%, 16%, 10%, 20%, and 53%, respectively. The STP dosimetry using the PBMS NLME method outperformed the Hänscheid and Madsen methods for all investigated time points. Conclusion: Our results show that a single measurement of SPECT/CT at 2 d after injection might be used to calculate accurate kidney-absorbed doses using the NLME method and PBMS.

Future trends for patient-specific dosimetry methodology in molecular radiotherapy

Molecular radiotherapy is rapidly expanding, and new radiotherapeutics are emerging. The majority of treatments is still performed using empirical fixed activities and not tailored for individual patients. Molecular radiotherapy dosimetry is often seen as a promising candidate that would allow personalisation of treatments as outcome should ultimately depend on the absorbed doses delivered and not the activities administered. The field of molecular radiotherapy dosimetry has made considerable progress towards the feasibility of routine clinical dosimetry with reasonably accurate absorbed-dose estimates for a range of molecular radiotherapy dosimetry applications. A range of challenges remain with respect to the accurate quantification, assessment of time-integrated activity and absorbed dose estimation. In this review, we summarise a range of technological and methodological advancements, mainly focussed on beta-emitting molecular radiotherapeutics, that aim to improve molecular radiotherapy dosimetry to achieve accurate, reproducible, and streamlined dosimetry. We describe how these new technologies can potentially improve the often time-consuming considered process of dosimetry and provide suggestions as to what further developments might be required.

Metabolic kinetic modeling of [11C]methionine based on total-body PET in multiple myeloma

PURPOSE

Multiple myeloma (MM) is a malignant disease characterized by the secretion of monoclonal immunoglobulins and has a high demand for amino acids. [11C]methionine total-body PET is capable of noninvasive dynamic monitoring of radiotracer in vivo, thus providing a way to reveal the dynamic changes of myeloma metabolism. This study aims to analyze the metabolic process of [11C]methionine based on kinetic modeling, and to preliminary reveal its application value in MM.

METHODS

Dynamic total-body [11C]methionine PET/CT was conducted with uEXPLORER in 12 subjects (9 MM patients and 3 controls). The tissue time activity curves (TACs) of organs and bone marrows were extracted. Model fitting of TACs was operated using PMOD Kinetic Modeling. After validation by Goodness of fit (GOF), the reversible two-tissue compartment model (2T4k) was used to further analysis. R software was used to analyze the correlation between kinetic parameters and clinical indicators.

RESULTS

The 2T4k has passed the criterion of GOF and was used to fit the data of 0-20 minutes. The [11C]methionine net uptake rate (Ki) was significantly higher in the MM lesions than in the non-myeloma controls (control: 0.040±0.007 mL/g/min, MM: 0.171±0.108 mL/g/min, p=0.009). The Ki values were found to be correlated with M protein levels in MM patients. MM patients with t(4;14) translocations had an elevated k4 value compared with t(4;14) negative patients.

CONCLUSION

MM lesions have a propensity for uptake of [11C]methionine. The serum levels of M protein are correlated with [11C]methionine uptake rate in myeloma. Metabolic classification based on the k4 value may be a promising strategy for risk stratification in MM.

Heterogeneity of absorbed dose distribution in kidney tissues and dose–response modelling of nephrotoxicity in radiopharmaceutical therapy with beta-particle emitters: A review

Absorbed dose heterogeneity in kidney tissues is an important issue in radiopharmaceutical therapy. The effect of absorbed dose heterogeneity in nephrotoxicity is, however, not fully understood yet, which hampers the implementation of treatment optimization by obscuring the interpretation of clinical response data and the selection of optimal treatment options. Although some dosimetry methods have been developed for kidney dosimetry to the level of microscopic renal substructures, the clinical assessment of the microscopic distribution of radiopharmaceuticals in kidney tissues currently remains a challenge. This restricts the anatomical resolution of clinical dosimetry, which hinders a thorough clinical investigation of the impact of absorbed dose heterogeneity. The potential of absorbed dose-response modelling to support individual treatment optimization in radiopharmaceutical therapy is recognized and gaining attraction. However, biophysical modelling is currently underexplored for the kidney, where particular modelling challenges arise from the convolution of a complex functional organization of renal tissues with the function-mediated dose distribution of radiopharmaceuticals. This article reviews and discusses the heterogeneity of absorbed dose distribution in kidney tissues and the absorbed dose-response modelling of nephrotoxicity in radiopharmaceutical therapy. The review focuses mainly on the peptide receptor radionuclide therapy with beta-particle emitting somatostatin analogues, for which the scientific literature reflects over two decades of clinical experience. Additionally, detailed research perspectives are proposed to address various identified challenges to progress in this field.

Population-based model selection for an accurate estimation of time-integrated activity using non-linear mixed-effects modelling

PURPOSE

Personalized treatment planning in Molecular Radiotherapy (MRT) with accurately determining the absorbed dose is highly desirable. The absorbed dose is calculated based on the Time-Integrated Activity (TIA) and the dose conversion factor. A crucial unresolved issue in MRT dosimetry is which fit function to use for the TIA calculation. A data-driven population-based fitting function selection could help solve this problem. Therefore, this project aims to develop and evaluate a method for accurately determining TIAs in MRT, which performs a Population-Based Model Selection within the framework of the Non-Linear Mixed-Effects (NLME-PBMS) model.

METHODS

Biokinetic data of a radioligand for the Prostate-Specific Membrane Antigen (PSMA) for cancer treatment were used. Eleven fit functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions' fixed and random effects parameters were fitted (in the NLME framework) to the biokinetic data of all patients. The goodness of fit was assumed acceptable based on the visual inspection of the fitted curves and the coefficients of variation of the fitted fixed effects. The Akaike weight, the probability that the model is the best among the whole set of considered models, was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. NLME-PBMS Model Averaging (MA) was performed with all functions having acceptable goodness of fit. The Root-Mean-Square Error (RMSE) of the calculated TIAs from individual-based model selection (IBMS), a shared-parameter population-based model selection (SP-PBMS) reported in the literature, and the functions from NLME-PBMS method to the TIAs from MA were calculated and analysed. The NLME-PBMS (MA) model was used as the reference as this model considers all relevant functions with corresponding Akaike weights.

RESULTS

The function [Formula: see text] was selected as the function most supported by the data with an Akaike weight of (54 ± 11) %. Visual inspection of the fitted graphs and the RMSE values show that the NLME model selection method has a relatively better or equivalent performance than the IBMS or SP-PBMS methods. The RMSEs of the IBMS, SP-PBMS, and NLME-PBMS (f3a) methods are 7.4%, 8.8%, and 2.4%, respectively.

CONCLUSION

A procedure including fitting function selection in a population-based 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 combines standard practice approaches in pharmacokinetics, i.e. an Akaike-weight-based model selection and the NLME model framework.

Single-time-point dosimetry using model selection and nonlinear mixed-effects modelling: a proof of concept

PURPOSE

This project aims to develop and evaluate a method for accurately determining time-integrated activities (TIAs) in single-time-point (STP) dosimetry for molecular radiotherapy. It performs a model selection (MS) within the framework of the nonlinear mixed-effects (NLME) model (MS-NLME).

METHODS

Biokinetic data of [¹¹¹In]In-DOTATATE activity in kidneys at T1 = (2.9 ± 0.6) h, T2 = (4.6 ± 0.4) h, T3 = (22.8 ± 1.6) h, T4 = (46.7 ± 1.7) h, and T5 = (70.9 ± 1.0) h post injection were obtained from eight patients using planar imaging. Eleven functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions' fixed and random effects parameters were fitted simultaneously (in the NLME framework) to the biokinetic data of all patients. The Akaike weights were used to select the fit function most supported by the data. The relative deviations (RD) and the root-mean-square error (RMSE) of the calculated TIAs for the STP dosimetry at T3 = (22.8 ± 1.6) h and T4 = (46.7 ± 1.7) h p.i. were determined for all functions passing the goodness-of-fit test.

RESULTS

The function [Formula: see text] with four adjustable parameters and [Formula: see text] was selected as the function most supported by the data with an Akaike weight of (45 ± 6) %. RD and RMSE values show that the MS-NLME method performs better than functions with three or five adjustable parameters. The RMSEs of TIA_NLME-PBMS and TIA_3-parameters were 7.8% and 10.9% (for STP at T3), and 4.9% and 10.7% (for STP at T4), respectively.

CONCLUSION

An MS-NLME method was developed to determine the best fit function for calculating TIAs in STP dosimetry for a given radiopharmaceutical, organ, and patient population. The proof of concept was demonstrated for biokinetic ¹¹¹In-DOTATATE data, showing that four-parameter functions perform better than three- and five-parameter functions.

Investigation of image-based lesion and kidney dosimetry protocols for 177Lu-PSMA-I&T therapy with and without a late SPECT/CT acquisition

BACKGROUND

¹⁷⁷Lu-PSMA therapy has been successfully used to prolong the survival of patients with metastatic castration-resistant prostate cancer. Patient-specific dosimetry based on serial quantitative SPECT/CT imaging can support the understanding of dose-effect relationships. However, multiple SPECT/CT measurements can be challenging for patients, which motivates the investigation of efficient sampling schedules and their impact on dosimetry. In this study, different time samplings with respect to the number and timing of SPECT/CT acquisitions with and without a late measurement were investigated.

MATERIALS AND METHODS

In total, 43 lesions and 10 kidneys of 5 patients receiving ¹⁷⁷Lu-PSMA-I&T therapy were investigated. Whole-body SPECT/CT measurements were performed at 1, 2, 3 and 7 days post-injection. For both lesions (isocontour-based segmentation) and kidneys (CT-based segmentation), a reference model was employed including all four time points. To identify the best-matching fit function out of a pre-defined set of models, visual inspection, coefficients of variation and sum of squared errors were considered as goodness-of-fit criteria. Biologically effective doses (BEDs) calculated with different time samplings (days 1, 2, 3/1, 2, 7/1, 3, 7/2, 3, 7 and 1, 2/1, 3/1, 7) were compared to the reference.

RESULTS

The best-fit function was found to be a mono-exponential model for lesions and a bi-exponential model with a population-based parameter and two free parameters for kidneys. The BEDs calculated with the time sampling 1, 3, 7 days showed the lowest deviations from the reference for lesions with 4 ± 5%. Without day 7, still 86% of all lesions showed deviations from the reference < 10%. The outlier deviations showed a positive correlation with the effective half-life of the respective lesions. For kidneys, including days 1, 2, 3 achieved the best results with 0 ± 1%. Generally, deviations for kidneys were found to be small for all time samplings (max. 13%).

CONCLUSIONS

For combined optimization of the SPECT/CT time sampling for kidney and lesion dosimetry during ¹⁷⁷Lu-PSMA-I&T therapy, the sampling with days 1, 3, 7 showed the smallest deviation from the reference. Without a late acquisition, using the schedule with days 1, 2, 3 is likewise feasible.

Single-time-point estimation of absorbed doses in PRRT using a non-linear mixed-effects model

INTRODUCTION

Estimation of accurate time-integrated activity coefficients (TIACs) and radiation absorbed doses (ADs) is desirable for treatment planning in peptide-receptor radionuclide therapy (PRRT). This study aimed to investigate the accuracy of a simplified dosimetry using a physiologically-based pharmacokinetic (PBPK) model, a nonlinear mixed effect (NLME) model, and single-time-point imaging to calculate the TIACs and ADs of ⁹⁰Y-DOTATATE in various organs of dosimetric interest and tumors.

MATERIALS & METHODS

Biokinetic data of ¹¹¹In-DOTATATE in tumors, kidneys, liver, spleen, and whole body were obtained from eight patients using planar scintigraphic imaging at T1 = (2.9 ± 0.6), T2 = (4.6 ± 0.4), T3 = (22.8 ± 1.6), T4 = (46.7 ± 1.7) and T5 = (70.9 ± 1.0) h post injection. Serum activity concentration was measured at 5 and 15 min; 0.5, 1, 2, and 4 h; and 1, 2, and 3 d p.i.. A published PBPK model for PRRT, NLME, and a single-time-point imaging datum at different time points were used to calculate TIACs in tumors, kidneys, liver, spleen, whole body, and serum. Relative deviations (RDs) (median [min, max]) between the calculated TIACs from single-time-point imaging were compared to the TIACs calculated from the all-time-points fit. The root mean square error (RMSE) of the difference between the computed ADs from the single-time-point imaging and reference ADs from the all-time point fittings were analyzed. A joint root mean square error RMSE_joint of the ADs was calculated with the RSME from both the tumor and kidneys to sort the time points concerning accurate results for the kidneys and tumor dosimetry. The calculations of TIACs and ADs from the single-time-point dosimetry were repeated using the sum of exponentials (SOE) approach introduced in the literature. The RDs and the RSME of the PBPK approach in our study were compared to the SOE approach.

RESULTS

Using the PBPK and NLME models and the biokinetic measurements resulted in a good fit based on visual inspection of the fitted curves and the coefficient of variation CV of the fitted parameters (<50%). T4 was identified being the time point with a relatively low median and range of TIACs RDs, i.e., 5 [1, 21]% and 2 [-15, 21]% for kidneys and tumors, respectively. T4 was found to be the time point with the lowest joint root mean square error RMSE_joint of the ADs. Based on the RD and RMSE, our results show a similar performance as the SOE and NLME model approach.

SUMMARY

In this study, we introduced a simplified calculation of TIACs/ADs using a PBPK model, an NLME model, and a single-time-point measurement. Our results suggest a single measurement might be used to calculate TIACs/ADs in the kidneys and tumors during PRRT.