Dependence of treatment planning accuracy in peptide receptor radionuclide therapy on the sampling schedule

A review of 177Lu dosimetry workflows: how to reduce the imaging workloads?

177 Lu radiopharmaceutical therapy is a standardized systemic treatment, with a typical dose of 7.4 GBq per injection, but its response varies from patient to patient. Dosimetry provides the opportunity to personalize treatment, but it requires multiple post-injection images to monitor the radiopharmaceutical's biodistribution over time. This imposes an additional imaging burden on centers with limited resources. This review explores methods to lessen this burden by optimizing acquisition types and minimizing the number and duration of imaging sessions. After summarizing the different steps of dosimetry and providing examples of dosimetric workflows for177 Lu -DOTATATE and177 Lu -PSMA, we examine dosimetric workflows based on a reduced number of acquisitions, or even just one. We provide a non-exhaustive description of simplified methods and their assumptions, as well as their limitations. Next, we detail the specificities of each normal tissue and tumors, before reviewing dose-response relationships in the literature. In conclusion, we will discuss the current limitations of dosimetric workflows and propose avenues for improvement.

Mathematical modeling of the synergistic interplay of radiotherapy and immunotherapy in anti-cancer treatments

Introduction

While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors.

Methods

We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions.

Results

Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions.

Discussion

Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to 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.

EANM guidance document: dosimetry for first-in-human studies and early phase clinical trials

The numbers of diagnostic and therapeutic nuclear medicine agents under investigation are rapidly increasing. Both novel emitters and novel carrier molecules require careful selection of measurement procedures. This document provides guidance relevant to dosimetry for first-in human and early phase clinical trials of such novel agents. The guideline includes a short introduction to different emitters and carrier molecules, followed by recommendations on the methods for activity measurement, pharmacokinetic analyses, as well as absorbed dose calculations and uncertainty analyses. The optimal use of preclinical information and studies involving diagnostic analogues is discussed. Good practice reporting is emphasised, and relevant dosimetry parameters and method descriptions to be included are listed. Three examples of first-in-human dosimetry studies, both for diagnostic tracers and radionuclide therapies, are given.

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.

Physiologically based radiopharmacokinetic (PBRPK) modeling to simulate and analyze radiopharmaceutical therapies: studies of non-linearities, multi-bolus injections, and albumin binding

BACKGROUND

We aimed to develop a publicly shared computational physiologically based pharmacokinetic (PBPK) model to reliably simulate and analyze radiopharmaceutical therapies (RPTs), including probing of hot-cold ligand competitions as well as alternative injection scenarios and drug designs, towards optimal therapies.

RESULTS

To handle the complexity of PBPK models (over 150 differential equations), a scalable modeling notation called the "reaction graph" is introduced, enabling easy inclusion of various interactions. We refer to this as physiologically based radiopharmacokinetic (PBRPK) modeling, fine-tuned specifically for radiopharmaceuticals. As three important applications, we used our PBRPK model to (1) study the effect of competition between hot and cold species on delivered doses to tumors and organs at risk. In addition, (2) we evaluated an alternative paradigm of utilizing multi-bolus injections in RPTs instead of prevalent single injections. Finally, (3) we used PBRPK modeling to study the impact of varying albumin-binding affinities by ligands, and the implications for RPTs. We found that competition between labeled and unlabeled ligands can lead to non-linear relations between injected activity and the delivered dose to a particular organ, in the sense that doubling the injected activity does not necessarily result in a doubled dose delivered to a particular organ (a false intuition from external beam radiotherapy). In addition, we observed that fractionating injections can lead to a higher payload of dose delivery to organs, though not a differential dose delivery to the tumor. By contrast, we found out that increased albumin-binding affinities of the injected ligands can lead to such a differential effect in delivering more doses to tumors, and this can be attributed to several factors that PBRPK modeling allows us to probe.

CONCLUSIONS

Advanced computational PBRPK modeling enables simulation and analysis of a variety of intervention and drug design scenarios, towards more optimal delivery of RPTs.

Lu-177-PSMA dosimetry for kidneys and tumors based on SPECT images at two imaging time points

Background

Personalized dosimetry for Lu-177-PSMA treatment requires multiple-time-point SPECT/CT scans to calculate time-integrated activity (TIA). This study evaluates two-time-point (TTP) methods for TIA calculation for kidneys and tumors.

Methods

A total of 18 patients treated with 3.7-7.4 GBq Lu-177 PSMA-617 were analyzed retrospectively, including 18 sets of left and right kidneys, as well as 45 tumors. Four quantitative SPECT/CT (4TP) were acquired at 2 h, 20 h, 40 h, 60 h (n = 11), or 200 h (n = 7) after treatment, and they were fit bi-exponentially as reference. The TTP method was fitted by a mono-exponential washout function using two selected imaging time points for kidneys. For tumors, one uptake and one washout phase were modeled, assuming linear (type I) and same (type II) uptake phase between 0 h to the first time point and mono-exponential washout thereafter. Two single-time-point (STP) methods were also implemented for comparison. TIA calculated by TTP and STP methods were compared with reference to the 4TP TIA.

Results

For the kidneys, the TTP methods using 20 h-60 h and 40 h-200 h had smaller mean absolute errors of 8.05 ± 6.05% and 4.95 ± 3.98%, respectively, as compared to other combinations of time points and STP methods. For tumors, the type I and type II TTP methods using 20h-60 h and 40-200 h had smaller mean absolute errors of 6.14 ± 5.19% and 12.22 ± 4.44%, and 8.31 ± 7.16% and 4.48 ± 7.10%, respectively, as compared to other TTP and STP methods.

Conclusion

The TTP methods based on later imaging time demonstrated fewer errors than the STP methods in kidney and tumor TIA. Imaging at 20 h-60 h and 40 h-200 h could simplify the dosimetry procedures with fewer TIA estimation errors.

Accuracy and uncertainty analysis of reduced time point imaging effect on time-integrated activity for 177Lu-DOTATATE PRRT in patients and clinically realistic simulations

BACKGROUND

Dosimetry promises many advantages for radiopharmaceutical therapies but repeat post-therapy imaging for dosimetry can burden both patients and clinics. Recent applications of reduced time point imaging for time-integrated activity (TIA) determination for internal dosimetry following ¹⁷⁷Lu-DOTATATE peptide receptor radionuclide therapy have shown promising results that allow for the simplification of patient-specific dosimetry. However, factors such as scheduling can lead to sub-optimal imaging time points, but the resulting impact on dosimetry accuracy is still under investigation. We use four-time point ¹⁷⁷Lu SPECT/CT data for a cohort of patients treated at our clinic to perform a comprehensive analysis of the error and variability in time-integrated activity when reduced time point methods with various combinations of sampling points are employed.

METHODS

The study includes 28 patients with gastroenteropancreatic neuroendocrine tumors who underwent post-therapy SPECT/CT imaging at approximately 4, 24, 96, and 168 h post-therapy (p.t.) following the first cycle of ¹⁷⁷Lu-DOTATATE. The healthy liver, left/right kidney, spleen and up to 5 index tumors were delineated for each patient. Time-activity curves were fit with either monoexponential or biexponential functions for each structure, based on the Akaike information criterion. This fitting was performed using all 4 time points as a reference and various combinations of 2 and 3 time points to determine optimal imaging schedules and associated errors. 2 commonly used methods of single time point (STP) TIA estimation are also evaluated. A simulation study was also performed with data generated by sampling curve fit parameters from log-normal distributions derived from the clinical data and adding realistic measurement noise to sampled activities. For both clinical and simulation studies, error and variability in TIA estimates were estimated with various sampling schedules.

RESULTS

The optimal post-therapy imaging time period for STP estimates of TIA was found to be 3-5 days (71-126 h) p.t. for tumor and organs, with one exception of 6-8 days (144-194 h) p.t. for spleen with one STP approach. At the optimal time point, STP estimates give mean percent errors (MPE) within ± 5% and SD < 9% across all structures with largest magnitude error for kidney TIA (MPE = - 4.1%) and highest variability also for kidney TIA (SD = 8.4%). The optimal sampling schedule for 2TP estimates of TIA is 1-2 days (21-52 h) p.t. followed by 3-5 days (71-126 h) p.t. for kidney, tumor, and spleen. Using the optimal sampling schedule, the largest magnitude MPE for 2TP estimates is 1.2% for spleen and highest variability is in tumor with SD = 5.8%. The optimal sampling schedule for 3TP estimates of TIA is 1-2 days (21-52 h) p.t. followed by 3-5 days (71-126 h) p.t. and 6-8 days (144-194 h) p.t. for all structures. Using the optimal sampling schedule, the largest magnitude MPE for 3TP estimates is 2.5% for spleen and highest variability is in tumor with SD = 2.1%. Simulated patient results corroborate these findings with similar optimal sampling schedules and errors. Many sub-optimal reduced time point sampling schedules also exhibit low error and variability.

CONCLUSIONS

We show that reduced time point methods can be used to achieve acceptable average TIA errors over a wide range of imaging time points and sampling schedules while maintaining low uncertainty. This information can improve the feasibility of dosimetry for ¹⁷⁷Lu-DOTATATE and elucidate the uncertainty associated with non-ideal conditions.

Theranostic Surrogacy of [123I]NaI for Differentiated Thyroid Cancer Radionuclide Therapy

Precise dosimetry has gained interest for interpreting the response assessments of novel therapeutic radiopharmaceuticals, as well as for improving conventional radiotherapies such as the "one dose fits all" approach. Although radioiodine as same-element isotope theranostic pairs has been used for differentiated thyroid cancer (DTC), there are insufficient studies on the determination of its dosing regimen for personalized medicine and on extrapolating strategies for companion diagnostic radiopharmaceuticals. In this study, DTC xenograft mouse models were generated after validating iodine uptakes via sodium iodine symporter proteins (NIS) through in vitro assays, and theranostic surrogacy of companion radiopharmaceuticals was investigated in terms of single photon emission computed tomography (SPECT) imaging and voxel-level dosimetry. Following a Monte Carlo simulation, the hypothetical energy deposition/dose distribution images were produced as [¹²³I]NaI SPECT scans with the use of ¹³¹I ion source simulation, and dose rate curves were used to estimate absorbed dose. For the tumor, a peak concentration of 96.49 ± 11.66% ID/g occurred 2.91 ± 0.42 h after [¹²³I]NaI injection, and absorbed dose for ¹³¹I therapy was estimated as 0.0344 ± 0.0088 Gy/MBq. The absorbed dose in target/off-target tissues was estimated by considering subject-specific heterogeneous tissue compositions and activity distributions. Furthermore, a novel approach was proposed for simplifying voxel-level dosimetry and suggested for determining the minimal/optimal scan time points of surrogates for pretherapeutic dosimetry. When two scan time points were set to T_max and 26 h and the group mean half-lives were applied to the dose rate curves, the most accurate absorbed dose estimates were determined [-22.96, 2.21%]. This study provided an experimental basis to evaluate dose distribution and is expected hopefully to improve the challenging dosimetry process for clinical use.

Accuracy and uncertainty analysis of reduced time point imaging effect on time-integrated activity for 177Lu-DOTATATE PRRT in clinical patients and realistic simulations

Background. Dosimetry promises many advantages for radiopharmaceutical therapies but repeat post-therapy imaging for dosimetry can burden both patients and clinics. Recent applications of reduced time point imaging for time-integrated activity (TIA) determination for internal dosimetry following ¹⁷⁷ Lu-DOTATATE peptide receptor radionuclide therapy have shown promising results that allow for the simplification of patient-specific dosimetry. However, factors such as scheduling can lead to undesirable imaging time points, but the resulting impact on dosimetry accuracy is unknown. We use four-time point ¹⁷⁷ Lu SPECT/CT data for a cohort of patients treated at our clinic to perform a comprehensive analysis of the error and variability in time-integrated activity when reduced time point methods with various combination of sampling points are employed. Methods. The study includes 28 patients with gastroenteropancreatic neuroendocrine tumors who underwent post-therapy SPECT/CT imaging at approximately 4, 24, 96, and 168 hours post-therapy (p.t.) following the first cycle of ¹⁷⁷ Lu-DOTATATE. The healthy liver, left/right kidney, spleen and up to 5 index tumors were delineated for each patient. Time-activity curves were fit with either monoexponential or biexponential functions for each structure, based on the Akaike information criterion. This fitting was performed using all 4 time points as a reference and various combinations of 2 and 3 time points to determine optimal imaging schedules and associated errors. 2 commonly used methods of single time point (STP) TIA estimation are also evaluated. A simulation study was also performed with data generated by sampling curve fit parameters from log-normal distributions derived from the clinical data and adding realistic measurement noise to sampled activities. For both clinical and simulation studies, error and variability in TIA estimates were estimated with various sampling schedules. Results . The optimal post-therapy imaging time period for STP estimates of TIA was found to be 3-5 days (71-126 h) p.t. for tumor and organs, with one exception of 6-8 days (144-194 h) p.t. for spleen with one STP approach. At the optimal time point, STP estimates give mean percent errors (MPE) within +/-5% and SD < 9% across all structures with largest magnitude error for kidney TIA (MPE=-4.1%) and highest variability also for kidney TIA (SD=8.4%). The optimal sampling schedule for 2TP estimates of TIA is 1-2 days (21-52 h) p.t. followed by 3-5 days (71-126 h) p.t. for kidney, tumor, and spleen. Using the optimal sampling schedule, the largest magnitude MPE for 2TP estimates is 1.2% for spleen and highest variability is in tumor with SD=5.8%. The optimal sampling schedule for 3TP estimates of TIA is 1-2 days (21-52 h) p.t. followed by 3-5 days (71-126 h) p.t. and 6-8 days (144-194 h) p.t. for all structures. Using the optimal sampling schedule, the largest magnitude MPE for 3TP estimates is 2.5% for spleen and highest variability is in tumor with SD=2.1%. Simulated patient results corroborate these findings with similar optimal sampling schedules and errors. Many sub-optimal reduced time point sampling schedules also exhibit low error and variability. Conclusions. We show that reduced time point methods can be used to achieve acceptable average TIA errors over a wide range of imaging time points and sampling schedules while maintaining low uncertainty. This information can improve the feasibility of dosimetry for ¹⁷⁷ Lu-DOTATATE and elucidate the uncertainty associated with non-ideal conditions.

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.

A physiologically based pharmacokinetic model for [68Ga]Ga-(HA-)DOTATATE to predict whole-body distribution and tumor sink effects in GEP-NET patients

BACKGROUND

Little is known about parameters that have a relevant impact on (dis)similarities in biodistribution between various ⁶⁸Ga-labeled somatostatin analogues. Additionally, the effect of tumor burden on organ uptake remains unclear. Therefore, the aim of this study was to describe and compare organ and tumor distribution of [⁶⁸Ga]Ga-DOTATATE and [⁶⁸Ga]Ga-HA-DOTATATE using a physiologically based pharmacokinetic (PBPK) model and to identify factors that might cause biodistribution and tumor uptake differences between both peptides. In addition, the effect of tumor burden on peptide biodistribution in gastroenteropancreatic (GEP) neuroendocrine tumor (NET) patients was assessed.

METHODS

A PBPK model was developed for [⁶⁸Ga]Ga-(HA-)DOTATATE in GEP-NET patients. Three tumor compartments were added, representing primary tumor, liver metastases and other metastases. Furthermore, reactions describing receptor binding, internalization and recycling, renal clearance and intracellular degradation were added to the model. Scan data from GEP-NET patients were used for evaluation of model predictions. Simulations with increasing tumor volumes were performed to assess the tumor sink effect.

RESULTS

Data of 39 and 59 patients receiving [⁶⁸Ga]Ga-DOTATATE and [⁶⁸Ga]Ga-HA-DOTATATE, respectively, were included. Evaluations showed that the model adequately described image-based patient data and that different receptor affinities caused organ uptake dissimilarities between both peptides. Sensitivity analysis indicated that tumor blood flow and blood volume impacted tumor distribution most. Tumor sink predictions showed a decrease in spleen uptake with increasing tumor volume, which seemed clinically relevant for patients with total tumor volumes higher than ~ 550 mL.

CONCLUSION

The developed PBPK model adequately predicted tumor and organ uptake for this GEP-NET population. Relevant organ uptake differences between [⁶⁸Ga]Ga-DOTATATE and [⁶⁸Ga]Ga-HA-DOTATATE were caused by different affinity profiles, while tumor uptake was mainly affected by tumor blood flow and blood volume. Furthermore, tumor sink predictions showed that for the majority of patients a tumor sink effect is not expected to be clinically relevant.

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.

Current use and future potential of (physiologically based) pharmacokinetic modelling of radiopharmaceuticals: a review

Rationale: Physiologically based pharmacokinetic (PBPK) and population pharmacokinetic (PK) modelling approaches are widely accepted in non-radiopharmaceutical drug development and research, while there is no major role for these approaches in radiopharmaceutical development yet. In this review, a literature search was performed to specify different research purposes and questions that have previously been answered using both PBPK and population PK modelling for radiopharmaceuticals. Methods: The literature search was performed using the databases PubMed and Embase. Wide search terms included radiopharmaceutical, tracer, radioactivity, physiologically based pharmacokinetic model, PBPK, population pharmacokinetic model and nonlinear mixed-effects model. Results: Eight articles and twenty articles were included for this review based on this literature search for population PK modelling and PBPK modelling, respectively. Included population PK analyses showed to have an added value to develop predictive models for a population and to describe individual variability sources. Main purposes of PBPK models appeared related to optimizing treatment (planning), or more specifically: to find the optimal combination of peptide amount and radioactivity, to optimize treatment planning by reducing the number of measurements, to individualize treatment, to get insights in differences between pre-therapeutic and therapeutic scans or to understand inter-patient differences. Other main research subjects were regarding radiopharmaceutical comparisons, selecting ligands based on their peptide characteristics and gaining a better understanding of drug-drug interactions. Conclusions: The use of PK modelling approaches in radiopharmaceutical research remains scarce, but can be expanded to obtain a better understanding of PK and whole-body distribution of radiopharmaceuticals in general. PK modelling of radiopharmaceuticals has great potential for the nearby future and could contribute to the evolving research of radiopharmaceuticals.

Simplified dosimetry for kidneys and tumors in 177Lu-labeled peptide receptor radionuclide therapy

Purpose

To evaluate if satisfactory post-therapeutic image-based dosimetry can be achieved for Lu-177-DOTATATE treatments using a reduced number of image acquisitions to improve patient comfort and reduce economical costs.

Methods

39 patients who underwent 147 treatment cycles of Lu-177-DOTATATE for neuroendocrine tumors were included in the study. A total of 291 and 284 absorbed doses were calculated to kidneys and tumors, respectively. Single-point dosimetry was performed using one SPECT/CT image acquired at 1 d or 7 d post-treatment using a fixed effective half-life (T_eff) or using a patient-specific T_eff determined for the initial cycle. Also, dose-per-activity values, (D/A)₁, were determined from the first cycle and used to calculate doses for subsequent cycles. All absorbed doses were evaluated against “true” doses calculated using both the 1 d and 7 d images. The relation between tumor grade and absorbed doses was also investigated. All dosimetry was performed on SPECT images.

Results

Absorbed doses to kidneys were most accurate when single-point dosimetry was performed using 1 d images with median ratios in relation to “true” doses in total dose of 1.00 (IQR: 0.97–1.03) when using fixed T_eff and 1.01 (IQR: 0.98–1.04) when using T_eff from the initial cycle. Calculations based on the 7 d image were most accurate for tumors with corresponding ratios in total absorbed dose of 0.98 (IQR: 0.96–1.00) and 1.00 (IQR: 0.99–1.01) when using a fixed T_eff or T_eff from the first cycle, respectively. The (D/A)₁ approach performed worse, as 2 of 77 total absorbed doses to the kidneys deviated with > 30%, and tumor-absorbed doses were increasingly overestimated with every cycle. Absorbed doses, T_eff and 1 d uptake were higher for G1 tumors than G2 tumors.

Conclusion

Dosimetry can be performed with satisfactory accuracy when using single SPECT/CT images acquired at 1 d for kidneys or at 7 d for tumors.

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

BACKGROUND

The calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [¹⁷⁷Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient.

METHODS

Renal biokinetics of [¹⁷⁷Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit.

RESULTS

The function [Formula: see text] with shared parameter [Formula: see text] was selected as the function most supported by the data with an Akaike weight of 97%. Parameters [Formula: see text] and [Formula: see text] were fitted individually for every patient while parameter [Formula: see text] was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037.

CONCLUSIONS

The presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.

A physiologically based pharmacokinetic (PBPK) model to describe organ distribution of 68Ga-DOTATATE in patients without neuroendocrine tumors

Background

Physiologically based pharmacokinetic (PBPK) models combine drug-specific information with prior knowledge on the physiology and biology at the organism level. Whole-body PBPK models contain an explicit representation of the organs and tissue and are a tool to predict pharmacokinetic behavior of drugs. The aim of this study was to develop a PBPK model to describe organ distribution of ⁶⁸Ga-DOTATATE in a population of patients without detectable neuroendocrine tumors (NETs).

Methods

Clinical ⁶⁸Ga-DOTATATE PET/CT data from 41 patients without any detectable somatostatin receptor (SSTR) overexpressing tumors were included. Scans were performed at 45 min (range 30–60 min) after intravenous bolus injection of ⁶⁸Ga-DOTATATE. Organ (spleen, liver, thyroid) and blood activity levels were derived from PET scans, and corresponding DOTATATE concentrations were calculated. A whole-body PBPK model was developed, including an internalization reaction, receptor recycling, enzymatic reaction for intracellular degradation and renal clearance. SSTR2 expression was added for several organs. Input parameters were fixed or estimated using a built-in Monte Carlo algorithm for parameter identification.

Results

⁶⁸Ga-DOTATATE was administered with a median peptide amount of 12.3 µg (range 8.05–16.9 µg) labeled with 92.7 MBq (range 43.4–129.9 MBq). SSTR2 amounts for spleen, liver and thyroid were estimated at 4.40, 7.80 and 0.0108 nmol, respectively. Variability in observed organ concentrations was best described by variability in SSTR2 expression and differences in administered peptide amounts.

Conclusions

To conclude, biodistribution of ⁶⁸Ga-DOTATATE was described with a whole-body PBPK model, where tissue distribution was mainly determined by variability in SSTR2 organ expression and differences in administered peptide amounts.

Monte Carlo simulation of the acquisition conditions for 177Lu molecular imaging of hepatic tumors

OBJECTIVE

To examine the impact of acquisition time on Lutetium-177 (177Lu) single-photon emission computed tomography (SPECT) images using Monte Carlo simulation.

METHODS

A gamma camera simulation based on the Monte Carlo method was performed to produce SPECT images. The phantom was modeled on a NEMA IEC BODY phantom including six spheres as tumors. After the administration of 7.4 GBq of 177Lu, radioactivity concentrations of the tumor/liver at 6, 24, and 72 h after administration were set to 1.85/0.201, 2.12/0.156, and 1.95/0.117 MBq/mL, respectively. In addition, the radioactivity concentrations of the tumor at 72 h after administration varied by 1/2, 1/4, and 1/8 when comparison was made. Acquisition times examined were 1.2, 1.5, 2, 3, 6, and 12 min. To assess the impact of collimators, SPECT data acquired at 72 h after the administration using six collimators of low-energy high-resolution (LEHR), extended low-energy general-purpose (ELEGP), medium-energy, and general-purpose (MEGP-1, MEGP-2, and MEGP-3) and high-energy general-purpose (HEGP) were examined. After prefiltering using a Butterworth filter, projection images were reconstructed using ordered subset expectation maximization. The detected photons were classified into direct rays, scattered rays, penetrating rays, and characteristic X-rays from lead. The image quality was evaluated through visual assessment, and physical assessment of contrast recovery coefficient (CRC) and contrast-to-noise ratio (CNR). In this study, the CNR threshold for detectability was assumed to be 5.0.

RESULTS

To compare collimators, the highest sensitivity was observed with ELEGP, followed by LEHR and MEGP-1. The highest ratio of direct ray was also observed in ELEGP followed by MEGP-1. In comparison of the radioactivity concentration ratios of tumor/liver, CRC and CNR were significantly decreased with smaller radioactivity concentration ratios. This effect was greater with larger spheres. According to the visual assessment, the acquisition time of 6, 6, and 3 min or longer was required using ELEGP collimator at 6, 24, and 72 h after administration, respectively. Physical assessment based on CNR and CRC also suggested that 6, 6, and 3 min or longer acquisition time was necessary at 6, 24, and 72 h after administration.

CONCLUSION

177Lu-SPECT images generated via the Monte Carlo simulation suggested that the recommended acquisition time was 6 min or longer at 6 and 24 h and 3 min or longer at 72 h after administration.

Important pharmacokinetic parameters for individualization of 177 Lu-PSMA therapy: A global sensitivity analysis for a physiologically-based pharmacokinetic model

PURPOSE

The knowledge of the contribution of anatomical and physiological parameters to interindividual pharmacokinetic differences could potentially be used to improve individualized treatment planning for radionuclide therapy. The aim of this study was therefore to identify the physiologically based pharmacokinetic (PBPK) model parameters that determine the interindividual variability of absorbed doses (ADs) to kidneys and tumor lesions in therapy with ¹⁷⁷ Lu-labeled PSMA-targeting radioligands.

METHODS

A global sensitivity analysis (GSA) with the extended Fourier Amplitude Sensitivity Test (eFAST) algorithm was performed. The whole-body PBPK model for PSMA-targeting radioligand therapy from our previous studies was used in this study. The model parameters of interest (input of the GSA) were the organ receptor densities [R₀ ], the organ blood flows f, and the organ release rates λ. These parameters were systematically sampled NE times according to their distribution in the patient population. The corresponding pharmacokinetics were simulated and the ADs (model output) to kidneys and tumor lesions were collected. The main effect S i and total effect S Ti were calculated using the eFAST algorithm based on the variability of the model output: The main effect S i of input parameter i represents the reduction in variance of the output if the "true" value of parameter i would be known. The total effect S Ti of an input parameter i represents the proportion of variance remaining if the "true" values of all other input parameters except for i are known. The numbers of samples NE were increased up to 8193 to check the stability (i.e., convergence) of the calculated main effects S i and total effects S Ti .

RESULTS

From the simulations, the relative interindividual variability of ADs in the kidneys (coefficient of variation CV = 31%) was lower than that of ADs in the tumors (CV up to 59%). Based on the GSA, the most important parameters that determine the ADs to the kidneys were kidneys flow ( S i  = 0.36, S Ti  = 0.43) and kidneys receptor density ( S i  = 0.25, S Ti  = 0.30). Tumor receptor density was identified as the most important parameter determining the ADs to tumors ( S i and S Ti up to 0.72).

CONCLUSIONS

The results suggest that an accurate measurement of receptor density and flow before therapy could be a promising approach for developing an individualized treatment with ¹⁷⁷ Lu-labeled PSMA-targeting radioligands.

Influence of sampling schedules on [177Lu]Lu-PSMA dosimetry

BACKGROUND

Individualized dosimetry is recommended for [¹⁷⁷Lu]Lu-PSMA radioligand therapy (RLT) which is resource-intensive and protocols are often not optimized. Therefore, a simulation study was performed focusing on the determination of efficient optimal sampling schedules (OSS) for renal and tumour dosimetry by investigating different numbers of time points (TPs).

METHODS

Sampling schedules with 1-4 TPs were investigated. Time-activity curves of the kidneys and two tumour lesions were generated based on a physiologically based pharmacokinetic (PBPK) model and biokinetic data of 13 patients who have undergone [¹⁷⁷Lu]Lu-PSMA I&T therapy. Systematic and stochastic noise of different ratios was considered when modelling time-activity data sets. Time-integrated activity coefficients (TIACs) were estimated by simulating the hybrid planar/SPECT method for schedules comprising at least two TPs. TIACs based on one single SPECT/CT measurement were estimated using an approximation for reducing the number of fitted parameters. For each sampling schedule, the root-mean-squared error (RMSE) of the deviations of the simulated TIACs from the ground truths for 1000 replications was used as a measure for accuracy and precision.

RESULTS

All determined OSS included a late measurement at 192 h p.i., which was necessary for accurate and precise tumour TIACs. OSS with three TPs were identified to be 3-4, 96-100 and 192 h with an additional SPECT/CT measurement at the penultimate TP. Kidney and tumour RMSE of 6.4 to 7.7% and 6.3 to 7.8% were obtained, respectively. Shortening the total time for dosimetry to e.g. 96 h resulted in kidney and tumour RMSE of 6.8 to 8.3% and 9.1 to 11%, respectively. OSS with four TPs showed similar results as with three TPs. Planar images at 4 and 68 h and a SPECT/CT shortly after the 68 h measurement led to kidney and tumour RMSE of 8.4 to 12% and 12 to 16%, respectively. One single SPECT/CT measurement at 52 h yielded good approximations for the kidney TIACs (RMSE of 7.0%), but led to biased tumour TIACs.

CONCLUSION

OSS allow improvements in accuracy and precision of renal and tumour dosimetry for [¹⁷⁷Lu]Lu-PSMA therapy with potentially less effort. A late TP is important regarding accurate tumour TIACs.

Technical Note: Optimal sampling schedules for kidney dosimetry based on the hybrid planar/SPECT method in 177 Lu-PSMA therapy

PURPOSE

Accurate and precise renal dosimetry during ¹⁷⁷ Lu-labeled prostate-specific membrane antigen (PSMA) radioligand therapy is crucial for therapy decisions. Sampling schedules for estimating the necessary time-integrated activity coefficients (TIACs) are not optimized and standardized for clinical practice. Therefore, a simulation study to determine optimal sampling schedules (OSSs) was performed on 13 virtual ¹⁷⁷ Lu-PSMA I&T therapy patients.

METHOD

A total of 880 clinically feasible sampling schedules for planar imaging (three time points) were investigated. To simulate the hybrid planar/SPECT method, an additional quantitative SPECT/CT measurement following one planar image was considered. For each sampling schedule and patient, the activity values were generated separately. Measurement noise was modeled by drawing random numbers of log-normal distributions. The used fractional standard deviations (FSD) differed depending on the imaging modality. For activity values assigned to planar imaging, systematic noise between 25% and 75% of the total noise was simulated. After fitting with a mono-exponential function, the root-mean-squared errors of the deviations of the simulated TIACs from the ground truth for 1000 replications were used to determine the OSS. The uncertainties of the TIACs and renal dose coefficients were estimated.

RESULTS

For the hybrid planar/SPECT method, OSSs were determined to be (3-4, 72-76, 124-144)  h post injection (p.i.) with the quantitative SPECT/CT scan shortly after the second measurement. The accuracy and precision of the determined TIACs were in the range of (-3.0 ±  6.2)% and (-1.0  ±  6.5)%. This precision was improved by a factor 2-3 compared to dosimetry based on planar images only. Similar results were obtained for the renal dose coefficients. The virtual patients' renal dose coefficients were (0.68  ± 0.24)  Gy/GBq indicating that a population-based method yields an uncertainty of 35%.

CONCLUSIONS

Dosimetry based on the hybrid planar/SPECT method with OSS outperforms dosimetry based on planar images. The high variability in dose coefficients between the virtual patients demonstrates the need for individualized dosimetry.

Translational Assessment of Drug-Induced Proximal Tubule Injury Using a Kidney Microphysiological System

Drug-induced kidney injury, a major cause of acute kidney injury, results in progressive kidney disease and is linked to increased mortality in hospitalized patients. Primary injury sites of drug-induced kidney injury are proximal tubules. Clinically, kidney injury molecule-1, an established tubule-specific biomarker, is monitored to assess the presence and progression of injury. The ability to accurately predict drug-related nephrotoxicity preclinically would reduce patient burden and drug attrition rates, yet state-of-the-art in vitro and animal models fail to do so. In this study, we demonstrate the use of kidney injury molecule-1 measurement in the kidney microphysiological system as a preclinical model for drug toxicity assessment. To show clinical relevance, we use quantitative systems pharmacology computational models for in vitro-in vivo translation of the experimental results and to identify favorable dosing regimens for one of the tested drugs.

A simulation-based method to determine optimal sampling schedules for dosimetry in radioligand therapy

AIM

For dosimetry in radioligand therapy, the time-integrated activity coefficients (TIACs) for organs at risk and for tumour lesions have to be determined. The used sampling scheme affects the TIACs and therefore the calculated absorbed doses. The aim of this work was to develop a general and flexible method, which analyses numerous clinically applicable sampling schedules using true time-activity curves (TACs) of virtual patients.

METHOD

Nine virtual patients with true TACs of the tumours were created using a physiologically-based pharmacokinetic (PBPK) model and individual biokinetic data of five patients with neuroendocrine tumours and four with meningioma. ¹¹¹In-DOTATATE was used for pre-therapeutic dosimetry. In total, 15,120 sampling schemes, each consisting of 4 time points, were investigated. Gaussian noise of different levels was added to the corresponding true time-activity points. A bi-exponential function was used to fit the simulated time-activity data. For each investigated sampling schedule, 1000 replications were performed. Patient-specific and population-specific optimal sampling schedules were determined using the relative root-mean-square error (rRMSE). Furthermore, the fractions of TIACs a˜ deviating >5% (f_Δa˜>5%) and >10% (f_Δa˜>10%) from the true TIAC a˜_true were used for additional evaluations e.g. to investigate the effect of varying single time points.

RESULTS

Almost all patient-specific and all population-specific optimal sampling schedules have t₄≥96h for all noise levels. Changing the latest time point from the population-specific optimal time to e.g. 48h leads to a median increase of f_Δa˜>10% from 0.1% to 88% for the lowest investigated noise level. Using the determined population-specific optimal schedules, results in more accurate and precise results than established schedules from the literature.

CONCLUSION

A method of determining the optimal sampling schedule for dosimetry, which considers clinical working hours and measurement uncertainties, has been developed and applied. The simulation study shows that optimised sampling schedules result in high accuracy and precision of the determined TIACs.

Dosimetry methods and clinical applications in peptide receptor radionuclide therapy for neuroendocrine tumours: a literature review

Background

The main challenge for systemic radiation therapy using radiopharmaceuticals (SRT) is to optimise the dose delivered to the tumour, while minimising normal tissue irradiation. Dosimetry could help to increase therapy response and decrease toxicity after SRT by individual treatment planning. Peptide receptor radionuclide therapy (PRRT) is an accepted SRT treatment option for irresectable and metastatic neuroendocrine tumours (NET). However, dosimetry in PRRT is not routinely performed, mainly due to the lack of evidence in literature and clinical implementation difficulties. The goal of this review is to provide insight in dosimetry methods and requirements and to present an overview of clinical aspects of dosimetry in PRRT for NET.

Methods

A PubMed query including the search criteria dosimetry, radiation dose, peptide receptor radionuclide therapy, and radionuclide therapy was performed. Articles were selected based on title and abstract, and description of dosimetric approach.

Results

A total of 288 original articles were included. The most important dosimetry methods, their main advantages and limitations, and implications in the clinical setting are discussed. An overview of dosimetry in clinical studies regarding PRRT treatment for NET is provided.

Conclusion

Clinical dosimetry in PRRT is feasible and can result in improved treatment outcomes. Current clinical dosimetry studies focus on safety and apply non-voxel-based dosimetry methods. Personalised treatment using sophisticated dosimetry methods to assess tumour and normal tissue uptake in clinical trials is the next step towards routine dosimetry in PRRT for NET.

Electronic supplementary material

The online version of this article (10.1186/s13550-018-0443-z) contains supplementary material, which is available to authorized users.

The Relevance of Dosimetry in Precision Medicine

The aim of this review is to provide an overview of the most recent technologic developments in state-of-the-art equipment and tools for dosimetry in radionuclide therapies. This includes, but is not restricted to, calibration methods for imaging systems. In addition, a summary of new developments that consider the influence of small-scale dosimetry and of biologic effects on radionuclide therapies is given. Finally, the current limitations of patient-specific dosimetry such as bone-marrow dosimetry or dosimetry of α-emitters are discussed.