Track structure modeling in liquid water: A review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit

MPEXS-DNA, a new GPU-based Monte Carlo simulator for track structures and radiation chemistry at subcellular scale

Purpose

Track structure simulation codes can accurately reproduce the stochastic nature of particle–matter interactions in order to evaluate quantitatively radiation damage in biological cells such as DNA strand breaks and base damage. Such simulations handle large numbers of secondary charged particles and molecular species created in the irradiated medium. Every particle and molecular species are tracked step‐by‐step using a Monte Carlo method to calculate energy loss patterns and spatial distributions of molecular species inside a cell nucleus with high spatial accuracy. The Geant4‐DNA extension of the Geant4 general‐purpose Monte Carlo simulation toolkit allows for such track structure simulations and can be run on CPUs. However, long execution times have been observed for the simulation of DNA damage in cells. We present in this work an improvement of the computing performance of such simulations using ultraparallel processing on a graphical processing unit (GPU).

Methods

A new Monte Carlo simulator named MPEXS‐DNA, allowing high computing performance by using a GPU, has been developed for track structure and radiolysis simulations at the subcellular scale. MPEXS‐DNA physics and chemical processes are based on Geant4‐DNA processes available in Geant4 version 10.02 p03. We have reimplemented the Geant4‐DNA process codes of the physics stage (electromagnetic processes of charged particles) and the chemical stage (diffusion and chemical reactions for molecular species) for microdosimetry simulation by using the CUDA language. MPEXS‐DNA can calculate a distribution of energy loss in the irradiated medium caused by charged particles and also simulate production, diffusion, and chemical interactions of molecular species from water radiolysis to quantitatively assess initial damage to DNA. The validation of MPEXS‐DNA physics and chemical simulations was performed by comparing various types of distributions, namely the radial dose distributions for the physics stage, and the G‐value profiles for each chemical product and their linear energy transfer dependency for the chemical stage, to existing experimental data and simulation results obtained by other simulation codes, including PARTRAC.

Results

For physics validation, radial dose distributions calculated by MPEXS‐DNA are consistent with experimental data and numerical simulations. For chemistry validation, MPEXS‐DNA can also reproduce G‐value profiles for each molecular species with the same tendency as existing experimental data. MPEXS‐DNA also agrees with simulations by PARTRAC reasonably well. However, we have confirmed that there are slight discrepancies in G‐value profiles calculated by MPEXS‐DNA for molecular species such as H₂ and H₂O₂ when compared to experimental data and PARTRAC simulations. The differences in G‐value profiles between MPEXS‐DNA and PARTRAC are caused by the different chemical reactions considered. MPEXS‐DNA can drastically boost the computing performance of track structure and radiolysis simulations. By using NVIDIA's GPU devices adopting the Volta architecture, MPEXS‐DNA has achieved speedup factors up to 2900 against Geant4‐DNA simulations with a single CPU core.

Conclusion

The MPEXS‐DNA Monte Carlo simulation achieves similar accuracy to Monte Carlo simulations performed using other codes such as Geant4‐DNA and PARTRAC, and its predictions are consistent with experimental data. Notably, MPEXS‐DNA allows calculations that are, at maximum, 2900 times faster than conventional simulations using a CPU.

TOPAS-nBio: An Extension to the TOPAS Simulation Toolkit for Cellular and Sub-cellular Radiobiology

The TOPAS Monte Carlo (MC) system is used in radiation therapy and medical imaging research, having played a significant role in making Monte Carlo simulations widely available for proton therapy related research. While TOPAS provides detailed simulations of patient scale properties, the fundamental unit of the biological response to radiation is a cell. Thus, our goal was to develop TOPAS-nBio, an extension of TOPAS dedicated to advance understanding of radiobiological effects at the (sub-)cellular, (i.e., the cellular and sub-cellular) scale. TOPAS-nBio was designed as a set of open source classes that extends TOPAS to model radiobiological experiments. TOPAS-nBio is based on and extends Geant4-DNA, which extends the Geant4 toolkit, the basis of TOPAS, to include very low-energy interactions of particles down to vibrational energies, explicitly simulates every particle interaction (i.e., without using condensed histories) and propagates radiolysis products. To further facilitate the use of TOPAS-nBio, a graphical user interface was developed. TOPAS-nBio offers full track-structure Monte Carlo simulations, integration of chemical reactions within the first millisecond, an extensive catalogue of specialized cell geometries as well as sub-cellular structures such as DNA and mitochondria, and interfaces to mechanistic models of DNA repair kinetics. We compared TOPAS-nBio simulations to measured and published data of energy deposition patterns and chemical reaction rates (G values). Our simulations agreed well within the experimental uncertainties. Additionally, we expanded the chemical reactions and species provided in Geant4-DNA and developed a new method based on independent reaction times (IRT), including a total of 72 reactions classified into 6 types between neutral and charged species. Chemical stage simulations using IRT were a factor of 145 faster than with step-by-step tracking. Finally, we applied the geometric/chemical modeling to obtain initial yields of double-strand breaks (DSBs) in DNA fibers for proton irradiations of 3 and 50 MeV and compared the effect of including chemical reactions on the number and complexity of DSB induction. Over half of the DSBs were found to include chemical reactions with approximately 5% of DSBs caused only by chemical reactions. In conclusion, the TOPAS-nBio extension to the TOPAS MC application offers access to accurate and detailed multiscale simulations, from a macroscopic description of the radiation field to microscopic description of biological outcome for selected cells. TOPAS-nBio offers detailed physics and chemistry simulations of radiobiological experiments on cells simulating the initially induced damage and links to models of DNA repair kinetics.

Optimized neuron models for estimation of charged particle energy deposition in hippocampus

The study of evaluating radiation risk on the central nervous system induced by space-born charged particles is very complex and challenging task in space radiobiology and radiation protection. To overcome computational difficulties in this field, we developed simplified neuron models with properties equivalent to realistic neuron morphology. Three-dimensional structure and parameters of simplified and complex neuron models with realistic morphology were obtained from the experimental data. The models implement uniform random distribution of spines along the dendritic branches in typical hippocampal neurons. Both types of models were implemented and tested using Geant4 Monte Carlo radiation transport code. Track structure simulations were performed for ion beams with typical fluxes of galactic cosmic rays expected for long-term interplanetary missions. The distribution of energy deposition events and percentage of irradiated volumes were obtained to be similar in both simplified and realistic models of pyramidal and granule cells of the rat hippocampus following irradiation. Significant increase of computational efficiency for detailed microdosimetry simulations of hippocampus using simplified neuron models was achieved. Using designed neuron models we have constructed 3D model of the rat hippocampus, including pyramidal cells, mature and immature granular cells, mossy cells, and neural stem cells. Computed energy deposition in irradiated hippocampal neurons following a track of iron ion suggests that most of energy is accumulated by dense population of granular cells in the dentate gyrus. Proposed approach could serve as a complementary computation technique for studying radiation-induced effects in large scale brain networks.

Clinically relevant nanodosimetric simulation of DNA damage complexity from photons and protons

Relative Biological Effectiveness (RBE), the ratio of doses between radiation modalities to produce the same biological endpoint, is a controversial and important topic in proton therapy. A number of phenomenological models incorporate variable RBE as a function of Linear Energy Transfer (LET), though a lack of mechanistic description limits their applicability. In this work we take a different approach, using a track structure model employing fundamental physics and chemistry to make predictions of proton and photon induced DNA damage, the first step in the mechanism of radiation-induced cell death. We apply this model to a proton therapy clinical case showing, for the first time, predictions of DNA damage on a patient treatment plan. Our model predictions are for an idealised cell and are applied to an ependymoma case, at this stage without any cell specific parameters. By comparing to similar predictions for photons, we present a voxel-wise RBE of DNA damage complexity. This RBE of damage complexity shows similar trends to the expected RBE for cell kill, implying that damage complexity is an important factor in DNA repair and therefore biological effect.

Relative Biological Effectiveness (RBE) is a controversial and important topic in proton therapy. This work uses Monte Carlo simulations of DNA damage for protons and photons to probe this phenomenon, providing a plausible mechanistic understanding.

Validation and investigation of reactive species yields of Geant4-DNA chemistry models

PURPOSE

Indirect biological damage due to reactive species produced in water radiolysis reactions is responsible for the majority of biological effect for low linear energy transfer (LET) radiation. Modeling water radiolysis and the subsequent interactions of reactive species, as well as track structures, is essential to model radiobiology on the microscale. Recently, chemistry models have been developed for Geant4-DNA to be used in combination with the comprehensive existing physics models. In the current work, the first detailed, independent, in silico validation of all species yields with published experimental observations and comparison with other radiobiological simulations is presented. Additionally, the effect of LET of protons and heavier ions on reactive species yield in the model was examined, as well as the completeness of the chemical reactions following the radiolysis within the time after physical interactions simulated in the model.

METHODS

Yields over time of reactive species were simulated for water radiolysis by incident electrons, protons, alpha particles, and ions with various LETs using Geant4 and RITRACKS simulation tools. Water dissociation and recombination was simulated using Geant4 to determine the completeness of chemical reactions at the end of the simulation. Yield validation was performed by comparing yields simulated using Geant4 with experimental observations and other simulations. Validation was performed for all species for low LET radiation and the solvated electron and hydroxyl radical for high LET ions.

RESULTS

It was found that the Geant4-DNA chemistry yields were generally in good agreement with experimental observations and other simulations. However, the Geant4-DNA yields for the hydroxyl radical and hydrogen peroxide at the end of the chemistry stage were found to be respectively considerably higher and lower than the experimentally observed yields. Increasing the LET of incident hadrons increased the yield of secondary species and decreased the yield of primary species. The effect of LET on the yield of the hydroxyl radical at 100 ns simulated with Geant4 was in good agreement with experimental measurements. Additionally, by the end of the simulation only 40% of dissociated water molecules had been recombined and the rate of recombination was slowing.

CONCLUSIONS

The yields simulated using Geant4 are within reasonable agreement with experimental observations. Higher LET radiation corresponds with increased yields of secondary species and decreased yields of primary species. These trends combined with the LET having similar effects on the 100 ns hydroxyl radical yield for Geant4 and experimental measurements indicate that Geant4 accurately models the effect of LET on radiolysis yields. The limited recombination within the modeled chemistry stage and the slowing rate of recombination at the end of the stage indicate potential long-range indirect biological damage.

A New Standard DNA Damage (SDD) Data Format

Our understanding of radiation-induced cellular damage has greatly improved over the past few decades. Despite this progress, there are still many obstacles to fully understand how radiation interacts with biologically relevant cellular components, such as DNA, to cause observable end points such as cell killing. Damage in DNA is identified as a major route of cell killing. One hurdle when modeling biological effects is the difficulty in directly comparing results generated by members of different research groups. Multiple Monte Carlo codes have been developed to simulate damage induction at the DNA scale, while at the same time various groups have developed models that describe DNA repair processes with varying levels of detail. These repair models are intrinsically linked to the damage model employed in their development, making it difficult to disentangle systematic effects in either part of the modeling chain. These modeling chains typically consist of track-structure Monte Carlo simulations of the physical interactions creating direct damages to DNA, followed by simulations of the production and initial reactions of chemical species causing so-called "indirect" damages. After the induction of DNA damage, DNA repair models combine the simulated damage patterns with biological models to determine the biological consequences of the damage. To date, the effect of the environment, such as molecular oxygen (normoxic vs. hypoxic), has been poorly considered. We propose a new standard DNA damage (SDD) data format to unify the interface between the simulation of damage induction in DNA and the biological modeling of DNA repair processes, and introduce the effect of the environment (molecular oxygen or other compounds) as a flexible parameter. Such a standard greatly facilitates inter-model comparisons, providing an ideal environment to tease out model assumptions and identify persistent, underlying mechanisms. Through inter-model comparisons, this unified standard has the potential to greatly advance our understanding of the underlying mechanisms of radiation-induced DNA damage and the resulting observable biological effects when radiation parameters and/or environmental conditions change.

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.

Geometrical structures for radiation biology research as implemented in the TOPAS-nBio toolkit

Computational simulations, such as Monte Carlo track structure simulations, offer a powerful tool for quantitatively investigating radiation interactions within cells. The modelling of the spatial distribution of energy deposition events as well as diffusion of chemical free radical species, within realistic biological geometries, can help provide a comprehensive understanding of the effects of radiation on cells. Track structure simulations, however, generally require advanced computing skills to implement. The TOPAS-nBio toolkit, an extension to TOPAS (TOol for PArticle Simulation), aims to provide users with a comprehensive framework for radiobiology simulations, without the need for advanced computing skills. This includes providing users with an extensive library of advanced, realistic, biological geometries ranging from the micrometer scale (e.g. cells and organelles) down to the nanometer scale (e.g. DNA molecules and proteins). Here we present the geometries available in TOPAS-nBio.

Multiphysics Modelling of Background Dose by Systemic Targeted Alpha Therapy

INTRODUCTION

Nontargeted molecules of alpha-immunoconjugate (AIC) intravenously injected in clinical trials of targeted alpha therapy (TAT) could be transported by convection and diffusion along with blood or lymphatic circulation.

MATERIALS AND METHODS

A coupled model based on the Geant4 Monte Carlo microdosimetry technique and computational fluid dynamics was established. The transient drug delivery process and background dose to the cells along the pathway were investigated using the model. A mesoscale numerical simulation in a simple 2D capillary was performed to determine the transient toxicity of the alpha-immunoconjugate to the DNA of a targeted cell.

RESULTS

The simulation results indicate that the multiphysics simulation is essential to improve the accuracy of TAT simulation.

CONCLUSION

In this work, a solution strategy for modelling AIC delivery in a blood vessel at a mesoscale level has been established. This work is the first to model different phenomena through the multiphysics simulation to investigate the whole picture of TAT.

Proton relative biological effectiveness (RBE): a multiscale problem

Proton radiotherapy is undergoing rapid expansion both within the UK and internationally, but significant challenges still need to be overcome if maximum benefit is to be realised from this technique. One major limitation is the persistent uncertainty in proton relative biological effectiveness (RBE). While RBE values are needed to link proton radiotherapy to our existing experience with photon radiotherapy, RBE remains poorly understood and is typically incorporated as a constant dose scaling factor of 1.1 in clinical plans. This is in contrast to extensive experimental evidence indicating that RBE is a function of dose, tissue type, and proton linear energy transfer, among other parameters. In this article, we discuss the challenges associated with obtaining clinically relevant values for proton RBE through commonly-used assays, and highlight the wide range of other experimental end points which can inform our understanding of RBE. We propose that accurate and robust optimization of proton radiotherapy ultimately requires a multiscale understanding of RBE, integrating subcellular, cellular, and patient-level processes.

Monte Carlo Simulation of the Oxygen Effect in DNA Damage Induction by Ionizing Radiation

DNA damage induced by ionizing radiation exposure is enhanced in the presence of oxygen (the "oxygen effect"). Despite its practical importance in radiotherapy, the oxygen effect has largely been excluded from models that predict DNA damage from radiation tracks. A Monte Carlo-based algorithm was developed in MATLAB software to predict DNA damage from physical and chemical tracks through a cell nucleus simulated in Geant4-DNA, taking into account the effects of cellular oxygenation (pO₂) on DNA radical chemistry processes. An initial spatial distribution of DNA base and sugar radicals was determined by spatially clustering direct events (that deposited at least 10.79 eV) and hydroxyl radical (^•OH) interactions. The oxygen effect was modeled by increasing the efficiency with which sugar radicals from direct-type effects were converted to strand breaks from 0.6 to 1, the efficiency with which sugar radicals from the indirect effect were converted to strand breaks from 0.28 to 1 and the efficiency of base-to-sugar radical transfer from ^•OH-mediated base radicals from 0 to 0.03 with increasing pO₂ from 0 to 760 mmHg. The DNA damage induction algorithm was applied to tracks from electrons, protons and alphas with LET values from 0.2 to 150 keV/μm under different pO₂ conditions. The oxygen enhancement ratio for double-strand break induction was 3.0 for low-LET radiation up to approximately 15 keV/μm, after which it gradually decreased to a value of 1.3 at 150 keV/μm. These values were consistent with a range of experimental data published in the literature. The DNA damage yields were verified using experimental data in the literature and results from other theoretical models. The spatial clustering approach developed in this work has low memory requirements and may be suitable for particle tracking simulations with a large number of cells.

Energy optimization in gold nanoparticle enhanced radiation therapy

Gold nanoparticles (GNPs) have been demonstrated as radiation dose enhancing agents. Kilovoltage external photon beams have been shown to yield the largest enhancement due to the high interaction probability with gold. While orthovoltage irradiations are feasible and promising, they suffer from a reduced tissue penetrating power. This study quantifies the effect of varying photon beam energies on various beam arrangements, body, tumor, and cellular GNP uptake geometries. Cell survival was modeled based on our previously developed GNP-local effect model with radial doses calculated using the TOPAS-nBio Monte Carlo code. Cell survival curves calculated for tumor sites with GNPs were used to calculate the relative biological effectiveness (RBE)-weighted dose. In order to evaluate the plan quality, the ratio of the mean dose between the tumor and normal tissue for 50-250 kVp beams with GNPs was compared to the standard of care using 6 MV photon beams without GNPs for breast and brain tumors. For breast using a single photon beam, kV  +  GNP was found to yield up to 2.73 times higher mean RBE-weighted dose to the tumor than two tangential megavoltage beams while delivering the same dose to healthy tissue. For irradiation of brain tumors using multiple photon beams, the GNP dose enhancement was found to be effective for energies above 50 keV. A small tumor at shallow depths was found to be the most effective treatment conditions for GNP enhanced radiation therapy. GNP uptake distributions in the cell (with or without nuclear uptake) and the beam arrangement were found to be important factors in determining the optimal photon beam energy.

Accounting for radiation-induced indirect damage on DNA with the Geant 4-DNA code

The use of Monte Carlo (MC) simulations remains a powerful tool to study the biological effects induced by ionizing radiation on living beings. Several MC codes are commonly used in research fields such as nanodosimetry, radiotherapy, radiation protection, and space radiation. This work presents an enhancement of an existing model [1] for radiobiological purposes, to account for the indirect DNA damage induced by ionizing particles. The Geant4-DNA simulation toolkit was used to simulate the physical, pre-chemical, and chemical stages of early DNA damage induced by protons and α-particles. Liquid water was used as the medium for simulations. Two phase-space files were generated, one containing the energy deposition events and another with the position of chemical species produced by water radiolysis from 0.1 ps up to 1 ns. These files were used as input in the radiobiological code that contains the genetic material model with atomic resolution, consisting of several copies of 30 nm chromatin fibers. The B-DNA configuration was used. This work focused on the indirect damage produced by the hydroxyl radical (OH) attack on the sugar-phosphate group. The approach followed to account for the indirect DNA damage was the same as those used by other radiobiological codes [2,3]. The critical parameter considered here was the reaction radius, which was calculated from the Smoluchowski's diffusion equation. Single, double, and total strand break yields produced by direct, indirect, and mixed mechanisms are reported. The obtained results are consistent with experimental and calculation data sets published in the literature.

Geant4-DNA example applications for track structure simulations in liquid water: A report from the Geant4-DNA Project

This Special Report presents a description of Geant4-DNA user applications dedicated to the simulation of track structures (TS) in liquid water and associated physical quantities (e.g., range, stopping power, mean free path…). These example applications are included in the Geant4 Monte Carlo toolkit and are available in open access. Each application is described and comparisons to recent international recommendations are shown (e.g., ICRU, MIRD), when available. The influence of physics models available in Geant4-DNA for the simulation of electron interactions in liquid water is discussed. Thanks to these applications, the authors show that the most recent sets of physics models available in Geant4-DNA (the so-called "option4" and "option 6" sets) enable more accurate simulation of stopping powers, dose point kernels, and W-values in liquid water, than the default set of models ("option 2") initially provided in Geant4-DNA. They also serve as reference applications for Geant4-DNA users interested in TS simulations.

Direct electron irradiation of DNA in a fully aqueous environment. Damage determination in combination with Monte Carlo simulations

We report on a study in which plasmid DNA in water was irradiated with 30 keV electrons generated by a scanning electron microscope and passed through a 100 nm thick Si₃N₄ membrane. The corresponding Monte Carlo simulations suggest that the kinetic energy spectrum of the electrons throughout the water is dominated by low energy electrons (<100 eV). The DNA radiation damage, single-strand breaks (SSBs) and double-strand breaks (DSBs), was determined by gel electrophoresis. The median lethal dose of D_1/2 = 1.7 ± 0.3 Gy was found to be much smaller as compared to partially or fully hydrated DNA irradiated under vacuum conditions. The ratio of the DSBs to SSBs was found to be 1 : 12 as compared to 1 : 88 found for hydrated DNA. Our method enables quantitative measurements of radiation damage to biomolecules (DNA, proteins) in solutions under varying conditions (pH, salinity, co-solutes) for an electron energy range which is difficult to probe by standard methods.

Targeted alpha therapy with 212Pb or 225Ac: Change in RBE from daughter migration

Targeted α-therapy (TAT) could be delivered early to patients who are at a high-risk for developing brain metastases, targeting the areas of the vasculature where tumor cells are penetrating into the brain. We have utilized a Monte Carlo model representing brain vasculature to calculate physical dose and DNA damage from the α-emitters ²²⁵Ac and ²¹²Pb. The micron-scale dose distributions from all radioactive decay products were modeled in Geant4, including the eV-scale interactions using the Geant4-DNA models. These interactions were then superimposed on an atomic-scale DNA model to estimate strand break yields. In addition to ²²⁵Ac having a higher dose per decay than ²¹²Pb, it also has a double strand break yield per decay that is 4.7 ± 0.5 times that of ²¹²Pb. However, the efficacy of both nuclides depends on retaining the daughter nuclei at the target location in the brain vasculature. The relative biological effectiveness (RBE) of ²²⁵Ac and ²¹²Pb are similar when the entire decay chains are included, with maxima of 2.7 ± 0.6 and 2.5 ± 0.5 (respectively), and RBE values of about 2 to a depth of 80 μm. If the initial daughter is lost, the RBE of ²¹²Pb is completely reduced to 1 or lower and the RBE of ²²⁵Ac is approximately 2 only for the first 40 μm.

Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio

Simulation of water radiolysis and the subsequent chemistry provides important information on the effect of ionizing radiation on biological material. The Geant4 Monte Carlo toolkit has added chemical processes via the Geant4-DNA project. The TOPAS tool simplifies the modeling of complex radiotherapy applications with Geant4 without requiring advanced computational skills, extending the pool of users. Thus, a new extension to TOPAS, TOPAS-nBio, is under development to facilitate the configuration of track-structure simulations as well as water radiolysis simulations with Geant4-DNA for radiobiological studies. In this work, radiolysis simulations were implemented in TOPAS-nBio. Users may now easily add chemical species and their reactions, and set parameters including branching ratios, dissociation schemes, diffusion coefficients, and reaction rates. In addition, parameters for the chemical stage were re-evaluated and updated from those used by default in Geant4-DNA to improve the accuracy of chemical yields. Simulation results of time-dependent and LET-dependent primary yields Gx (chemical species per 100 eV deposited) produced at neutral pH and 25 °C by short track-segments of charged particles were compared to published measurements. The LET range was 0.05-230 keV µm-1. The calculated Gx values for electrons satisfied the material balance equation within 0.3%, similar for protons albeit with long calculation time. A smaller geometry was used to speed up proton and alpha simulations, with an acceptable difference in the balance equation of 1.3%. Available experimental data of time-dependent G-values for [Formula: see text] agreed with simulated results within 7%  ±  8% over the entire time range; for [Formula: see text] over the full time range within 3%  ±  4%; for H2O2 from 49%  ±  7% at earliest stages and 3%  ±  12% at saturation. For the LET-dependent Gx, the mean ratios to the experimental data were 1.11  ±  0.98, 1.21  ±  1.11, 1.05  ±  0.52, 1.23  ±  0.59 and 1.49  ±  0.63 (1 standard deviation) for [Formula: see text], [Formula: see text], H2, H2O2 and [Formula: see text], respectively. In conclusion, radiolysis and subsequent chemistry with Geant4-DNA has been successfully incorporated in TOPAS-nBio. Results are in reasonable agreement with published measured and simulated data.

Intratumoral Injection of Low-Energy Photon-Emitting Gold Nanoparticles: A Microdosimetric Monte Carlo-Based Model

Gold nanoparticles (Au NPs) distributed in the vicinity of low-dose rate (LDR) brachytherapy seeds could multiply their efficacy thanks to the secondary emissions induced by the photoelectric effect. Injections of radioactive LDR gold nanoparticles (LDR Au NPs), instead of conventional millimeter-size radioactive seeds surrounded by Au NPs, could further enhance the dose by distributing the radioactivity more precisely and homogeneously in tumors. However, the potential of LDR Au NPs as an emerging strategy to treat cancer is strongly dependent on the macroscopic diffusion of the NPs in tumors, as well as on their microscopic internalization within the cells. Understanding the relationship between interstitial and intracellular distribution of NPs, and the outcomes of dose deposition in the cancer tissue is essential for considering future applications of radioactive Au NPs in oncology. Here, LDR Au NPs (¹⁰³Pd:Pd@Au-PEG NPs) were injected in prostate cancer tumors. The particles were visualized at time-points by computed tomography imaging ( in vivo), transmission electron microscopy ( ex vivo), and optical microscopy ( ex vivo). These data were used in a Monte Carlo-based dosimetric model to reveal the dose deposition produced by LDR Au NPs both at tumoral and cellular scales. ¹⁰³Pd:Pd@Au-PEG NPs injected in tumors produce a strong dose enhancement at the intracellular level. However, energy deposition is mainly confined around vesicles filled with NPs, and not necessarily close to the nuclei. This suggests that indirect damage caused by the production of reactive oxygen species might be the leading therapeutic mechanism of tumor growth control, over direct damage to the DNA.

Geant4-DNA track-structure simulations for gold nanoparticles: The importance of electron discrete models in nanometer volumes

PURPOSE

Gold nanoparticles (GNPs) are known to enhance the absorbed dose in their vicinity following photon-based irradiation. To investigate the therapeutic effectiveness of GNPs, previous Monte Carlo simulation studies have explored GNP dose enhancement using mostly condensed-history models. However, in general, such models are suitable for macroscopic volumes and for electron energies above a few hundred electron volts. We have recently developed, for the Geant4-DNA extension of the Geant4 Monte Carlo simulation toolkit, discrete physics models for electron transport in gold which include the description of the full atomic de-excitation cascade. These models allow event-by-event simulation of electron tracks in gold down to 10 eV. The present work describes how such specialized physics models impact simulation-based studies on GNP-radioenhancement in a context of x-ray radiotherapy.

METHODS

The new discrete physics models are compared to the Geant4 Penelope and Livermore condensed-history models, which are being widely used for simulation-based NP radioenhancement studies. An ad hoc Geant4 simulation application has been developed to calculate the absorbed dose in liquid water around a GNP and its radioenhancement, caused by secondary particles emitted from the GNP itself, when irradiated with a monoenergetic electron beam. The effect of the new physics models is also quantified in the calculation of secondary particle spectra, when originating in the GNP and when exiting from it.

RESULTS

The new physics models show similar backscattering coefficients with the existing Geant4 Livermore and Penelope models in large volumes for 100 keV incident electrons. However, in submicron sized volumes, only the discrete models describe the high backscattering that should still be present around GNPs at these length scales. Sizeable differences (mostly above a factor of 2) are also found in the radial distribution of absorbed dose and secondary particles between the new and the existing Geant4 models. The degree to which these differences are due to intrinsic limitations of the condensed-history models or to differences in the underling scattering cross sections requires further investigation.

CONCLUSIONS

Improved physics models for gold are necessary to better model the impact of GNPs in radiotherapy via Monte Carlo simulations. We implemented discrete electron transport models for gold in Geant4 that is applicable down to 10 eV including the modeling of the full de-excitation cascade. It is demonstrated that the new model has a significant positive impact on particle transport simulations in gold volumes with submicron dimensions compared to the existing Livermore and Penelope condensed-history models of Geant4.

Observation of dose-rate dependence in a Fricke dosimeter irradiated at low dose rates with monoenergetic X-rays

Absolute measurements of the radiolytic yield of Fe3+ in a ferrous sulphate dosimeter formulation (6 mM Fe2+), with a 20 keV x-ray monoenergetic beam, are reported. Dose-rate suppression of the radiolytic yield was observed at dose rates lower than and different in nature to those previously reported with x-rays. We present evidence that this effect is most likely to be due to recombination of free radicals radiolytically produced from water. The method used to make these measurements is also new and it provides radiolytic yields which are directly traceable to the SI standards system. The data presented provides new and exacting tests of radiation chemistry codes.

Average stopping powers for electron and photon sources for radiobiological modeling and microdosimetric applications

This study concerns calculation of the average electronic stopping power for photon and electron sources. It addresses two problems that have not yet been fully resolved. The first is defining the electron spectrum used for averaging in a way that is most suitable for radiobiological modeling. We define it as the spectrum of electrons entering the sensitive to radiation volume (SV) within the cell nucleus, at the moment they enter the SV. For this spectrum we derive a formula that combines linearly the fluence spectrum and the source spectrum. The latter is the distribution of initial energies of electrons produced by a source. Previous studies used either the fluence or source spectra, but not both, thereby neglecting a part of the complete spectrum. Our derived formula reduces to these two prior methods in the case of high and low energy sources, respectively. The second problem is extending electron spectra to low energies. Previous studies used an energy cut-off on the order of 1 keV. However, as we show, even for high energy sources, such as 60Co, electrons with energies below 1 keV contribute about 30% to the dose. In this study all the spectra were calculated with Geant4-DNA code and a cut-off energy of only 11 eV. We present formulas for calculating frequency- and dose-average stopping powers, numerical results for several important electron and photon sources, and tables with all the data needed to use our formulas for arbitrary electron and photon sources producing electrons with initial energies up to  ∼1 MeV.

Simulation of Radiation Damage to Neural Cells with the Geant4-DNA Toolkit

To help in understanding the physical and biological mechanisms underlying effects of cosmic and therapeutic types of radiation on the central nervous system (CNS), we have developed an original neuron application based on the Geant4 Monte Carlo simulation toolkit, in particular on its biophysical extension Geant4-DNA. The applied simulation technique provides a tool for the simulation of physical, physico-chemical and chemical processes (e.g. production of water radiolysis species in the vicinity of neurons) in realistic geometrical model of neural cells exposed to ionizing radiation. The present study evaluates the microscopic energy depositions and water radiolysis species yields within a detailed structure of a selected neuron taking into account its soma, dendrites, axon and spines following irradiation with carbon and iron ions.

Microdosimetry in 3D realistic mitochondria phantoms: Geant4 Monte Carlo tracking of 250keV photons in phantoms reconstructed from microscopic images

Mitochondria are considered to be sensitive radiation targets since they control processes vital to the cell's functioning. These organelles are starting to get attention and some studies are investigating the radiation dose inside them. In previous studies, mitochondria are represented as simple ellipsoids inside the cell not taking into consideration the complexity of their shape. In this study, realistic phantoms are built based on deconvolved widefield fluorescent microscopic images of the mitochondrial networks of fibroblast cells. The phantoms are imported into Geant4 as tessellated volumes taking into account the geometrical complexity of these organelles. Irradiation with 250keV photons is performed and the lineal energy is calculated. The lineal energy distributions inside the produced phantoms are compared with those calculated inside simple volumes, a sphere and an ellipsoid, where the effect of the shape and volume is clearly seen on lineal energies.

Numerical insight into the Dual Radiation Action Theory

This work studies the first and second order mechanisms for the induction of lethal lesions in DNA after irradiation with protons and α-particles. The purpose is to numerically study the mechanisms behind the Dual Radiation Action Theory (DRAT) for these heavy particles. A genetic material geometrical model with atomic resolution is used. It accounts for the explicit position of 5.47 × 10⁹ base pairs, organized up to the chromatin level. The GEANT4-DNA Monte Carlo code was employed to simulate the interaction of these ions with the genetic material model. The number of lethal lesions induced by one- and two-track mechanisms was determined as a function of dose. Values of the α/β ratio were estimated as well as corresponding relative biological effectiveness (RBE). The number of lethal lesions produced by one-track and two-track mechanisms depends on the dose and squared dose, respectively, as predicted by the DRAT. RBE values consistent with experimental results were found, at least for LET below ∼100 keV/μm. Double strand break spatial distributions are qualitatively analyzed. According to this work, the α parameter determined from cellular surviving curves depends on both the physical α and β parameters introduced here, and on the specific energy deposited by a single track into the region of interest. We found an increment of the β parameter with LET, yet at a slower rate than α so that the α/β ratio increases with LET. In addition, we observed and explained the saturation of the α parameter as the dose increases above ∼6 Gy.

Simulation of early DNA damage after the irradiation of a fibroblast cell nucleus using Geant4-DNA

In order to improve the understanding of the mechanisms involved in the generation of early DNA damage, a new calculation chain based on the Geant4-DNA toolkit was developed. This work presents for the first time the simulation of the physical, physicochemical and chemical stages of early radiation damage at the scale of an entire human genome (fibroblast, male) and using Geant4-DNA models. The DnaFabric software was extended to generate and export this nucleus model to a text file with a specific format that can be read by Geant4 user applications. This calculation chain was used to simulate the irradiation of the nucleus by primary protons of different energies (0,5; 0,7; 0,8; 1; 1,5; 2; 3; 4; 5; 10; 20 MeV) and the results, in terms of DNA double strand breaks, agree with experimental data found in the literature (pulsed field electrophoresis technique). These results show that the simulation is consistent and that its parameters are well balanced. Among the different parameters that can be adjusted, our results demonstrate that the criterion used to select direct strand break appears to have a very significant role on the final number of simulated double strand breaks.

Study on dependence of dose enhancement on cluster morphology of gold nanoparticles in radiation therapy using a body-centred cubic model

Gold nanoparticles (GNPs) injected in a body for dose enhancement in radiation therapy are known to form clusters. We investigated the dependence of dose enhancement on the GNP morphology using Monte-Carlo simulations and compared the model predictions with experimental data. The cluster morphology was approximated as a body-centred cubic (BCC) structure by placing GNPs at the 8 corners and the centre of a cube with an edge length of 0.22-1.03 µm in a 4  ×  4  ×  4 µm³ water-filled phantom. We computed the dose enhancement ratio (DER) for 50 and 260 kVp photons as a function of the distance from the cube centre for 12 different cube sizes. A 10 nm-wide concentric shell shaped detector was placed up to 100 nm away from a GNP at the cube centre. For model validation, simulations based on BCC and nanoparticle random distribution (NRD) models were performed using parameters that corresponded to the experimental conditions, which measured increases in the relative biological effect due to GNPs. We employed the linear quadratic model to compute cell surviving fraction (SF) and sensitizer enhancement ratio (SER). The DER is inversely proportional to the distance to the GNPs. The largest DERs were 1.97 and 1.80 for 50 kVp and 260 kVp photons, respectively. The SF predicted by the BCC model agreed with the experimental value within 10%, up to a 5 Gy dose, while the NRD model showed a deviation larger than 10%. The SERs were 1.21  ±  0.13, 1.16  ±  0.11, and 1.08  ±  0.11 according to the experiment, BCC, and NRD models, respectively. We most accurately predicted the GNP radiosensitization effect using the BCC approximation and suggest that the BCC model is effective for use in nanoparticle dosimetry.

A general mechanistic model enables predictions of the biological effectiveness of different qualities of radiation

Predicting the responses of biological systems to ionising radiation is extremely challenging, particularly when comparing X-rays and heavy charged particles, due to the uncertainty in their Relative Biological Effectiveness (RBE). Here we assess the power of a novel mechanistic model of DNA damage repair to predict the sensitivity of cells to X-ray, proton or carbon ion exposures in vitro against over 800 published experiments. By specifying the phenotypic characteristics of cells, the model was able to effectively stratify X-ray radiosensitivity (R² = 0.74) without the use of any cell-specific fitting parameters. This model was extended to charged particle exposures by integrating Monte Carlo calculated dose distributions, and successfully fit to cellular proton radiosensitivity using a single dose-related parameter (R² = 0.66). Using these parameters, the model was also shown to be predictive of carbon ion RBE (R² = 0.77). This model can effectively predict cellular sensitivity to a range of radiations, and has the potential to support developments of personalised radiotherapy independent of radiation type.

Nanodosimetric Simulation of Direct Ion-Induced DNA Damage Using Different Chromatin Geometry Models

Monte Carlo based simulation has proven useful in investigating the effect of proton-induced DNA damage and the processes through which this damage occurs. Clustering of ionizations within a small volume can be related to DNA damage through the principles of nanodosimetry. For simulation, it is standard to construct a small volume of water and determine spatial clusters. More recently, realistic DNA geometries have been used, tracking energy depositions within DNA backbone volumes. Traditionally a chromatin fiber is built within the simulation and identically replicated throughout a cell nucleus, representing the cell in interphase. However, the in vivo geometry of the chromatin fiber is still unknown within the literature, with many proposed models. In this work, the Geant4-DNA toolkit was used to build three chromatin models: the solenoid, zig-zag and cross-linked geometries. All fibers were built to the same chromatin density of 4.2 nucleosomes/11 nm. The fibers were then irradiated with protons (LET 5-80 keV/μm) or alpha particles (LET 63-226 keV/μm). Nanodosimetric parameters were scored for each fiber after each LET and used as a comparator among the models. Statistically significant differences were observed in the double-strand break backbone size distributions among the models, although nonsignificant differences were noted among the nanodosimetric parameters. From the data presented in this article, we conclude that selection of the solenoid, zig-zag or cross-linked chromatin model does not significantly affect the calculated nanodosimetric parameters. This allows for a simulation-based cell model to make use of any of these chromatin models for the scoring of direct ion-induced DNA damage.

Flagged uniform particle splitting for variance reduction in proton and carbon ion track-structure simulations

Flagged uniform particle splitting was implemented with two methods to improve the computational efficiency of Monte Carlo track structure simulations with TOPAS-nBio by enhancing the production of secondary electrons in ionization events. In method 1 the Geant4 kernel was modified. In method 2 Geant4 was not modified. In both methods a unique flag number assigned to each new split electron was inherited by its progeny, permitting reclassification of the split events as if produced by independent histories. Computational efficiency and accuracy were evaluated for simulations of 0.5-20 MeV protons and 1-20 MeV u^-1 carbon ions for three endpoints: (1) mean of the ionization cluster size distribution, (2) mean number of DNA single-strand breaks (SSBs) and double-strand breaks (DSBs) classified with DBSCAN, and (3) mean number of SSBs and DSBs classified with a geometry-based algorithm. For endpoint (1), simulation efficiency was 3 times lower when splitting electrons generated by direct ionization events of primary particles than when splitting electrons generated by the first ionization events of secondary electrons. The latter technique was selected for further investigation. The following results are for method 2, with relative efficiencies about 4.5 times lower for method 1. For endpoint (1), relative efficiency at 128 split electrons approached maximum, increasing with energy from 47.2  ±  0.2 to 66.9  ±  0.2 for protons, decreasing with energy from 51.3  ±  0.4 to 41.7  ±  0.2 for carbon. For endpoint (2), relative efficiency increased with energy, from 20.7  ±  0.1 to 50.2  ±  0.3 for protons, 15.6  ±  0.1 to 20.2  ±  0.1 for carbon. For endpoint (3) relative efficiency increased with energy, from 31.0  ±  0.2 to 58.2  ±  0.4 for protons, 23.9  ±  0.1 to 26.2  ±  0.2 for carbon. Simulation results with and without splitting agreed within 1% (2 standard deviations) for endpoints (1) and (2), within 2% (1 standard deviation) for endpoint (3). In conclusion, standard particle splitting variance reduction techniques can be successfully implemented in Monte Carlo track structure codes.

Metallic nanoparticles irradiated by low-energy protons for radiation therapy: Are there significant physical effects to enhance the dose delivery?

PURPOSE

To identify which physical properties of nanoparticles are correlated with the survival fraction of cells exposed in vitro to low-energy protons in combination with nanoparticles.

METHODS

The Geant4 simulation toolkit (version 10.3) was used to model nanoparticles of different sizes (5-50 nm) and materials (Ti, Zr, Hf, Ta, Au, Pt), with or without an organic capping ensuring biocompatibility and to irradiate them with 1.3 or 4 MeV protons and 5.3 MeV alpha particles. The spectra of secondary electrons inside and at the nanoparticle surface were computed, as well as electron yields, Auger and organic capping contribution, trapping in metal bulk and linear energy transfer profiles as a function of distance from the nanoparticle center. In a next step, an in silico cell model was designed and loaded with gold nanoparticles, according to experimental uptake values. Dose to the cell was evaluated macroscopically and microscopically in 100 × 100 × 100 nm³ voxels for different radiation qualities.

RESULTS

The cell geometry showed that radiation enhancement is negligible for the gold concentration used and for any radiation quality. However, when the single nanoparticle geometry is considered, we observed a local LET in its vicinity considerably higher than for the water equivalent case (up to 5 keV/μm at the titanium nanoparticle surface compared to 2.5 keV/μm in the water case). The yield of secondary electrons per primary interaction with 1.3 MeV protons was found to be most favorable for titanium (1.54), platinum (1.44), and gold (1.32), although results for higher Z metals are probably underestimated due to the incomplete simulation of de-excitation cascade in outer shells. It was also found that the organic capping contributed mostly to the production of low-energy electrons, adding a spike of dose near the nanoparticle surface. Indeed, the yield for the coated gold nanoparticle increased to 1.53 when exposed to 1.3 MeV protons. Although most electrons are retained inside larger nanoparticles (50 nm), it was shown that their yield is comparable to smaller sizes and that the linear energy transfer profile is better. From a combination of ballistic and nanoparticle size factors, it was concluded that 10-nm gold nanoparticles were better inducers of additional cell killing than 5-nm gold nanoparticles, matching our previous in vitro study.

CONCLUSIONS

Although effects from a physical standpoint are limited, the high linear energy transfer profile at the nanoparticle surface generates detrimental events in the cell, in particular ROS-induced damage and local heating.

Monte Carlo Electron Track Structure Calculations in Liquid Water Using a New Model Dielectric Response Function

Monte Carlo track structure codes provide valuable information for understanding radiation effects down to the DNA level, where experimental measurements are most difficult or unavailable. It is well recognized that the performance of such codes, especially at low energies and/or subcellular level, critically depends on the reliability of the interaction cross sections that are used as input in the simulation. For biological media such as liquid water, one of the most challenging issues is the role of condensed-phase effects. For inelastic scattering, such effects can be conveniently accounted for through the complex dielectric response function of the media. However, for this function to be useful it must fulfill some important sum rules and have a simple analytic form for arbitrary energy- and momentum-transfer. The Emfietzoglou-Cucinotta-Nikjoo (ECN) model offers a practical, self-consistent and fully analytic parameterization of the dielectric function of liquid water based on the best available experimental data. An important feature of the ECN model is that it includes, in a phenomenological manner, exchange and correlation effects among the screening electrons, thus, going beyond the random-phase approximation implicit in earlier models. In this work, inelastic cross sections beyond the plane wave Born approximation are calculated for low-energy electrons (10 eV-10 keV) based on the ECN model, and used for Monte Carlo track structure simulations of physical quantities relevant to the microdosimetry of low-energy electrons in liquid water. Important new developments in the physics of inelastic scattering are discussed and their effect on electron track structure is investigated by a comparison against simulations (under otherwise identical conditions) using the Born approximation and a simpler form of the dielectric function based on the Oak Ridge National Laboratory model. The results reveal that both the dielectric function and the corrections to the Born approximation may have a sizeable effect on track structure calculations at the nanometer scale (DNA level), where the details of inelastic scattering and the role of low-energy electrons are most critical.