Physics and small-scale dosimetry of α $\alpha$ -emitters for targeted radionuclide therapy: The case of 211 At $^{211}{\rm At}$

BACKGROUND

Monte Carlo simulations have been considered for a long time the gold standard for dose calculations in conventional radiotherapy and are currently being applied for the same purpose in innovative radiotherapy techniques such as targeted radionuclide therapy (TRT).

PURPOSE

We present in this work a benchmarking study of the latest version of the Transport d'Ions Lourds Dans l'Aqua & Vivo (TILDA-V ) Monte Carlo track structure code, highlighting its capabilities for describing the full slowing down of α $\alpha$ -particles in water and the energy deposited in cells by α $\alpha$ -emitters in the context of TRT.

METHODS

We performed radiation transport simulations of α $\alpha$ -particles (10 keVu - 1 ${\rm u}^{-1}$ -100 MeVu - 1 ${\rm u}^{-1}$ ) in water with TILDA-V and the Particle and Heavy Ion Transport code System (PHITS) version 3.33. We compared the predictions of each code in terms of track parameters (stopping power, range and radial dose profiles) and cellular S-values of the promising radionuclide astatine-211 (211 At $^{211}{\rm At}$ ). Additional comparisons were made with available data in the literature.

RESULTS

The stopping power, range and radial dose profiles of α $\alpha$ -particles computed with TILDA-V were in excellent agreement with other calculations and available data. Overall, minor differences with PHITS were ascribed to phase effects, that is, related to the use of interaction cross sections computed for water vapor or liquid water. However, important discrepancies were observed in the radial dose profiles of monoenergetic α $\alpha$ -particles, for which PHITS results showed a large underestimation of the absorbed dose compared to other codes and experimental data. The cellular S-values of211 At $^{211}{\rm At}$ computed with TILDA-V  agreed within 4% with the values predicted by PHITS and MIRDcell.

CONCLUSIONS

The validation of the TILDA-V code presented in this work opens the possibility to use it as an accurate simulation tool for investigating the interaction of α $\alpha$ -particles in biological media down to the nanometer scale in the context of medical research. The code may help nuclear medicine physicians in their choice of α $\alpha$ -emitters for TRT. Further research will focus on the application of TILDA-V for quantifying radioinduced damage on the deoxyribonucleic acid (DNA) molecule.

Modelling tissue specific RBE for different radiation qualities based on a multiscale characterization of energy deposition

PURPOSE

We present the nanoCluE model, which uses nano- and microdosimetric quantities to model RBE for protons and carbon ions. Under the hypothesis that nano- and microdosimetric quantities correlates with the generation of complex DNA double strand breakes, we wish to investigate whether an improved accuracy in predicting LQ parameters may be achieved, compared to some of the published RBE models.

METHODS

The model is based on experimental LQ data for protons and carbon ions. We generated a database of track structure data for a number of proton and carbon ion kinetic energies with the Geant4-DNA Monte Carlo code. These data were used to obtain both a nanodosimetric quantity and a set of microdosimetric quantities. The latter were tested with different parameterizations versus experimental LQ-data to select the variable and parametrization that yielded the best fit.

RESULTS

For protons, the nanoCluE model yielded, for the ratio of the linear LQ term versus the test data, a root mean square error (RMSE) of 1.57 compared to 1.31 and 1.30 for two earlier other published proton models. For carbon ions the RMSE was 2.26 compared to 3.24 and 5.24 for earlier published carbon ion models.

CONCLUSION

These results demonstrate the feasibility of the nanoCluE RBE model for carbon ions and protons. The increased accuracy for carbon ions as compared to two other considered models warrants further investigation.

Review of the Geant4-DNA Simulation Toolkit for Radiobiological Applications at the Cellular and DNA Level

Simple Summary

A brief description of the methodologies to simulate ionizing radiation transport in biologically relevant matter is presented. Emphasis is given to the physical, chemical, and biological models of Geant4-DNA that enable mechanistic radiobiological modeling at the cellular and DNA level, important to improve the efficacy of existing and novel radiotherapeutic modalities for the treatment of cancer.

Abstract

The Geant4-DNA low energy extension of the Geant4 Monte Carlo (MC) toolkit is a continuously evolving MC simulation code permitting mechanistic studies of cellular radiobiological effects. Geant4-DNA considers the physical, chemical, and biological stages of the action of ionizing radiation (in the form of x- and γ-ray photons, electrons and β^±-rays, hadrons, α-particles, and a set of heavier ions) in living cells towards a variety of applications ranging from predicting radiotherapy outcomes to radiation protection both on earth and in space. In this work, we provide a brief, yet concise, overview of the progress that has been achieved so far concerning the different physical, physicochemical, chemical, and biological models implemented into Geant4-DNA, highlighting the latest developments. Specifically, the “dnadamage1” and “molecularDNA” applications which enable, for the first time within an open-source platform, quantitative predictions of early DNA damage in terms of single-strand-breaks (SSBs), double-strand-breaks (DSBs), and more complex clustered lesions for different DNA structures ranging from the nucleotide level to the entire genome. These developments are critically presented and discussed along with key benchmarking results. The Geant4-DNA toolkit, through its different set of models and functionalities, offers unique capabilities for elucidating the problem of radiation quality or the relative biological effectiveness (RBE) of different ionizing radiations which underlines nearly the whole spectrum of radiotherapeutic modalities, from external high-energy hadron beams to internal low-energy gamma and beta emitters that are used in brachytherapy sources and radiopharmaceuticals, respectively.

Development and validation of proton track-structure model applicable to arbitrary materials

A novel transport algorithm performing proton track-structure calculations in arbitrary materials was developed. Unlike conventional algorithms, which are based on the dielectric function of the target material, our algorithm uses a total stopping power formula and single-differential cross sections of secondary electron production. The former was used to simulate energy dissipation of incident protons and the latter was used to consider secondary electron production. In this algorithm, the incident proton was transmitted freely in matter until the proton produced a secondary electron. The corresponding ionising energy loss was calculated as the sum of the ionisation energy and the kinetic energy of the secondary electron whereas the non-ionising energy loss was obtained by subtracting the ionising energy loss from the total stopping power. The most remarkable attribute of this model is its applicability to arbitrary materials, i.e. the model utilises the total stopping power and the single-differential cross sections for secondary electron production rather than the material-specific dielectric functions. Benchmarking of the stopping range, radial dose distribution, secondary electron energy spectra in liquid water, and lineal energy in tissue-equivalent gas, against the experimental data taken from literature agreed well. This indicated the accuracy of the present model even for materials other than liquid water. Regarding microscopic energy deposition, this model will be a robust tool for analysing the irradiation effects of cells, semiconductors and detectors.

Verification of KURBUC-based ion track structure mode for proton and carbon ions in the PHITS code

The particle and heavy ion transport code system (PHITS) is a general-purpose Monte Carlo radiation transport simulation code. It has the ability to handle diverse particle types over a wide range of energy. The latest PHITS development enables the generation of track structure for proton and carbon ions (¹H⁺, ¹²C⁶⁺) based on the algorithms in the KURBUC code, which is considered as one of the most verified track-structure codes worldwide. This ion track-structure mode is referred to as the PHITS-KURBUC mode. In this study, the range, radial dose distributions, and microdosimetric distributions were calculated using the PHITS-KURBUC mode. Subsequently, they were compared with the corresponding data obtained from the original KURBUC and from other studies. These comparative studies confirm the successful inclusion of the KURBUC code in the PHITS code. As results of the synergistic effect between the macroscopic and microscopic radiation transport codes, this implementation enabled the detailed calculation of the microdosimetric and nanodosimetric quantities under complex radiation fields, such as proton beam therapy with the spread-out Bragg peak.

Ionizing Radiation and Complex DNA Damage: Quantifying the Radiobiological Damage Using Monte Carlo Simulations

Ionizing radiation is a common tool in medical procedures. Monte Carlo (MC) techniques are widely used when dosimetry is the matter of investigation. The scientific community has invested, over the last 20 years, a lot of effort into improving the knowledge of radiation biology. The present article aims to summarize the understanding of the field of DNA damage response (DDR) to ionizing radiation by providing an overview on MC simulation studies that try to explain several aspects of radiation biology. The need for accurate techniques for the quantification of DNA damage is crucial, as it becomes a clinical need to evaluate the outcome of various applications including both low- and high-energy radiation medical procedures. Understanding DNA repair processes would improve radiation therapy procedures. Monte Carlo simulations are a promising tool in radiobiology studies, as there are clear prospects for more advanced tools that could be used in multidisciplinary studies, in the fields of physics, medicine, biology and chemistry. Still, lot of effort is needed to evolve MC simulation tools and apply them in multiscale studies starting from small DNA segments and reaching a population of cells.

A Simplified Cluster Analysis of Electron Track Structure for Estimating Complex DNA Damage Yields

Complex DNA damage, defined as at least two vicinal lesions within 10-20 base pairs (bp), induced after exposure to ionizing radiation, is recognized as fatal damage to human tissue. Due to the difficulty of directly measuring the aggregation of DNA damage at the nano-meter scale, many cluster analyses of inelastic interactions based on Monte Carlo simulation for radiation track structure in liquid water have been conducted to evaluate DNA damage. Meanwhile, the experimental technique to detect complex DNA damage has evolved in recent decades, so both approaches with simulation and experiment get used for investigating complex DNA damage. During this study, we propose a simplified cluster analysis of ionization and electronic excitation events within 10 bp based on track structure for estimating complex DNA damage yields for electron and X-ray irradiations. We then compare the computational results with the experimental complex DNA damage coupled with base damage (BD) measured by enzymatic cleavage and atomic force microscopy (AFM). The computational results agree well with experimental fractions of complex damage yields, i.e., single and double strand breaks (SSBs, DSBs) and complex BD, when the yield ratio of BD/SSB is assumed to be 1.3. Considering the comparison of complex DSB yields, i.e., DSB + BD and DSB + 2BD, between simulation and experimental data, we find that the aggregation degree of the events along electron tracks reflects the complexity of induced DNA damage, showing 43.5% of DSB induced after 70 kVp X-ray irradiation can be classified as a complex form coupled with BD. The present simulation enables us to quantify the type of complex damage which cannot be measured through in vitro experiments and helps us to interpret the experimental detection efficiency for complex BD measured by AFM. This simple model for estimating complex DNA damage yields contributes to the precise understanding of the DNA damage complexity induced after X-ray and electron irradiations.

Simulating the radial dose distribution for charged particles in water medium by a semi-empirical model: An analytical approach

A computational semi-empirical model based on electronic radiation damage to medium has been presented to simulate the radial dose distribution. An analytical approach was used to calculate the deposited energy in water per unit mass within a cylindrical shell of unit length around the ion path at a radial distance between r and r + dr, the so-called radial dose distribution, RDD. Detail steps were given and the final radial dose integration over the electron range between R_min and R_max was solved numerically using the Mid-Point Method. A validation for the present model was presented by integrating the RDD over all possible radial distances, r to yield the tabulated LET of the ion. The validation was presented for a range of proton ions of different energies. The RDD for heavy charged particles of proton, alpha, Carbon and Oxygen ions of different energies in liquid water were obtained. Good agreement between the present model and experimental, theoretical, and Monte Carlo (Geant4-DNA) data were obtained for all ions under investigations.

Target Size Variation in Microdosimetric Distributions and its Impact on the Linear-Quadratic Parameterization of Cell Survival

The linear-quadratic (LQ) parameterization of survival fraction [SF( D)] inherently assumes that all cells in a population receive the same dose ( D), albeit the distribution of specific energy z over the individual cells f( z, D) can be very wide. From these microdosimetric distributions, which are target size dependent, we estimate the size of the cellular sensitive volume by analyzing its influence on the LQ parameterization of cell survival. A Monte Carlo track structure code was used to simulate detailed tracks from a ⁶⁰Co source as well as proton and carbon ions of various energies. From these tracks, f( z, D) distributions were calculated for spherical targets with diameters ranging from 10 nm to 12 μm. A cell survival function based on f( z, D) was fitted to experimental LQ α values, revealing an intrinsic limitation that target size imposes on the usage of f( z, D) to describe the linear term of the LQ parameterization. The results indicate that such threshold volume arises naturally from the relationship between the particle's probability of no-hit and the probability of cell survival. Further analysis led to the proposal of a radiobiological property [Formula: see text], defined as the mean lineal energy corresponding to the target size that allows equivalence between the mean inactivation dose (MID) and the mean specific energy [Formula: see text]. The fact that [Formula: see text] is an increasing continuous function of target size within the range of biological targets of interest in radiobiology, ensures the uniqueness of [Formula: see text] for any radiation quality, thus, its potential usefulness in modeling. In conclusion, an accurate estimation of such threshold volumes may be useful for improving modeling of cell survival curves.

Radial dose distributions from carbon ions of therapeutic energies calculated with Geant4-DNA

We report on radial dose distributions [Formula: see text] for carbon ions calculated with Geant4-DNA code. These distributions characterize ion tracks on a nanoscale and are important for understanding the biological effects of ion beams. We present data for carbon ion beams in the energy range from 20 to 400 MeV u^-1. To approximate the Monte Carlo results, we developed a simple formula that combines the well-known inverse square distance dependence with a factor correcting [Formula: see text] for small [Formula: see text]. The proposed formula can be used to calculate [Formula: see text] for any energy within the above range and for distances [Formula: see text] from 1 nm to 2 μm with a maximum error not exceeding 14%. This range of distances corresponds to a dose range of over seven orders of magnitude. Differences between our results and those of previously published analytical models are discussed.

Reply to the comment on 'Monte Carlo calculated microdosimetric spread for cell nucleus-sized targets exposed to brachytherapy 125I and 192Ir sources and 60Co cell irradiation'

A discrepancy between the Monte Carlo derived relative standard deviation [Formula: see text] (microdosimetric spread) and experimental data was reported by Villegas et al (2013 Phys. Med. Biol. 58 6149-62) suggesting wall effects as a plausible explanation. The comment by Lindborg et al (2015 Phys. Med. Biol. 60 8621-4) concludes that this is not a likely explanation. A thorough investigation of the Monte Carlo (MC) transport code used for track simulation revealed a critical bug. The corrected MC version yielded [Formula: see text] values that are now within experimental uncertainty. Other microdosimetric findings are hereby communicated.

Microdosimetric spread for cell-sized targets exposed to ⁶⁰Co, ¹⁹²Ir and ¹²⁵I sources

The magnitude of the spread in specific energy deposition per cell may be a confounding factor in dose-response analysis motivating derivation of explicit data for the most common brachytherapy isotopes (125)I and (192)Ir, and for (60)Co radiation frequently used as reference in RBE studies. The aim of this study is to analyse the microdosimetric spread as given by the frequency distribution of specific energy for a range of doses imparted by (125)I, (192)Ir and (60)Co sources. An upgraded version of the Monte Carlo code PENELOPE was used for scoring energy deposition distributions in liquid water for each of the radiation qualities. Frequency distributions of specific energy were calculated according to the formalism of Kellerer and Chmelevsky. Results indicate that the magnitude of the microdosimetric spread increases with decreasing target size and decreasing energy of the radiation quality. Within the clinical relevant dose range (1 to 100 Gy), the spread does not exceed 4 % for (60)Co, 5 % for (192)Ir and 6 % for (125)I. The frequency distributions can be accurately approximated with symmetrical normal distributions at doses down to 0.2 Gy for (60)Co, 0.1 Gy for (192)Ir and 0.08 Gy for (125)I.