Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio

Modelling radiobiology

Radiotherapy has played an essential role in cancer treatment for over a century, and remains one of the best-studied methods of cancer treatment. Because of its close links with the physical sciences, it has been the subject of extensive quantitative mathematical modelling, but a complete understanding of the mechanisms of radiotherapy has remained elusive. In part this is because of the complexity and range of scales involved in radiotherapy-from physical radiation interactions occurring over nanometres to evolution of patient responses over months and years. This review presents the current status and ongoing research in modelling radiotherapy responses across these scales, including basic physical mechanisms of DNA damage, the immediate biological responses this triggers, and genetic- and patient-level determinants of response. Finally, some of the major challenges in this field and potential avenues for future improvements are also discussed.

Localized in vivo prodrug activation using radionuclides

Radionuclides used for imaging and therapy can show high molecular specificity in the body with appropriate targeting ligands. We hypothesized that local energy delivered by molecularly targeted radionuclides could chemically activate prodrugs at disease sites while avoiding activation in off-target sites of toxicity. As proof-of-principle, we tested whether this strategy of " RA dionuclide i nduced D rug E ngagement for R elease" ( RAiDER ) could locally deliver combined radiation and chemotherapy to maximize tumor cytotoxicity while minimizing exposure to activated chemotherapy in off-target sites.

Methods

We screened the ability of radionuclides to chemically activate a model radiation-activated prodrug consisting of the microtubule destabilizing monomethyl auristatin E caged by a radiation-responsive phenyl azide ("caged-MMAE") and interpreted experimental results using the radiobiology computational simulation suite TOPAS-nBio. RAiDER was evaluated in syngeneic mouse models of cancer using fibroblast activation protein inhibitor (FAPI) agents 99m Tc-FAPI-34 and 177 Lu-FAPI-04, the prostate-specific membrane antigen (PSMA) agent 177 Lu-PSMA-617, combined with caged-MMAE or caged-exatecan. Biodistribution in mice, combined with clinical dosimetry, estimated the relationship between radiopharmaceutical uptake in patients and anticipated concentrations of activated prodrug using RAiDER.

Results

RAiDER efficiency varied by 250-fold across radionuclides ( 99m Tc> 177 Lu> 64 Cu> 68 Ga> 223 Ra> 18 F), yielding up to 1.22µM prodrug activation per Gy of exposure from 99m Tc. Computational simulations implicated low-energy electron-mediated free radical formation as driving prodrug activation. Clinically relevant radionuclide concentrations chemically activated caged-MMAE restored its ability to destabilize microtubules and increased its cytotoxicity by up to 600-fold compared to non-irradiated prodrug. Mice treated with 99m Tc-FAPI-34 and caged-MMAE accumulated up to 3000× greater concentrations of activated MMAE in tumors compared to other tissues. RAiDER with 99m Tc-FAPI-34 or 177 Lu-FAPI-04 delayed tumor growth, while monotherapies did not ( P <0.03). Clinically-guided dosimetry suggests sufficient radiation doses can be delivered to activate therapeutically meaningful levels of prodrug.

Conclusion

This proof-of-concept study shows that RAiDER is compatible with multiple radionuclides commonly used in nuclear medicine and has the potential to improve the efficacy of radiopharmaceutical therapies to treat cancer safely. RAiDER thus shows promise as an effective strategy to treat disseminated malignancies and broadens the capability of radiopharmaceuticals to trigger diverse biological and therapeutic responses.

Abstract Figure

Review of chemical models and applications in Geant4-DNA: Report from the ESA BioRad III Project

A chemistry module has been implemented in Geant4-DNA since Geant4 version 10.1 to simulate the radiolysis of water after irradiation. It has been used in a number of applications, including the calculation of G-values and early DNA damage, allowing the comparison with experimental data. Since the first version, numerous modifications have been made to the module to improve the computational efficiency and extend the simulation to homogeneous kinetics in bulk solution. With these new developments, new applications have been proposed and released as Geant4 examples, showing how to use chemical processes and models. This work reviews the models implemented and application developments for modeling water radiolysis in Geant4-DNA as reported in the ESA BioRad III Project.

Primary study of the relative and compound biological effectiveness model for boron neutron capture therapy based on nanodosimetry

BACKGROUND

The current radiobiological model employed for boron neutron capture therapy (BNCT) treatment planning, which relies on microdosimetry, fails to provide an accurate representation the biological effects of BNCT. The precision in calculating the relative biological effectiveness (RBE) and compound biological effectiveness (CBE) plays a pivotal role in determining the therapeutic efficacy of BNCT. Therefore, this study focuses on how to improve the accuracy of the biological effects of BNCT.

PURPOSE

The purpose of this study is to propose new radiation biology models based on nanodosimetry to accurately assess RBE and CBE for BNCT.

METHODS

Nanodosimetry, rooted in ionization cluster size distributions (ICSD), introduces a novel approach to characterize radiation quality by effectively delineating RBE through the ion track structure at the nanoscale. In the context of prior research, this study presents a computational model for the nanoscale assessment of RBE and CBE. We establish a simplified model of DNA chromatin fiber using the Monte Carlo code TOPAS-nBio to evaluate the applicability of ICSD to BNCT and compute nanodosimetric parameters.

RESULTS

Our investigation reveals that both homogeneous and heterogeneous nanodosimetric parameters, as well as the corresponding biological model coefficients α and β, along with RBE values, exhibit variations in response to varying intracellular 10B concentrations. Notably, the nanodosimetric parameterM 1 C 2 $M_1^{{{\mathrm{C}}}_2}$ effectively captures the fluctuations in model coefficients α and RBE.

CONCLUSION

Our model facilitates a nanoscale analysis of BNCT, enabling predictions of nanodosimetric quantities for secondary ions as well as RBE, CBE, and other essential biological metrics related to the distribution of boron. This contribution significantly enhances the precision of RBE calculations and holds substantial promise for future applications in treatment planning.

Comparison of two methods simulating inter-track interactions using the radiobiological Monte Carlo toolkit TOPAS-nBio

Objective.To compare two independently developed methods that enable modelling inter-track interactions in TOPAS-nBio by examining the yield of radiolytic species in radiobiological Monte Carlo track structure simulations. One method uses a phase space file to assign more than one primary to one event, allowing for inter-track interaction between these primary particles. This method has previously been developed by this working group and published earlier. Using the other method, chemical reactions are simulated based on a new version of the independent reaction time approach to allow inter-track interactions.Approach.G-values were calculated and compared using both methods for different numbers of tracks able to undergo inter-track interactions.Main results.Differences in theG-values simulated with the two methods strongly depend on the molecule type, and deviations can range up to 3.9% (H2O2), although, on average, the deviations are smaller than 1.5%.Significance.Both methods seem to be suitable for simulating inter-track interactions, as they provide comparableG-values even though both techniques were developed independently of each other.

Effects of Differing Underlying Assumptions in In Silico Models on Predictions of DNA Damage and Repair

The induction and repair of DNA double-strand breaks (DSBs) are critical factors in the treatment of cancer by radiotherapy. To investigate the relationship between incident radiation and cell death through DSB induction many in silico models have been developed. These models produce and use custom formats of data, specific to the investigative aims of the researchers, and often focus on particular pairings of damage and repair models. In this work we use a standard format for reporting DNA damage to evaluate combinations of different, independently developed, models. We demonstrate the capacity of such inter-comparison to determine the sensitivity of models to both known and implicit assumptions. Specifically, we report on the impact of differences in assumptions regarding patterns of DNA damage induction on predicted initial DSB yield, and the subsequent effects this has on derived DNA repair models. The observed differences highlight the importance of considering initial DNA damage on the scale of nanometres rather than micrometres. We show that the differences in DNA damage models result in subsequent repair models assuming significantly different rates of random DSB end diffusion to compensate. This in turn leads to disagreement on the mechanisms responsible for different biological endpoints, particularly when different damage and repair models are combined, demonstrating the importance of inter-model comparisons to explore underlying model assumptions.

Single-cell DNA sequencing-a potential dosimetric tool

We hypothesised that single-cell whole-genome sequencing has the potential to detect mutational differences in the genomes of the cells that are irradiated with different doses of radiation and we set out to test our hypothesis using in silico and in vitro experiments. In this manuscript, we present our findings from a Monte Carlo single-cell irradiation simulation performed in TOPAS-nBio using a custom-built geometric nuclear deoxyribonucleic acid (DNA) model, which predicts a significant dose dependence of the number of cluster damages per cell as a function of radiation dose. We also present preliminary experimental results, obtained from single-cell whole-genome DNA sequencing analysis performed on cells irradiated with different doses of radiation, showing promising agreement with the simulation results.

Prospects of nanoparticle-based radioenhancement for radiotherapy

Radiotherapy is a key pillar of solid cancer treatment. Despite a high level of conformal dose deposition, radiotherapy is limited due to co-irradiation of organs at risk and subsequent normal tissue toxicities. Nanotechnology offers an attractive opportunity for increasing the efficacy and safety of cancer radiotherapy. Leveraging the freedom of design and the growing synthetic capabilities of the nanomaterial-community, a variety of engineered nanomaterials have been designed and investigated as radiosensitizers or radioenhancers. While research so far has been primarily focused on gold nanoparticles and other high atomic number materials to increase the absorption cross section of tumor tissue, recent studies are challenging the traditional concept of high-Z nanoparticle radioenhancers and highlight the importance of catalytic activity. This review provides a concise overview on the knowledge of nanoparticle radioenhancement mechanisms and their quantification. It critically discusses potential radioenhancer candidate materials and general design criteria for different radiation therapy modalities, and concludes with research priorities in order to advance the development of nanomaterials, to enhance the efficacy of radiotherapy and to increase at the same time the therapeutic window.

A new approach for simulating inhomogeneous chemical kinetics

In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling [Formula: see text]- and [Formula: see text]-radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method's efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach's capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method's suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

Calculation of the DNA damage yield and relative biological effectiveness in boron neutron capture therapy via the Monte Carlo track structure simulation

Objective.Boron neutron capture therapy (BNCT) is an advanced cellular-level hadron therapy that has exhibited remarkable therapeutic efficacy in the treatment of locally invasive malignancies. Despite its clinical success, the intricate nature of relative biological effectiveness (RBE) and mechanisms responsible for DNA damage remains elusive. This work aims to quantify the RBE of compound particles (i.e. alpha and lithium) in BNCT based on the calculation of DNA damage yields via the Monte Carlo track structure (MCTS) simulation.Approach. The TOPAS-nBio toolkit was employed to conduct MCTS simulations. The calculations encompassed four steps: determination of the angle and energy spectra on the nuclear membrane, quantification of the database containing DNA damage yields for ions with specific angle and energy, accumulation of the database and spectra to obtain the DNA damage yields of compound particles, and calculation of the RBE by comparison yields of double-strand break (DSB) with the reference gamma-ray. Furthermore, the impact of cell size and microscopic boron distribution was thoroughly discussed.Main results. The DSB yields induced by compound particles in three types of spherical cells (radius equal to 10, 8, and 6μm) were found to be 13.28, 17.34, 22.15 Gy Gbp-1for boronophenylalanine (BPA), and 1.07, 3.45, 8.32 Gy Gbp-1for sodium borocaptate (BSH). The corresponding DSB-based RBE values were determined to be 1.90, 2.48, 3.16 for BPA and 0.15, 0.49, 1.19 for BSH. The calculated DSB-based RBE showed agreement with experimentally values of compound biological effectiveness for melanoma and gliosarcoma. Besides, the DNA damage yield and DSB-based RBE value exhibited an increasing trend as the cell radius decreased. The impact of the boron concentration ratio on RBE diminished once the drug enrichment surpasses a certain threshold.Significance. This work is potential to provide valuable guidance for accurate biological-weighted dose evaluation in BNCT.

A theoretical study of H2 O2 as the surrogate of dose in minibeam radiotherapy, with a diffusion model considering radical removal process

BACKGROUND

Minibeam radiation therapy (MBRT) is an innovative dose delivery method with the potential to spare normal tissue while achieving similar tumor control as conventional radiotherapy. However, it is difficult to use a single dose parameter, such as mean dose, to compare different patterns of MBRT due to the spatially fractionated radiation. Also, the mechanism leading to the biological effects is still unknown.

PURPOSE

This study aims to demonstrate that the hydrogen peroxide (H2 O2 ) distribution could serve as a surrogate of dose distribution when comparing different patterns of MBRT.

METHODS

A free diffusion model (FDM) for H2 O2 developed with Fick's second law was compared with a previously published model based on Monte Carlo & convolution method. Since cells form separate compartments that can eliminate H2 O2 radicals diffusing inside the cell, a term describing the elimination was introduced into the equation. The FDM and the diffusion model considering removal (DMCR) were compared by simulating various dose rate irradiation schemes and uniform irradiation. Finally, the DMCR was compared with previous microbeam and minibeam animal experiments.

RESULTS

Compared with a previous Monte Carlo & Convolution method, this analytical method provides more accurate results. Furthermore, the new model shows H2 O2 concentration distribution instead of the time to achieve a certain H2 O2 uniformity. The comparison between FDM and DMCR showed that H2 O2 distribution from FDM varied with dose rate irradiation, while DMCR had consistent results. For uniform irradiation, FDM resulted in a Gaussian distribution, while the H2 O2 distribution from DMCR was close to the dose distribution. The animal studies' evaluation showed a correlation between the H2 O2 concentration in the valley region and treatment outcomes.

CONCLUSION

DMCR is a more realistic model for H2 O2 simulation than the FDM. In addition, the H2 O2 distribution can be a good surrogate of dose distribution when the minibeam effect could be observed.

Modeling ultra-high dose rate electron and proton FLASH effect with the physicochemical approach

Objective. A physicochemical model built on the radiochemical kinetic theory was recently proposed in (Labarbeet al2020) to explain the FLASH effect. We performed extensive simulations to scrutinize its applicability for oxygen depletion studies and FLASH-related experiments involving both proton and electron beams.Approach. Using the dose and beam delivery parameters for each FLASH experiment, we numerically solved the radiochemical rate equations comprised of a set of coupled nonlinear ordinary differential equations to obtain the area under the curve (AUC) of radical concentrations.Main results. The modeled differences in AUC induced by ultra-high dose rates appeared to correlate well with the FLASH effect. (i) For the whole brain irradiation of mice performed in (Montay-Gruelet al2017), the threshold dose rate values for memory preservation coincided with those at which AUC started to decrease much less rapidly. (ii) For the proton pencil beam scanning FLASH of (Cunninghamet al2021), we found linear correlations between radicals' AUC and the biological endpoints: TGF-β1, leg contracture and plasma level of cytokine IL-6. (iii) Compatible with the findings of the proton FLASH experiment in (Kimet al2021), we found that radicals' AUC at the entrance and mid-Spread-Out Bragg peak regions were highly similar. In addition, our model also predicted ratios of oxygen depletionG-values between normal and UHDR irradiation similar to those observed in (Caoet al2021) and (El Khatibet al2022).Significance. Collectively, our results suggest that the normal tissue sparing conferred by UHDR irradiation may be due to the lower degree of exposure to peroxyl and superoxide radicals. We also found that the differential effect of dose rate on the radicals' AUC was less pronounced at lower initial oxygen levels, a trait that appears to align with the FLASH differential effect on normal versus tumor tissues.

The complexity of DNA damage by radiation follows a Gamma distribution: insights from the Microdosimetric Gamma Model

Introduction

DNA damage is the main predictor of response to radiation therapy for cancer. Its Q8 quantification and characterization are paramount for treatment optimization, particularly in advanced modalities such as proton and alpha-targeted therapy.

Methods

We present a novel approach called the Microdosimetric Gamma Model (MGM) to address this important issue. The MGM uses the theory of microdosimetry, specifically the mean energy imparted to small sites, as a predictor of DNA damage properties. MGM provides the number of DNA damage sites and their complexity, which were determined using Monte Carlo simulations with the TOPAS-nBio toolkit for monoenergetic protons and alpha particles. Complexity was used together with a illustrative and simplistic repair model to depict the differences between high and low LET radiations.

Results

DNA damage complexity distributions were were found to follow a Gamma distribution for all monoenergetic particles studied. The MGM functions allowed to predict number of DNA damage sites and their complexity for particles not simulated with microdosimetric measurements (yF) in the range of those studied.

Discussion

Compared to current methods, MGM allows for the characterization of DNA damage induced by beams composed of multi-energy components distributed over any time configuration and spatial distribution. The output can be plugged into ad hoc repair models that can predict cell killing, protein recruitment at repair sites, chromosome aberrations, and other biological effects, as opposed to current models solely focusing on cell survival. These features are particularly important in targeted alpha-therapy, for which biological effects remain largely uncertain. The MGM provides a flexible framework to study the energy, time, and spatial aspects of ionizing radiation and offers an excellent tool for studying and optimizing the biological effects of these radiotherapy modalities.

An integrated Monte Carlo track-structure simulation framework for modeling inter and intra-track effects on homogenous chemistry

Objective. The TOPAS-nBio Monte Carlo track structure simulation code, a wrapper of Geant4-DNA, was extended for its use in pulsed and longtime homogeneous chemistry simulations using the Gillespie algorithm.Approach. Three different tests were used to assess the reliability of the implementation and its ability to accurately reproduce published experimental results: (1) a simple model with a known analytical solution, (2) the temporal evolution of chemical yields during the homogeneous chemistry stage, and (3) radiolysis simulations conducted in pure water with dissolved oxygen at concentrations ranging from 10μM to 1 mM with [H2O2] yields calculated for 100 MeV protons at conventional and FLASH dose rates of 0.286 Gy s-1and 500 Gy s-1, respectively. Simulated chemical yield results were compared closely with data calculated using the Kinetiscope software which also employs the Gillespie algorithm.Main results. Validation results in the third test agreed with experimental data of similar dose rates and oxygen concentrations within one standard deviation, with a maximum of 1% difference for both conventional and FLASH dose rates. In conclusion, the new implementation of TOPAS-nBio for the homogeneous long time chemistry simulation was capable of recreating the chemical evolution of the reactive intermediates that follow water radiolysis.Significance. Thus, TOPAS-nBio provides a reliable all-in-one chemistry simulation of the physical, physico-chemical, non-homogeneous, and homogeneous chemistry and could be of use for the study of FLASH dose rate effects on radiation chemistry.

Monte Carlo simulation of gold nanoparticles for X-ray enhancement application

BACKGROUND

Gold nanoparticles (Au NPs) are regarded as potential agents that enhance the radiosensitivity of tumor cells for theranostic applications. To elucidate the biological mechanisms of radiation dose enhancement effects of Au NPs as well as DNA damage attributable to the inclusion of Au NPs, Monte Carlo (MC) simulations have been deployed in a number of studies.

SCOPE OF REVIEW

This review paper concisely collates and reviews the information reported in the simulation research in terms of MC simulation of radiosensitization and dose enhancement effects caused by the inclusion of Au NPs in tumor cells, simulation mechanisms, benefits and limitations.

MAJOR CONCLUSIONS

In this review, we first explore the recent advances in MC simulation on Au NPs radiosensitization. The MC methods, physical dose enhancement and enhanced chemical and biological effects is discussed, followed by some results regarding the prediction of dose enhancement. We then review Multi-scale MC simulations of Au NP-induced DNA damages for X-ray irradiation. Moreover, we explain and look at Multi-scale MC simulations of Au NP-induced DNA damages for X-ray irradiation.

GENERAL SIGNIFICANCE

Using advanced chemical module-implemented MC simulations, there is a need to assess the radiation-induced chemical radicals that contribute to the dose-enhancing and biological effects of multiple Au NPs.

Effects of incoming particle energy and cluster size on the G-value of hydrated electrons

In hydrated electron (e^-_aq) dosimetry, absorbed radiation dose to water is measured by monitoring the concentration of radiation-induced e^-_aq. However, to obtain accurate dose, the radiation chemical yield of e^-_aq, G(e^-_aq), is needed for the radiation quality/setup under investigation. The aim of this study was to investigate the time-evolution of the G-values for the main generated reactive species during water radiolysis using GEANT4-DNA. The effects of cluster size and linear energy transfer (LET) on G(e^-_aq) were examined. Validity of GEANT4-DNA for calculation of G(e^-_aq) for clinically relevant energies was studied. Three scenarios were investigated with different phantom sizes and incoming electron energies (1 keV to 1 MeV). The time evolution of G(e^-_aq) was in good agreement with published data and did not change with decreasing phantom size. The time-evolution of the G-values increases with increasing LET for all radiolytic species. The particle tracks formed with high-energy electrons are separated and the resulting reactive species develop independently in time. With decreasing energy, the mean separation distance between reactive species decreases. The particle tracks might not initially overlap but will overlap shortly thereafter due to diffusion of reactive species, increasing the probability of e^-_aq recombination with other species. This also explains the decrease of G(e^-_aq) with cluster size and LET. Finally, if all factors are kept constant, as the incoming electron energy increases to clinically relevant energies, G(e^-_aq) remains similar to its value at 1 MeV, hence GEANT4-DNA can be used for clinically relevant energies.

Investigating the potential contribution of inter-track interactions within ultra-high dose-rate proton therapy

Objective. Laser-accelerated protons offer an alternative delivery mechanism for proton therapy. This technique delivers dose-rates of ≥10⁹Gy s^-1, many orders of magnitude greater than used clinically. Such ultra-high dose-rates reduce delivery time to nanoseconds, equivalent to the lifetime of reactive chemical species within a biological medium. This leads to the possibility of inter-track interactions between successive protons within a pulse, potentially altering the yields of damaging radicals if they are in sufficient spatial proximity. This work investigates the temporal evolution of chemical species for a range of proton energies and doses to quantify the circumstances required for inter-track interactions, and determine any relevance within ultra-high dose-rate proton therapy.Approach. The TOPAS-nBio Monte Carlo toolkit was used to investigate possible inter-track interactions. Firstly, protons between 0.5 and 100 MeV were simulated to record the radial track dimensions throughout the chemical stage from 1 ps to 1μs. Using the track areas, the geometric probability of track overlap was calculated for various exposures and timescales. A sample of irradiations were then simulated in detail to compare any change in chemical yields for independently and instantaneously delivered tracks, and validate the analytic model.Main results. Track overlap for a clinical 2 Gy dose was negligible for biologically relevant timepoints for all energies. Overlap probability increased with time after irradiation, proton energy and dose, with a minimum 23 Gy dose required before significant track overlap occurred. Simulating chemical interactions confirmed these results with no change in radical yields seen up to 8 Gy for independently and instantaneously delivered tracks.Significance. These observations suggest that the spatial separation between incident protons is too large for physico-chemical inter-track interactions, regardless of the delivery time, indicating such interactions would not play a role in any potential changes in biological response between laser-accelerated and conventional proton therapy.

Monte-Carlo techniques for radiotherapy applications I: introduction and overview of the different Monte-Carlo codes

Introduction:

The dose calculation plays a crucial role in many aspects of contemporary clinical radiotherapy treatment planning process. It therefore goes without saying that the accuracy of the dose calculation is of very high importance. The gold standard for absorbed dose calculation is the Monte-Carlo algorithm.

Methods:

This first of two papers gives an overview of the main openly available and supported codes that have been widely used for radiotherapy simulations.

Results:

The paper aims to provide an overview of Monte-Carlo in the field of radiotherapy and point the reader in the right direction of work that could help them get started or develop their existing understanding and use of Monte-Carlo algorithms in their practice.

Conclusions:

It also serves as a useful companion to a curated collection of papers on Monte-Carlo that have been published in this journal.

Monte-Carlo techniques for radiotherapy applications II: equipment and source modelling, dose calculations and radiobiology

Introduction:

This is the second of two papers giving an overview of the use of Monte-Carlo techniques for radiotherapy applications.

Methods:

The first paper gave an introduction and introduced some of the codes that are available to the user wishing to model the different aspects of radiotherapy treatment. It also aims to serve as a useful companion to a curated collection of papers on Monte-Carlo that have been published in this journal.

Results and Conclusions:

This paper focuses on the application of Monte-Carlo to specific problems in radiotherapy. These include radiotherapy and imaging beam production, brachytherapy, phantom and patient dosimetry, detector modelling and track structure calculations for micro-dosimetry, nano-dosimetry and radiobiology.

Nano-scale simulation of neuronal damage by galactic cosmic rays

The effects of realistic, deep space radiation environments on neuronal function remain largely unexplored.In silicomodeling studies of radiation-induced neuronal damage provide important quantitative information about physico-chemical processes that are not directly accessible through radiobiological experiments. Here, we present the first nano-scale computational analysis of broad-spectrum galactic cosmic ray irradiation in a realistic neuron geometry. We constructed thousands ofin silicorealizations of a CA1 pyramidal neuron, each with over 3500 stochastically generated dendritic spines. We simulated the entire 33 ion-energy beam spectrum currently in use at the NASA Space Radiation Laboratory galactic cosmic ray simulator (GCRSim) using the TOol for PArticle Simulation (TOPAS) and TOPAS-nBio Monte Carlo-based track structure simulation toolkits. We then assessed the resulting nano-scale dosimetry, physics processes, and fluence patterns. Additional comparisons were made to a simplified 6 ion-energy spectrum (SimGCRSim) also used in NASA experiments. For a neuronal absorbed dose of 0.5 Gy GCRSim, we report an average of 250 ± 10 ionizations per micrometer of dendritic length, and an additional 50 ± 10, 7 ± 2, and 4 ± 2 ionizations per mushroom, thin, and stubby spine, respectively. We show that neuronal energy deposition by proton andα-particle tracks declines approximately hyperbolically with increasing primary particle energy at mission-relevant energies. We demonstrate an inverted exponential relationship between dendritic segment irradiation probability and neuronal absorbed dose for each ion-energy beam. We also find that there are no significant differences in the average physical responses between the GCRSim and SimGCRSim spectra. To our knowledge, this is the first nano-scale simulation study of a realistic neuron geometry using the GCRSim and SimGCRSim spectra. These results may be used as inputs to theoretical models, aid in the interpretation of experimental results, and help guide future study designs.

Radical Production with Pulsed Beams: Understanding the Transition to FLASH

Ultra-high dose rate (UHDR) irradiation regimes have the potential to spare normal tissue while keeping equivalent tumoricidal capacity than conventional dose rate radiotherapy (CONV-RT). This has been called the FLASH effect. In this work, we present a new simulation framework aiming to study the production of radical species in water and biological media under different irradiation patterns. The chemical stage (heterogeneous phase) is based on a nonlinear reaction-diffusion model, implemented in GPU. After the first 1 μs, no further radical diffusion is assumed, and radical evolution may be simulated over long periods of hundreds of seconds. Our approach was first validated against previous results in the literature and then employed to assess the influence of different temporal microstructures of dose deposition in the expected biological damage. The variation of the Normal Tissue Complication Probability (NTCP), assuming the model of Labarbe et al., where the integral of the peroxyl radical concentration over time (AUC-ROO) is taken as surrogate for biological damage, is presented for different intra-pulse dose rate and pulse frequency configurations, relevant in the clinical scenario. These simulations yield that overall, mean dose rate and the dose per pulse are the best predictors of biological effects at UHDR.

Impact of DNA Geometry and Scoring on Monte Carlo Track-Structure Simulations of Initial Radiation-Induced Damage

Track structure Monte Carlo simulations are a useful tool to investigate the damage induced to DNA by ionizing radiation. These simulations usually rely on simplified geometrical representations of the DNA subcomponents. DNA damage is determined by the physical and physicochemical processes occurring within these volumes. In particular, damage to the DNA backbone is generally assumed to result in strand breaks. DNA damage can be categorized as direct (ionization of an atom part of the DNA molecule) or indirect (damage from reactive chemical species following water radiolysis). We also consider quasi-direct effects, i.e., damage originated by charge transfers after ionization of the hydration shell surrounding the DNA. DNA geometries are needed to account for the damage induced by ionizing radiation, and different geometry models can be used for speed or accuracy reasons. In this work, we use the Monte Carlo track structure tool TOPAS-nBio, built on top of Geant4-DNA, for simulation at the nanometer scale to evaluate differences among three DNA geometrical models in an entire cell nucleus, including a sphere/spheroid model specifically designed for this work. In addition to strand breaks, we explicitly consider the direct, quasi-direct, and indirect damage induced to DNA base moieties. We use results from the literature to determine the best values for the relevant parameters. For example, the proportion of hydroxyl radical reactions between base moieties was 80%, and between backbone, moieties was 20%, the proportion of radical attacks leading to a strand break was 11%, and the expected ratio of base damages and strand breaks was 2.5-3. Our results show that failure to update parameters for new geometric models can lead to significant differences in predicted damage yields.

TOPAS-nBio simulation of temperature-dependent indirect DNA strand break yields

Current Monte Carlo simulations of DNA damage have been reported only at ambient temperature. The aim of this work is to use TOPAS-nBio to simulate the yields of DNA single-strand breaks (SSBs) and double-strand breaks (DSBs) produced in plasmids under low-LET irradiation incorporating the effect of the temperature changes in the environment. A new feature was implemented in TOPAS-nBio to incorporate reaction rates used in the simulation of the chemical stage of water radiolysis as a function of temperature. The implemented feature was verified by simulating temperature-dependent G-values of chemical species in liquid water from 20 °C to 90 °C. For radiobiology applications, temperature dependent SSB and DSB yields were calculated from 0 °C to 42 °C, the range of available published measured data. For that, supercoiled DNA plasmids dissolved in aerated solutions containing EDTA irradiated by Cobalt-60 gamma-rays were simulated. TOPAS-nBio well reproduced published temperature-dependent G-values in liquid water and the yields of SSB and DSB for the temperature range considered. For strand break simulations, the model shows that the yield of SSB and DSB increased linearly with the temperature at a rate of (2.94 ± 0.17) × 10−10 Gy–1 Da–1 °C–1 (R 2 = 0.99) and (0.13 ± 0.01) × 10−10 Gy–1 Da–1 °C–1 (R 2 = 0.99), respectively. The extended capability of TOPAS-nBio is a complementary tool to simulate realistic conditions for a large range of environmental temperatures, allowing refined investigations of the biological effects of radiation.

CPU-GPU coupling independent reaction times method in NASIC and application in water radiolysis by FLASH irradiation

The mechanism of the FLASH effect remains unclear and could be revealed by studying chemical reactions during irradiation. Monte Carlo simulation of the radiolytic species is an effective tool to analyze chemical reactions, but the simulation is limited by computing costs of the step-by-step simulation of radiolytic species, especially when considering beam with complex time structure. The complexity of the time structure of beams from accelerators in FLASH radiotherapy requires a high-performance Monte Carlo code. In this work, we develop a CPU-GPU coupling accelerating code with the independent reaction times (IRT) method to extend the chemical module of our nanodosimetry Monte Carlo code NASIC. Every chemical molecule in the microenvironment contains time information to consider the reactions from different tracks and simulate beams with complex time structures. Performance test shows that our code significantly improved the computing efficiency of the chemical module by four orders of magnitude. Then the code is used to study the oxygen depletion hypothesis in FLASH radiotherapy for different conditions by setting different parameters. The transient oxygen consumption rate values in the water are calculated when the pulses width ranges from 2 ps to 2 μs, the total dose ranges from 0.5 Gy to 100 Gy and the initial oxygen concentration ranges from 0.1% to 21%. The time evolution curves are simulated to study the effect of the time structure of an electron linear accelerator. Results show that the total dose in several microseconds is a better indicator reflecting the radiolytic oxygen consumption rate than the dose rate. The initial oxygen greatly affects the oxygen consumption rate because of the reaction competition. The diffusion of oxygen determined by the physiological parameters is the key factor affecting oxygen depletion during the radiation using electron linear accelerators. Our code provides an efficient tool for simulating water radiolysis in different conditions

Comparing Geant4 physics models for proton-induced dose deposition and radiolysis enhancement from a gold nanoparticle

Gold nanoparticles (GNPs) are materials that make the tumor cells more radiosensitive when irradiated with ionizing radiation. The present study aimed to evaluate the impact of different physical interaction models on the dose calculations and radiochemical results around the GNP. By applying the Geant4 Monte Carlo (MC) toolkit, a single 50-nm GNP was simulated, which was immersed in a water phantom and irradiated with 5, 50, and 150 MeV proton beams. The present work assessed various parameters including the secondary electron spectra, secondary photon spectra, radial dose distribution (RDD), dose enhancement factor (DEF), and radiochemical yields around the GNP. The results with an acceptable statistical uncertainty of less than 1% indicated that low-energy electrons deriving from the ionization process formed a significant part of the total number of secondary particles generated in the presence of GNP; the Penelope model produced a larger number of these electrons by a factor of about 30%. Discrepancies of the secondary electron spectrum between Livermore and Penelope were more obvious at energies of less than 1 keV and reached the factor of about 30% at energies between 250 eV and 1 keV. The RDDs for Livermore and Penelope models were very similar with small variations within the first 6 nm from NP surface by a factor of 10%. In addition, neither the G-value nor the REF was affected by the choice of physical interaction models with the same energy cut-off. This work illustrated the similarity of the Livermore and Penelope models (within 15%) available in Geant4 for future simulation studies of GNP enhanced proton therapy with physical, physicochemical, and chemical mechanisms.

Evaluating Iodine-125 DNA Damage Benchmarks of Monte Carlo DNA Damage Models

A wide range of Monte Carlo models have been applied to predict yields of DNA damage based on nanoscale track structure calculations. While often similar on the macroscopic scale, these models frequently employ different assumptions which lead to significant differences in nanoscale dose deposition. However, the impact of these differences on key biological readouts remains unclear. A major challenge in this area is the lack of robust datasets which can be used to benchmark models, due to a lack of resolution at the base pair level required to deeply test nanoscale dose deposition. Studies investigating the distribution of strand breakage in short DNA strands following the decay of incorporated 125I offer one of the few benchmarks for model predictions on this scale. In this work, we have used TOPAS-nBio to evaluate the performance of three Geant4-DNA physics models at predicting the distribution and yield of strand breaks in this irradiation scenario. For each model, energy and OH radical distributions were simulated and used to generate predictions of strand breakage, varying energy thresholds for strand breakage and OH interaction rates to fit to the experimental data. All three models could fit well to the observed data, although the best-fitting strand break energy thresholds ranged from 29.5 to 32.5 eV, significantly higher than previous studies. However, despite well describing the resulting DNA fragment distribution, these fit models differed significantly with other endpoints, such as the total yield of breaks, which varied by 70%. Limitations in the underlying data due to inherent normalisation mean it is not possible to distinguish clearly between the models in terms of total yield. This suggests that, while these physics models can effectively fit some biological data, they may not always generalise in the same way to other endpoints, requiring caution in their extrapolation to new systems and the use of multiple different data sources for robust model benchmarking.

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.

DNA damage modeled with Geant4-DNA: effects of plasmid DNA conformation and experimental conditions

The chemical stage of the Monte Carlo track-structure (MCTS) code Geant4-DNA was extended for its use in DNA strand break (SB) simulations and compared against published experimental data. Geant4-DNA simulations were performed using pUC19 plasmids (2686 base pairs) in a buffered solution of DMSO irradiated by⁶⁰Co or¹³⁷Csγ-rays. A comprehensive evaluation of SSB yields was performed considering DMSO, DNA concentration, dose and plasmid supercoiling. The latter was measured using the super helix density value used in a Brownian dynamics plasmid generation algorithm. The Geant4-DNA implementation of the independent reaction times method (IRT), developed to simulate the reaction kinetics of radiochemical species, allowed to score the fraction of supercoiled, relaxed and linearized plasmid fractions as a function of the absorbed dose. The percentage of the number of SB after •OH + DNA and H• + DNA reactions, referred as SSB efficiency, obtained using MCTS were 13.77% and 0.74% respectively. This is in reasonable agreement with published values of 12% and 0.8%. The SSB yields as a function of DMSO concentration, DNA concentration and super helix density recreated the expected published experimental behaviors within 5%, one standard deviation. The dose response of SSB and DSB yields agreed with published measurements within 5%, one standard deviation. We demonstrated that the developed extension of IRT in Geant4-DNA, facilitated the reproduction of experimental conditions. Furthermore, its calculations were strongly in agreement with experimental data. These two facts will facilitate the use of this extension in future radiobiological applications, aiding the study of DNA damage mechanisms with a high level of detail.

Application of High-Z Gold Nanoparticles in Targeted Cancer Radiotherapy-Pharmacokinetic Modeling, Monte Carlo Simulation and Radiobiological Effect Modeling

High-Z gold nanoparticles (AuNPs) conjugated to a targeting antibody can help to improve tumor control in radiotherapy while simultaneously minimizing radiotoxicity to adjacent healthy tissue. This paper summarizes the main findings of a joint research program which applied AuNP-conjugates in preclinical modeling of radiotherapy at the Klinikum rechts der Isar, Technical University of Munich and Helmholtz Zentrum München. A pharmacokinetic model of superparamagnetic iron oxide nanoparticles was developed in preparation for a model simulating the uptake and distribution of AuNPs in mice. Multi-scale Monte Carlo simulations were performed on a single AuNP and multiple AuNPs in tumor cells at cellular and molecular levels to determine enhancements in the radiation dose and generation of chemical radicals in close proximity to AuNPs. A biologically based mathematical model was developed to predict the biological response of AuNPs in radiation enhancement. Although simulations of a single AuNP demonstrated a clear dose enhancement, simulations relating to the generation of chemical radicals and the induction of DNA strand breaks induced by multiple AuNPs showed only a minor dose enhancement. The differences in the simulated enhancements at molecular and cellular levels indicate that further investigations are necessary to better understand the impact of the physical, chemical, and biological parameters in preclinical experimental settings prior to a translation of these AuNPs models into targeted cancer radiotherapy.

Multi-scale Monte Carlo simulations of gold nanoparticle-induced DNA damages for kilovoltage X-ray irradiation in a xenograft mouse model using TOPAS-nBio

Background

Gold nanoparticles (AuNPs) are considered as promising agents to increase the radiosensitivity of tumor cells. However, the biological mechanisms of radiation enhancement effects of AuNPs are still not well understood. We present a multi-scale Monte Carlo simulation framework within TOPAS-nBio to investigate the increase of DNA damage due to the presence of AuNPs in mouse tumor models.

Methods

A tumor was placed inside a voxel mouse model and irradiated with either 100 kVp or 200 kVp x-ray beams. Phase spaces were employed to transfer particles from the macroscopic (voxel) scale to the microscopic scale, which consists of a cell geometry including a detailed mouse DNA model. Radiosensitizing effects were calculated in the presence and absence of hybrid nanoparticles with a Fe2O3 core surrounded by a gold layer (AuFeNPs). To simulate DNA damage even for very small energy tracks, Geant4-DNA physics and chemistry models were used on microscopic scale.

Results

An AuFeNP induced enhancement of both dose and DNA strand breaks has been established for different scenarios. Produced chemical radicals including hydroxyl molecules, which were assumed to be responsible for DNA damage through chemical reactions, were found to be significantly increased. We further observed a dependency of the results on the location of the cells within the tumor for 200 kVp x-ray beams.

Conclusions

Our multi-scale approach allows to study irradiation induced physical and chemical effects on cells. We showed a potential increase in cell radiosensitization caused by relatively small concentrations of AuFeNPs. Our new methodology allows the individual adjustment of parameters in each simulation step and therefore can be used for other studies investigating the radiosensitizing effects of AuFeNPs or AuNPs in living cells.

TOPAS-nBio validation for simulating water radiolysis and DNA damage under low-LET irradiation

The chemical stage of the Monte Carlo track-structure simulation code Geant4-DNA has been revised and validated. The root-mean-square (RMS) empirical parameter that dictates the displacement of water molecules after an ionization and excitation event in Geant4-DNA has been shortened to better fit experimental data. The pre-defined dissociation channels and branching ratios were not modified, but the reaction rate coefficients for simulating the chemical stage of water radiolysis were updated. The evaluation of Geant4-DNA was accomplished with TOPAS-nBio. For that, we compared predicted time-dependentGvalues in pure liquid water for^·OH, e^-_aq, and H₂with published experimental data. For H₂O₂and H^·, simulation of added scavengers at different concentrations resulted in better agreement with measurements. In addition, DNA geometry information was integrated with chemistry simulation in TOPAS-nBio to realize reactions between radiolytic chemical species and DNA. This was used in the estimation of the yield of single-strand breaks (SSB) induced by¹³⁷Csγ-ray radiolysis of supercoiled pUC18 plasmids dissolved in aerated solutions containing DMSO. The efficiency of SSB induction by reaction between radiolytic species and DNA used in the simulation was chosen to provide the best agreement with published measurements. An RMS displacement of 1.24 nm provided agreement with measured data within experimental uncertainties for time-dependentGvalues and under the presence of scavengers. SSB efficiencies of 24% and 0.5% for^·OH and H^·, respectively, led to an overall agreement of TOPAS-nBio results within experimental uncertainties. The efficiencies obtained agreed with values obtained with published non-homogeneous kinetic model and step-by-step Monte Carlo simulations but disagreed by 12% with published direct measurements. Improvement of the spatial resolution of the DNA damage model might mitigate such disagreement. In conclusion, with these improvements, Geant4-DNA/TOPAS-nBio provides a fast, accurate, and user-friendly tool for simulating DNA damage under low linear energy transfer irradiation.

Geant4-DNA simulation of the pre-chemical stage of water radiolysis and its impact on initial radiochemical yields

This paper demonstrates the impact of the pre-chemical stage, especially the dissociation scheme and the associated probabilities, on water radiolysis simulation using the Geant4-DNA Monte Carlo track structure simulation toolkit. The models and parameters provided by TRACs have been collected and implemented into Geant4-DNA. In order to evaluate their influence on water radiolysis simulation, the radiochemical yields (G-values) are evaluated as a function of time and LET using the "chem6" Geant4-DNA example, and they are compared with published experimental and calculated data. The new pre-chemical models lead to a better agreement with literature data than the default pre-chemical models of Geant4-DNA, especially for OH radicals and H2O2. The revised chemistry constructor "G4EmDNAChemistry_option3" is available in Geant4-DNA version 10.7.

The relation between microdosimetry and induction of direct damage to DNA by alpha particles

In radiopharmaceutical treatmentsα-particles are employed to treat tumor cells. However, the mechanism that drives the biological effect induced is not well known. Being ionizing radiation,α-particles can affect biological organisms by producing damage to the DNA, either directly or indirectly. Following the principle that microdosimetry theory accounts for the stochastic way in which radiation deposits energy in sub-cellular sized volumes via physical collisions, we postulate that microdosimetry represents a reasonable framework to characterize the statistical nature of direct damage induction byα-particles to DNA. We used the TOPAS-nBio Monte Carlo package to simulate direct damage produced by monoenergetic alpha particles to different DNA structures. In separate simulations, we obtained the frequency-mean lineal energy (yF) and dose-mean lineal energy (yD) of microdosimetric distributions sampled with spherical sites of different sizes. The total number of DNA strand breaks, double strand breaks (DSBs) and complex strand breaks per track were quantified and presented as a function of eitheryForyD.The probability of interaction between a track and the DNA depends on how the base pairs are compacted. To characterize this variability on compactness, spherical sites of different size were used to match these probabilities of interaction, correlating the size-dependent specific energy (z) with the damage induced. The total number of DNA strand breaks per track was found to linearly correlate withyFandzFwhen using what we defined an effective volume as microdosimetric site, while the yield of DSB per unit dose linearly correlated withyDorzD,being larger for compacted than for unfolded DNA structures. The yield of complex breaks per unit dose exhibited a quadratic behavior with respect toyDand a greater difference among DNA compactness levels. Microdosimetric quantities correlate with the direct damage imparted on DNA.

Development of a DNA damage model that accommodates different cellular oxygen concentrations and radiation qualities

PURPOSE

Research regarding cellular responses at different oxygen concentrations (OCs) is of immense interest within the field of radiobiology. Therefore, this study aimed to develop a mechanistic model to analyze cellular responses at different OCs.

METHODS

A DNA damage model (the different cell oxygen level DNA damage [DICOLDD] model) that examines the oxygen effect was developed based on the oxygen fixation hypothesis, which states that dissolved oxygen can modify the reaction kinetics of DNA-derived radicals generated by ionizing radiation. The generation of DNA-derived radicals was simulated using the Monte Carlo method. The decay of DNA-derived radicals due to the competing processes of chemical repair, oxygen fixation, and intrinsic damaging was described using differential equations. The DICOLDD model was fitted to the previous experimental data obtained under different irradiation configurations and validated by calculating the yields of DNA double-strand breaks (DSBs) after exposure to ¹³⁷ Cs as well as cell survival fractions (SFs) using a mechanistic model of cellular survival. Moreover, we used the DICOLDD model to calculate DNA DSB damage yields after irradiation with 0.5-50 MeV protons.

RESULTS

Generally, DSB yields calculated after exposure to ¹³⁷ Cs at different OCs correspond to statistical uncertainties of previous experimental results. Calculated SFs of CHO and V79 cells exposed to photons, protons, and alpha particles at different OCs generally concur with those obtained in previous studies. Our results demonstrated that the variation in DSB yields was less than 10% when the cellular OC decreased from 21% to 5%. Additionally, DSB yields changed drastically when OC dropped below 1%.

CONCLUSIONS

We developed a DNA damage model to evaluate the oxygen effect and provide evidence that a reaction-kinetic model of DNA-derived radicals induced by ionizing radiation suffices to explain the observed oxygen effects. Therefore, the DICOLDD model is a powerful tool for the analysis of cellular responses at different OCs after exposure to different types of radiation.

A review of simulation codes and approaches for radiation chemistry

Historically, the field of radiation chemistry began shortly after the discovery of radioactivity, and its development has been closely related to discoveries in other related fields such as radiation and nuclear physics. Radiolysis of water and radiation chemistry have been very important in elucidating how radiation affects living matter and how it induces DNA damage. Nowadays, we recognize the importance of chemistry to understanding the effects of radiation on cells; however, it took several decades to obtain this insight, and much is still unknown. The radiolysis of water and aqueous solutions have been the subject of much experimental and theoretical research for many decades. One important concept closely related to radiation chemistry is radiation track structure. Track structure results from early physical and physicochemical events that lead to a highly non-homogenous distribution of radiolytic species. Because ionizing radiation creates unstable species that are distributed non-homogenously, the use of conventional reaction kinetics methods does not describe this chemistry well. In recent years, several methods have been developed for simulating radiation chemistry. In this review, we give a brief history of the field and the development of the simulation codes. We review the current methods used to simulate radiolysis of water and radiation chemistry, and we describe several radiation chemistry codes and their applications.

Modeling the effect of oxygen on the chemical stage of water radiolysis using GPU-based microscopic Monte Carlo simulations, with an application in FLASH radiotherapy

Oxygen plays a critical role in determining the initial DNA damages induced by ionizing radiation. It is important to mechanistically model the oxygen effect in the water radiolysis process. However, due to the computational costs from the many body interaction problem, oxygen is often ignored or treated as a constant continuum radiolysis-scavenger background in the simulations using common microscopic Monte Carlo tools. In this work, we reported our recent progress on the modeling of the chemical stage of the water radiolysis with an explicit consideration of the oxygen effect, based upon our initial development of an open-source graphical processing unit (GPU)-based MC simulation tool, gMicroMC. The inclusion of oxygen mainly reduces the yields of [Formula: see text] and [Formula: see text] chemical radicals, turning them into highly toxic [Formula: see text] and [Formula: see text] species. To demonstrate the practical value of gMicroMC in large scale simulation problems, we applied the oxygen-simulation-enabled gMicroMC to compute the yields of chemical radicals under a high instantaneous dose rate [Formula: see text] to study the oxygen depletion hypothesis in FLASH radiotherapy. A decreased oxygen consumption rate (OCR) was found associated with a reduced initial oxygen concentration level due to reduced probabilities of reactions. With respect to dose rate, for the oxygen concentration of 21% and electron energy of 4.5 [Formula: see text], OCR remained approximately constant (∼0.22 [Formula: see text]) for [Formula: see text]'s of [Formula: see text], [Formula: see text] and reduced to 0.19 [Formula: see text] at [Formula: see text], because the increased dose rate improved the mutual reaction frequencies among radicals, hence reducing their reactions with oxygen. We computed the time evolution of oxygen concentration under the FLASH irradiation setups. At the dose rate of [Formula: see text] and initial oxygen concentrations from 0.01% to 21%, the oxygen is unlikely to be fully depleted with an accumulative dose of 30 Gy, which is a typical dose used in FLASH experiments. The computational efficiency of gMicroMC when considering oxygen molecules in the chemical stage was evaluated through benchmark work to GEANT4-DNA with simulating an equivalent number of radicals. With an initial oxygen concentration of 3% (∼10⁵ molecules), a speedup factor of 1228 was achieved for gMicroMC on a single GPU card when comparing with GEANT4-DNA on a single CPU.

Cellular Response to Proton Irradiation: A Simulation Study with TOPAS-nBio

The cellular response to ionizing radiation continues to be of significant research interest in cancer radiotherapy, and DNA is recognized as the critical target for most of the biologic effects of radiation. Incident particles can cause initial DNA damages through physical and chemical interactions within a short time scale. Initial DNA damages can undergo repair via different pathways available at different stages of the cell cycle. The misrepair of DNA damage results in genomic rearrangement and causes mutations and chromosome aberrations, which are drivers of cell death. This work presents an integrated study of simulating cell response after proton irradiation with energies of 0.5-500 MeV (LET of 60-0.2 keV/µm). A model of a whole nucleus with fractal DNA geometry was implemented in TOPAS-nBio for initial DNA damage simulations. The default physics and chemistry models in TOPAS-nBio were used to describe interactions of primary particles, secondary particles, and radiolysis products within the nucleus. The initial DNA double-strand break (DSB) yield was found to increase from 6.5 DSB/Gy/Gbp at low-linear energy transfer (LET) of 0.2 keV/µm to 21.2 DSB/Gy/Gbp at high LET of 60 keV/µm. A mechanistic repair model was applied to predict the characteristics of DNA damage repair and dose response of chromosome aberrations. It was found that more than 95% of the DSBs are repaired within the first 24 h and the misrepaired DSB fraction increases rapidly with LET and reaches 15.8% at 60 keV/µm with an estimated chromosome aberration detection threshold of 3 Mbp. The dicentric and acentric fragment yields and the dose response of micronuclei formation after proton irradiation were calculated and compared with experimental results.

Independent reaction times method in Geant4-DNA: Implementation and performance

PURPOSE

The simulation of individual particle tracks and the chemical stage following water radiolysis in biological tissue is an effective means of improving our knowledge of the physico-chemical contribution to the biological effect of ionizing radiation. However, the step-by-step simulation of the reaction kinetics of radiolytic species is the most time-consuming task in Monte Carlo track-structure simulations, with long simulation times that are an impediment to research. In this work, we present the implementation of the independent reaction times (IRT) method in Geant4-DNA Monte Carlo toolkit to improve the computational efficiency of calculating G-values, defined as the number of chemical species created or lost per 100 eV of deposited energy.

METHODS

The computational efficiency of IRT, as implemented, is compared to that from available Geant4-DNA step-by-step simulations for electrons, protons and alpha particles covering a wide range of linear energy transfer (LET). The accuracy of both methods is verified using published measured data from fast electron irradiations for ^• OH and e aq - for time-dependent G-values. For IRT, simulations in the presence of scavengers irradiated by cobalt-60 γ-ray and 2 MeV protons are compared with measured data for different scavenging capacities. In addition, a qualitative assessment comparing measured LET-dependent G-values with Geant4-DNA calculations in pure liquid water is presented.

RESULTS

The IRT improved the computational efficiency by three orders of magnitude relative to the step-by-step method while differences in G-values by 3.9% at 1 μs were found. At 7 ps, ^• OH and e aq - yields calculated with IRT differed from recent published measured data by 5% ± 4% and 2% ± 4%, respectively. At 1 μs, differences were 9% ± 5% and 6% ± 7% for ^• OH and e aq - , respectively. Uncertainties are one standard deviation. Finally, G-values at different scavenging capacities and LET-dependent G-values reproduced the behavior of measurements for all radiation qualities.

CONCLUSION

The comprehensive validation of the Geant4-DNA capabilities to accurately simulate the chemistry following water radiolysis is an ongoing work. The implementation presented in this work is a necessary step to facilitate performing such a task.

LET-Dependent Intertrack Yields in Proton Irradiation at Ultra-High Dose Rates Relevant for FLASH Therapy

FLASH radiotherapy delivers a high dose (≥10 Gy) at a high rate (≥40 Gy/s). In this way, particles are delivered in pulses as short as a few nanoseconds. At that rate, intertrack reactions between chemical species produced within the same pulse may affect the heterogeneous chemistry stage of water radiolysis. This stochastic process suits the capabilities of the Monte Carlo method, which can model intertrack effects to aid in radiobiology research, including the design and interpretation of experiments. In this work, the TOPAS-nBio Monte Carlo track-structure code was expanded to allow simulations of intertrack effects in the chemical stage of water radiolysis. Simulation of the behavior of radiolytic yields over a long period of time (up to 50 s) was verified by simulating radiolysis in a Fricke dosimeter irradiated by 60Co γ rays. In addition, LET-dependent G values of protons delivered in single squared pulses of widths, 1 ns, 1 µs and 10 µs, were obtained and compared to simulations using no intertrack considerations. The Fricke simulation for the calculated G value of Fe3+ ion at 50 s was within 0.4% of the accepted value from ICRU Report 34. For LET-dependent G values at the end of the chemical stage, intertrack effects were significant at LET values below 2 keV/µm. Above 2 keV/µm the reaction kinetics remained limited locally within each track and thus, effects of intertrack reactions remained low. Therefore, when track structure simulations are used to investigate the biological damage of FLASH irradiation, these intertrack reactions should be considered. The TOPAS-nBio framework with the expansion to intertrack chemistry simulation provides a useful tool to assist in this task.

Monte Carlo track-structure for the radionuclide Copper-64: characterization of S-values, nanodosimetry and quantification of direct damage to DNA

TOPAS-nBio was used to simulate, collision-to-collision, the complete trajectories of electrons in water generated during the explicit simulation of ⁶⁴Cu decay. S-values and direct damage to the DNA were calculated representing the cell (C) and the cell nucleus (N) with concentric spheres of 5 μm and 4 μm in radius, respectively. The considered 'target'←'source' configurations, including the cell surface (Cs) and cytoplasm (Cy), were: C←C, C←Cs, N←N, N←Cy and N←Cs. Ionization cluster size distributions were also calculated in a cylinder immersed in water corresponding to a DNA segment of 10 base-pairs in length (diameter 2.3 nm, length 3.4 nm), modeling a radioactive point source moving from the central axis to the edge of the cylinder. For that, the first moment (M₁) and cumulative probability of having a cluster size of 2 or more ionizations in the cylindrical volume (F₂) were obtained. Finally, the direct damage to the DNA was estimated by quantifying double-strand breaks (DSBs) using the clustering algorithm DBSCAN. The S-values obtained with TOPAS-nBio for ⁶⁴Cu were 7.879 × 10^-4 ± 5 × 10^-7, 4.351 × 10^-4 ± 6 × 10^-7, 1.442 × 10^-3 ± 1 × 10^-6, 2.596 × 10^-4 ± 8 × 10^-7, 1.127 × 10^-4 ± 4 × 10^-7 Gy Bq-s^-1 for the configurations C←C, C←Cs, N←N, N←Cy and N←Cs, respectively. The difference of these values, compared with previously reported S-values for ⁶⁴Cu with the code MNCP and software MIRDCell, ranged from -4% to -25% for the configurations N←N and N←Cs, respectively. On the other hand, F₂ was maximum with the source at the center of the cylinder 0.373 ± 0.001, and monotonically decreased until reaching a value of 0.058 ± 0.001 at 2.3 nm. The same behavior was observed for M₁ with values ranging from 2.188 ± 0.004 to 0.242 ± 0.002. Finally, the DBSCAN algorithm showed that the mean number of DNA DSBs per decay were 0.187 ± 0.001, 0.0317 ± 0.0005, and 0.0125 ± 0.0002 DSB-(Bq-s)^-1 for the configurations N←N, N←Cs, and N←Cy, respectively. In conclusion, the results of the S-values show that the absorbed dose strongly depends on the distribution of the radionuclide in the cell, the dose being higher when ⁶⁴Cu is internalized in the cell nucleus, which is reinforced by the nanodosimetric study by the presence of DNA DSBs attributable to the Auger electrons emitted during the decay of ⁶⁴Cu.

A parameter sensitivity study for simulating DNA damage after proton irradiation using TOPAS-nBio

Monte Carlo (MC) track structure simulation tools are commonly used for predicting radiation induced DNA damage by modeling the physical and chemical reactions at the nanometer scale. However, the outcome of these MC simulations is particularly sensitive to the adopted parameters which vary significantly across studies. In this study, a previously developed full model of nuclear DNA was used to describe the DNA geometry. The TOPAS-nBio MC toolkit was used to investigate the impact of physics and chemistry models as well as three key parameters (the energy threshold for direct damage, the chemical stage time length, and the probability of damage between hydroxyl radical reactions with DNA) on the induction of DNA damage. Our results show that the difference in physics and chemistry models alone can cause differences up to 34% and 16% in the DNA double strand break (DSB) yield, respectively. Additionally, changing the direct damage threshold, chemical stage length, and hydroxyl damage probability can cause differences of up to 28%, 51%, and 71% in predicted DSB yields, respectively, for the configurations in this study.

A new open-source GPU-based microscopic Monte Carlo simulation tool for the calculations of DNA damages caused by ionizing radiation - Part II: sensitivity and uncertainty analysis

PURPOSE

Calculations of deoxyribonucleic acid (DNA) damages involve many parameters in the computation process. As these parameters are often subject to uncertainties, it is of central importance to comprehensively quantify their impacts on DNA single-strand break (SSB) and double-strand break (DSB) yields. This has been a challenging task due to the required large number of simulations and the relatively low computational efficiency using CPU-based MC packages. In this study, we present comprehensive evaluations on sensitivities and uncertainties of DNA SSB and DSB yields on 12 parameters using our GPU-based MC tool, gMicroMC.

METHODS

We sampled one electron at a time in a water sphere containing a human lymphocyte nucleus and transport the electrons and generated radicals until 2 Gy dose was accumulated in the nucleus. We computed DNA damages caused by electron energy deposition events in the physical stage and the hydroxyl radicals at the end of the chemical stage. We repeated the computations by varying 12 parameters: (a) physics cross section, (b) cutoff energy for electron transport, (c)-(e) three branching ratios of hydroxyl radicals in the de-excitation of excited water molecules, (f) temporal length of the chemical stage, (g)-(h) reaction radii for direct and indirect damages, (i) threshold energy defining the threshold damage model to generate a physics damage, (j)-(k) minimum and maximum energy values defining the linear-probability damage model to generate a physics damage, and (l) probability to generate a damage by a radical. We quantified sensitivity of SSB and DSB yields with respect to these parameters for cases with 1.0 and 4.5 keV electrons. We further estimated uncertainty of SSB and DSB yields caused by uncertainties of these parameters.

RESULTS

Using a threshold of 10% uncertainty as a criterion, threshold energy in the threshold damage model, maximum energy in the linear-probability damage model, and probability for a radical to generate a damage were found to cause large uncertainties in both SSB and DSB yields. The scaling factor of the cross section, cutoff energy, physics reaction radius, and minimum energy in the linear-probability damage model were found to generate large uncertainties in DSB yields.

CONCLUSIONS

We identified parameters that can generate large uncertainties in the calculations of SSB and DSB yields. Our study could serve as a guidance to reduce uncertainties of parameters and hence uncertainties of the simulation results.

Modelling variable proton relative biological effectiveness for treatment planning

Dose in proton radiotherapy is generally prescribed by scaling the physical proton dose by a constant value of 1.1. Relative biological effectiveness (RBE) is defined as the ratio of doses required by two radiation modalities to cause the same level of biological effect. The adoption of an RBE of 1.1. assumes that the biological efficacy of protons is similar to photons, allowing decades of clinical dose prescriptions from photon treatments and protocols to be utilized in proton therapy. There is, however, emerging experimental evidence that indicates that proton RBE varies based on technical, tissue and patient factors. The notion that a single scaling factor may be used to equate the effects of photons and protons across all biological endpoints and doses is too simplistic and raises concern for treatment planning decisions. Here, we review the models that have been developed to better predict RBE variations in tissue based on experimental data as well as using a mechanistic approach.

Nanodosimetric quantities and RBE of a clinically relevant carbon-ion beam

PURPOSE

Although carbon-ion therapy is becoming increasingly attractive to the treatment of tumors, details about the ionization pattern formed by therapeutic carbon-ion beam in tissue have not been fully investigated. In this work, systematic calculations for the nanodosimetric quantities and relative biological effectiveness (RBE) of a clinically relevant carbon-ion beam were studied for the first time.

METHODS

The method combining both track structure and condensed history Monte Carlo (MC) simulations was adopted to calculate the nanodosimetric quantities. Fragments and energy spectra at different positions of the radiation field of a clinically relevant carbon-ion pencil beam were generated by means of MC simulations in water. Nanodosimetric quantities such as mean ionization cluster size ( M 1 ), the first moment of conditional cluster size ( M 1 C 2 ), cumulative probability ( F 2 ), and conditional cumulative probability ( F 3 C 2 ) at these positions were then acquired based on the spectra and the pre-calculated nanodosimetric database created by track structure MC simulations. What's more, a novel approach to calculate RBE based on the said nanodosimetric quantities was introduced. The RBE calculations were then conducted for the carbon-ion beam at different water-equivalent depths.

RESULTS

Lateral distributions at various water-equivalent depths of both the nanodosimetric quantities and RBE values were obtained. The values of M 1 , M 1 C 2 , F 2 , and F 3 C 2 were 1.49, 2.67, 0.30, and 0.38 at the plateau at the beam central axis and maximized at 2.79, 5.69, 0.47, and 0.68 at the depths around the Bragg peak, respectively. At a given depth, M 1 and F 2 decreased laterally with increasing the distance to the beam central axis while M 1 C 2 and F 3 C 2 remained nearly unchanged at first and then decreased except for M 1 C 2 at the rising edge of the Bragg peak. The calculated RBE values were 1.07 at the plateau and 3.13 around the Bragg peak. Good agreement between the calculated RBE values and experimental data was obtained.

CONCLUSIONS

Different nanodosimetric quantities feature the track structure of therapeutic carbon-ion beam in different manners. Detailed ionization patterns generated by carbon-ion beam could be characterized by nanodosimetric quantities. Moreover the combined method adopted in this work to calculate nanodosimetric quantities is not only valid but also convenient. Nanodosimetric quantities are significantly helpful for the RBE calculations in carbon-ion therapy.

Modulation of gold nanoparticle mediated radiation dose enhancement through synchronization of breast tumor cell population

OBJECTIVE

The incorporation of high atomic number materials such as gold nanoparticles (GNPs) into tumor cells is being tested to enhance the local radiotherapy (RT) dose. It is also known that the radiosensitivity of tumor cells depends on the phase of their cell cycle. Triple combination of GNPs, phase of tumor cell population, and RT for improved outcomes in cancer treatment.

METHODS

We used a double-thymidine block method for synchronization of the tumor cell population. GNPs of diameters 17 and 46 nm were used to capture the size dependent effects. A radiation dose of 2 Gy with 6 MV linear accelerator was used to assess the efficacy of this proposed combined treatment. A triple negative breast cancer cell line, MDA-MB-231 was chosen as the model cell line. Monte Carlo (MC) calculations were done to predict the GNP-mediated cell death using the experimental GNP uptake data.

RESULTS

There was a 1.5- and 2- fold increase in uptake of 17 and 46 nm GNPs in the synchronized cell population, respectively. A radiation dose of 2 Gy with clinically relevant 6 MV photons resulted in a 62 and 38 % enhancement in cell death in the synchronized cell population with the incorporation of 17 and 46 nm GNPs, respectively. MC data supported the experimental data, but to a lesser extent.

CONCLUSION

A triple combination of GNPs, cell cycle synchronization, and RT could pave the way to enhance the local radiation dose while minimizing side effects to the surrounding healthy tissue.

ADVANCES IN KNOWLEDGE

This is the first study to show that the combined use of GNPs, phase of tumor cell population, and RT could enhance tumor cell death.

Monte Carlo Processing on a Chip (MCoaC)-preliminary experiments toward the realization of optimal-hardware for TOPAS/Geant4 to drive discovery

Amongst the scientific frameworks powered by the Monte Carlo (MC) toolkit Geant4 (Agostinelli et al., 2003), the TOPAS (Tool for Particle Simulation) (Perl et al., 2012) is one. TOPAS focuses on providing ease of use, and has significant implementation in the radiation oncology space at present. TOPAS functionality extends across the full capacity of Geant4, is freely available to non-profit users, and is being extended into radiobiology via TOPAS-nBIO (Ramos-Mendez et al., 2018). A current "grand problem" in cancer therapy is to convert the dose of treatment from physical dose to biological dose, optimized ultimately to the individual context of administration of treatment. Biology MC calculations are some of the most complex and require significant computational resources. In order to enhance TOPAS's ability to become a critical tool to explore the definition and application of biological dose in radiation therapy, we chose to explore the use of Field Programmable Gate Array (FPGA) chips to speedup the Geant4 calculations at the heart of TOPAS, because this approach called "Reconfigurable Computing" (RC), has proven able to produce significant (around 90x) (Sajish et al., 2012) speed increases in scientific computing. Here, we describe initial steps to port Geant4 and TOPAS to be used on FPGA. We provide performance analysis of the current TOPAS/Geant4 code from an RC implementation perspective. Baseline benchmarks are presented. Achievable performance figures of the subsections of the code on optimal hardware are presented; Aspects of practical implementation of "Monte Carlo on a chip" are also discussed.

Mechanistic Modelling of Radiation Responses

Radiobiological modelling has been a key part of radiation biology and therapy for many decades, and many aspects of clinical practice are guided by tools such as the linear-quadratic model. However, most of the models in regular clinical use are abstract and empirical, and do not provide significant scope for mechanistic interpretation or making predictions in novel cell lines or therapies. In this review, we will discuss the key areas of ongoing mechanistic research in radiation biology, including physical, chemical, and biological steps, and review a range of mechanistic modelling approaches which are being applied in each area, highlighting the possible opportunities and challenges presented by these techniques.

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.

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.

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.