A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy

Computational Nuclear Oncology Toward Precision Radiopharmaceutical Therapies: Current Tools, Techniques, and Uncharted Territories

Radiopharmaceutical therapy (RPT), with its targeted delivery of cytotoxic ionizing radiation, demonstrates significant potential for treating a wide spectrum of malignancies, with particularly unique benefits for metastatic disease. There is an opportunity to optimize RPTs and enhance the precision of theranostics by moving beyond a one-size-fits-all approach and using patient-specific image-based dosimetry for personalized treatment planning. Such an approach, however, requires accurate methods and tools for the mathematic modeling and prediction of dose and clinical outcome. To this end, the SNMMI AI-Dosimetry Working Group is promoting the paradigm of computational nuclear oncology: mathematic models and computational tools describing the hierarchy of etiologic mechanisms involved in RPT dose response. This includes radiopharmacokinetics for image-based internal dosimetry and radiobiology for the mapping of dose response to clinical endpoints. The former area originates in pharmacotherapy, whereas the latter originates in radiotherapy. Accordingly, models and methods developed in these predecessor disciplines serve as a foundation on which to develop a repurposed set of tools more appropriate to RPT. Over the long term, this computational nuclear oncology framework also promises to facilitate widespread cross-fertilization of ideas between nuclear medicine and the greater mathematic and computational oncology communities.

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

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

Beyond Average: α-Particle Distribution and Dose Heterogeneity in Bone Metastatic Prostate Cancer

α-particle emitters are emerging as a potent modality for disseminated cancer therapy because of their high linear energy transfer and localized absorbed dose profile. Despite great interest and pharmaceutical development, there is scant information on the distribution of these agents at the scale of the α-particle pathlength. We sought to determine the distribution of clinically approved [223Ra]RaCl2 in bone metastatic castration-resistant prostate cancer at this resolution, for the first time to our knowledge, to inform activity distribution and dose at the near-cell scale. Methods: Biopsy specimens and blood were collected from 7 patients 24 h after administration. 223Ra activity in each sample was recorded, and the microstructure of biopsy specimens was analyzed by micro-CT. Quantitative autoradiography and histopathology were segmented and registered with an automated procedure. Activity distributions by tissue compartment and dosimetry calculations based on the MIRD formalism were performed. Results: We revealed the activity distribution differences across and within patient samples at the macro- and microscopic scales. Microdistribution analysis confirmed localized high-activity regions in a background of low-activity tissue. We evaluated heterogeneous α-particle emission distribution concentrated at bone-tissue interfaces and calculated spatially nonuniform absorbed-dose profiles. Conclusion: Primary patient data of radiopharmaceutical therapy distribution at the small scale revealed that 223Ra uptake is nonuniform. Dose estimates present both opportunities and challenges to enhance patient outcomes and are a first step toward personalized treatment approaches and improved understanding of α-particle radiopharmaceutical therapies.

Influence on voxel-based dosimetry: noise effect on absorbed dose dosimetry at single time-point versus sequential single-photon emission computed tomography

OBJECTIVE

The purpose of this study was to evaluate how statistical fluctuation in single-photon emission computed tomography (SPECT) images propagate to absorbed dose maps.

METHODS

SPECT/computed tomography (CT) images of iodine-131 filled phantoms, using different acquisition and processing protocols, were evaluated using STRATOS software to assess the absorbed dose distribution at the voxel level. Absorbed dose values and coefficient of variation (COV) were analyzed for dosimetry based on single time-point SPECT images and time-integrated activities of SPECT sequences with low and high counts.

RESULTS

Considering dosimetry based on a single time-point, the mean absorbed dose was not significantly affected by total counts or reconstruction parameters, but the uniformity of the absorbed dose maps had an almost linear correlation with SPECT noise. When high- and low-count SPECT sequences were used to generate an absorbed dose map, the absorbed dose COV for each of the temporal sequences was slightly lower than the absorbed dose COV based on the single SPECT image with the highest count included in the sequence.

CONCLUSION

The impact of changes in SPECT counts and reconstruction parameters is almost linear when dosimetry is based on isolated SPECT images, but less pronounced when dosimetry is based on sequential SPECTs.

Heterogeneity of dose distribution in normal tissues in case of radiopharmaceutical therapy with alpha-emitting radionuclides

Heterogeneity of dose distribution has been shown at different spatial scales in diagnostic nuclear medicine. In cancer treatment using new radiopharmaceuticals with alpha-particle emitters, it has shown an extensive degree of dose heterogeneity affecting both tumour control and toxicity of organs at risk. This review aims to provide an overview of generalized internal dosimetry in nuclear medicine and highlight the need of consideration of the dose heterogeneity within organs at risk. The current methods used for patient dosimetry in radiopharmaceutical therapy are summarized. Bio-distribution and dose heterogeneities of alpha-particle emitting pharmaceutical 223Ra (Xofigo) within bone tissues are presented as an example. In line with the strategical research agendas of the Multidisciplinary European Low Dose Initiative (MELODI) and the European Radiation Dosimetry Group (EURADOS), future research direction of pharmacokinetic modelling and dosimetry in patient radiopharmaceutical therapy are recommended.

MIRD Pamphlet No. 27: MIRDcell V3, a Revised Software Tool for Multicellular Dosimetry and Bioeffect Modeling

Radiopharmaceutical therapy is growing rapidly. However, yet to be addressed is the implementation of methods to plan treatments for circulating tumor cells, disseminated tumor cells, and micrometastases. Given the capacity of radiopharmaceuticals to specifically target and kill single cells and multicellular clusters, a quality not available in chemotherapy and external-beam radiation therapy, it is important to develop dosimetry and bioeffect modeling tools that can inform radiopharmaceutical design and predict their effect on microscopic disease. This pamphlet describes a new version of MIRDcell, a software tool that was initially released by the MIRD committee several years ago. Methods: Version 3 (V3) of MIRDcell uses a combination of analytic and Monte Carlo methods to conduct dosimetry and bioeffect modeling for radiolabeled cells within planar colonies and multicellular clusters. A worked example is provided to assist users to learn old and new features of MIRDcell and test its capacity to recapitulate published responses of tumor cell spheroids to radiopharmaceutical treatments. Prominent capabilities of the new version include radially dependent activity distributions, user-imported activity distributions, cold regions within the cluster, complex bioeffect modeling that accounts for radiation type and subcellular distribution, and a rich table of output data for subsequent analysis. Results: MIRDcell V3 effectively reproduces experimental responses of multicellular spheroids to uniform and nonuniform distributions of therapeutic radiopharmaceuticals. Conclusion: MIRDcell is a versatile software tool that can be used for educational purposes and design of radiopharmaceutical therapies.

Using radial distribution functions to calculate cellular cross-absorbed dose forβemitters: comparison with reference methods and application for18F-FDG cell labeling

To further improve the understanding ofin vitrobiological effects of incorporated radionuclides, it is essential to accurately determine cellular absorbed doses. In the case ofβemitters, the cross-dose is a major contribution, and can involve up to millions of cells. Realistic and efficient computational models are needed for that purpose. Conventionally, distances between each cell are calculated and the related dose contributions are cumulated to get the total cross-dose (standard method). In this work, we developed a novel approach for the calculation of the cross-absorbed dose, based on the use of the radial distribution function (rdf)) that describes the spatial properties of the cellular model considered. The dynamic molecular tool LAMMPS was used to create 3D cellular models and computerdfsfor various conditions of cell density, volume size, and configuration type (lattice and randomized geometry). The novel method is suitable for any radionuclide of nuclear medicine. Here, the model was applied for the labeling of cells with¹⁸F-FDG used for PET imaging, and first validated by comparison with other reference methods. MeanS_crossvalues calculated with the novel approach versus the standard method agreed very well (relative differences less that 0.1%). Implementation of therdf-based approach with LAMMPS allowed to achieved results considerably faster than with the standard method, the computing time decreasing from hours to seconds for 10⁶cells. Therdf-based approach was also faster and easier to accommodate more complex cellular models than the standard and other published methods. Finally, a comparative study of the meanS_crossfor different types of configuration was carried out, as a function of the cell density and the volume size, allowing to better understand the impact of the configuration on the cross-absorbed dose.

A cell-based dosimetry model for radium-223 dichloride therapy using bone micro-CT images and GATE simulations

Dosimetry at the cellular level has outperformed macrodosimetry in terms of agreement with toxicity effects in clinical studies. This fact has encouraged dosimetry studies aiming to quantify the absorbed doses needed to reach radiotoxicity at the cellular level and to inform recommendations on the administration of radium-223. The aim of this work is to qualitatively and quantitatively evaluate the absorbed doses of radium-223 and the interactions of the doses at the cellular level. The analysis was performed by Monte Carlo simulations in GATE using micro-CT image of a mouse. Two physics lists available in the GATE code were tested. The influence of single and multiple scattering models on the absorbed dose distribution and number of particle hits was also studied. In addition, the fuzzy c-means clustering method was used for data segmentation. The segmentation method was suitable for these analyses, particularly given that it was unsupervised. There was no significant difference in the estimated absorbed dose between the two proposed physics lists. The absorbed dose values were not significantly influenced by scattering, although single scattering resulted in twice as many interactions as multiple scattering. The absorbed dose histogram at the voxel level shows heterogeneous absorbed dose values within each shell, but the observations from the graph of the medians were comparable to those in the literature. The interaction histogram indicates 10⁴ events, although some voxels had no interactions with alpha particles. However, the voxels did not show absorbed doses capable of deterministic effects in the deepest part of the bone marrow. The absorbed dose distribution in images of mouse trabecular bone was compatible with simple geometric models, with absorbed doses capable of deterministic effects near the bone surface. The interaction distributions need to be correlated with in vivo studies for better interpretation.

Radiopharmaceutical Therapy

Radiopharmaceutical therapy involves the use of radionuclides that are either conjugated to tumor-targeting agents (e.g., nanoscale constructs, antibodies, peptides, and small molecules) or that concentrate in tumors through natural physiological mechanisms that occur predominantly in neoplastic cells. In the latter category, radioiodine therapy of thyroid cancer is the prototypical and most widely implemented radiopharmaceutical therapy. In the category of radionuclide-ligand conjugates, antibody and peptide conjugates have been studied extensively. The efficacy of radiopharmaceutical therapy relies on the ability to deliver cytotoxic radiation to tumor cells without causing prohibitive normal tissue toxicity. After some 30 y of preclinical and clinical research, a number of recent developments suggest that radiopharmaceutical therapy is poised to emerge as an important and widely recognized therapeutic modality. These developments include the substantial investment in antibodies by the pharmaceutical industry and the compelling rationale to build upon this already existing and widely tested platform. In addition, the growing recognition that the signaling pathways responsible for tumor cell survival and proliferation are less easily and durably inhibited than originally envisioned has also provided a rationale for identifying agents that are cytotoxic rather than inhibitory. A number of radiopharmaceutical agents are currently undergoing clinical trial investigation; these include beta-particle emitters, such as Lu, that are being used to label antisomatostatin receptor peptides for neuroendocrine cancers and also prostate-specific membrane antigen targeting small molecules for prostate cancer. Alpha-particle-emitting radionuclides have also been studied for radiopharmaceutical therapy; these include At for glioblastoma, Ac for leukemias and prostate cancer, Pb for breast cancer, and Ra for prostate cancer. The alpha emitters have tended to show particular promise, and there is substantial interest in further developing these agents for therapy of cancers that are particularly difficult to treat.

Targeting Micrometastases: The Effect of Heterogeneous Radionuclide Distribution on Tumor Control Probability

The spatial distribution of radiopharmaceuticals that emit short-range high linear-energy-transfer electrons greatly affects the absorbed dose and their biological effectiveness. The purpose of this study was to investigate the effect of heterogeneous radionuclide distribution on tumor control probability (TCP) in a micrometastases model. Methods: Cancer cell lines; MDA-MB-468, SQ20B and 231-H2N were grown as spheroids to represent micrometastases. The intracellular distribution of a representative radiopeptide (111In-labelled epidermal growth factor, EGF) and radioimmunotherapeutic (111In-labelled Trastuzumab) was determined in cell internalization experiments. The intratumoral distribution was evaluated by microautoradiography of spheroids. γH2AX staining was performed on spheroid sections to correlate DNA damage with radionuclide distribution. Experimental surviving fractions (SFexp ) were obtained using clonogenic assays. A random closed-packed algorithm, which models the random packing behavior of cells and reflects variation in the radii of cells and nuclei, was used to simulate 3-D spheroids. Calculated survival fractions (SFcal ) were generated using an iterative modelling method based on Monte Carlo determined absorbed dose with the PENELOPE code and were compared to (SFexp ). Radiobiological parameters deduced from experimental results and MC simulations were used to predict the TCP for a 3-D spheroid model. Results: Calculated SFs were in good agreement with experimental data, particularly when an increased value for relative biological effectiveness (RBE) was applied to self-dose deposited by sources located in the nucleus and when radiobiological parameters were adjusted to account for dose protraction. Only in MDA-MB-468 spheroids treated with 111In-EGF was a TCP>0.5 achieved, indicating that for this cell type the radiopeptide would be curative when targeting micrometastases. This is attributed to the relative radiosensitivity of MDA-MB-468 cells, high nuclear uptake of the radiopeptide and uniform distribution of radioactivity throughout the spheroid. Conclusion: It is imperative to include biological endpoints when evaluating the distribution of radionuclides in models emulating micrometastatic disease. The spatial distribution of radioactivity is a clear determinant of biological effect and TCP as demonstrated in this study.

Dosimetric Effects of Magnetic Resonance Imaging-assisted Radiotherapy Planning: Dose Optimization for Target Volumes at High Risk and Analytic Radiobiological Dose Evaluation

Based on the assumption that apparent diffusion coefficients (ADCs) define high-risk clinical target volume (aCTVHR) in high-grade glioma in a cellularity-dependent manner, the dosimetric effects of aCTVHR-targeted dose optimization were evaluated in two intensity-modulated radiation therapy (IMRT) plans. Diffusion-weighted magnetic resonance (MR) images and ADC maps were analyzed qualitatively and quantitatively to determine aCTVHR in a high-grade glioma with high cellularity. After confirming tumor malignancy using the average and minimum ADCs and ADC ratios, the aCTVHR with double- or triple-restricted water diffusion was defined on computed tomography images through image registration. Doses to the aCTVHR and CTV defined on T1-weighted MR images were optimized using a simultaneous integrated boost technique. The dosimetric benefits for CTVs and organs at risk (OARs) were compared using dose volume histograms and various biophysical indices in an ADC map-based IMRT (IMRTADC) plan and a conventional IMRT (IMRTconv) plan. The IMRTADC plan improved dose conformity up to 15 times, compared to the IMRTconv plan. It reduced the equivalent uniform doses in the visual system and brain stem by more than 10% and 16%, respectively. The ADC-based target differentiation and dose optimization may facilitate conformal dose distribution to the aCTVHR and OAR sparing in an IMRT plan.

MIRD pamphlet No. 25: MIRDcell V2.0 software tool for dosimetric analysis of biologic response of multicellular populations

Patients undergoing nuclear medicine procedures for cancer therapy are administered radiopharmaceuticals that emit various types of radiation. Because radiation has differential delivery to and uptake by cells in tissue, radiation exposures are often highly nonuniform. Some cell populations in a tissue may contain widely different amounts of radioactivity, whereas other cell populations in the same tissue may contain no radioactivity, referred to as labeled and unlabeled cells, respectively. Furthermore, the toxicity of the radiations emitted can depend on the location of the radioactive decay within the cell (e.g., nucleus vs. cytoplasm). Therefore, the response of a given cell depends on the absorbed dose received from radiations emitted by decays within the cell (self-dose) and emitted by decays in neighboring cells (cross-dose), among other factors. Taken together, these variables make it difficult to predict the response of cell populations to radiopharmaceuticals. Accordingly, to assist in designing treatment plans for therapeutic radiopharmaceuticals, an applet software application called MIRDcell was developed. This applet models the distribution of radiopharmaceuticals in tissues, calculates the distribution of radiation dose, models responses on a cell-by-cell basis, and predicts the surviving fraction of the labeled and unlabeled cell populations. MIRDcell can be accessed at http://mirdcell.njms.rutgers.edu/.

Accelerated event-by-event Monte Carlo microdosimetric calculations of electrons and protons tracks on a multi-core CPU and a CUDA-enabled GPU

For microdosimetric calculations event-by-event Monte Carlo (MC) methods are considered the most accurate. The main shortcoming of those methods is the extensive requirement for computational time. In this work we present an event-by-event MC code of low projectile energy electron and proton tracks for accelerated microdosimetric MC simulations on a graphic processing unit (GPU). Additionally, a hybrid implementation scheme was realized by employing OpenMP and CUDA in such a way that both GPU and multi-core CPU were utilized simultaneously. The two implementation schemes have been tested and compared with the sequential single threaded MC code on the CPU. Performance comparison was established on the speed-up for a set of benchmarking cases of electron and proton tracks. A maximum speedup of 67.2 was achieved for the GPU-based MC code, while a further improvement of the speedup up to 20% was achieved for the hybrid approach. The results indicate the capability of our CPU-GPU implementation for accelerated MC microdosimetric calculations of both electron and proton tracks without loss of accuracy.

Microdosimetry for targeted alpha therapy of cancer

Targeted alpha therapy (TAT) has the advantage of delivering therapeutic doses to individual cancer cells while reducing the dose to normal tissues. TAT applications relate to hematologic malignancies and now extend to solid tumors. Results from several clinical trials have shown efficacy with limited toxicity. However, the dosimetry for the labeled alpha particle is challenging because of the heterogeneous antigen expression among cancer cells and the nature of short-range, high-LET alpha radiation. This paper demonstrates that it is inappropriate to investigate the therapeutic efficacy of TAT by macrodosimetry. The objective of this work is to review the microdosimetry of TAT as a function of the cell geometry, source-target configuration, cell sensitivity, and biological factors. A detailed knowledge of each of these parameters is required for accurate microdosimetric calculations.

Tumour control probability derived from dose distribution in homogeneous and heterogeneous models: assuming similar pharmacokinetics, (125)Sn-(177)Lu is superior to (90)Y-(177)Lu in peptide receptor radiotherapy

Clinical trials on (177)Lu-(90)Y therapy used empirical activity ratios. Radionuclides (RN) with larger beta maximal range could favourably replace (90)Y. Our aim is to provide RN dose-deposition kernels and to compare the tumour control probability (TCP) of RN combinations. Dose kernels were derived by integration of the mono-energetic beta-ray dose distributions (computed using Monte Carlo) weighted by their respective beta spectrum. Nine homogeneous spherical tumours (1-25 mm in diameter) and four spherical tumours including a lattice of cold, but alive, spheres (1, 3, 5, 7 mm in diameter) were modelled. The TCP for (93)Y, (90)Y and (125)Sn in combination with (177)Lu in variable proportions (that kept constant the renal cortex biological effective dose) were derived by 3D dose kernel convolution. For a mean tumour-absorbed dose of 180 Gy, 2 mm homogeneous tumours and tumours including 3 mm diameter cold alive spheres were both well controlled (TCP > 0.9) using a 75-25% combination of (177)Lu and (90)Y activity. However, (125)Sn-(177)Lu achieved a significantly better result by controlling 1 mm-homogeneous tumour simultaneously with tumours including 5 mm diameter cold alive spheres. Clinical trials using RN combinations should use RN proportions tuned to the patient dosimetry. (125)Sn production and its coupling to somatostatin analogue appear feasible. Assuming similar pharmacokinetics (125)Sn is the best RN for combination with (177)Lu in peptide receptor radiotherapy justifying pharmacokinetics studies in rodent of (125)Sn-labelled somatostatin analogues.

A nephron-based model of the kidneys for macro-to-micro α-particle dosimetry

Targeted α-particle therapy is a promising treatment modality for cancer. Due to the short path-length of α-particles, the potential efficacy and toxicity of these agents is best evaluated by microscale dosimetry calculations instead of whole-organ, absorbed fraction-based dosimetry. Yet time-integrated activity (TIA), the necessary input for dosimetry, can still only be quantified reliably at the organ or macroscopic level. We describe a nephron- and cellular-based kidney dosimetry model for α-particle radiopharmaceutical therapy, more suited to the short range and high linear energy transfer of α-particle emitters, which takes as input kidney or cortex TIA and through a macro to micro model-based methodology assigns TIA to micro-level kidney substructures. We apply a geometrical model to provide nephron-level S-values for a range of isotopes allowing for pre-clinical and clinical applications according to the medical internal radiation dosimetry (MIRD) schema. We assume that the relationship between whole-organ TIA and TIA apportioned to microscale substructures as measured in an appropriate pre-clinical mammalian model also applies to the human. In both, the pre-clinical and the human model, microscale substructures are described as a collection of simple geometrical shapes akin to those used in the Cristy-Eckerman phantoms for normal organs. Anatomical parameters are taken from the literature for a human model, while murine parameters are measured ex vivo. The murine histological slides also provide the data for volume of occupancy of the different compartments of the nephron in the kidney: glomerulus versus proximal tubule versus distal tubule. Monte Carlo simulations are run with activity placed in the different nephron compartments for several α-particle emitters currently under investigation in radiopharmaceutical therapy. The S-values were calculated for the α-emitters and their descendants between the different nephron compartments for both the human and murine models. The renal cortex and medulla S-values were also calculated and the results compared to traditional absorbed fraction calculations. The nephron model enables a more optimal implementation of treatment and is a critical step in understanding toxicity for human translation of targeted α-particle therapy. The S-values established here will enable a MIRD-type application of α-particle dosimetry for α-emitters, i.e. measuring the TIA in the kidney (or renal cortex) will provide meaningful and accurate nephron-level dosimetry.

A bone marrow toxicity model for ²²³Ra alpha-emitter radiopharmaceutical therapy

Ra-223, an α-particle emitting bone-seeking radionuclide, has recently been used in clinical trials for osseous metastases of prostate cancer. We investigated the relationship between absorbed fraction-based red marrow dosimetry and cell level-dosimetry using a model that accounts for the expected localization of this agent relative to marrow cavity architecture. We show that cell level-based dosimetry is essential to understanding potential marrow toxicity. The GEANT4 software package was used to create simple spheres representing marrow cavities. Ra-223 was positioned on the trabecular bone surface or in the endosteal layer and simulated for decay, along with the descendants. The interior of the sphere was divided into cell-size voxels and the energy was collected in each voxel and interpreted as dose cell histograms. The average absorbed dose values and absorbed fractions were also calculated in order to compare those results with previously published values. The absorbed dose was predominantly deposited near the trabecular surface. The dose cell histogram results were used to plot the percentage of cells that received a potentially toxic absorbed dose (2 or 4 Gy) as a function of the average absorbed dose over the marrow cavity. The results show (1) a heterogeneous distribution of cellular absorbed dose, strongly dependent on the position of the cell within the marrow cavity; and (2) that increasing the average marrow cavity absorbed dose, or equivalently, increasing the administered activity resulted in only a small increase in potential marrow toxicity (i.e. the number of cells receiving more than 4 or 2 Gy), for a range of average marrow cavity absorbed doses from 1 to 20 Gy. The results from the trabecular model differ markedly from a standard absorbed fraction method while presenting comparable average dose values. These suggest that increasing the amount of radioactivity may not substantially increase the risk of toxicity, a result unavailable to the absorbed fraction method of dose calculation.