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

Theranostic digital twins: Concept, framework and roadmap towards personalized radiopharmaceutical therapies

Radiopharmaceutical therapy (RPT) is a rapidly developing field of nuclear medicine, with several RPTs already well established in the treatment of several different types of cancers. However, the current approaches to RPTs often follow a somewhat inflexible "one size fits all" paradigm, where patients are administered the same amount of radioactivity per cycle regardless of their individual characteristics and features. This approach fails to consider inter-patient variations in radiopharmacokinetics, radiation biology, and immunological factors, which can significantly impact treatment outcomes. To address this limitation, we propose the development of theranostic digital twins (TDTs) to personalize RPTs based on actual patient data. Our proposed roadmap outlines the steps needed to create and refine TDTs that can optimize radiation dose to tumors while minimizing toxicity to organs at risk. The TDT models incorporate physiologically-based radiopharmacokinetic (PBRPK) models, which are additionally linked to a radiobiological optimizer and an immunological modulator, taking into account factors that influence RPT response. By using TDT models, we envisage the ability to perform virtual clinical trials, selecting therapies towards improved treatment outcomes while minimizing risks associated with secondary effects. This framework could empower practitioners to ultimately develop tailored RPT solutions for subgroups and individual patients, thus improving the precision, accuracy, and efficacy of treatments while minimizing risks to patients. By incorporating TDT models into RPTs, we can pave the way for a new era of precision medicine in cancer treatment.

Quantification of biochemical PSA dynamics after radioligand therapy with [177Lu]Lu-PSMA-I&T using a population pharmacokinetic/pharmacodynamic model

BACKGROUND

There is an unmet need for prediction of treatment outcome or patient selection for [177Lu]Lu-PSMA therapy in patients with metastatic castration-resistant prostate cancer (mCRPC). Quantification of the tumor exposure-response relationship is pivotal for further treatment optimization. Therefore, a population pharmacokinetic (PK) model was developed for [177Lu]Lu-PSMA-I&T using SPECT/CT data and, subsequently, related to prostate-specific antigen (PSA) dynamics after therapy in patients with mCRPC using a pharmacokinetic/pharmacodynamic (PKPD) modelling approach.

METHODS

A population PK model was developed using quantitative SPECT/CT data (406 scans) of 76 patients who received multiple cycles [177Lu]Lu-PSMA-I&T (± 7.4 GBq with either two- or six-week interval). The PK model consisted of five compartments; central, salivary glands, kidneys, tumors and combined remaining tissues. Covariates (tumor volume, renal function and cycle number) were tested to explain inter-individual variability on uptake into organs and tumors. The final PK model was expanded with a PD compartment (sequential fitting approach) representing PSA dynamics during and after treatment. To explore the presence of a exposure-response relationship, individually estimated [177Lu]Lu-PSMA-I&T tumor concentrations were related to PSA changes over time.

RESULTS

The population PK model adequately described observed data in all compartments (based on visual inspection of goodness-of-fit plots) with adequate precision of parameters estimates (< 36.1% relative standard error (RSE)). A significant declining uptake in tumors (k14) during later cycles was identified (uptake decreased to 73%, 50% and 44% in cycle 2, 3 and 4-7, respectively, compared to cycle 1). Tumor growth (defined by PSA increase) was described with an exponential growth rate (0.000408 h-1 (14.2% RSE)). Therapy-induced PSA decrease was related to estimated tumor concentrations (MBq/L) using both a direct and delayed drug effect. The final model adequately captured individual PSA concentrations after treatment (based on goodness-of-fit plots). Simulation based on the final PKPD model showed no evident differences in response for the two different dosing regimens currently used.

CONCLUSIONS

Our population PK model accurately described observed [177Lu]Lu-PSMA-I&T uptake in salivary glands, kidneys and tumors and revealed a clear declining tumor uptake over treatment cycles. The PKPD model adequately captured individual PSA observations and identified population response rates for the two dosing regimens. Hence, a PKPD modelling approach can guide prediction of treatment response and thus identify patients in whom radioligand therapy is likely to fail.

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.

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.

A PBPK model for PRRT with [177Lu]Lu-DOTA-TATE: Comparison of model implementations in SAAM II and MATLAB/SimBiology

Physiologically based pharmacokinetic (PBPK) models offer the ability to simulate and predict the biodistribution of radiopharmaceuticals and have the potential to enable individualised treatment planning in molecular radiotherapy. The objective of this study was to develop and implement a whole-body compartmental PBPK model for peptide receptor radionuclide therapy (PRRT) with [177Lu]Lu-DOTA-TATE in SimBiology to allow for more complex analyses. The correctness of the model implementation was ensured by comparing its outputs, such as the time-integrated activity (TIA), with those of a PBPK model implemented in SAAM II software.

METHODS

A combined PBPK model for [68Ga]Ga-DOTA-TATE and [177Lu]Lu-DOTA-TATE was developed and implemented in both SAAM II and SimBiology. A retrospective analysis of 12 patients with metastatic neuroendocrine tumours (NETs) was conducted. First, time-activity curves (TACs) and TIAs from the two software were calculated and compared for identical parameter values. Second, pharmacokinetic parameters were fitted to activity concentrations, analysed and compared.

RESULTS

The PBPK model implemented in SimBiology produced TIA results comparable to those generated by the model implemented in SAAM II, with a relative deviation of less than 0.5% when using the same input parameters. The relative deviation of the fitted TIAs was less than 5% when model parameter values were fitted to the measured activity concentrations.

CONCLUSION

The proposed PBPK model implemented in SimBiology can be used for dosimetry in radioligand therapy and TIA prediction. Its outputs are similar to those generated by the PBPK model implemented in SAAM II, confirming the correctness of the model implementation in SimBiology.

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.

Time-Activity data fitting in molecular Radiotherapy: Methodology and pitfalls

Absorbed radiation doses are essential in assessing the effects, e.g. safety and efficacy, of radiopharmaceutical therapy (RPT). Patient-specific absorbed dose calculations in the target or the organ at risk require multiple inputs. These include the number of disintegrations in the organ, i.e. the time-integrated activities (TIAs) of the organs, as well as other parameters describing the process of radiation energy deposition in the target tissue (i.e. mean energy per disintegration, radiation dose constants, etc). TIAs are then estimated by incorporating the area under the radiopharmaceutical's time-activity curve (TAC), which can be obtained by quantitative measurements of the biokinetics in the patient (typically based on imaging data such as planar scintigraphy, SPECT/CT, PET/CT, or blood and urine samples). The process of TAC determination/calculation for RPT generally depends on the user, e.g., the chosen number and schedule of measured time points, the selection of the fit function, the error model for the data and the fit algorithm. These decisions can strongly affect the final TIA values and thus the accuracy of calculated absorbed doses. Despite the high clinical importance of the TIA values, there is currently no consensus on processing time-activity data or even a clear understanding of the influence of uncertainties and variations in personalised RPT dosimetry related to user-dependent TAC calculation. As a first step towards minimising site-dependent variability in RPT dosimetry, this work provides an overview of quality assurance and uncertainty management considerations of the TIA estimation.

Predicting [177Lu]Lu-HA-DOTATATE kidney and tumor accumulation based on [68Ga]Ga-HA-DOTATATE diagnostic imaging using semi-physiological population pharmacokinetic modeling

BACKGROUND

Prediction of [177Lu]Lu-HA-DOTATATE kidney and tumor uptake based on diagnostic [68Ga]Ga-HA-DOTATATE imaging would be a crucial step for precision dosing of [177Lu]Lu-HA-DOTATATE. In this study, the population pharmacokinetic (PK) differences between [177Lu]Lu-HA-DOTATATE and [68Ga]Ga-HA-DOTATATE were assessed and subsequently [177Lu]Lu-HA-DOTATATE was predicted based on [68Ga]Ga-HA-DOTATATE imaging.

METHODS

A semi-physiological nonlinear mixed-effects model was developed for [68Ga]Ga-HA-DOTATATE and [177Lu]Lu-HA-DOTATATE, including six compartments (representing blood, spleen, kidney, tumor lesions, other somatostatin receptor expressing organs and a lumped rest compartment). Model parameters were fixed based on a previously developed physiologically based pharmacokinetic model for [68Ga]Ga-HA-DOTATATE. For [177Lu]Lu-HA-DOTATATE, PK parameters were based on literature values or estimated based on scan data (four time points post-injection) from nine patients. Finally, individual [177Lu]Lu-HA-DOTATATE uptake into tumors and kidneys was predicted based on individual [68Ga]Ga-HA-DOTATATE scan data using Bayesian estimates. Predictions were evaluated compared to observed data using a relative prediction error (RPE) for both area under the curve (AUC) and absorbed dose. Lastly, to assess the predictive value of diagnostic imaging to predict therapeutic exposure, individual prediction RPEs (using Bayesian estimation) were compared to those from population predictions (using the population model).

RESULTS

Population uptake rate parameters for spleen, kidney and tumors differed by a 0.29-fold (15% relative standard error (RSE)), 0.49-fold (15% RSE) and 1.43-fold (14% RSE), respectively, for [177Lu]Lu-HA-DOTATATE compared to [68Ga]Ga-HA-DOTATATE. Model predictions adequately described observed data in kidney and tumors for both peptides (based on visual inspection of goodness-of-fit plots). Individual predictions of tumor uptake were better (RPE AUC -40 to 28%) compared to kidney predictions (RPE AUC -53 to 41%). Absorbed dose predictions were less predictive for both tumor and kidneys (RPE tumor and kidney -51 to 44% and -58 to 82%, respectively). For most patients, [177Lu]Lu-HA-DOTATATE tumor accumulation predictions based on individual PK parameters estimated from diagnostic imaging outperformed predictions based on population parameters.

CONCLUSION

Our semi-physiological PK model indicated clear differences in PK parameters for [68Ga]Ga-HA-DOTATATE and [177Lu]Lu-HA-DOTATATE. Diagnostic images provided additional information to individually predict [177Lu]Lu-HA-DOTATATE tumor uptake compared to using a population approach. In addition, individual predictions indicated that many aspects, apart from PK differences, play a part in predicting [177Lu]Lu-HA-DOTATATE distribution.

An anthropomorphic body phantom for the determination of calibration factor in radionuclide treatment dosimetry

The aim of this study is to create an inhomogeneous human-like phantom, whose attenuation and scattering effects are similar to the human body, as an alternative to the homogeneous phantoms traditionally used in calibration factor (CF) determination. The phantom was designed to include the thorax, abdomen and upper pelvis regions sized to represent a 75-kg male with a body mass index of 25. Measurements using Lu-177 with 50- and 100-mL lesion volumes were performed using inhomogeneous anthropomorphic body phantom (ABP) and homogeneous NEMA PET body phantom. There was a difference of 5.7% of Calibration Factor including attenuation and scatter effect between ABP and NEMA PET body phantom. Because it better reflects the attenuation and scatter effect, it is recommended to use a human-like inhomogeneous phantom for determination of CF instead of a homogeneous phantom.

Clinical Pharmacokinetics of Radiopharmaceuticals from SPECT/CT Image Acquisition by Contouring in Patients with Gastroenteropancreatic Neuroendocrine Tumors: Lu-177 DOTATATE (Lutathera®) Case

BACKGROUND AND OBJECTIVE

Lu-177 DOTATATE (Lutathera^®) is a radiolabeled analog of somatostatin administered intravenously in patients with somatostatin receptor-positive gastroenteropancreatic neuroendocrine tumors. Biodistribution of Lu-177 DOTATATE in tumor and healthy tissues can be monitored by serial post-injection scintigraphy imaging. Patient exposure to the drug is variable with the recommended fixed dosage, and hence there is a variable response to treatment. The aim of this work was to study the pharmacokinetics of Lu-177 DOTATATE by a population modeling approach, based on single-photon emission computed tomography (SPECT)/computed tomography (CT) images used as surrogate of plasma concentrations to study the interindividual variability and finally optimize an individual dosage.

METHODS

From a retrospective study, SPECT/CT images were acquired at 4 h, 24 h, 72 h, and 192 h postadministration. From these images, volumic activities were calculated in blood and bone marrow. An individual non-compartmental pharmacokinetic analysis was performed, and the mean pharmacokinetic parameters of each tissue were compared together and with reference data. Blood volumic activities were then used to perform a population pharmacokinetic analysis (NONMEM).

RESULTS

The pharmacokinetic parameters (non-compartmental analysis) obtained from blood (clearance [CL] = 2.65 L/h, volume of distribution at steady state [Vss] = 309 L, elimination half-life [t_1/2] = 86.3 h) and bone marrow (CL =1.68 L/h, Vss = 233 L, t_1/2 = 98.8 h) were statistically different from each other and from reference values (CL = 4.50 L/h, Vss = 460 L, t_1/2 = 71.0 h) published in the literature. SPECT/CT blood images were used as a surrogate of plasma concentrations to develop a population pharmacokinetic model. Weight was identified as covariate on volume of the central compartment, reducing the interindividual variability of all population pharmacokinetic parameters.

CONCLUSION

This study is a proof of concept that obtaining pharmacokinetic parameters with image-based blood concentration is possible. Obtaining observed concentrations from SPECT/CT images, without the need for blood sampling, is a real advantage for the patient and the drug monitoring. Pharmacokinetic modeling could be combined with a deep learning model for automatic contouring and allow precise patient-specific dose adjustment in a non-invasive manner.