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.

Cellular lethal damage of 64Cu incorporated in mammalian genome evaluated with Monte Carlo methods

Purpose

Targeted Radionuclide Therapy (TRT) with Auger Emitters (AE) is a technique that allows targeting specific sites on tumor cells using radionuclides. The toxicity of AE is critically dependent on its proximity to the DNA. The aim of this study is to quantify the DNA damage and radiotherapeutic potential of the promising AE radionuclide copper-64 (64Cu) incorporated into the DNA of mammalian cells using Monte Carlo track-structure simulations.

Methods

A mammalian cell nucleus model with a diameter of 9.3 μm available in TOPAS-nBio was used. The cellular nucleus consisted of double-helix DNA geometrical model of 2.3 nm diameter surrounded by a hydration shell with a thickness of 0.16 nm, organized in 46 chromosomes giving a total of 6.08 giga base-pairs (DNA density of 14.4 Mbp/μm3). The cellular nucleus was irradiated with monoenergetic electrons and radiation emissions from several radionuclides including 111In, 125I, 123I, and 99mTc in addition to 64Cu. For monoenergetic electrons, isotropic point sources randomly distributed within the nucleus were modeled. The radionuclides were incorporated in randomly chosen DNA base pairs at two positions near to the central axis of the double-helix DNA model at (1) 0.25 nm off the central axis and (2) at the periphery of the DNA (1.15 nm off the central axis). For all the radionuclides except for 99mTc, the complete physical decay process was explicitly simulated. For 99mTc only total electron spectrum from published data was used. The DNA Double Strand Breaks (DSB) yield per decay from direct and indirect actions were quantified. Results obtained for monoenergetic electrons and radionuclides 111In, 125I, 123I, and 99mTc were compared with measured and calculated data from the literature for verification purposes. The DSB yields per decay incorporated in DNA for 64Cu are first reported in this work. The therapeutic effect of 64Cu (activity that led 37% cell survival after two cell divisions) was determined in terms of the number of atoms incorporated into the nucleus that would lead to the same DSBs that 100 decays of 125I. Simulations were run until a 2% statistical uncertainty (1 standard deviation) was achieved.

Results

The behavior of DSBs as a function of the energy for monoenergetic electrons was consistent with published data, the DSBs increased with the energy until it reached a maximum value near 500 eV followed by a continuous decrement. For 64Cu, when incorporated in the genome at evaluated positions (1) and (2), the DSB were 0.171 ± 0.003 and 0.190 ± 0.003 DSB/decay, respectively. The number of initial atoms incorporated into the genome (per cell) for 64Cu that would cause a therapeutic effect was estimated as 3,107 ± 28, that corresponds to an initial activity of 47.1 ± 0.4 × 10-3 Bq.

Conclusion

Our results showed that TRT with 64Cu has comparable therapeutic effects in cells as that of TRT with radionuclides currently used in clinical practice.

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.

A method to implement inter-track interactions in Monte Carlo simulations with TOPAS-nBio and their influence on simulated radical yields following water radiolysis

OBJECTIVE

In FLASH radiotherapy (dose rates ≥ 40 Gy/s), a reduced normal tissue toxicity has been observed, while maintaining the same tumor control compared to conventional radiotherapy (dose rates ≤ 0.03 Gy/s). This protecting effect could not be fully explained yet. One assumption is that interactions between the chemicals of different primary ionizing particles, so-called inter-track interactions, trigger this outcome. In this work, we included inter-track interactions in Monte Carlo track structure simulations and investigated the yield of chemicals (G-value) produced by ionizing particles. 
Approach: For the simulations, we used the Monte Carlo toolkit TOPAS, in which inter-track interactions cannot be implemented without further effort. Thus, we developed a method enabling the simultaneous simulation of N original histories in one event allowing chemical species to interact with each other. To investigate the effect of inter-track interactions we analyzed the G-value of different chemicals using various radiation sources. We used electrons with an energy of 60 eV in different spatial arrangements as well as a 10 MeV and 100 MeV proton source. For electrons we set N between 1 and 60, for protons between 1 and 100.
Main results: In all simulations, the total G-value decreases with increasing N. In detail, the G-value for^●OH, H₃O and e_aqdecreases with increasing N, whereas the G-value of OH^-, H₂O₂and H₂increases slightly. The reason is that with increasing N, the concentration of chemical radicals increases allowing for more chemical reactions between the radicals resulting in a change of the dynamics of the chemical stage.
Signifcance: Inter-track interactions resulting in a variation of the yield of chemical species, may be a factor explaining the FLASH effect. To verify this hypothesis, further simulations are necessary in order to evaluate the impact of varying G-values on the yield of DNA damages.

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 10 µM to 1 mM with [H2O2] yields calculated for 100 MeV protons at conventional and FLASH dose rates of 0.286 Gy/s and 500 Gy/s, 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.

A study of indirect action's impact on simulated neutron-induced DNA damage

OBJECTIVE

The risk of radiobiological stochastic effects associated with neutrons is strongly energy dependent. Recent Monte Carlo studies simulating neutron-irradiated nuclear DNA have demonstrated that this energy dependence is correlated with the relative biological effectiveness (RBE) of neutrons to inflict DNA damage clusters that contain difficult-to-repair double-strand breaks. However, these previous investigations were either limited to modeling direct radiation action or considered the effects of both direct and indirect action together without distinguishing between the two. In this study, we aimed to quantify the influence of indirect action in neutron irradiation scenarios and acquire novel estimations of the energy-dependent neutron RBE for inducing DNA damage clusters due to both direct and indirect action.

Approach: We explored the role of indirect action in neutron-induced DNA damage by integrating a validated indirect action model into our existing simulation pipeline. Using this pipeline, we performed track-structure simulations of monoenergetic neutron irradiations (1 eV to 10 MeV) in a nuclear DNA model and analyzed the resulting simple and clustered DNA lesions. We repeated the irradiation simulations for 250 keV X-rays that acted as our reference radiation.

Main results: Including indirect action significantly increased the occurrence of DNA lesions. We found that indirect action tends to amplify the damage due to direct action by inducing DNA lesions in the vicinity of directly-induced lesions, resulting in additional and larger damage clusters. Our neutron RBE results are qualitatively similar to but lower in magnitude than the established radiation protection factors and the results of previous similar investigations, due to the greater relative impact of indirect action in photon-induced damage than in neutron-induced damage.

Significance: Although our model for neutron-induced DNA damage has some important limitations, our findings suggest that the energy-dependent risk of neutron-induced stochastic effects may not be completely modeled alone by the relative potential of neutrons to inflict clustered lesions via direct and indirect action in DNA damage.

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.

Towards the characterization of neutron carcinogenesis through direct action simulations of clustered DNA damage

Neutron exposure poses a unique radiation protection concern because neutrons have a large, energy-dependent relative biological effectiveness (RBE) for stochastic effects. Recent computational studies on the microdosimetric properties of neutron dose deposition have implicated clustered DNA damage as a likely contributor to this marked energy dependence. So far, publications have focused solely on neutron RBE for inducing clusters of DNA damage containing two or more DNA double strand breaks (DSBs). In this study, we have conducted a novel assessment of neutron RBE for inducing all types of clustered DNA damage that contain two or more lesions, stratified by whether the clusters contain DSBs (complex DSB clusters) or not (non-DSB clusters). This assessment was conducted for eighteen initial neutron energies between 1 eV and 10 MeV as well as a reference radiation of 250 keV x-rays. We also examined the energy dependence of cluster length and cluster complexity because these factors are believed to impact the DNA repair process. To carry out our investigation, we developed a user-friendly TOPAS-nBio application that includes a custom nuclear DNA model and a novel algorithm for recording clustered DNA damage. We found that neutron RBE for inducing complex DSB clusters exhibited similar energy dependence to the canonical neutron RBE for stochastic radiobiological effects, at multiple depths in human tissue. Qualitatively similar results were obtained for non-DSB clusters, although the quantitative agreement was lower. Additionally we identified a significant neutron energy dependence in the average length and complexity of clustered lesions. These results support the idea that many types of clustered DNA damage contribute to the energy dependence of neutron RBE for stochastic radiobiological effects and imply that the size and constituent lesions of individual clusters should be taken into account when modeling DNA repair. Our results were qualitatively consistent for (i) multiple radiation doses (including a low-dose 0.1 Gy irradiation), (ii) variations in the maximal lesion separation distance used to define a cluster, and (iii) two distinct collections of physics models used to govern particle transport. Our complete TOPAS-nBio application has been released under an open-source license to enable others to independently validate our work and to expand upon it.

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.

Investigating the feasibility of TOPAS-nBio for Monte Carlo track structure simulations by adapting GEANT4-DNA examples application

Purpose.The purpose of this work is to investigate the feasibility of TOPAS-nBio for track structure simulations using tuple scoring and ROOT/Python-based post-processing.Materials and methods.There are several example applications implemented in GEANT4-DNA demonstrating track structure simulations. These examples are not implemented by default in TOPAS-nBio. In this study, the tuple scorer was used to re-simulate these examples. The simulations contained investigations of different physics lists, calculation of energy-dependent range, stopping power, mean free path andW-value. Additionally, further applications of the TOPAS-nBio tool were investigated, focusing on physical interactions and deposited energies of electrons with initial energies in the range of 10-60 eV, not covered in the recently published GEANT4-DNA simulations. Low-energetic electrons are currently of great interest in the radiobiology research community due to their high effectiveness towards the induction of biological damage.Results.The quantities calculated with TOPAS-nBio show a good agreement with the simulations of GEANT4-DNA with deviations of 5% at maximum. Thus, we have presented a feasible way to implement the example applications included in GEANT4-DNA in TOPAS-nBio. With the extended simulations, an insight could be given, which further tracking information can be gained with the track structure code and how cross sections and physics models influence a particle's fate.Conclusion.With our results, we could show the potentials of applying the tuple scorer in TOPAS-nBio Monte Carlo track structure simulations. Using this scorer, a large amount of information about the track structure can be accessed, which can be analyzed as preferred after the simulation.

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.

Radiobiological impact of gadolinium neutron capture from proton therapy and alternative neutron sources using TOPAS-nBio

PURPOSE

A multi-scale investigation of the biological properties of gadolinium neutron capture (GdNC) therapy with applications in particle therapy is conducted using the TOPAS Monte Carlo (MC) simulation code. The simulation results are used to quantify the amount of gadolinium dose enhancement produced as a result of the secondary neutron production from proton therapy scaled by measured data.

MATERIALS AND METHODS

MC modeling was performed using the radiobiology extension TOol for PArticle Simulation TOPAS-nBio MC simulation code to study the radiobiological effects produced from GdNC on a segment of DNA, a spherical cellular model, and from the modeling of previous experimental measurements. The average RBE values were calculated from two methods, microdosimetric kinematic (MK) and biological weighting r(y) within a 2 nm DNA segment for GdNC. The single-strand breaks (SSBs) and double-strand breaks (DSBs) were calculated from within the nucleus of a 20 µm diameter, spherical cell model. From a previous experimental proton therapy measurement using a spread-out Bragg peak (SOBP) of 4.5-9.5 cm and a delivered absorbed dose of 10.4 Gy, the amount of Gd neutron captures was calculated and used to quantify the amount of GdNC absolute dose from particle therapy.

RESULTS

The average RBE from microdosimetric kinematic and biological weighting was 1.35, and 1.70 for a 10% cell survival on HSG cell-line and weighting function data from early intestinal tolerance of mice. From a central isotropic GdNC source, the energy deposition is found to decrease from roughly 2.7 eV per capture down to approximately 0.01 eV per capture, a drop of two orders of magnitude within 50 nm. This result suggests that Gd needs to be close to the DNA (within 10-20 nm) in order for neutron capture to induce a significant dose enhancement due to the short-range electrons emitted after Gd neutron capture. Within a spherical cell model, the SSBs, and DSBs were determined to be 39 and 1.5 per neutron capture, respectively. From the total neutron captures produced from an experimental proton therapy measurement on a 3000 PPM Gd solution, an insignificant absolute Gd dose enhancement was quantified to be 5.4 × 10^-6  Gy per Gy of administered proton dose.

CONCLUSION

From this study and literature review, the production of secondary thermal neutrons from proton therapy is determined to be a limiting factor and unlikely to produce a clinically useful dose enhancement for secondary neutron capture therapy. Moreover, alternative neutron sources, such as, a compact deuterium-tritium (D-T) neutron generator, a "high yield" deuterium-deuterium (D-D) generator, or an industrial strength (100 mg) ²⁵² Cf source were investigated, with the ²⁵² Cf source the most likely to be capable of producing enough neutrons for 1 Gy of localized GdNC absolute dose within a reasonable treatment time.