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

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.

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.

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.

Evolution of Portable Sensors for In-Vivo Dose and Time-Activity Curve Monitoring as Tools for Personalized Dosimetry in Molecular Radiotherapy

Treatment personalization in Molecular Radiotherapy (MRT) relies on pre- and post-treatment SPECT/ PET-based images and measurements to obtain a patient-specific absorbed dose-rate distribution map and its evolution over time. Unfortunately, the number of time points that are available per patient to investigate individual pharmacokinetics is often reduced by limited patient compliance or SPECT or PET/CT scanner availability for dosimetry in busy departments. The adoption of portable sensors for in-vivo dose monitoring during the entire treatment could improve the assessment of individual biokinetics in MRT and, thus, the treatment personalization. The evolution of portable devices, non-SPECT/PET-based options, already used for monitoring radionuclide activity transit and accumulation during therapy with radionuclides (i.e., MRT or brachytherapy), is presented to identify valuable ones, which combined with conventional nuclear medicine imaging systems could be effective in MRT. External probes, integration dosimeters and active detecting systems were included in the study. The devices and their technology, the range of applications, the features and limitations are discussed. Our overview of the available technologies encourages research and development of portable devices and dedicated algorithms for MRT patient-specific biokinetics study. This would represent a crucial advancement towards personalized treatment in MRT.

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.

Is a single late SPECT/CT based kidney 177Lu-dosimetry superior to hybrid dosimetry with sequential multiple time-point whole-body planar scans in combination with an early SPECT/CT?

PURPOSE

The aim is to assess the impact of different imaging-protocols on image-based kidney dosimetry in ¹⁷⁷Lu labelled peptide receptor radiotherapies.

METHODS

Kidney data of five [¹⁷⁷Lu]Lu-OPS201 injected pigs and a 3D printed phantom were used for comparing the absorbed doses and time-integrated activity coefficients calculated based on the following imaging-protocols: A-) multiple time-point SPECT/CTs, B-) multiple time-point planar scans in combination with one SPECT/CT, C-) single time-point SPECT/CT. In addition, the influence of late scan time-points on kidney dosimetry was investigated by sequentially eliminating scan data at > 100 h from the pig/phantom datasets for imaging-protocols A and B.

RESULTS

Compared to imaging-protocol A, absorbed doses based on imaging-protocols B and C (scans at > 24 h post-injection) were always lower (differences > 34%). The best agreement in absorbed dose was achieved by imaging-protocol C at ∼ 100 h post-injection (difference: 4%). Regarding the phantom/pig experiments, eliminating scan data at > 100 h post-injection increased the time-integrated activity coefficients calculated based on imaging-protocols A and B by up to 83%.

CONCLUSION

While imaging-protocol A is accurate if scans at >∼100 h are included, it is time-consuming. In addition to being time-consuming, imaging-protocol B shows high differences associated with organ-count overlay, a lack of accuracy concerning the geometric mean based 2D attenuation correction, and 2D background subtraction due to the inhomogeneous and time-varying background contributions. Our findings indicate that dosimetry based on imaging-protocol C, if appropriately performed, provides similar kidney absorbed doses compared to imaging-protocol A, while only a single scan time-point is necessary.

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.