Inelastic cross-sections for electron transport in liquid water: a comparison of dielectric models

Inversion model for extracting chemically resolved depth profiles across liquid interfaces of various configurations from XPS data: PROPHESY

PROPHESY, a technique for the reconstruction of surface-depth profiles from X-ray photoelectron spectroscopy data, is introduced. The inversion methodology is based on a Bayesian framework and primal-dual convex optimization. The acquisition model is developed for several geometries representing different sample types: plane (bulk sample), cylinder (liquid microjet) and sphere (droplet). The methodology is tested and characterized with respect to simulated data as a proof of concept. Possible limitations of the method due to uncertainty in the attenuation length of the photo-emitted electron are illustrated.

Prediction of DNA rejoining kinetics and cell survival after proton irradiation for V79 cells using Geant4-DNA

PURPOSE

Track structure Monte Carlo (MC) codes have achieved successful outcomes in the quantitative investigation of radiation-induced initial DNA damage. The aim of the present study is to extend a Geant4-DNA radiobiological application by incorporating a feature allowing for the prediction of DNA rejoining kinetics and corresponding cell surviving fraction along time after irradiation, for a Chinese hamster V79 cell line, which is one of the most popular and widely investigated cell lines in radiobiology.

METHODS

We implemented the Two-Lesion Kinetics (TLK) model, originally proposed by Stewart, which allows for simulations to calculate residual DNA damage and surviving fraction along time via the number of initial DNA damage and its complexity as inputs.

RESULTS

By optimizing the model parameters of the TLK model in accordance to the experimental data on V79, we were able to predict both DNA rejoining kinetics at low linear energy transfers (LET) and cell surviving fraction.

CONCLUSION

This is the first study to demonstrate the implementation of both the cell surviving fraction and the DNA rejoining kinetics with the estimated initial DNA damage, in a realistic cell geometrical model simulated by full track structure MC simulations at DNA level and for various LET. These simulation and model make the link between mechanistic physical/chemical damage processes and these two specific biological endpoints.

Research on the proximity functions of microdosimetry of low energy electrons in liquid water based on different Monte Carlo codes

PURPOSE

The proximity function is an important index in microdosimetry for describing the spatial distribution of energy, which is closely related to the biological effects of organs or tissues in the target area. In this work, the impact of parameters, such as physic models, cut-off energy, and initial energy, on the proximity function are quantitated and compared.

METHODS

According to the track structure (TS) and condensed history (CH) low-energy electromagnetic models, this paper chooses a variety of Monte Carlo (Monte Carlo, MC) codes (Geant4-DNA, PHITS, and Penelope) to simulate the track structure of low-energy electrons in liquid water and evaluates the influence of the electron initial energy, cut-off energy, energy spectrum, and physical model factors on the differential proximity function.

RESULTS

The results show that the initial energy of electrons in the low-energy part (especially less than 1 keV) has a greater impact on the differential proximity function, and the choice of cut-off energy has a greater impact on the differential proximity function corresponding to small radius sites (generally less than 10 nm). The difference in the electronic energy spectrum has little effect on the result, and the proximity functions of different physics models show better consistency under large radius sites.

CONCLUSIONS

This work comprehensively compares the differential proximity functions under different codes by setting a variety of simulation conditions and has basic guiding significance for helping users simulate and analyze the deposition characteristics of microscale electrons according to the selection of an appropriate methodology and cut-off energy.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage

Modelling the inelastic scattering of electrons in water is fundamental, given their crucial role in biological damage. In Monte Carlo track-structure (MC-TS) codes used to assess biological damage, the energy loss function (ELF), from which cross sections are extracted, is derived from different semi-empirical optical models. Only recently have first ab initio results for the ELF and cross sections in water become available. For benchmarking purpose, in this work, we present ab initio linear-response time-dependent density functional theory calculations of the ELF of liquid water. We calculated the inelastic scattering cross sections, inelastic mean free paths, and electronic stopping power and compared our results with recent calculations and experimental data showing a good agreement. In addition, we provide an in-depth analysis of the contributions of different molecular orbitals, species and orbital angular momenta to the total ELF. Moreover, we present single-differential cross sections computed for each molecular orbital channel, which should prove useful for MC-TS simulations.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage

Modelling the inelastic scattering of electrons in water is fundamental, given their crucial role in biological damage. In Monte Carlo track-structure (MC-TS) codes used to assess biological damage, the energy loss function (ELF), from which cross sections are extracted, is derived from different semi-empirical optical models. Only recently have first ab initio results for the ELF and cross sections in water become available. For benchmarking purpose, in this work, we present ab initio linear-response time-dependent density functional theory calculations of the ELF of liquid water. We calculated the inelastic scattering cross sections, inelastic mean free paths, and electronic stopping power and compared our results with recent calculations and experimental data showing a good agreement. In addition, we provide an in-depth analysis of the contributions of different molecular orbitals, species and orbital angular momenta to the total ELF. Moreover, we present single-differential cross sections computed for each molecular orbital channel, which should prove useful for MC-TS simulations.

Low-energy electron distributions from the photoionization of liquid water: a sensitive test of electron mean free paths

The availability of accurate mean free paths for slow electrons (<50 eV) in water is central to the understanding of many electron-driven processes in aqueous solutions, but their determination poses major challenges to experiment and theory alike. Here, we describe a joint experimental and theoretical study demonstrating a novel approach for testing, and, in the future, refining such mean free paths. We report the development of Monte-Carlo electron-trajectory simulations including elastic and inelastic electron scattering, as well as energy loss and secondary-electron production to predict complete photoelectron spectra of liquid water. These simulations are compared to a new set of photoelectron spectra of a liquid-water microjet recorded over a broad range of photon energies in the extreme ultraviolet (20-57 eV). Several previously published sets of scattering parameters are investigated, providing direct and intuitive insights on how they influence the shape of the low-energy electron spectra. A pronounced sensitivity to the escape barrier is also demonstrated. These simulations considerably advance our understanding of the origin of the prominent low-energy electron distributions in photoelectron spectra of liquid water and clarify the influence of scattering parameters and the escape barrier on their shape. They moreover describe the reshaping and displacement of low-energy photoelectron bands caused by vibrationally inelastic scattering. Our work provides a quantitative basis for the interpretation of the complete photoelectron spectra of liquids and opens the path to fully predictive simulations of low-energy scattering in liquid water.

Performance Evaluation for Repair of HSGc-C5 Carcinoma Cell Using Geant4-DNA

Track-structure Monte Carlo simulations are useful tools to evaluate initial DNA damage induced by irradiation. In the previous study, we have developed a Gean4-DNA-based application to estimate the cell surviving fraction of V79 cells after irradiation, bridging the gap between the initial DNA damage and the DNA rejoining kinetics by means of the two-lesion kinetics (TLK) model. However, since the DNA repair performance depends on cell line, the same model parameters cannot be used for different cell lines. Thus, we extended the Geant4-DNA application with a TLK model for the evaluation of DNA damage repair performance in HSGc-C5 carcinoma cells which are typically used for evaluating proton/carbon radiation treatment effects. For this evaluation, we also performed experimental measurements for cell surviving fractions and DNA rejoining kinetics of the HSGc-C5 cells irradiated by 70 MeV protons at the cyclotron facility at the National Institutes for Quantum and Radiological Science and Technology (QST). Concerning fast- and slow-DNA rejoining, the TLK model parameters were adequately optimized with the simulated initial DNA damage. The optimized DNA rejoining speeds were reasonably agreed with the experimental DNA rejoining speeds. Using the optimized TLK model, the Geant4-DNA simulation is now able to predict cell survival and DNA-rejoining kinetics for HSGc-C5 cells.

A Mathematical Radiobiological Model (MRM) to Predict Complex DNA Damage and Cell Survival for Ionizing Particle Radiations of Varying Quality

Predicting radiobiological effects is important in different areas of basic or clinical applications using ionizing radiation (IR); for example, towards optimizing radiation protection or radiation therapy protocols. In this case, we utilized as a basis the ‘MultiScale Approach (MSA)’ model and developed an integrated mathematical radiobiological model (MRM) with several modifications and improvements. Based on this new adaptation of the MSA model, we have predicted cell-specific levels of initial complex DNA damage and cell survival for irradiation with ¹¹Β, ¹²C, ¹⁴Ν, ¹⁶Ο, ²⁰Νe, ⁴⁰Αr, ²⁸Si and ⁵⁶Fe ions by using only three input parameters (particle’s LET and two cell-specific parameters: the cross sectional area of each cell nucleus and its genome size). The model-predicted survival curves are in good agreement with the experimental ones. The particle Relative Biological Effectiveness (RBE) and Oxygen Enhancement Ratio (OER) are also calculated in a very satisfactory way. The proposed integrated MRM model (within current limitations) can be a useful tool for the assessment of radiation biological damage for ions used in hadron-beam radiation therapy or radiation protection purposes.

Excitation and ionisation cross-sections in condensed-phase biomaterials by electrons down to very low energy: application to liquid water and genetic building blocks

A model is presented for computing electron-impact electronic excitation and ionisation cross-sections for arbitrary condensed-phase biomaterials in a wide energy range, showing a general good agreement with the available experimental data.

Analytical proposal for the assessment of the molecular excitation levels contribution to the mean excitation energy: Application to the water molecule

The mean excitation energy 〈I〉 is a fundamental quantity in radiation physics, concerning energy deposition in matter and absorbed dose analytical estimations for charged particles. The stopping of charged particles in different materials strongly depends on this parameter among others. This work intends to contribute with insights for some issues, usually treated not in detail in the theory of stopping power, as the analytic and theoretic assessment of 〈I〉-value for different relevant materials. A methodology is proposed and described aimed at providing the procedure for the 〈I〉 calculation framework, based on the definition of the mean excitation energy using the dielectric response function is analytically integrable if the inelastic cross section parameters are known. Some dielectric models were studied, aimed at calculating the 〈I〉-value for liquid water by theoretical means, reaching the conclusion that a decay at least of the order of ω^-2 in frequency (energy) is needed as weak condition of the optical energy-loss function for the integrals to converge. Afterwards, the first four discrete excitation levels and the diffuse bands for water are treated in a fully analytical scheme, and further compared with numerical results, providing the contribution of these levels to 〈I〉, with the aim of testing the proposed analytical model.

Fully integrated Monte Carlo simulation for evaluating radiation induced DNA damage and subsequent repair using Geant4-DNA

Ionising radiation induced DNA damage and subsequent biological responses to it depend on the radiation’s track-structure and its energy loss distribution pattern. To investigate the underlying biological mechanisms involved in such complex system, there is need of predicting biological response by integrated Monte Carlo (MC) simulations across physics, chemistry and biology. Hence, in this work, we have developed an application using the open source Geant4-DNA toolkit to propose a realistic “fully integrated” MC simulation to calculate both early DNA damage and subsequent biological responses with time. We had previously developed an application allowing simulations of radiation induced early DNA damage on a naked cell nucleus model. In the new version presented in this work, we have developed three additional important features: (1) modeling of a realistic cell geometry, (2) inclusion of a biological repair model, (3) refinement of DNA damage parameters for direct damage and indirect damage scoring. The simulation results are validated with experimental data in terms of Single Strand Break (SSB) yields for plasmid and Double Strand Break (DSB) yields for plasmid/human cell. In addition, the yields of indirect DSBs are compatible with the experimental scavengeable damage fraction. The simulation application also demonstrates agreement with experimental data of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}γ-H2AX yields for gamma ray irradiation. Using this application, it is now possible to predict biological response along time through track-structure MC simulations.

Experimental validation of an analytical microdosimetric model based on Geant4-DNA simulations by using a silicon-based microdosimeter

PURPOSE

To study the agreement between proton microdosimetric distributions measured with a silicon-based cylindrical microdosimeter and a previously published analytical microdosimetric model based on Geant4-DNA in-water Monte Carlo simulations for low energy proton beams.

METHODS AND MATERIAL

Distributions for lineal energy (y) are measured for four proton monoenergetic beams with nominal energies from 2.0 MeV to 4.5 MeV, with a tissue equivalent proportional counter (TEPC) and a silicon-based microdosimeter. The actual energy for protons traversing the silicon-based microdosimeter is simulated with SRIM. Monoenergetic beams with these energies are simulated with Geant4-DNA code by simulating a water cylinder site of dimensions equal to those of the microdosimeter. The microdosimeter response is calibrated by using the distribution peaks obtained from the TEPC. Analytical calculations fory ¯ F andy ¯ D using our methodology based on spherical sites are also performed choosing the equivalent sphere to be checked against experimental results.

RESULTS

Distributions for y at silicon are converted into tissue equivalent and compared to the Geant4-DNA simulated, yielding maximum deviations of 1.03% fory ¯ F and 1.17% fory ¯ D . Our analytical method generates maximum deviations of 1.29% and 3.33%, respectively, with respect to experimental results.

CONCLUSION

Simulations in Geant4-DNA with ideal cylindrical sites in liquid water produce similar results to the measurements in an actual silicon-based cylindrical microdosimeter properly calibrated. The found agreement suggests the possibility to experimentally verify the calculated clinicaly ¯ D with our analytical method.

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.

A microdosimetric analysis of the interactions of mono-energetic neutrons with human tissue

Nuclear reactions induced during high-energy radiotherapy produce secondary neutrons that, due to their carcinogenic potential, constitute an important risk for the development of iatrogenic cancer. Experimental and epidemiological findings indicate a marked energy dependence of neutron relative biological effectiveness (RBE) for carcinogenesis, but little is reported on its physical basis. While the exact mechanism of radiation carcinogenesis is yet to be fully elucidated, numerical microdosimetry can be used to predict the biological consequences of a given irradiation based on its microscopic pattern of energy depositions. Building on recent studies, this work investigated the physics underlying neutron RBE by using the microdosimetric quantity dose-mean lineal energy (y‾_D) as a proxy. A simulation pipeline was constructed to explicitly calculate the y‾_D of radiation fields that consisted of (i) the open source Monte Carlo toolkit Geant4, (ii) its radiobiological extension Geant4-DNA, and (iii) a weighted track-sampling algorithm. This approach was used to study mono-energetic neutrons with initial kinetic energies between 1 eV and 10 MeV at multiple depths in a tissue-equivalent phantom. Spherical sampling volumes with diameters between 2 nm and 1 μm were considered. To obtain a measure of RBE, the neutron y‾_D values were divided by those of 250 keV X-rays that were calculated in the same way. Qualitative agreement was found with published radiation protection factors and simulation data, allowing for the dependencies of neutron RBE on depth and energy to be discussed in the context of the neutron interaction cross sections and secondary particle distributions in human tissue.

A new open-source GPU-based microscopic Monte Carlo simulation tool for the calculations of DNA damages caused by ionizing radiation --- Part I: Core algorithm and validation

PURPOSE

Monte Carlo (MC) simulation of radiation interactions with water medium at physical, physicochemical, and chemical stages, as well as the computation of biologically relevant quantities such as DNA damages, are of critical importance for the understanding of microscopic basis of radiation effects. Due to the large problem size and many-body simulation problem in the chemical stage, existing CPU-based computational packages encounter the problem of low computational efficiency. This paper reports our development on a GPU-based microscopic Monte Carlo simulation tool gMicroMC using advanced GPU-acceleration techniques.

METHODS

gMicroMC simulated electron transport in the physical stage using an interaction-by-interaction scheme to calculate the initial events generating radicals in water. After the physicochemical stage, initial positions of all radicals were determined. Simulation of radicals' diffusion and reactions in the chemical stage was achieved using a step-by-step model using GPU-accelerated parallelization together with a GPU-enabled box-sorting algorithm to reduce the computations of searching for interaction pairs and therefore improve efficiency. A multi-scale DNA model of the whole lymphocyte cell nucleus containing ~6.2 Gbp of DNA was built.

RESULTS

Accuracy of physical stage simulation was demonstrated by computing stopping power and track length. The results agreed with published data and the data produced by GEANT4-DNA (version 10.3.3) simulations with 10 -20% difference in most cases. Difference of yield values of major radiolytic species from GEANT4-DNA results was within 10%. We computed DNA damages caused by monoenergetic 662 keV photons, approximately representing ¹³⁷ Cs decay. Single-strand break (SSB) and double-strand break (DSB) yields were 196 ± 8 SSB/Gy/Gbp and 7.3 ± 0.7 DSB/Gy/Gbp, respectively, which agreed with the result of 188 SSB/Gy/Gbp and 8.4 DSB/Gy/Gbp computed by Hsiao et al. Compared to computation using a single CPU, gMicroMC achieved a speedup factor of ~540x using an NVidia TITAN Xp GPU card.

CONCLUSIONS

The achieved accuracy and efficiency demonstrated that gMicroMC can facilitate research on microscopic radiation transport simulation and DNA damage calculation. gMicroMC is an open-source package available to the research community.

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.

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.

Energy Spectra of Protons and Generated Secondary Electrons around the Bragg Peak in Materials of Interest in Proton Therapy

The number and energy of secondary electrons generated around the trajectories of swift protons interacting with biological materials are highly relevant in proton therapy, due to the prominent role of low-energy electrons in the production of biodamage. For a given material, electron energy distributions are determined by the proton energy; and it is imperative that the distribution of proton energy at depths around the Bragg peak region be described as accurately as possible. With this objective, we simulated the energy distributions of proton beams of clinically relevant energies (50-300 MeV) at depths around the Bragg peak in liquid water and the water-equivalent polymer poly(methyl methacrylate) (PMMA). By using a simple model, this simulation has been conveniently extended to account for nuclear fragmentation reactions, providing depth-dose curves in excellent agreement with available experimental data. Special care has been taken to describe the electronic excitation spectrum of the target, taking into account its condensed phase nature. A predictive formula has been obtained for the mean value and the width of the proton energy distribution at the Bragg peak depth, quantities which are found to grow linearly with the initial energy of the beam, in good agreement with available data. To accurately characterize (in number and energy) the electrons generated around the proton paths, the energy distributions of the latter at each depth have been convoluted with the energy-dependent ionization inverse mean free paths. This results in a number of low-energy electrons around the Bragg peak larger than when only the proton beam average energy at the given depths is considered. The convoluted ionization inverse mean free path closely resembles the Bragg curve shape. The average energy of the secondary electrons is nearly constant (∼55 eV for liquid water and ∼43 eV for PMMA) in the plateau of the Bragg curve, independent of the proton incident energy and suddenly decaying once the Bragg peak is reached. These findings highlight the importance of a precise calculation of the proton beam energy distribution as a function of the target depth to reliably characterize the secondary electrons generated around the Bragg peak region.

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

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

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Implementation of new physics models for low energy electrons in liquid water in Geant4-DNA

A new alternative set of elastic and inelastic cross sections has been added to the very low energy extension of the Geant4 Monte Carlo simulation toolkit, Geant4-DNA, for the simulation of electron interactions in liquid water. These cross sections have been obtained from the CPA100 Monte Carlo track structure code, which has been a reference in the microdosimetry community for many years. They are compared to the default Geant4-DNA cross sections and show better agreement with published data. In order to verify the correct implementation of the CPA100 cross section models in Geant4-DNA, simulations of the number of interactions and ranges were performed using Geant4-DNA with this new set of models, and the results were compared with corresponding results from the original CPA100 code. Good agreement is observed between the implementations, with relative differences lower than 1% regardless of the incident electron energy. Useful quantities related to the deposited energy at the scale of the cell or the organ of interest for internal dosimetry, like dose point kernels, are also calculated using these new physics models. They are compared with results obtained using the well-known Penelope Monte Carlo code.

Technical Note: Improvements in geant4 energy-loss model and the effect on low-energy electron transport in liquid water

PURPOSE

The geant4-DNA physics models are upgraded by a more accurate set of electron cross sections for ionization and excitation in liquid water. The impact of the new developments on low-energy electron transport simulations by the geant4 Monte Carlo toolkit is examined for improving its performance in dosimetry applications at the subcellular and nanometer level.

METHODS

The authors provide an algorithm for an improved implementation of the Emfietzoglou model dielectric response function of liquid water used in the geant4-DNA existing model. The algorithm redistributes the imaginary part of the dielectric function to ensure a physically motivated behavior at the binding energies, while retaining all the advantages of the original formulation, e.g., the analytic properties and the fulfillment of the f-sum-rule. In addition, refinements in the exchange and perturbation corrections to the Born approximation used in the geant4-DNA existing model are also made.

RESULTS

The new ionization and excitation cross sections are significantly different from those of the geant4-DNA existing model. In particular, excitations are strongly enhanced relative to ionizations, resulting in higher W-values and less diffusive dose-point-kernels at sub-keV electron energies.

CONCLUSIONS

An improved energy-loss model for the excitation and ionization of liquid water by low-energy electrons has been implemented in geant4-DNA. The suspiciously low W-values and the unphysical long tail in the dose-point-kernel have been corrected owing to a different partitioning of the dielectric function.

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

Understanding the fundamental mechanisms involved in the induction of biological damage by ionizing radiation remains a major challenge of today's radiobiology research. The Monte Carlo simulation of physical, physicochemical and chemical processes involved may provide a powerful tool for the simulation of early damage induction. The Geant4-DNA extension of the general purpose Monte Carlo Geant4 simulation toolkit aims to provide the scientific community with an open source access platform for the mechanistic simulation of such early damage. This paper presents the most recent review of the Geant4-DNA extension, as available to Geant4 users since June 2015 (release 10.2 Beta). In particular, the review includes the description of new physical models for the description of electron elastic and inelastic interactions in liquid water, as well as new examples dedicated to the simulation of physicochemical and chemical stages of water radiolysis. Several implementations of geometrical models of biological targets are presented as well, and the list of Geant4-DNA examples is described.

Electron attenuation in free, neutral ethane clusters

The electron effective attenuation length (EAL) in free, neutral ethane clusters has been determined at 40 eV kinetic energy by combining carbon 1s x-ray photoelectron spectroscopy and theoretical lineshape modeling. More specifically, theory is employed to form model spectra on a grid in cluster size (N) and EAL (λ), allowing N and λ to be determined by optimizing the goodness-of-fit χ(2)(N, λ) between model and observed spectra. Experimentally, the clusters were produced in an adiabatic-expansion setup using helium as the driving gas, spanning a range of 100-600 molecules in mean cluster size. The effective attenuation length was determined to be 8.4 ± 1.9 Å, in good agreement with an independent estimate of 10 Å formed on the basis of molecular electron-scattering data and Monte Carlo simulations. The aggregation state of the clusters as well as the cluster temperature and its importance to the derived EAL value are discussed in some depth.

Monte Carlo calculations of energy deposition distributions of electrons below 20 keV in protein

The distributions of energy depositions of electrons in semi-infinite bulk protein and the radial dose distributions of point-isotropic mono-energetic electron sources [i.e., the so-called dose point kernel (DPK)] in protein have been systematically calculated in the energy range below 20 keV, based on Monte Carlo methods. The ranges of electrons have been evaluated by extrapolating two calculated distributions, respectively, and the evaluated ranges of electrons are compared with the electron mean path length in protein which has been calculated by using electron inelastic cross sections described in this work in the continuous-slowing-down approximation. It has been found that for a given energy, the electron mean path length is smaller than the electron range evaluated from DPK, but it is large compared to the electron range obtained from the energy deposition distributions of electrons in semi-infinite bulk protein. The energy dependences of the extrapolated electron ranges based on the two investigated distributions are given, respectively, in a power-law form. In addition, the DPK in protein has also been compared with that in liquid water. An evident difference between the two DPKs is observed. The calculations presented in this work may be useful in studies of radiation effects on proteins.

Semiempirical model for the ion impact ionization of complex biological media

We present a semiempirical model for calculating the electron emission from any organic compound after ion impact. With only the input of the density and composition of the target we are able to evaluate its ionization cross sections using plausible approximations. Results for protons impacting in the most representative biological targets (such as water or DNA components) show a very good comparison with experimental data. Because of its simplicity and great predictive effectiveness, the method can be immediately extended to any combination of biological target and charged particle of interest in ion beam cancer therapy.

Absolute cross sections for vibrational excitations of cytosine by low energy electron impact

The absolute cross sections (CSs) for vibrational excitations of cytosine by electron impact between 0.5 and 18 eV were measured by electron-energy loss (EEL) spectroscopy of the molecule deposited at monolayer coverage on an inert Ar substrate. The vibrational energies compare to those that have been reported from IR spectroscopy of cytosine isolated in Ar matrix, IR and Raman spectra of polycrystalline cytosine, and ab initio calculation. The CSs for the various H bending modes at 142 and 160 meV are both rising from their energy threshold up to 1.7 and 2.1 × 10(-17) cm(2) at about 4 eV, respectively, and then decrease moderately while maintaining some intensity at 18 eV. The latter trend is displayed as well for the CS assigned to the NH(2) scissor along with bending of all H at 179 meV. This overall behavior in electron-molecule collision is attributed to direct processes such as the dipole, quadrupole, and polarization contributions, etc. of the interaction of the incident electron with a molecule. The CSs for the ring deformation at 61 meV, the ring deformation with N-H symmetric wag at 77 meV, and the ring deformations with symmetric bending of all H at 119 meV exhibit common enhancement maxima at 1.5, 3.5, and 5.5 eV followed by a broad hump at about 12 eV, which are superimposed on the contribution due to the direct processes. At 3.5 eV, the CS values for the 61-, 77-, and 119-meV modes reach 4.0, 3.0, and 4.5 × 10(-17) cm(2), respectively. The CS for the C-C and C-O stretches at 202 meV, which dominates in the intermediate EEL region, rises sharply until 1.5 eV, reaches its maximum of 5.7 × 10(-17) cm(2) at 3.5 eV and then decreases toward 18 eV. The present vibrational enhancements, correspond to the features found around 1.5 and 4.5 eV in electron transmission spectroscopy (ETS) and those lying within 1.5-2.1 eV, 5.2-6.8 eV, and 9.5-10.9 eV range in dissociative electron attachment (DEA) experiments with cytosine in gas phase. While the ETS features are ascribed to shape resonances associated with the electron occupation of the second and third antibonding π-orbitals of the molecule in its ground state, the correspondence with DEA features suggests the existence of common precursor anion states decaying with certain probabilities into the vibrationally excited ground state.

A new calculation on spectrum of direct DNA damage induced by low-energy electrons

In this work, direct DNA damage induced by low-energy electrons (<5 keV) is simulated using Monte Carlo methods, and the resulting yield of various strand breaks and base damages in cellular environment is presented. The simulation is based on a new inelastic cross section for the production of electron track structure in liquid water, and on ionization cross sections of DNA bases to generate base radical. Especially, a systematic approach of simulating detailed base damage is suggested. This approach includes improvement of a volume model of DNA, generation of the DNA base sequence, conversion of ionization events in liquid water at hit site to the ionization interaction of electrons with DNA bases and development of an algorithm to convert a base radical to a damage. The results obtained in terms of strand breaks are compared with those of experiments and other theoretical calculations, and good agreement was obtained. The yield of detailed base damages and clustered DNA damages caused by the combination of various strand breaks and base damages is presented, and the corresponding distribution characteristics are analyzed. The influence of the relative content of base pairs A-T and G-C in a DNA segment on the yield of both strand breaks and base damages is also explored. The present work provides fundamental information on DNA damage and represents the first effort toward the goal of obtaining the spectrum of clustered DNA damage including detailed base damages, for the mechanistic interpretation and prediction of radiation effects.

Accurate electron inelastic cross sections and stopping powers for liquid water over the 0.1-10 keV range based on an improved dielectric description of the Bethe surface

Electron inelastic cross sections and stopping powers for liquid water over the 0.1-10 keV range are presented based on a recently developed dielectric response model for liquid water (D. Emfietzoglou, F. Cucinotta and H. Nikjoo, Radiat. Res. 164, 202-211, 2005) that is consistent with the experimental data over the whole energy-momentum plane. Both exchange and second-order Born corrections are included in a material-specific way using the dielectric functions of liquid water. The numerical results are fitted by simple analytic functions to facilitate their further use. Compared to previous studies, differential cross sections are shifted toward smaller energy losses resulting in smaller inelastic and stopping cross sections with differences reaching, on average, the approximately 20% and approximately 50% level, respectively. Contrary to higher energies, it is shown that the dispersion model for the momentum dependence of the dielectric functions (Bethe ridge) is as important as the optical model used. Within the accuracy of the experimental data (a few percent) upon which our dielectric model is based, the calculations are "exact" to first order, while the uncertainty of the results beyond first order is estimated at the 5-10% level. The present work overcomes the limitations of Bethe's theory at low energies by a self-consistent account of inner-shell effects and may serve to extend the ICRU electron stopping power database for liquid water down to 100 eV with a level of uncertainty similar to that for the higher-energy values.

Electron stopping power and inelastic mean free path in amino acids and protein over the energy range of 20-20,000 eV

Systematic calculations of stopping power (SPs) and inelastic mean free path (IMFP) values for 20-20,000 eV electrons in a group of 15 amino acids and a simple protein have been performed. The calculations are based on the dielectric response model and take into account the exchange effect between the incident electron and target electrons. The optical energy-loss functions for the 15 investigated amino acids and the protein are evaluated by using an empirical approach, because of the lack of experimental optical data. For all the considered materials, the calculated mean ionization potentials are in good agreement with those given by Bragg's rule, and the evaluated SP values at 20 keV converge well to the Bethe-Bloch predictions. The data shown represent the first results of SP and IMFP, for these 15 amino acids and the protein in the energy range below 20 keV, and might be useful for studies of various radiation effects in these materials. In addition, the average energy deposited by inelastic scattering of the electrons on this group of 15 amino acids, on the protein, on Formvar and on DNA, respectively, has been estimated for energies below 20 keV. The dependences of the average energy deposition on the electron energy are given. These results are important for any detailed studies of radiation-induced inactivation of proteins and the DNA.

A comparative study of dielectric response function models for liquid water

Various methodologies that aim at an analytic representation of the dielectric response function (DRF) of liquid water with emphasis on the Bethe ridge region are compared. The use of optical data is a common feature to all models presented providing an empirical ground for modelling the valence energy losses where many-body (and phase) effects are expected to be most prevalent. The dispersion models used for describing the momentum dependence of the DRF are evaluated against the recent inelastic X-ray scattering (IXS) spectroscopy data. Recent developments along the lines of Ritchie's extended-Drude scheme for an improved representation of the experimental Bethe ridge are presented.

A Monte-Carlo code for the detailed simulation of electron and light-ion tracks in condensed matter

In an effort to understand the basic mechanism of the action of charged particles in solid radiation dosimeters, we extend our Monte-Carlo code (MC4) to condensed media (liquids/solids) and present new track-structure calculations for electrons and protons. Modeling the energy dissipation process is based on a model dielectric function, which accounts in a semi-empirical and self-consistent way for condensed-phase effects which are computationally intractable. Importantly, these effects mostly influence track-structure characteristics at the nanometer scale, which is the focus of radiation action models. Since the event-by-event scheme for electron transport is impractical above several kilo-electron volts, a condensed-history random-walk scheme has been implemented to transport the energetic delta rays produced by energetic ions. Based on the above developments, new track-structure calculations are presented for two representative dosimetric materials, namely, liquid water and silicon. Results include radial dose distributions in cylindrical and spherical geometries, as well as, clustering distributions, which, among other things, are important in predicting irreparable damage in biological systems and prompt electric-fields in microelectronics.

Track structure: time evolution from physics to chemistry

This review discusses interaction cross sections of charged particles (electrons, protons, light ions) with atoms and molecules. The focus is on biological relevant targets like liquid water which serves as a substitute of soft tissue in most Monte Carlo codes. The spatial distribution of energy deposition patterns by different radiation qualities and their importance to the time evolution from the physical to the chemical stage or radiation response is discussed. The determination of inelastic interaction cross sections for charged particles in condensed matter is discussed within the relativistic plane-wave Born approximation and semi-empirical models. The dielectric-response-function of liquid water is discussed.

A complete dielectric response model for liquid water: a solution of the Bethe ridge problem

We present a complete yet computationally simple model for the dielectric response function of liquid water over the energy-momentum plane, which, in contrast to earlier models, is consistent with the recent inelastic X-ray scattering spectroscopy data at both zero and finite momentum transfer values. The model follows Ritchie's extended-Drude algorithm and is particularly effective at the region of the Bethe ridge, substantially improving previous models. The present development allows for a more accurate simulation of the inelastic scattering and energy deposition process of low-energy electrons in liquid water and other biomaterials. As an example, we calculate the stopping power of liquid water for electrons over the 0.1-10 keV range where direct experimental measurements are still impractical and the Bethe stopping formula is inaccurate. The new stopping power values are up to 30-40% lower than previous calculations. Within the range of validity of the first Born approximation, the new values are accurate to within the experimental uncertainties (a few percent). At the low end, the introduction of Born corrections raises the uncertainty to perhaps approximately 10%. Thus the present model helps extend the ICRU electron stopping power database for liquid water down to about two orders of magnitude with a comparable level of uncertainty.

The effect of model approximations on single-collision distributions of low-energy electrons in liquid water

The development of cross sections for the inelastic interaction of low-energy electrons with condensed tissue-like media is best accomplished within the framework of the dielectric theory. In this work we investigate the degree to which various model approximations, used in the above methodology, influence electron single-collision distributions. These distributions are of major importance to Monte Carlo track structure codes, namely, the energy-loss spectrum, the inelastic inverse mean free path, and the ionization efficiency. In particular, we make quantitative assessment of the influence of (1) the optical data set, (2) the dispersion algorithm, and (3) the perturbation and exchange Born corrections. It is shown that, although the shape and position of the energy-loss spectrum remains almost fixed, its peak height may vary by up to a factor of 1.5. Discrepancies in the calculated inelastic inverse mean free path are largely within 20-30% above 100 eV; they increase drastically, though, at lower energies. Exchange and perturbation Born corrections increase gradually below 1 keV leading to a approximately 30 to 40% reduction of the inverse mean free path at 100 eV. The perturbation effect contributes more than the exchange effect to this reduction. Similar to the dispersion situation, the effect of Born corrections at lower energies is also unclear since the models examined disagree strongly below 100 eV. In comparison, the vapor data are higher than the liquid calculations by 20 to 50% as the energy decreases from 1 to 0.1 keV, respectively. The excitation contribution is the main cause of this difference, since the ionization efficiency in the liquid levels off at approximately 90%, whereas the plateau value for the vapor is approximately 70%. It is concluded that electron inelastic distributions for liquid water, although in some respects distinctively different from the vapor phase, have associated uncertainties that are comparable in magnitude to the phase differences. The situation below 100 eV is uncertain.

Monte-Carlo calculations of radial dose and restricted-let for protons in water

A new Monte-Carlo code for event-by-event simulation of the transport of energetic non-relativistic protons (approximately 0.5-10 MeV) and all their secondary electrons (down to 1 Ry) in both the vapour and liquid phases of water is presented. A unified particle-water inelastic model for both phases of water has been developed based on experimental optical data and elements of the Bethe theory. The model applies to both electrons and heavy-charged particles and is particularly suitable for extension to other media of biological relevance (organic polymers, DNA, etc.). Condensed-phase effects are included in the liquid version (MC4L) by means of the dielectric functions which, essentially, substitute the oscillator-strength used in the vapour version (MC4V). The results in the form of radial dose distributions and spatially restricted linear energy transfer are presented and compared with the literature.

Monte Carlo simulation of the energy loss of low-energy electrons in liquid water

A Monte Carlo code that performs detailed (i.e. event-by-event) simulation of the transport and energy loss of low-energy electrons (approximately 50-10 000 eV) in water in the liquid phase is presented. The inelastic model for energy loss is based on a semi-empirical dielectric-response function for the valence-shells of the liquid whereas an exchange corrected semi-classical formula was used for K-shell ionization. Following a methodology widely used for the vapour phase, we succeeded in parametrizing the dielectric cross-sections of the liquid in accordance with the Bethe asymptote, thus providing a unified approach for both phases of water and greatly facilitating the computations. Born-corrections at lower energies have been implemented in terms of a second-order perturbation term with a simple Coulomb-field correction and the use of a Mott-type exchange modification. Angular deflections were determined by empirical schemes established from vapour data. Electron tracks generated by the code were used to calculate energy- and interaction-point-kernel distributions at low electron energies in liquid water. The effect of various model assumptions (e.g., dispersion, Born-corrections, phase) on both the single-collision and slowing-down distributions is examined.