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

Radiation Track Structure: How the Spatial Distribution of Energy Deposition Drives Biological Response

Ionising radiation is incredibly effective at causing biological effects. This is due to the unique way energy is deposited along highly structured tracks of ionisation and excitation events, which results in correlation with sites of DNA damage from the nanometre to the micrometre scale. Correlation of these events along the track on the nanometre scale results in clustered damage, which not only results in the formation of DNA double-strand breaks (DSB), but also more difficult to repair complex DSB, which include additional damage within a few base pairs. The track structure varies significantly with radiation quality and the increase in relative biological effectiveness observed with increasing linear energy transfer in part corresponds to an increase in the probability and complexity of clustered DNA damage produced. Likewise, correlation over larger scales, associated with packing of DNA and associated chromosomes within the cell nucleus, can also have a major impact on the biological response. The proximity of the correlated damage along the track increases the probability of miss-repair through pairwise interactions resulting in an increase in probability and complexity of DNA fragments/deletions, mutations and chromosomal rearrangements. Understanding the mechanisms underlying the biological effectiveness of ionising radiation can provide an important insight into ways of increasing the efficacy of radiotherapy, as well as the risks associated with exposure. This requires a multi-scale approach for modelling, not only considering the physics of the track structure from the millimetre scale down to the nanometre scale, but also the structural packing of the DNA within the nucleus, the resulting chemistry in the context of the highly reactive environment of the nucleus, together with the subsequent biological response.

Minibeam radiation therapy: A micro- and nano-dosimetry Monte Carlo study

PURPOSE

Minibeam radiation therapy (MBRT) is an innovative strategy based on a distinct dose delivery method that is administered using a series of narrow (submillimetric) parallel beams. To shed light on the biological effects of MBRT irradiation, we explored the micro- and nanodosimetric characteristics of three promising MBRT modalities (photon, electron, and proton) using Monte Carlo (MC) calculations.

METHODS

Irradiation with proton (100 MeV), electron (300 MeV), and photon (effective energy of 69 keV) minibeams were simulated using Geant4 MC code and the Geant4-DNA extension, which allows the simulation of energy transfer points with nanometric accuracy. As the target of the simulations, cells containing spherical nuclei with or without a detailed description of the DNA (deoxyribonucleic acid) geometry were placed at different depths in peak and valley regions in a water phantom. The energy deposition and number of events in the cell nuclei were recorded in the microdosimetry study, and the number of DNA breaks and their complexity were determined in the nanodosimetric study, where a multi-scale simulation approach was used for the latter. For DNA damage assessment, an adapted DBSCAN clustering algorithm was used. To compare the photon MBRT (xMBRT), electron MBRT (eMBRT), and proton MBRT (pMBRT) approaches, we considered the treatment of a brain tumor located at a depth of 75 mm.

RESULTS

Both mean energy deposition at micrometric scale and DNA damage in the "valley" cell nuclei were very low as compared with these parameters in the peak region at all depths for xMBRT and at depths of 0 to 30 mm and 0 to 50 mm for eMBRT and pMBRT, respectively. Only the charged minibeams were favorable for tumor control by producing similar effects in peak and valley cells after 70 mm. At the micrometer scale, the energy deposited per event pointed to a potential advantage of proton beams for tumor control, as more aggressive events could be expected at the end of their tracks. At the nanometer scale, all three MBRT modalities produced direct clustered DNA breaks, although the majority of damage (>93%) was composed of isolated single strand breaks. The pMBRT led to a significant increase in the proportion of clustered single strand breaks and double-strand breaks at the end of its range as compared to the entrance (7% at 75 mm vs 3% at 10 mm) in contrast to eMBRT and xMBRT. In the latter cases, the proportions of complex breaks remained constant, irrespective of the depth and region (peak or valley).

CONCLUSIONS

Enhanced normal tissue sparing can be expected with these three MBRT techniques. Among the three modalities, pMBRT offers an additional gain for radioresistant tumors, as it resulted in a higher number of complex DNA damage clusters in the tumor region. These results can aid understanding of the biological mechanisms of MBRT.

The influence of Geant4-DNA toolkit parameters on electron microdosimetric track structure

The influence of different physical process factors on tracks of low-energy electrons in liquid water was analyzed and evaluated based on the Geant4-DNA toolkit of Geant4 version 10.4, and it provides theoretical support for obtaining the basic parameters of microdosimetry concerned with radiotherapy and radiation protection. According to the characteristics of different models, five physics constructors of Geant4-DNA toolkit were selected to simulate monoenergetic electrons in microscopic scale. Details of track structure of different Geant4-DNA physics constructors were compared, including total number of interaction processes, number and energy percentage of excitation and ionization; analyzing the impacts of mean lineal energy of several factors, including Geant4-DNA physics constructors, initial energy, radius of scoring spheres, interaction processes and cut-off energy. Firstly, 'G4EmDNAPhysics' (hereinafter referred to as 'dna') is well consistent with 'G4EmDNAPhysics_option 2' (hereinafter referred to as 'option 2'), and 'G4EmDNAPhysics_option 4' (hereinafter referred to as 'option 4') is well consistent with 'G4EmDNAPhysics_option 5' (hereinafter referred to as 'option 5'); secondly, there are differences for the information of track structure and mean lineal energy between 'option 2' 'option 4' and 'G4EmDNAPhysics_option 6' (hereinafter referred to as 'option 6'); thirdly, the influence of the model on the mean lineal energy decreases with the increase of the radius of the scoring spheres, whereas mean lineal energy increases as the tracking cut increases. Several alternative discrete physics constructors of Geant4-DNA are comprehensively discussed overlaying multiple perspectives under different conditions in this work.

Intercomparison of dose enhancement ratio and secondary electron spectra for gold nanoparticles irradiated by X-rays calculated using multiple Monte Carlo simulation codes

PURPOSE

Targeted radiation therapy has seen an increased interest in the past decade. In vitro and in vivo experiments showed enhanced radiation doses due to gold nanoparticles (GNPs) to tumors in mice and demonstrated a high potential for clinical application. However, finding a functionalized molecular formulation for actively targeting GNPs in tumor cells is challenging. Furthermore, the enhanced energy deposition by secondary electrons around GNPs, particularly by short-ranged Auger electrons is difficult to measure. Computational models, such as Monte Carlo (MC) radiation transport codes, have been used to estimate the physical quantities and effects of GNPs. However, as these codes differ from one to another, the reliability of physical and dosimetric quantities needs to be established at cellular and molecular levels, so that the subsequent biological effects can be assessed quantitatively.

METHODS

In this work, irradiation of single GNPs of 50 nm and 100 nm diameter by X-ray spectra generated by 50 and 100 peak kilovoltages was simulated for a defined geometry setup, by applying multiple MC codes in the EURADOS framework.

RESULTS

The mean dose enhancement ratio of the first 10 nm-thick water shell around a 100 nm GNP ranges from 400 for 100 kVp X-rays to 600 for 50 kVp X-rays with large uncertainty factors up to 2.3.

CONCLUSIONS

It is concluded that the absolute dose enhancement effects have large uncertainties and need an inter-code intercomparison for a high quality assurance; relative properties may be a better measure until more experimental data is available to constrain the models.

The physical stage of radiolysis of solvated DNA by high-energy-transfer particles: insights from new first principles simulations

Electron dynamics simulations based on density functional theory are carried out on nanometric molecular systems to decipher the primary processes following irradiation of bio-macromolecules by high energy transfer charged particles.

In Silico Models of DNA Damage and Repair in Proton Treatment Planning: A Proof of Concept

There is strong in vitro cell survival evidence that the relative biological effectiveness (RBE) of protons is variable, with dependence on factors such as linear energy transfer (LET) and dose. This is coupled with the growing in vivo evidence, from post-treatment image change analysis, of a variable RBE. Despite this, a constant RBE of 1.1 is still applied as a standard in proton therapy. However, there is a building clinical interest in incorporating a variable RBE. Recently, correlations summarising Monte Carlo-based mechanistic models of DNA damage and repair with absorbed dose and LET have been published as the Manchester mechanistic (MM) model. These correlations offer an alternative path to variable RBE compared to the more standard phenomenological models. In this proof of concept work, these correlations have been extended to acquire RBE-weighted dose distributions and calculated, along with other RBE models, on a treatment plan. The phenomenological and mechanistic models for RBE have been shown to produce comparable results with some differences in magnitude and relative distribution. The mechanistic model found a large RBE for misrepair, which phenomenological models are unable to do. The potential of the MM model to predict multiple endpoints presents a clear advantage over phenomenological models.

A comparative study on Monte Carlo simulations of electron emission from liquid water

PURPOSE

Liquid water being the major constituent of the human body, is of fundamental importance in radiobiological research. Hence, the knowledge of electron-water interaction physics and particularly the secondary electron yield is essential. However, to date, only very little is known experimentally on the low energy electron interaction with liquid water because of certain practical limitations. The purpose of this study was to gain some useful information about electron emission from water using a Monte Carlo (MC) simulation technique that can numerically model electron transport trajectories in water.

METHODS

In this study, we have performed MC simulations of electron emission from liquid water in the primary energy range of 50 eV-30 keV by using two different codes, i.e., a classical trajectory MC (CMC) code developed in our laboratory and the Geant4-DNA (G4DNA) code. The calculated secondary electron yield and electron backscattering coefficient are compared with experimental results wherever applicable to verify the validity of physical models for the electron-water interaction.

RESULTS

The secondary electron yield vs. primary energy curves calculated using the two codes present the same generic curve shape as that of metals but in rather different absolute values. G4DNA underestimates the secondary electron yield due to the application of one step thermalization model by setting a cutoff energy at 10 eV so that the low energy losses due to phonon excitations are omitted. Our CMC code, using a full energy loss spectrum to model electron inelastic scattering, allows the simulation of individual phonon scattering events for very low energy losses down to 10 meV, which then enables the calculated secondary electron yields much closer to the experimental data and also gives quite reasonable energy distribution curve of secondary electrons.

CONCLUSIONS

It is concluded that full dielectric function data at low energy loss values below 10 eV are recommended for modeling of low energy electrons in liquid water.

Stochastic multicellular modeling of x-ray irradiation, DNA damage induction, DNA free-end misrejoining and cell death

The repair or misrepair of DNA double-strand breaks (DSBs) largely determines whether a cell will survive radiation insult or die. A new computational model of multicellular, track structure-based and pO₂-dependent radiation-induced cell death was developed and used to investigate the contribution to cell killing by the mechanism of DNA free-end misrejoining for low-LET radiation. A simulated tumor of 1224 squamous cells was irradiated with 6 MV x-rays using the Monte Carlo toolkit Geant4 with low-energy Geant4-DNA physics and chemistry modules up to a uniform dose of 1 Gy. DNA damage including DSBs were simulated from ionizations, excitations and hydroxyl radical interactions along track segments through cell nuclei, with a higher cellular pO₂ enhancing the conversion of DNA radicals to strand breaks. DNA free-ends produced by complex DSBs (cDSBs) were able to misrejoin and produce exchange-type chromosome aberrations, some of which were asymmetric and lethal. A sensitivity analysis was performed and conditions of full oxia and anoxia were simulated. The linear component of cell killing from misrejoining was consistently small compared to values in the literature for the linear component of cell killing for head and neck squamous cell carcinoma (HNSCC). This indicated that misrejoinings involving DSBs from the same x-ray (including all associated secondary electrons) were rare and that other mechanisms (e.g. unrejoined ends) may be important. Ignoring the contribution by the indirect effect toward DNA damage caused the DSB yield to drop to a third of its original value and the cDSB yield to drop to a tenth of its original value. Track structure-based cell killing was simulated in all 135306 viable cells of a 1 mm³ hypoxic HNSCC tumor for a uniform dose of 1 Gy.

Assessment of Radio-Induced Damage in Endothelial Cells Irradiated with 40 kVp, 220 kVp, and 4 MV X-rays by Means of Micro and Nanodosimetric Calculations

The objective of this work was to study the differences in terms of early biological effects that might exist between different X-rays energies by using a mechanistic approach. To this end, radiobiological experiments exposing cell monolayers to three X-ray energies were performed in order to assess the yields of early DNA damage, in particular of double-strand breaks (DSBs). The simulation of these irradiations was set in order to understand the differences in the obtained experimental results. Hence, simulated results in terms of microdosimetric spectra and early DSB induction were analyzed and compared to the experimental data. Human umbilical vein endothelial cells (HUVECs) were irradiated with 40, 220 kVp, and 4 MV X-rays. The Geant4 Monte Carlo simulation toolkit and its extension Geant4-DNA were used for the simulations. Microdosimetric calculations aiming to determine possible differences in the variability of the energy absorbed by the irradiated cell population for those photon spectra were performed on 10,000 endothelial cell nuclei representing a cell monolayer. Nanodosimetric simulations were also carried out using a computation chain that allowed the simulation of physical, physico-chemical, and chemical stages on a single realistic endothelial cell nucleus model including both heterochromatin and euchromatin. DNA damage was scored in terms of yields of prompt DSBs per Gray (Gy) and per giga (10⁹) base pair (Gbp) and DSB complexity was derived in order to be compared to experimental data expressed as numbers of histone variant H2AX (γ-H2AX) foci per cell. The calculated microdosimetric spread in the irradiated cell population was similar when comparing between 40 and 220 kVp X-rays and higher when comparing with 4 MV X-rays. Simulated yields of induced DSB/Gy/Gbp were found to be equivalent to those for 40 and 220 kVp but larger than those for 4 MV, resulting in a relative biological effectiveness (RBE) of 1.3. Additionally, DSB complexity was similar between the considered photon spectra. Simulated results were in good agreement with experimental data obtained by IRSN (Institut de radioprotection et de sûreté nucléaire) radiobiologists. Despite differences in photon energy, few differences were observed when comparing between 40 and 220 kVp X-rays in microdosimetric and nanodosimetric calculations. Nevertheless, variations were observed when comparing between 40/220 kVp and 4 MV X-rays. Thanks to the simulation results, these variations were able to be explained by the differences in the production of secondary electrons with energies below 10 keV.

Track Structure Study for Energy Dependency of Electrons and X-rays on DNA Double-Strand Break Induction

Radiation weighting factor wR for photons and electrons has been defined as unity independently of the energy of the particles. However, the biological effects depend on the incident energies according to in vitro experimental data. In this study, we have quantified the energy concentration along electron tracks in terms of dose-mean lineal energy (yD) on chromosome (micro-meter) and DNA (nano-meter) order scales by Monte Carlo simulations, and evaluated the impact of photon energies on DNA double-strand break (DNA-DSB) induction from an experimental study of irradiated cells. Our simulation result shows that the yD values for diagnostic X-rays (60-250 kVp) are higher than that for therapeutic X-rays (linac 6 MV), which agrees well with the tissue equivalent proportional counter (TEPC) measurements. The relation between the yD values and the numbers of γ-H2AX foci for various photon energy spectra suggests that low energy X-rays induce DNA-DSB more efficiently than higher energy X-rays even at the same absorbed dose (e.g., 1.0 Gy). The relative biological effectiveness based on DNA-DSBs number (RBEDSB) is proportionally enhanced as the yD value increases, demonstrating that the biological impact of the photon irradiation depends on energy concentration along radiation tracks of electrons produced in the bio-tissues. Ultimately, our study implies that the value of wR for photons varies depending on their energies.

Radiolysis reduction in liquid solution targets for the production of 89Zr

Increased interest in radiometals for nuclear medicine and imaging can be hampered by radionuclide supply. ⁸⁹Zr for example, is a PET imaging nuclide for which no radionuclide generator exists. One method to produce ⁸⁹Zr involves irradiating aqueous solutions of yttrium nitrate salt on small medical cyclotrons. However, in irradiating these solutions the radiolysis of water can cause significant H₂ and O₂ gas buildup, which can eventually rupture a sealed target vessel. We examine the role of nitrate and nitrite in radiolysis. Here, we find that using copper-coated cadmium pellets to chemically reduce nitrate to nitrite in solution prior to irradiation can reduce in-target radiolysis by approximately 60% as compared to other published methods of radiolysis reduction, but only in acidic solutions. We hypothesize that during irradiation, nitrate is converted to nitrite, consuming free radicals which would otherwise be available to eliminate molecular gas species. Performing this conversion before irradiation may limit the consumption of these beneficial free radicals.

Computational approach to determine the relative biological effectiveness of fast neutrons using the Geant4-DNA toolkit and a DNA atomic model from the Protein Data Bank

This study proposes an innovative approach to estimate relative biological effectiveness (RBE) of fast neutrons using the Geant4 toolkit. The Geant4-DNA version cannot track heavy ions below 0.5 MeV/nucleon. In order to explore the impact of this issue, secondary particles are simulated instead of the primary low-energy neutrons. The Evaluated Nuclear Data File library is used to determine the cross sections for the elastic and inelastic interactions of neutrons with water and to find the contribution of each secondary particle spectrum. Two strategies are investigated in order to find the best possible approach and results. The first one takes into account only light particles, protons produced from elastic scattering, and α particles from inelastic scattering. Geantino particles are shot instead of heavy ions; hence all heavy ions are considered in the simulations, though their physical effects on DNA not. The second strategy takes into account all the heavy and light ions, although heavy ions cannot be tracked down to very low energies (E<0.5 MeV/nucleon). Our model is based on the combination of an atomic resolution DNA geometrical model and a Monte Carlo simulation toolkit for tracking particles. The atomic coordinates of the DNA double helix are extracted from the Protein Data Bank. Since secondary particle spectra are used instead of simulating the interaction of neutrons explicitly, this method reduces the computation times dramatically. Double-strand break induction is used as the end point for the estimation of the RBE of fast neutrons. ^{60}Co γ rays are used as the reference radiation quality. Both strategies succeed in reproducing the behavior of the RBE_{max} as a function of the incident neutron energy ranging from 0.1 to 14 MeV, including the position of its peak. A comparison of the behavior of the two strategies shows that for neutrons with energies less than 0.7 MeV, the effect of heavy ions would not be very significant, but above 0.7 MeV, heavy ions have an important role in neutron RBE.

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.

Ionizing Radiation and Complex DNA Damage: From Prediction to Detection Challenges and Biological Significance

Biological responses to ionizing radiation (IR) have been studied for many years, generally showing the dependence of these responses on the quality of radiation, i.e., the radiation particle type and energy, types of DNA damage, dose and dose rate, type of cells, etc. There is accumulating evidence on the pivotal role of complex (clustered) DNA damage towards the determination of the final biological or even clinical outcome after exposure to IR. In this review, we provide literature evidence about the significant role of damage clustering and advancements that have been made through the years in its detection and prediction using Monte Carlo (MC) simulations. We conclude that in the future, emphasis should be given to a better understanding of the mechanistic links between the induction of complex DNA damage, its processing, and systemic effects at the organism level, like genomic instability and immune responses.

Radio-Enhancing Properties of Bimetallic Au:Pt Nanoparticles: Experimental and Theoretical Evidence

The use of nanoparticles, in combination with ionizing radiation, is considered a promising method to improve the performance of radiation therapies. In this work, we engineered mono- and bimetallic core-shell gold–platinum nanoparticles (NPs) grafted with poly (ethylene glycol) (PEG). Their radio-enhancing properties were investigated using plasmids as bio-nanomolecular probes and gamma radiation. We found that the presence of bimetallic Au:Pt-PEG NPs increased by 90% the induction of double-strand breaks, the signature of nanosize biodamage, and the most difficult cell lesion to repair. The radio-enhancement of Au:Pt-PEG NPs were found three times higher than that of Au-PEG NPs. This effect was scavenged by 80% in the presence of dimethyl sulfoxide, demonstrating the major role of hydroxyl radicals in the damage induction. Geant4-DNA Monte Carlo simulations were used to elucidate the physical processes involved in the radio-enhancement. We predicted enhancement factors of 40% and 45% for the induction of nanosize damage, respectively, for mono- and bimetallic nanoparticles, which is attributed to secondary electron impact processes. This work contributed to a better understanding of the interplay between energy deposition and the induction of nanosize biomolecular damage, being Monte Carlo simulations a simple method to guide the synthesis of new radio-enhancing agents.

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.

Preliminary results coupling "Stochastic Mean Field" and "Boltzmann-Langevin One Body" models with Geant4

PURPOSE

Monte Carlo (MC) simulations are widely used for medical applications and nuclear reaction models are fundamental for the simulation of the particle interactions with patients in ion therapy. Therefore, it is of utmost importance to have reliable models in MC simulations for such interactions. Geant4 is one of the most used toolkits for MC simulation. However, its models showed severe limitations in reproducing the yields measured in the interaction of ion beams below 100 MeV/u with thin targets. For this reason, we interfaced two models, SMF ("Stochastic Mean Field") and BLOB ("Boltzmann-Langevin One Body"), dedicated to simulate such reactions, with Geant4.

METHODS

Both SMF and BLOB are semi-classical, one-body approaches to solve the Boltzmann-Langevin equation. They include an identical treatment of the mean-field propagation, on the basis of the same effective interaction, but they differ in the way fluctuations are included. Furthermore, we tested a correction to the excitation energy calculated for the light fragments emerging from the simulations and a simple coalescence model.

RESULTS

While both SMF and BLOB have been developed to simulate heavy ion interactions, they show very good results in reproducing the experimental yields of light fragments, up to alpha particles, obtained in the interaction of ¹²C with a thin carbon target at 62 MeV/u.

CONCLUSIONS

BLOB in particular gives promising results and this stresses the importance of integrating it into the Geant4 toolkit.

Systematic microdosimetric data for protons of therapeutic energies calculated with Geant4-DNA

The purpose of this study was to generate physical data needed for microdosimetry-based models of proton RBE. Our focus was on the frequency and dose average lineal energies, y  F and y  D . We report data for proton energies from 0.1 to 100 MeV, for spherical volumes 2-103 nm in diameter. These data were calculated using Geant4-DNA Monte Carlo software. The physics implemented in Geant4-DNA has been extensively tested for this type of calculations but data on y  F and y  D for protons generated with this code have been very limited. An innovative aspect of our study is that we introduced a straightforward procedure for calculation of y  F and y  D for polyenergetic beams and presented the data in a format that simplifies these calculations. We compared our data with previous studies that used different Monte Carlo codes and with experimental data.

Radio-enhancement effects by radiolabeled nanoparticles

In cancer radiation therapy, dose enhancement by nanoparticles has to date been investigated only for external beam radiotherapy (EBRT). Here, we report on an in silico study of nanoparticle-enhanced radiation damage in the context of internal radionuclide therapy. We demonstrate the proof-of-principle that clinically relevant radiotherapeutic isotopes (i.e. 213Bi, 223Ra, 90Y, 177Lu, 67Cu, 64Cu and 89Zr) labeled to clinically relevant superparamagnetic iron oxide nanoparticles results in enhanced radiation damage effects localized to sub-micron scales. We find that radiation dose can be enhanced by up to 20%, vastly outperforming nanoparticle dose enhancement in conventional EBRT. Our results demonstrate that in addition to the favorable spectral characteristics of the isotopes and their proximity to the nanoparticles, clustering of the nanoparticles results in a nonlinear collective effect that amplifies nanoscale radiation damage effects by electron-mediated inter-nanoparticle interactions. In this way, optimal radio-enhancement is achieved when the inter-nanoparticle distance is less than the mean range of the secondary electrons. For the radioisotopes studied here, this corresponds to inter-nanoparticle distances <50 nm, with the strongest effects within 20 nm. The results of this study suggest that radiolabeled nanoparticles offer a novel and potentially highly effective platform for developing next-generation theranostic strategies for cancer medicine.

Progress of Geant4 electromagnetic physics developments and applications

We report on developments of the Geant4 electromagnetic physics sub-libraries of Geant4 release 10.4 and beyond. Modifications are introduced to the models of photoelectric effect, bremsstrahlung, gamma conversion, single and multiple scattering. The theory-based Goudsmit-Saunderson model of electron/positron multiple scattering has been recently reviewed and a new improved version, providing the most accurate results for scattering of electrons and positrons, was made available. The updated interfaces, models and configurations have already been integrated into LHC applications and may be useful for any type of simulations.

Gold Nanoparticle Enhanced Proton Therapy: Monte Carlo Modeling of Reactive Species' Distributions Around a Gold Nanoparticle and the Effects of Nanoparticle Proximity and Clustering

Gold nanoparticles (GNPs) are promising radiosensitizers with the potential to enhance radiotherapy. Experiments have shown GNP enhancement of proton therapy and indicated that chemical damage by reactive species plays a major role. Simulations of the distribution and yield of reactive species from 10 ps to 1 µs produced by a single GNP, two GNPs in proximity and a GNP cluster irradiated with a proton beam were performed using the Geant4 Monte Carlo toolkit. It was found that the reactive species distribution at 1 µs extended a few hundred nm from a GNP and that the largest enhancement occurred over 50 nm from the nanoparticle. Additionally, the yield for two GNPs in proximity and a GNP cluster was reduced by up to 17% and 60% respectively from increased absorption. The extended range of action from the diffusion of the reactive species may enable simulations to model GNP enhanced proton therapy. The high levels of absorption for a large GNP cluster suggest that smaller clusters and diffuse GNP distributions maximize the total radiolysis yield within a cell. However, this must be balanced against the high local yields near a cluster particularly if the cluster is located adjacent to a biological target.

Determining dose enhancement factors of high-Z nanoparticles from simulations where lateral secondary particle disequilibrium exists

Nanoparticles (NPs) containing high atomic number (high-Z) materials have been shown to enhance the radiobiological effectiveness of ionizing radiation. This effect is often attributed to an enhancement of the absorbed dose in the vicinity of the NPs, based on Monte Carlo simulations that show a significant local enhancement of the energy deposition on the microscopic scale. The results of such simulations may be significantly biased and lead to a severe overestimation of the dose enhancement if the condition of secondary particle equilibrium is not met in the simulation setup. This current work shows an approach to estimate a 'realistic' dose enhancement from the results of such biased simulations which is based on published photon interaction data and provides a way for correcting biased results.

Monte Carlo single-cell dosimetry using Geant4-DNA: the effects of cell nucleus displacement and rotation on cellular S values

Investigation of biological effects of low-dose ionizing radiation at the (sub-) cellular level, which is referred to as microdosimetry, remains a major challenge of today's radiobiology research. Monte Carlo simulation of radiation tracks can provide a detailed description of the physical processes involved in dimensions as small as the critical substructures of the cell. Hereby, in the present study, microdosimetric calculations of cellular S values for mono-energetic electrons and six Auger-emitting radionuclides were performed in single-cell models of liquid water using Geant4-DNA. The effects of displacement and rotation of the nucleus within the cell on the cellular S values were studied in spherical and ellipsoidal geometries. It was found that for the examined electron energies and radionuclides, in the case of nucleus cross-absorption where the radioactivity is either localized in the cytoplasm of the cell or distributed on the cell surface, rotation of the nucleus within the cell affects cellular S values less than displacement of the nucleus. Especially, the considerable differences observed in S(nucleus ← cell surface) values between an eccentric and a concentric cell-nucleus configuration in spherical and ellipsoidal geometries (up to 63% and up to 44%, respectively) suggests that the approximation of concentricity should be used with caution, at least for localized irradiation of the cell membrane by an Auger-emitter in targeted radionuclide cancer therapy. The obtained results, which are based on a more realistic modeling of the cell than was done before, provide more accurate information about nuclear dose. This can be useful for theranostic applications.

Monte-Carlo dosimetry and real-time imaging of targeted irradiation consequences in 2-cell stage Caenorhabditis elegans embryo

Charged-particle microbeams (CPMs) provide a unique opportunity to investigate the effects of ionizing radiation on living biological specimens with a precise control of the delivered dose, i.e. the number of particles per cell. We describe a methodology to manipulate and micro-irradiate early stage C. elegans embryos at a specific phase of the cell division and with a controlled dose using a CPM. To validate this approach, we observe the radiation-induced damage, such as reduced cell mobility, incomplete cell division and the appearance of chromatin bridges during embryo development, in different strains expressing GFP-tagged proteins in situ after irradiation. In addition, as the dosimetry of such experiments cannot be extrapolated from random irradiations of cell populations, realistic three-dimensional models of 2 cell-stage embryo were imported into the Geant4 Monte-Carlo simulation toolkit. Using this method, we investigate the energy deposit in various chromatin condensation states during the cell division phases. The experimental approach coupled to Monte-Carlo simulations provides a way to selectively irradiate a single cell in a rapidly dividing multicellular model with a reproducible dose. This method opens the way to dose-effect investigations following targeted irradiation.

Approaches to combat hypoxia in cancer therapy and the potential for in silico models in their evaluation

AIM

The negative impact of tumour hypoxia on cancer treatment outcome has been long-known, yet there has been little success combating it. This paper investigates the potential role of in silico modelling to help test emerging hypoxia-targeting treatments in cancer therapy.

METHODS

A Medline search was undertaken on the current landscape of in silico models that simulate cancer therapy and evaluate their ability to test hypoxia-targeting treatments. Techniques and treatments to combat tumour hypoxia and their current challenges are also presented.

RESULTS

Hypoxia-targeting treatments include tumour reoxygenation, hypoxic cell radiosensitization with nitroimidazoles, hypoxia-activated prodrugs and molecular targeting. Their main challenges are toxicity and not achieving adequate delivery to hypoxic regions of the tumour. There is promising research toward combining two or more of these techniques. Different types of in silico therapy models have been developed ranging from temporal to spatial and from stochastic to deterministic models. Numerous models have compared the effectiveness of different radiotherapy fractionation schedules for controlling hypoxic tumours. Similarly, models could help identify and optimize new treatments for overcoming hypoxia that utilize novel hypoxia-targeting technology.

CONCLUSION

Current therapy models should attempt to incorporate more sophisticated modelling of tumour angiogenesis/vasculature and vessel perfusion in order to become more useful for testing hypoxia-targeting treatments, which typically rely upon the tumour vasculature for delivery of additional oxygen, (pro)drugs and nanoparticles.

Using the Proton Energy Spectrum and Microdosimetry to Model Proton Relative Biological Effectiveness

PURPOSE

We introduce a methodology to calculate the microdosimetric quantity dose-mean lineal energy for input into the microdosimetric kinetic model (MKM) to model the relative biological effectiveness (RBE) of proton irradiation experiments.

METHODS AND MATERIALS

The data from 7 individual proton RBE experiments were included in this study. In each experiment, the RBE at several points along the Bragg curve was measured. Monte Carlo simulations to calculate the lineal energy probability density function of 172 different proton energies were carried out with use of Geant4 DNA. We calculated the fluence-weighted lineal energy probability density function (fw(y)), based on the proton energy spectra calculated through Monte Carlo at each experimental depth, calculated the dose-mean lineal energy yD¯ for input into the MKM, and then computed the RBE. The radius of the domain (rd) was varied to reach the best agreement between the MKM-predicted RBE and experimental RBE. A generic RBE model as a function of dose-averaged linear energy transfer (LETD) with 1 fitting parameter was presented and fit to the experimental RBE data as well to facilitate a comparison to the MKM.

RESULTS

Both the MKM and LETD-based models modeled the RBE from experiments well. Values for rd were similar to those of other cell lines under proton irradiation that were modeled with the MKM. Analysis of the performance of each model revealed that neither model was clearly superior to the other.

CONCLUSIONS

Our 3 key accomplishments include the following: (1) We developed a method that uses the proton energy spectra and lineal energy distributions of those protons to calculate dose-mean lineal energy. (2) We demonstrated that our application of the MKM provides theoretical validation of proton irradiation experiments that show that RBE is significantly greater than 1.1. (3) We showed that there is no clear evidence that the MKM is better than LETD-based RBE models.

Physical Radiation Enhancement Effects Around Clinically Relevant Clusters of Nanoagents in Biological Systems

Here we show that the determining factor for physical radiation enhancement effects for a clinically realistic cluster of heavy-atom bearing nanoparticles is the total number of heavy atoms packed into the cluster. We do this through a multiscale Monte Carlo approach which permits the consideration of radiation transport through clusters of millions of nanoparticles. The finding is in contrast to that predicted when isolated nanoparticles are considered and is a direct consequence of the Auger electrons playing less of a role for clusters compared to isolate nanoparticles. We further show that this result is agnostic to selection of the subcellular region considered to be sensitive to the effects of radiation, provided the inside the cluster of nanoparticles is not considered to be biologically active.

IMPACT OF NANOPARTICLE CLUSTERING ON DOSE RADIO-ENHANCEMENT

High atomic number nanoparticles (NPs) have been shown to enhance the effects of radiation in vitro and in vivo. However, NPs are often observed to cluster together, leading to inhomogeneous distribution within the tissue and within cells themselves. The effect of this clustering on the capability of NPs to enhance radiation dose has not yet been fully investigated. In this Monte Carlo simulation study, the dependence of radio-enhancement on a separation parameter characterising NP clustering was investigated. A target water cube of side length 100 μm was simulated containing gold NPs constituting ~1% by mass. The NPs were placed in a cubic grid pattern and the separation distance between nanoparticles was varied. For NPs of 100 nm radius widely separated 2 μm apart, 91% of the total energy deposit was found to occur in the surrounding water, compared to only 56% when the NPs were moved closer together to 0.2 μm. The remaining energy deposit was absorbed by the NPs themselves. A similar trend was observed for NPs of radius 50 nm. The clustering effect was found to persist to greater separations for the larger NPs. The proportion of energy deposit in the available water of the target impacts the potential for cellular damage. Energy deposited within nanoparticles is unlikely to cause biological damage, as ionisations in the surrounding water are required to create radical oxygen species which then progress to cause the biological response to radiation. Clustering of nanoparticles is therefore expected to decrease their effectiveness for enhancing radiotherapy.

From Energy Deposition of Ionizing Radiation to Cell Damage Signaling: Benchmarking Simulations by Measured Yields of Initial DNA Damage after Ion Microbeam Irradiation

Advances in accelerator technology, which have enabled conforming radiotherapy with charged hadronic species, have brought benefits as well as potential new risks to patients. To better understand the effects of ionizing radiation on tumor and surrounding tissue, it is important to investigate and quantify the relationship between energy deposition at the nanometric scale and the initial biological events. Monte Carlo track structure simulation codes provide a powerful tool for investigating this relationship; however, their success and reliability are dependent on their improvement and development accordingly to the dedicated biological data to which they are challenged. For this aim, a microbeam facility that allows for fluence control, down to one ion per cell nucleus, was used to evaluate relative frequencies of DNA damage after interaction between the incoming ion and DNA according to radiation quality. Primary human cells were exposed to alpha particles of three different energies with respective linear energy transfers (LETs) of approximately 36, 85 or 170 keV·µm^-1 at the cells' center position, or to protons (19 keV·µm^-1). Statistical evaluation of nuclear foci formation (53BP1/γ-H2AX), observed using immunofluorescence and related to a particle traversal, was undertaken in a large population of cell nuclei. The biological results were adjusted to consider the factors that drive the experimental uncertainties, then challenged with results using Geant4-DNA code modeling of the ionizing particle interactions on a virtual phantom of the cell nucleus with the same mean geometry and DNA density as the cells used in our experiments. Both results showed an increase of relative frequencies of foci (or simulated DNA damage) in cell nuclei as a function of increasing LET of the traversing particles, reaching a quasi-plateau when the LET exceeded 80-90 keV·µm^-1. For the LET of an alpha particle ranging from 80-90 to 170 keV·µm^-1, 10-30% of the particle hits did not lead to DNA damage inducing 53BP1 or γ-H2AX foci formation.

Experimental measurements validate the use of the binary encounter approximation model to accurately compute proton induced dose and radiolysis enhancement from gold nanoparticles

In protontherapy, it has been suggested that nanoparticles of high-Z material like gold (GNP) could be used as radiosensitizers. The origin of this enhancement phenomenon for proton radiation is not yet well understood and additional mechanistic insights are required. Previous works have highlighted the good capabilities of TRAX to reproduce secondary electron emission from gold material. Therefore, TRAX cross sections obtained with the binary encounter approximation (BEA) model for proton ionization were implemented within Geant4 for gold material. Based on the TRAX cross sections, improved Geant4 simulations have been developed to investigate the energy deposition and radical species production around a spherical gold nanoparticle (5 and 10 nm in diameter) placed in a water volume during proton irradiation. Simulations were performed for incident 2 MeV proton. The dose enhancement factor and the radiolysis enhancement factor were quantified. Results obtained with the BEA model were compared with results obtained with condensed-history models. Experimental irradiation of 200 nm gold films were performed to validate the secondary electron emission reproduction capabilities of physical models used in Monte Carlo (MC) simulations. TRAX simulations reproduced the experimental backscattered electron energy spectrum from gold film with better agreement than Geant4. Results on gold film obtained with the BEA model enabled to estimate the electron emission from GNPs. Results obtained in our study tend to support that the use of the BEA discrete model leads to a significant increase of the dose in the near vicinity of GNPs (<20 nm), while condensed history models used in Geant4 seem to overestimate the dose and the number of chemical species for increasing distances from the GNP. Based on discrete BEA model results, no enhancement effect due to secondary electron emitted from the GNP is expected if the GNP is not in close proximity to key cellular functional elements (DNA, mitochondria…).

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.