Investigating the Effect of Ligand Amount and Injected Therapeutic Activity: A Simulation Study for 177Lu-Labeled PSMA-Targeting Peptides

Mathematical Modeling Unveils Optimization Strategies for Targeted Radionuclide Therapy of Blood Cancers

Targeted radionuclide therapy is based on injections of cancer-specific molecules conjugated with radioactive nuclides. Despite the specificity of this treatment, it is not devoid of side-effects limiting its use and is especially harmful for rapidly proliferating organs well perfused by blood, like bone marrow. Optimization of radioconjugates administration accounting for toxicity constraints can increase treatment efficacy. Based on our experiments on disseminated multiple myeloma mouse model treated by 225Ac-DOTA-daratumumab, we developed a mathematical model which investigation highlighted the following principles for optimization of targeted radionuclide therapy. 1) Nuclide to antibody ratio importance. The density of radioconjugates on cancer cells determines the density of radiation energy deposited in them. Low labeling ratio as well as accumulation of unlabeled antibodies and antibodies attached to decay products in the bloodstream can mitigate cancer radiation damage due to excessive occupation of specific receptors by antibodies devoid of radioactive nuclides. 2) Cancer binding capacity-based dosing. The rate of binding of drug to cancer cells depends on the total number of their specific receptors, which therefore can be estimated from the pharmacokinetic curve of diagnostic radioconjugates. Injection of doses significantly exceeding cancer binding capacity should be avoided since radioconjugates remaining in the bloodstream have negligible efficacy to toxicity ratio. 3) Particle range-guided multi-dosing. The use of short-range particle emitters and high-affinity antibodies allows for robust treatment optimization via initial saturation of cancer binding capacity, enabling redistribution of further injected radioconjugates and deposited dose towards still viable cells that continue expressing specific receptors.

Radiopharmaceutical transport in solid tumors via a 3-dimensional image-based spatiotemporal model

Lutetium-177 prostate-specific membrane antigen (177Lu-PSMA)-targeted radiopharmaceutical therapy is a clinically approved treatment for patients with metastatic castration-resistant prostate cancer (mCRPC). Even though common practice reluctantly follows "one size fits all" approach, medical community believes there is significant room for deeper understanding and personalization of radiopharmaceutical therapies. To pursue this aim, we present a 3-dimensional spatiotemporal radiopharmaceutical delivery model based on clinical imaging data to simulate pharmacokinetic of 177Lu-PSMA within the prostate tumors. The model includes interstitial flow, radiopharmaceutical transport in tissues, receptor cycles, association/dissociation with ligands, synthesis of PSMA receptors, receptor recycling, internalization of radiopharmaceuticals, and degradation of receptors and drugs. The model was studied for a range of values for injection amount (100-1000 nmol), receptor density (10-500 nmol•l-1), and recycling rate of receptors (10-4 to 10-1 min-1). Furthermore, injection type, different convection-diffusion-reaction mechanisms, characteristic time scales, and length scales are discussed. The study found that increasing receptor density, ligand amount, and labeled ligands improved radiopharmaceutical uptake in the tumor. A high receptor recycling rate (0.1 min-1) increased radiopharmaceutical concentration by promoting repeated binding to tumor cell receptors. Continuous infusion results in higher radiopharmaceutical concentrations within tumors compared to bolus administration. These insights are crucial for advancing targeted therapy for prostate cancer by understanding the mechanism of radiopharmaceutical distribution in tumors. Furthermore, measures of characteristic length and advection time scale were computed. The presented spatiotemporal tumor transport model can analyze different physiological parameters affecting 177Lu-PSMA delivery.

Spatiotemporal modeling of radiopharmaceutical transport in solid tumors: Application to 177Lu-PSMA therapy of prostate cancer

BACKGROUND AND OBJECTIVE

177Lu-labeled prostate-specific membrane antigen (PSMA) radiopharmaceutical therapy (RPT) represents a pivotal advancement in addressing prostate cancer. However, existing therapies, while promising, remain incompletely understood and optimized. Computational models offer potential insights into RPTs, aiding in clinical drug delivery enhancement. In this study, we investigate the impact of various physiological parameters on the delivery of 177Lu-PSMA-617 RPT using the convection-diffusion-reaction (CDR) model.

METHODS

Our investigation encompasses tumor geometry and surrounding tissue, characterized by well-defined boundaries and initial conditions. Utilizing the finite element method, we solve governing equations across a range of parameters: dissociation constant KD (1, 0.1, 0.01 [nM]), internalization rate (0.01-0.0001 [min-1]), diverse tumor shapes, and variable necrotic zone sizes. This model can provide an accurate analysis of radiopharmaceutical delivery from the injection site to the tumor cell, including drug transport in the vascular, interstitial, and intracellular spaces, and considering important parameters (e.g., drug extravasation from microvessels or to lymphatic vessels, the extracellular matrix, receptors, and intracellular space).

RESULTS

Our findings reveal significant enhancements in tumor-absorbed doses as KD decreases. This outcome can be attributed to the higher affinity of radiopharmaceuticals for PSMA receptors as KD diminishes, facilitating a more efficient binding and retention of the therapeutic agent within the tumor microenvironment. Additionally, tumor-absorbed doses for KD ∼ 1 [nM] show an upward trend with higher internalization rates. This observation can be rationalized by considering that a greater internalization rate would result in a higher proportion of radiopharmaceuticals being taken up by tumor cells after binding to receptors on the cell surface. Notably, tumor shape and necrotic zone size exhibit limited influence on tumor absorbed dose.

CONCLUSIONS

The present study employs the CDR model to explore the role of physiological parameters in shaping 177Lu-PSMA-617 RPT delivery. These findings provide insights for improving prostate cancer therapy by understanding radiopharmaceutical transport dynamics. This computational approach contributes to advancing our understanding of radiopharmaceutical delivery mechanisms and has implications for enhancing treatment efficacy.

Localized radiotherapy of solid tumors using radiopharmaceutical loaded implantable system: insights from a mathematical model

Introduction

Computational models yield valuable insights into biological interactions not fully elucidated by experimental approaches. This study investigates an innovative spatiotemporal model for simulating the controlled release and dispersion of radiopharmaceutical therapy (RPT) using 177Lu-PSMA, a prostate-specific membrane antigen (PSMA) targeted radiopharmaceutical, within solid tumors via a dual-release implantable delivery system. Local delivery of anticancer agents presents a strategic approach to mitigate adverse effects while optimizing therapeutic outcomes.

Methods

This study evaluates various factors impacting RPT efficacy, including hypoxia region extension, binding affinity, and initial drug dosage, employing a novel 3-dimensional computational model. Analysis gauges the influence of these factors on radiopharmaceutical agent concentration within the tumor microenvironment. Furthermore, spatial and temporal radiopharmaceutical distribution within both the tumor and surrounding tissue is explored.

Results

Analysis indicates a significantly higher total concentration area under the curve within the tumor region compared to surrounding normal tissue. Moreover, drug distribution exhibits notably superior efficacy compared to the radiation source. Additionally, low microvascular density in extended hypoxia regions enhances drug availability, facilitating improved binding to PSMA receptors and enhancing therapeutic effectiveness. Reductions in the dissociation constant (KD) lead to heightened binding affinity and increased internalized drug concentration. Evaluation of initial radioactivities (7.1×107, 7.1×108, and 7.1×109 [Bq]) indicates that an activity of 7.1×108 [Bq] offers a favorable balance between tumor cell elimination and minimal impact on normal tissues.

Discussion

These findings underscore the potential of localized radiopharmaceutical delivery strategies and emphasize the crucial role of released drugs relative to the radiation source (implant) in effective tumor treatment. Decreasing the proximity of the drug to the microvascular network and enhancing its distribution within the tumor promote a more effective therapeutic outcome. The study furnishes valuable insights for future experimental investigations and clinical trials, aiming to refine medication protocols and minimize reliance on in vivo testing.

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.

Predicting the effect of different folate doses on [68Ga]Ga-PSMA-11 organ and tumor uptake using physiologically based pharmacokinetic modeling

BACKGROUND

Folate intake might reduce [⁶⁸Ga]Ga-PSMA-11 uptake in tissues due to a competitive binding to the PSMA receptor. For diagnostic imaging, this could impact decision making, while during radioligand therapy this could affect treatment efficacy. The relationship between folate dose, timing of dosing and tumor and organ uptake is not well established. The aim of this study was to develop a physiologically based pharmacokinetic (PBPK) model to predict the effect of folates on [⁶⁸Ga]Ga-PSMA-11 PET/CT uptake in salivary glands, kidneys and tumors.

METHODS

A PBPK model was developed for [⁶⁸Ga]Ga-PSMA-11 and folates (folic acid and its metabolite 5-MTHF), with compartments added that represent salivary glands and tumor. Reactions describing receptor binding, internalization and intracellular degradation were included. Model evaluation for [⁶⁸Ga]Ga-PSMA-11 was performed by using patient scan data from two different studies (static and dynamic), while for folates data from the literature were used for evaluation. Simulations were performed to assess the effect of different folate doses (150 µg, 400 µg, 5 mg and 10 mg) on accumulation in salivary glands, kidney and tumor, also for patients with different tumor volumes (10, 100, 500 and 1000 mL).

RESULTS

Final model evaluation showed that predictions adequately described data for both [⁶⁸Ga]Ga-PSMA-11 and folates. Predictions of a 5-MTFH dose of 150 µg and folic acid dose of 400 µg (in case of administration at the same time as [⁶⁸Ga]Ga-PSMA-11 (t = 0)) showed no clinically relevant effect on salivary glands and kidney uptake. However, the effect of a decrease in salivary glands and kidney uptake was determined to be clinically relevant for doses of 5 mg (34% decrease for salivary glands and 32% decrease for kidney) and 10 mg (36% decrease for salivary glands and 34% decrease for kidney). Predictions showed that tumor uptake was not relevantly affected by the co-administration of folate for all different folate doses (range 150 µg-10 mg). Lastly, different tumor volumes did not impact the folate effect on [⁶⁸Ga]Ga-PSMA-11 biodistribution.

CONCLUSION

Using a PBPK model approach, high doses of folate (5 and 10 mg) were predicted to show a decrease of [⁶⁸Ga]Ga-PSMA-11 salivary glands and kidney uptake, while intake by means of folate containing food or vitamin supplements showed no relevant effects. In addition, tumor uptake was not affected by folate administration in the simulated dose ranges (150 µg-10 mg). Differences in tumor volume are not expected to impact folate effects on [⁶⁸Ga]Ga-PSMA-11 organ uptake.

Improved quality control of [177Lu]Lu-PSMA I&T

BACKGROUND

Targeted radionuclide therapy with [¹⁷⁷Lu]Lu-PSMA I&T (zadavotide guraxetan) has proven high efficacy and safety in treating patients with advanced prostate cancer worldwide. Several methods to determine the radiochemical purity have been reported but also limitations in the HPLC analysis due to retention of the sample and tailing effects when using standard gradients containing trifluoroacetic acid (TFA). We here report on the validation of a method for quality control of [¹⁷⁷Lu]Lu-PSMA I&T including determination of radiochemical purity, identity testing and limit test for PSMA I&T by HPLC using a Phosphate buffer /Acetonitrile gradient system, complemented with a TLC system with 0.1N Citrate buffer pH 5 as mobile phase including validation of the methods, batch and stability data as well as identification of the main radiochemical impurity by mass spectrometry.

RESULTS

The described HPLC method met the defined acceptance criteria in terms of accuracy, specificity, robustness, linearity, range and LOQ. HPLC analysis revealed symmetrical peaks and quantitative recovery from the column. Batch data showed a radiochemical purity > 95% as determined by HPLC, stability data a pronounced degradation due to radiolysis, which could be limited by addition of ascorbic acid, dilution and storage at low temperatures. The main radiochemical impurity was found to be the de-iodinated form of [¹⁷⁷Lu]Lu-PSMA I&T. TLC analysis allowed to determine the amount of free Lu-177 even in the presence of DTPA in the final formulation.

CONCLUSION

Overall the described combination of HPLC and TLC provides a reliable tool for quality control of [¹⁷⁷Lu]Lu-PSMA I&T.

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.

Theranostic digital twins for personalized radiopharmaceutical therapies: Reimagining theranostics via computational nuclear oncology

This work emphasizes that patient data, including images, are not operable (clinically), but that digital twins are. Based on the former, the latter can be created. Subsequently, virtual clinical operations can be performed towards selection of optimal therapies. Digital twins are beginning to emerge in the field of medicine. We suggest that theranostic digital twins (TDTs) are amongst the most natural and feasible flavors of digitals twins. We elaborate on the importance of TDTs in a future where 'one-size-fits-all' therapeutic schemes, as prevalent nowadays, are transcended in radiopharmaceutical therapies (RPTs). Personalized RPTs will be deployed, including optimized intervention parameters. Examples include optimization of injected radioactivities, sites of injection, injection intervals and profiles, and combination therapies. Multi-modal multi-scale images, combined with other data and aided by artificial intelligence (AI) techniques, will be utilized towards routine digital twinning of our patients, and will enable improved deliveries of RPTs and overall healthcare.

Impact of the mouse model and molar amount of injected ligand on the tissue distribution profile of PSMA radioligands

Purpose

Various preclinical study designs are described in the literature for the evaluation of PSMA radioligands. In this study, [¹⁷⁷Lu]Lu-Ibu-DAB-PSMA, an albumin-binding radioligand, and [¹⁷⁷Lu]Lu-PSMA-617 were investigated and compared under variable experimental conditions.

Methods

In vitro cell uptake studies were performed with PC-3 PIP and LNCaP tumor cells using a range of molar concentrations (0.75–500 nM) of both radioligands. Biodistribution and SPECT/CT imaging studies were carried out with the respective tumor mouse models using 0.05 nmol and 1.0 nmol injected ligand per mouse.

Results

In both tumor cell lines, the uptake of the radioligands was increased when using low molar concentrations of the respective ligand. The observed saturation effect at high ligand concentrations was more pronounced for LNCaP cells that express PSMA at lower levels than for PC-3 PIP cells. At all investigated timepoints, the in vivo uptake of both radioligands was higher in PC-3 PIP tumors than in LNCaP tumors. A low molar amount of injected ligand increased the PC-3 PIP tumor uptake mainly for [¹⁷⁷Lu]Lu-Ibu-DAB-PSMA; however, the molar amount of ligand was relevant for both radioligands when using LNCaP tumors. Renal retention of both radioligands was, however, up to fourfold higher during the first hours after application of a low ligand amount compared to the high ligand amount.

Conclusion

The results of this preclinical study underline the relevance of the tumor model and applied ligand amount for the characterization of PSMA radioligands. The application of equal preclinical study designs is crucial to allow the comparison of novel radioligands with existing ones and, thus, predict potential advantages of new radioligands in view of a clinical application.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00259-021-05446-5.

An in silico study on the effect of the radionuclide half-life on PET/CT imaging with PSMA-targeting radioligands

AIM

 The aim of this work was to systematically investigate the influence of the radionuclide half-life and affinity of prostate-specific membrane antigen (PSMA)-targeting ligands on the activity concentration for PET/CT imaging.

METHODS

 A whole-body physiologically-based pharmacokinetic (PBPK) model with individually estimated parameters of 13 patients with metastatic castration-resistant prostate cancer (mCRPC) was used to simulate the pharmacokinetics of PSMA-targeting radioligands. The simulations were performed with 68Ga (T1/2 = 1.13 h), 18F (T1/2 = 1.83 h), 64Cu (T1/2 = 12.7 h) and for different affinities (dissociation constants KD of 1-0.01 nM) and a commonly used ligand amount of 3 nmol. The activity concentrations were calculated at 1, 2, 3, 4, 8, 12, and 16 h after injection.

RESULTS

 The highest tumor uptake was achieved 1 h p. i. for 68Ga-PSMA. For 18F-PSMA, the highest tumor uptake was at 1 h p. i. and 2 h p.i for dissociation constants KD  = 1 nM and KD  = 0.1-0.01 nM, respectively. For 64Cu-PSMA, the highest tumor uptake was at 4 h p. i. for dissociation constant KD  = 1 nM and at 4 h p. i. (9 patients) and 8 h p. i. (4 patients) for higher affinities. Compared to 68Ga-PSMA (1 h p. i.), the activity concentrations in the tumor for 18F-PSMA (2 h p. i.) increased maximum 1.3-fold with minor differences for all affinities. For 64Cu-PSMA (4 h p. i.), the improvements were in the range of 2.8 to 3.2-fold for all affinities.

CONCLUSIONS

 The simulations indicate that the highest tumor-to-background ratio can be achieved after 4 hours in PET/CT using high-affinity 64Cu-PSMA.

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.

Effect of Tumor Perfusion and Receptor Density on Tumor Control Probability in 177Lu-DOTATATE Therapy: An In Silico Analysis for Standard and Optimized Treatment

The aim of this work was to determine a minimal tumor perfusion and receptor density for ¹⁷⁷Lu-DOTATATE therapy using physiologically based pharmacokinetic (PBPK) modeling considering, first, a desired tumor control probability (TCP) of 99% and, second, a maximal tolerated biologically effective dose (BED_max) for organs at risk (OARs) in the treatment of neuroendocrine tumors and meningioma. Methods: A recently developed PBPK model was used. Nine virtual patients (i.e., individualized PBPK models) were used to perform simulations of pharmacokinetics for different combinations of perfusion (0.001-0.1 mL/g/min) and receptor density (1-100 nmol/L). The TCP for each combination was determined for 3 different treatment strategies: a standard treatment (4 cycles of 7.4 GBq and 105 nmol), a treatment maximizing the number of cycles based on BED_max for red marrow and kidneys, and a treatment having 4 cycles with optimized ligand amount and activity. The red marrow and the kidneys (BED_max of 2 Gy₁₅ and 40 Gy_2.5, respectively) were assumed to be OARs. Additionally, the influence of varying glomerular filtration rates, kidney somatostatin receptor densities, tumor volumes, and release rates was investigated. Results: To achieve a TCP of at least 99% in the standard treatment, a minimal tumor perfusion of 0.036 ± 0.023 mL/g/min and receptor density of 34 ± 20 nmol/L were determined for the 9 virtual patients. With optimization of the number of cycles, the minimum values for perfusion and receptor density were considerably lower, at 0.022 ± 0.012 mL/g/min and 21 ± 11 nmol/L, respectively. However, even better results (perfusion, 0.018 ± 0.009 mL/g/min; receptor density, 18 ± 10 nmol/L) were obtained for strategy 3. The release rate of ¹⁷⁷Lu (or labeled metabolites) from tumor cells had the strongest effect on the minimal perfusion and receptor density for standard and optimized treatments. Conclusion: PBPK modeling and simulations represent an elegant approach to individually determine the minimal tumor perfusion and minimal receptor density required to achieve an adequate TCP. This computational method can be used in the radiopharmaceutical development process for ligand and target selection for specific types of tumors. In addition, this method could be used to optimize clinical trials.

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.

Investigating PSMA-Targeted Radioligand Therapy Efficacy as a Function of Cellular PSMA Levels and Intratumoral PSMA Heterogeneity

PURPOSE

Prostate-specific membrane antigen (PSMA) targeting radioligands deliver radiation to PSMA-expressing cells. However, the relationship between PSMA levels and intralesion heterogeneity of PSMA expression, and cytotoxic radiation by radioligand therapy (RLT) is unknown. Here we investigate RLT efficacy as function of PSMA levels/cell, and the fraction of PSMA+ cells in a tumor.

EXPERIMENTAL DESIGN

RM1 cells expressing different levels of PSMA (PSMA-, PSMA+, PSMA++, PSMA+++; study 1) or a mix of PSMA+ and PSMA- RM1 (study 2, 4) or PC-3/PC-3-PIP (study 3) cells at various ratios were injected into mice. Mice received 177Lu- (studies 1-3) or 225Ac- (study 4) PSMA617. Tumor growth was monitored. Two days post-RLT, tumors were resected in a subset of mice. Radioligand uptake and DNA damage were quantified.

RESULTS

177Lu-PSMA617 efficacy increased with increasing PSMA levels (study 1) and fractions of PSMA positive cells (studies 2, 3) in both, the RM1 and PC-3-PIP models. In tumors resected 2 days post-RLT, PSMA expression correlated with 177Lu-PSMA617 uptake and the degree of DNA damage. Compared with 177Lu-PSMA617, 225Ac-PSMA617 improved overall antitumor effectiveness and tended to enhance the differences in therapeutic efficacy between experimental groups.

CONCLUSIONS

In the current models, both the degree of PSMA expression and the fraction of PSMA+ cells correlate with 177Lu-/225Ac-PSMA617 tumor uptake and DNA damage, and thus, RLT efficacy. Low or heterogeneous PSMA expression represents a resistance mechanism to RLT.See related commentary by Ravi Kumar and Hofman, p. 2774.

The effect of ligand amount, affinity and internalization on PSMA-targeted imaging and therapy: A simulation study using a PBPK model

The aim of this work was to investigate the effect of ligand amount, affinity and internalization of prostate-specific membrane antigen (PSMA)-specific ligands on the activity concentrations for PET/CT imaging and on the absorbed doses for therapy. A physiologically-based pharmacokinetic (PBPK) model for PSMA-specific ligands was implemented. Thirteen virtual patients with metastatic castration-resistant prostate cancer were analysed. Simulations were performed for different combinations of association rates k_on (0.1-0.01 L/nmol/min), dissociation rates k_off (0.1-0.0001 min^-1), internalization rates λ_int (0.01-0.0001 min^-1) and ligand amounts (1-1000 nmol). For imaging the activity was normalized to volume and injected activity (⁶⁸Ga-PSMA at 1 h). For therapy the absorbed dose was calculated for 7.3 ± 0.3 GBq ¹⁷⁷Lu-PSMA. The effect of the investigated parameters on therapy were larger compared to imaging. For imaging, the combination of properties leading to the highest tumour uptake was k_on = 0.1 L/nmol/min, k_off = 0.01 min^-1 for typical ligand amounts (1-10 nmol). For therapy, the higher the internalization rate, the larger was the required ligand amount for optimal tumour-to-kidney ratios. The higher the affinity, the more important was the choice of the optimal ligand amount. PBPK modelling provides insight into the pharmacokinetics of PSMA-specific ligands. Further in silico and in vivo studies are required to verify the influence of the analysed parameters.

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.

Radionuclide Therapy of Metastatic Prostate Cancer

The current mainstay of treatment in metastatic prostate cancer is based on hormonal manipulations. Standard androgen deprivation therapy and novel androgen axis drugs are commonly well tolerable and can stabilize metastatic hormone-sensitive prostate cancers for years. However, metastatic castration-resistant prostate cancer is still challenging to treat. Except taxanes, prostate cancer presents intrinsic resistance against conventional chemotherapies. The typically elderly patient population excludes more aggressive treatment regimens. First clinical trials evaluating immunotherapy or tyrosine-kinase-inhibitors against prostate cancer failed. In contrast, prostate cancer can be radiosensitive and external beam radiotherapy is effective in localized prostate cancer, thus providing a good rationale for the use of systemic radiopharmaceuticals in the metastatic setting. Beta-particle emitting "bone-seekers" have a long history and are effective as analgesics but do not improve survival because they are limited by red-marrow dose. Alpha emitting ²²³Radium can be used in a dose that prolongs survival but is restricted to bone-confined patients. Currently radiolabeled high-affinity ligands to the prostate-specific membrane antigen are in clinical evaluation. While radioimmunotherapy approaches were limited by the long circulation time and slow tumor-accumulation of antibodies, low molecular weight PSMA-specific ligands offer an approx. ten-fold improved tumor to red-marrow ratio in comparison to the unspecific bone-seekers. Early clinical studies demonstrate that regarding surrogate markers, such as >50% PSA reduction (60%) and radiologic response (80%), PSMA-therapy exceeds the antitumor activity of all approved or other recently tested compounds; for example, PSA-response was only observed in approx. a total of 10% of patients treated with ipilimumab, sunitinib, cabozantinib, or xofigo, respectively and in approx. 30, 40, 50% of patients treated with abiraterone, cabazitaxel, or enzalutamide. Also progression free and overall survivals of these single-arm studies appear promising when compared to historical controls. Consecutively, the first PSMA-RLT recently advanced into phase-3 (¹⁷⁷Lu-PSMA-617; VISION-trial). Future developments aim to avoid off-target radiation by ligand-optimization and to outperform the antitumor activity of beta-emitter PSMA-RLT by labeling with highly focused, high energy transferring alpha-nuclides; however the latter potentially also increasing the risk of side-effects and additional early phase studies are needed to improve treatment protocols. Academically clinical research is developing prognostic tools to improve treatment benefit by selecting the most appropriate patients in advance.

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.

Molar Activity of Ga-68 Labeled PSMA Inhibitor Conjugates Determines PET Imaging Results

Radiopharmaceuticals targeting the enzyme prostate-specific membrane antigen (PSMA; synonyms: glutamate carboxypeptidase II, NAALADase; EC 3.4.17.21) have recently emerged as powerful agents for diagnosis and therapy (theranostics) of prostate carcinoma (PCa). The radiation doses for therapeutic application of such compounds are limited by substantial uptakes in kidneys and salivary glands, with excess doses reportedly leading to radiotoxicity-related adverse effects, such as kidney insufficiency or xenostomia. On the basis of the triazacyclononane-triphosphinate (TRAP) chelator, monomeric to trimeric conjugates of the PSMA inhibitor motif lysine-urea-glutamic acid (KuE) were synthesized by means of Cu(I)-mediated (CuAAC) or 5-aza-dibenzocyclooctyne (DBCO)-driven, strain-promoted click chemistry (SPAAC), which were labeled with gallium-68 for application in positron emission tomography (PET), and characterized in terms of PSMA affinity (determined in cellular displacement assays against I-125-BA) and lipophilicity (expressed as log D). Using subcutaneous murine LNCaP (PSMA-positive human prostate carcinoma) xenografts, the influence of ligand multiplicity, affinity, polarity, and molar activity (i.e., mass dose) on the uptakes in tumor, kidney, salivary, and background (muscle) was analyzed by means of region-of-interest (ROI) based quantification of small-animal PET imaging data. As expected, trimerization of the KuE motif resulted in high PSMA affinities (IC₅₀ ranging from 6.0-1.5 nM). Of all parameters, molar activity/cold mass had the most pronounced influence on PET uptakes. Because accumulation in nontumor tissues was effected to a larger extent than tumor uptakes, lower molar activities resulted in substantially better tumor-to-organ ratios. For example, for one trimer, ⁶⁸Ga-AhxKuE₃ (IC₅₀ = 1.5 ± 0.3 nM, log D = -3.8 ± 0.1), a higher overall amount of active compound (12 pmol vs 2 nmol, equivalent to molar activities of 1200 and 8 MBq/nmol) resulted in a remarkable reduction of the kidney-to-tumor ratio from 11.4 to 1.4, respectively, at 60 min p.i. Our study suggests that, for PSMA-targeting radiopharmaceuticals, molar activity has a more pronounced influence on small-animal PET imaging results than structural or in vitro parameters.

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.

Treatment planning algorithm for peptide receptor radionuclide therapy considering multiple tumor lesions and organs at risk

PURPOSE

Peptide receptor radionuclide therapy (PRRT) has shown promising results in the treatment of tumors with high expression of somatostatin receptors such as neuroendocrine tumors (NETs) and meningioma. However, PRRT potentially produces high renal and red marrow (RM) toxicity, the kidneys usually being the dose-limiting organ. Previously, it was shown that an improved therapeutic index can be achieved by choosing an optimal combination of injected activity and peptide molar amount. The aim of this work was to develop a clinically applicable algorithm for treatment planning in PRRT. To demonstrate the applicability and possible advantages of the algorithm thus developed, an in silico clinical trial applying the algorithm to 177 Lu-DOTATATE therapy in nine virtual patients was conducted.

METHODS

An algorithm for treatment planning in PRRT was developed, which simultaneously considers multiple tumor lesions, maximum tolerated biologically effective doses (BEDs) for multiple organs at risk (OARs) and a maximum achievable molar activity. The algorithm, subject to the abovementioned constraints, aims at maximizing the total number of killed tumor cells in the considered lesions/metastases. An in silico clinical trial was conducted with nine virtual patients. For each virtual patient, simulations increasing the molar dose of 177 Lu-DOTATATE from 2 to 2048 nmol by factors of 25 were performed. Maximum tolerated BEDs per cycle for the kidneys (10 Gy2.5 ) and for the RM (0.5 Gy15 ) were defined based on a planned total treatment of four cycles. A maximum achievable molar activity of 420 MBq/nmol was assumed. Optimal combinations of molar dose and activity were determined by applying the developed algorithm. For comparison, simulations for a typical plan with 177 Lu-DOTATATE (7.4 GBq, 265 nmol) were performed and BEDs for the OARs and for individual tumor lesions were calculated. Furthermore, to determine treatment efficacy, overall tumor control probability (oTCP) values after a four-cycle treatment were estimated for the optimal and typical plans.

RESULTS

The conducted in silico clinical trial yielded optimal molar doses and activities ranging from 24 to 512 nmol and from 6 to 30 GBq, respectively. Tumor BEDs ranged from 2 to 107 Gy10 and from 1 to 65 Gy10 for the optimal and typical plans, respectively. The estimated oTCP values showed that the optimal plans may produce adequate tumor control in six of the nine virtual patients after four cycles of 177 Lu-DOTATATE while the typical plan may be sufficient in only two virtual patients.

CONCLUSIONS

The algorithm presented can derive plans with higher tumor control than the typically delivered plan. Therefore, we propose this algorithm for clinical validation and possibly future implementation in treatment planning in molecular radiotherapy.

The Effect of Total Tumor Volume on the Biologically Effective Dose to Tumor and Kidneys for 177Lu-Labeled PSMA Peptides

The aim of this work was to simulate the effect of prostate-specific membrane antigen (PSMA)-positive total tumor volume (TTV) on the biologically effective doses (BEDs) to tumors and organs at risk in patients with metastatic castration-resistant prostate cancer who are undergoing ¹⁷⁷Lu-PSMA radioligand therapy. Methods: A physiologically based pharmacokinetic model was fitted to the data of 13 patients treated with ¹⁷⁷Lu-PSMA I&T (a PSMA inhibitor for imaging and therapy). The tumor, kidney, and salivary gland BEDs were simulated for TTVs of 0.1-10 L. The activity and peptide amounts leading to an optimal tumor-to-kidneys BED ratio were also investigated. Results: When the TTV was increased from 0.3 to 3 L, the simulated BEDs to tumors, kidneys, parotid glands, and submandibular glands decreased from 22 ± 15 to 11.0 ± 6.0 Gy_1.49, 6.5 ± 2.3 to 3.7 ± 1.4 Gy_2.5, 11.0 ± 2.7 to 6.4 ± 1.9 Gy_4.5, and 10.9 ± 2.7 to 6.3 ± 1.9 Gy_4.5, respectively (where the subscripts denote that an α/β of 1.49, 2.5, or 4.5 Gy was used to calculate the BED). The BED to the red marrow increased from 0.17 ± 0.05 to 0.32 ± 0.11 Gy₁₅ For patients with a TTV of more than 0.3 L, the optimal amount of peptide was 273 ± 136 nmol and the optimal activity was 10.4 ± 4.4 GBq. Conclusion: This simulation study suggests that in patients with large PSMA-positive tumor volumes, higher activities and peptide amounts can be safely administered to maximize tumor BEDs without exceeding the tolerable BED to the organs at risk.