Inelastic scattering and energy loss of swift electron beams in biologically relevant materials

Analytic and Monte Carlo calculations of dose-mean lineal energy for 1 MeV-1 GeV protons with application to radiation protection quality factor

Radiation quality for determining biological effects is commonly linked to the microdosimetric quantity lineal energy ( y ) and to the dose-mean lineal energy ( y D ). Calculations of y D are typically performed by specialised Monte Carlo track-structure (MCTS) codes, which can be time-intensive. Thus, microdosimetry-based analytic models are potentially useful for practical calculations. Analytic model calculations of proton y D and radiation protection quality factor ( Q ) values in sub-micron liquid water spheres (diameter 10-1000 nm) over a broad energy range (1 MeV-1 GeV) are compared against MCTS simulations by PHITS, RITRACKS, and Geant4-DNA. Additionally, an improved analytic microdosimetry model is proposed. The original analytic model of Xapsos is refined and model parameters are updated based on Geant4-DNA physics model. Direct proton energy deposition is described by an alternative energy-loss straggling distribution and the contribution of secondary electrons is calculated using the dielectric formulation of the relativistic Born approximation. MCTS simulations of proton y D values using the latest versions of the PHITS, RITRACKS, and Geant4-DNA are reported along with the Monte Carlo Damage Simulation (MCDS) algorithm. The y D datasets are then used within the Theory of Dual Radiation Action (TDRA) to illustrate variations in Q with proton energy. By a careful selection of parameters, overall differences at the ~ 10% level between the proposed analytic model and the MCTS codes can be attained, significantly improving upon existing models. MCDS estimates of y D are generally much lower than estimates from MCTS simulations. The differences of Q among the examined methods are somewhat smaller than those of y D . Still, estimates of proton Q values by the present model are in better agreement with MCTS-based estimates than the existing analytic models. An improved microdosimetry-based analytic model is presented for calculating proton y D values over a broad range of proton energies (1 MeV-1 GeV) and target sizes (10-1000 nm) in very good agreement with state-of-the-art MCTS simulations. It is envisioned that the proposed model might be used as an alternative to CPU-intensive MCTS simulations and advance practical microdosimetry and quality factor calculations in medical, accelerator, and space radiation applications.

Electron interaction with DNA constituents in aqueous phase

Electron driven chemistry of biomolecules in aqueous phase presents the realistic picture to study molecular processes. In this study we have investigated the interactions of electrons with the DNA constituents in their aqueous phase in order to obtain the quantities useful for DNA damage assessment. We have computed the inelastic mean free path (IMFP), mass stopping power (MSP) and absorbed dose (D) for the DNA constituents (Adenine, Cytosine, Guanine, Thymine and Uracil) in the aqueous medium from ionisation threshold to 5000 eV. We have modified complex optical potential formalism to include band gap of the systems to calculate inelastic cross sections which are used to estimate these entities. This is the maiden attempt to report these important quantities for the aqueous DNA constituents. We have compared our results with available data in gas and other phase and have observed explicable accord for IMFP and MSP. Since these are the first results of absorbed dose (D) for these compounds, we have explored present results vis-a-vis dose absorption in water.

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.

Sub-keV corrections to binary encounter cross section models for electron ionization of liquid water with application to the Geant4-DNA Monte Carlo code

INTRODUCTION

The electron ionization cross section of water is one of the most important input in Monte Carlo studies of cellular radiobiological effects. Analytical cross section models of the binary-encounter type have the potential of reducing simulation time and facilitate application to a variety of biological materials (other than water). The Binary-Encounter-Bethe (BEB) and Binary-Encounter-Dipole (BED) models of NIST are perhaps the most popular of such models giving reliable results for atoms and molecules in the gas-phase over a wide energy range. However, the use of such models to sub-keV electron energies in liquid water raises concerns due to the neglect of condensed phase effects that leads to a significant overestimation when compared to medium-specific dielectric models.

PURPOSE

To modify the BEB and BED models towards better agreement with the recommended low-energy dielectric model of Geant4-DNA (Option 4). To implement the new modifications to the existing BEB model of the Option 6 physics constructor of Geant4-DNA and re-evaluate fundamental transport quantities for sub-keV electrons.

METHODS

In analogy to a Yukawa potential a simple, yet physically-motivated, modification of the Burgess correction term is proposed to account for the reduction of the Coulomb interaction due to the polarizability of the target. The magnitude of the correction is guided by the dielectric-based ionization cross section implemented in Option 4.

RESULTS

Differential, total and stopping ionization cross sections for low-energy electrons in liquid water are presented. When combined with the Vriens correction (which is not included in Option 6), the proposed modification to the BEB and BED models brings the ionization and stopping cross sections in much better agreement against those used in the Option 4 dielectric model of Geant4-DNA, with up to 30% and 10% deviation, respectively. Implementation of the new correction to the Option 6 constructor of Geant4-DNA and re-evaluation of fundamental transport quantities, such as electron penetration ranges and dose-point-kernels, reduced the discrepancies from Option 4 at sub-keV energies from 20 to 100% (or more) to well below 10% in most cases.

CONCLUSIONS

A simple modification to the BEB and BED analytic models was found to improve their performance for sub-keV electrons in liquid water medium. Implementation of the new modification to the Option 6 constructor of Geant4-DNA significantly improved the agreement with the recommended low-energy Option 4 constructor for a variety of fundamental quantities related to electron transport.

Electron Impact with the Liquid-Vapor Interface

Reaction dynamics in the liquid-vapor interface is one of the crucial physical sciences but is still starving for in-depth exploration. It is challenging to selectively detect the interfacial species or the yields of chemical reaction therein, meanwhile shielding or reducing the interference from the vapor and liquid bulk. Mass spectrometry is a straightforward method but is also frustrated in such a selective detection. Using a liquid microjet in combination with a pulsed electron beam, a linear time-of-flight mass spectrometer, and a quadrupole mass filter, we recently innovated time-delayed mass spectrometry for investigations of the liquid-vapor interface. In this Account, we illustrate how this unique method succeeds in disentangling different sources, i.e., the vapor and liquid-vapor interface, of the ionic yields of the electron impacts with a liquid beam of alcohol in vacuum. These achievements are basically attributed to the application of an onion-peeling strategy in the ion detection. Concretely, the microsecond time scale of molecular volatilization can be resolved well by tuning the delay time between the nanosecond pulses of incident electron bunch and ion attractor. First, the specific orientation of the interfacial molecule, i.e., a well-known fact about the hydrophobic hydrocarbon groups pointing outside the liquid surface of alcohol, is validated again. More importantly, the dynamic features of time-delayed mass spectra, in particular, for the ionic yields from the liquid-vapor interface, are rationalized explicitly. Moreover, we demonstrate evidence of in situ molecular dimers in the liquid-vapor interface of 1-propanol. As the first example of electron-induced reaction in the liquid-vapor interface, dimethyl ether can be synthesized in the liquid methanol interface due to local interfacial acidification by high-energy electron impacts. On the contrary, the low energy electron can lead to local basicity through dissociative electron attachment (DEA). Besides the primary low-energy electrons, the low-energy secondary and inelastically scattered electrons in the higher-energy impacts of the primary electrons can also participate in the DEA process. In contrast to the gas- or solid-phase DEAs, that in the liquid-vapor interface shows distinct differences in both the types and efficiencies of anionic products. With these and efforts in the future, we develop a molecular-level understanding of how the chemical reactions happen in the liquid-vapor interface.

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.

Review of the Geant4-DNA Simulation Toolkit for Radiobiological Applications at the Cellular and DNA Level

Simple Summary

A brief description of the methodologies to simulate ionizing radiation transport in biologically relevant matter is presented. Emphasis is given to the physical, chemical, and biological models of Geant4-DNA that enable mechanistic radiobiological modeling at the cellular and DNA level, important to improve the efficacy of existing and novel radiotherapeutic modalities for the treatment of cancer.

Abstract

The Geant4-DNA low energy extension of the Geant4 Monte Carlo (MC) toolkit is a continuously evolving MC simulation code permitting mechanistic studies of cellular radiobiological effects. Geant4-DNA considers the physical, chemical, and biological stages of the action of ionizing radiation (in the form of x- and γ-ray photons, electrons and β^±-rays, hadrons, α-particles, and a set of heavier ions) in living cells towards a variety of applications ranging from predicting radiotherapy outcomes to radiation protection both on earth and in space. In this work, we provide a brief, yet concise, overview of the progress that has been achieved so far concerning the different physical, physicochemical, chemical, and biological models implemented into Geant4-DNA, highlighting the latest developments. Specifically, the “dnadamage1” and “molecularDNA” applications which enable, for the first time within an open-source platform, quantitative predictions of early DNA damage in terms of single-strand-breaks (SSBs), double-strand-breaks (DSBs), and more complex clustered lesions for different DNA structures ranging from the nucleotide level to the entire genome. These developments are critically presented and discussed along with key benchmarking results. The Geant4-DNA toolkit, through its different set of models and functionalities, offers unique capabilities for elucidating the problem of radiation quality or the relative biological effectiveness (RBE) of different ionizing radiations which underlines nearly the whole spectrum of radiotherapeutic modalities, from external high-energy hadron beams to internal low-energy gamma and beta emitters that are used in brachytherapy sources and radiopharmaceuticals, respectively.

Stopping power and CSDA range calculations of electrons and positrons over the 20 eV-1 GeV energy range in some water equivalent polymer gel dosimeters

In this study, the stopping power, CSDA range and radiation yield calculations of electrons and positrons over the 20 eV-1 GeV energy range in some water equivalent polymer gel dosimeters were performed. For collision stopping power calculations of electrons and positrons the effective charge concept proposed by Sugiyama were considered. Here, both the effective charge of incident electrons and positrons (z*) and the effective charge (Z*) and the effective mean excitation energy (I*) of the target material were calculated. For the density effect correction the Fano model was selected. For the radiative stopping power analytical model based on the ratio between the collision and the radiative stopping power discribed by Attix was considered. For CSDA range and radition yield the continuous slowing down approximation (CSDA) was considered and the calculations were performed using numerical integral methods. Because of their water equivalent and 3D dose distribution properties, MAGIC and MAGAS polymer gels were selected as a target materials. The calculations were performed by programming all the equations discribed in this study as a computational code. The results of the stopping power, range and radiation yield were compared with those of ESTAR program and PENELOPE Monte Carlo modelling. Some deviations in low and high energy region between the calculated and reference data were observed. However, the similarity between calculated and reference data is remarkable. For the collision stopping power and CSDA range a good agreement between the calculated and reference data was observed for energies >1 keV. Whereas, for the radiative stopping power a good agreement was observed for energies >100 keV.

Electronic excitation spectra of cerium oxides: from ab initio dielectric response functions to Monte Carlo electron transport simulations

Nanomaterials made of cerium oxides CeO₂ and Ce₂O₃ have a broad range of applications, from catalysts in automotive, industrial or energy operations to promising materials to enhance hadrontherapy effectiveness in oncological treatments. To elucidate the physico-chemical mechanisms involved in these processes, it is of paramount importance to know the electronic excitation spectra of these oxides, which are obtained here through high-accuracy linear-response time-dependent density functional theory calculations. In particular, the macroscopic dielectric response functions  of both bulk CeO₂ and Ce₂O₃ are derived, which compare remarkably well with the available experimental data. These results stress the importance of appropriately accounting for local field effects to model the dielectric function of metal oxides. Furthermore, we reckon the energy loss functions Im(-1/) of the materials, including the accurate evaluation of the momentum transfer dispersion from first-principles calculations. In this respect, by using Mermin-type parametrization we are able to model the contribution of different electronic excitations to the dielectric loss function. Finally, from the knowledge of the electron inelastic mean free path, together with the elastic mean free path provided by the relativistic Mott theory, we carry out statistical Monte Carlo (MC) electron transport simulations to reproduce the major features of the reported experimental reflection electron energy loss (REEL) spectra of cerium oxides. The good agreement with REEL experimental data strongly supports our approach based on MC modelling, whose main inputs were obtained using ab initio calculated electronic excitation spectra in a broad range of momentum and energy transfers.

Mean Free Paths and Cross Sections for Electron Scattering from Liquid Water

Electron collision with liquid water is theoretically investigated and reported in this article. The range of projectile energy considered is 10-5000 eV, covering all major channels, viz., ionization, inelastic, elastic, and total scattering. The liquid phase electron charge density and static potential are generated and used in the calculation under a spherical complex optical potential formalism to achieve the goals. For the ionization channel, the complex scattering potential-ionization contribution method is used. The agreement with available theoretical data is satisfactory. The study on the total electron scattering from liquid water, using a common method for elastic and inelastic cross sections, is new and requires further attempts to support the reported data.

Future directions on low-energy radiation dosimetry

For more than one century, low-energy (< 100 keV) photons (x-rays and gamma) have been widely used in different areas including biomedical research and medical applications such as mammography, fluoroscopy, general radiography, computed tomography, and brachytherapy treatment, amongst others. It has been demonstrated that most of the electrons produced by low photon energy beams have energies below 10 keV. However, the physical processes by which these low energy electrons interact with matter are not yet well understood. Besides, it is generally assumed that all the energy deposited within a dosimeter sensitive volume is transformed into a response. But such an assumption could be incorrect since part of the energy deposited might be used to create defects or damages at the molecular and atomic level. Consequently, the relationship between absorbed dose and dosimeter response can be mistaken. During the last few years, efforts have been made to identify models that allow to understand these interaction processes from a quantum mechanical point of view. Some approaches are based on electron-beam − solid-state-interaction models to calculate electron scattering cross-sections while others consider the density functional theory method to localize low energy electrons and evaluate the energy loss due to the creations of defects and damages in matter. The results obtained so far could be considered as a starting point. This paper presents some methodologies based on fundamental quantum mechanics which can be considered useful for dealing with low-energy interactions.

IDDRRA: A novel platform, based on Geant4-DNA to quantify DNA damage by ionizing radiation

PURPOSE

This study proposes a novel computational platform that we refer to as IDDRRA (DNA Damage Response to Ionizing RAdiation), which uses Monte Carlo (MC) simulations to score radiation induced DNA damage. MC simulations provide results of high accuracy on the interaction of radiation with matter while scoring the energy deposition based on state-of-the-art physics and chemistry models and probabilistic methods.

METHODS

The IDDRRA software is based on the Geant4-DNA toolkit together with new tools that were developed for the purpose of this study, including a new algorithm that was developed in Python for the design of the DNA molecules. New classes were developed in C++ to integrate the GUI and produce the simulation's output in text format. An algorithm was also developed to analyze the simulation's output in terms of energy deposition, Single Strand Breaks (SSB), Double Strand Breaks (DSB) and Cluster Damage Sites (CDS). Finally, a new tool was developed to implement probabilistic SSB and DSB repair models using MC techniques.

RESULTS

This article provides the first benchmarks that the user of the IDDRRA tool can use to validate the functionality of the software as well as to provide a starting point to produce different types of DNA simulations. These benchmarks incorporate different kind of particles (e-, e+, protons, electron spectrum) and DNA molecules.

CONCLUSION

We have developed the IDDRRA tool and demonstrated its use to study various aspects of the modeling and simulation of a DNA irradiation experiment. The tool is expandable and can be expanded by other users with new benchmarks and applications based on the user's needs and experience. New functionality will be added over time, including the quantification of the indirect damage.

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.

Electron Inelastic Mean Free Paths for LiF, CaF2, Al2O3, and Liquid Water from 433 keV down to the Energy Gap

We report new calculations, which include the influence of the band gap and exciton states, of the electron inelastic mean free path (IMFP) for liquid water, LiF, CaF₂, and Al₂O₃ from the band gap to 433 keV. Among compounds, liquid water is the most studied due to its role in radiobiological research, whereas LiF and CaF₂ are the most widely used thermoluminescent dosimeters in environmental monitoring and medical and space dosimetry. Due to its sensitivity, the optically stimulated luminescent dosimeter, Al₂O₃, has recently begun to be used for personnel monitoring. Previous treatments have modified the integration domain to consider the indistinguishability between the incident electron and the ejected one or the bandgap energy for nonconductors but not to accommodate exciton states within the band gap, and no published IMFP data are available for CaF₂. Our calculation was carried out using an electron-beam-solid-state interaction model through the relativistic full Penn algorithm. Integration limits that consider the band gap, the valence band width, and exciton interactions have been used. The results suggest that, at electron energies below 100 eV, the different choices of models for integration limits and the exciton interaction can affect the IMFP by 9-29%. At higher energies, the differences associated with the choice of energy-loss function and other input parameters are around 2.5-7.5%.

Microdosimetric calculations of the direct DNA damage induced by low energy electrons using the Geant4-DNA Monte Carlo code

To calculate the yield of direct DNA damage induced by low energy electrons using Monte Carlo generated microdosimetric spectra at the nanometer scale and examine the influence of various simulation inputs. The potential of classical microdosimetry to offer a viable and simpler alternative to more elaborate mechanistic approaches for practical applications is discussed. Track-structure simulations with the Geant4-DNA low-energy extension of the Geant4 Monte Carlo toolkit were used for calculating lineal energy spectra in spherical volumes with dimensions relevant to double-strand-break (DSB) induction. The microdosimetric spectra were then used to calculate the yield of simple and clustered DSB based on literature values of the threshold energy of DNA damage. The influence of the different implementations of the dielectric function of liquid water available in Geant4-DNA (Option 2 and Option 4 constructors), as well as the effect of particle tracking cutoff energy and target size are examined. Frequency- and dose-mean lineal energies in liquid-water spheres of 2, 2.3, 2.6, and 3.4 nm diameter, as well as, number of simple and clustered DSB/Gy/cell are presented for electrons over the 100 eV to 100 keV energy range. Results are presented for both the 'default' (Option 2) and 'Ioannina' (Option 4) physics models of Geant4-DNA applying several commonly used tracking cutoff energies (10, 20, 50, 100 eV). Overall, the choice of the physics model and target diameter has a moderate effect (up to ~10%-30%) on the DSB yield whereas the effect of the tracking cutoff energy may be significant (>100%). Importantly, the yield of both simple and clustered DSB was found to vary significantly (by a factor of 2 or more) with electron energy over the examined range. The yields of electron-induced simple and clustered DSB exhibit a strong energy dependence over the 100 eV-100 keV range with implications to radiation quality issues. It is shown that a classical microdosimetry approach for the calculation of DNA damage based on lineal energy spectra in nanometer-size targets predicts comparable results to computationally intensive mechanistic approaches which use detailed atomistic DNA geometries, thus, offering a relatively simple and robust alternative for some practical applications.

Alternative Approach for the Determination of Mean Free Paths of Electron Scattering in Liquid Water Based on Experimental Data

Mean free paths of low-energy electrons in liquid water are of importance for modeling many physicochemical processes, but neither theoretical predictions nor experimental results have converged for these parameters. We therefore introduce an approach to determine elastic and inelastic mean free paths (EMFP, IMFP) based on experimental data. We show that ab initio calculations of electron scattering with water clusters converge with cluster size, thus providing access to condensed-phase scattering. The results are used in Monte Carlo simulations to extract EMFP and IMFP from recent liquid-microjet experiments that determined the effective attenuation length (EAL) and the photoelectron angular distribution (PAD) following oxygen 1s-ionization of liquid water. For electron kinetic energies from 10 to 300 eV, we find that the IMFP is noticeably larger than the EAL. The EMFP is longer than that of gas-phase water and the IMFP is longer compared to latest theoretical estimations, but both EMFP and IMFP are much shorter than suggested by experimental measurements of integral cross sections for amorphous ice.

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.

Unveiling the principle descriptor for predicting the electron inelastic mean free path based on a machine learning framework

The TPP-2M formula is the most popular empirical formula for the estimation of the electron inelastic mean free paths (IMFPs) in solids from several simple material parameters. The TPP-2M formula, however, poorly describes several materials because it relies heavily on the traditional least-squares analysis. Herein, we propose a new framework based on machine learning to overcome the weakness. This framework allows a selection from an enormous number of combined terms (descriptors) to build a new formula that describes the electron IMFPs. The resulting framework not only provides higher average accuracy and stability but also reveals the physics meanings of several newly found descriptors. Using the identified principle descriptors, a complete physics picture of electron IMFPs is obtained, including both single and collective electron behaviors of inelastic scattering. Our findings suggest that machine learning is robust and efficient to predict the IMFP and has great potential in building a regression framework for data-driven problems. Furthermore, this method could be applicable to find empirical formula for given experimental data using a series of parameters given a priori, holds potential to find a deeper connection between experimental data and a priori parameters.

Simple and universal model for electron-impact ionization of complex biomolecules

We present a simple and universal approach to calculate the total ionization cross section (TICS) for electron impact ionization in DNA bases and other biomaterials in the condensed phase. Evaluating the electron impact TICS plays a vital role in ion-beam radiobiology simulation at the cellular level, as secondary electrons are the main cause of DNA damage in particle cancer therapy. Our method is based on extending the dielectric formalism. The calculated results agree well with experimental data and show a good comparison with other theoretical calculations. This method only requires information of the chemical composition and density and an estimate of the mean binding energy to produce reasonably accurate TICS of complex biomolecules. Because of its simplicity and great predictive effectiveness, this method could be helpful in situations where the experimental TICS data are absent or scarce, such as in particle cancer therapy.

Low-energy electron inelastic mean free paths for liquid water

We improve the Mermin-Penn algorithm (MPA) for determining the energy loss function (ELF) within the dielectric formalism. The present algorithm is applicable not only to real metals, but also to materials that have an energy gap in the excitation spectrum. Applying the improved MPA to liquid water, we show that the present algorithm is able to address the ELF overestimation at the energy gap, and the calculated results are in good agreement with experimental data.

Mechanistic DNA damage simulations in Geant4-DNA Part 2: Electron and proton damage in a bacterial cell

We extended a generic Geant4 application for mechanistic DNA damage simulations to an Escherichia coli cell geometry, finding electron damage yields and proton damage yields largely in line with experimental results. Depending on the simulation of radical scavenging, electrons double strand breaks (DSBs) yields range from 0.004 to 0.010 DSB Gy-1 Mbp-1, while protons have yields ranging from 0.004 DSB Gy-1 Mbp-1 at low LETs and with strict assumptions concerning scavenging, up to 0.020 DSB Gy-1 Mbp-1 at high LETs and when scavenging is weakest. Mechanistic DNA damage simulations can provide important limits on the extent to which physical processes can impact biology in low background experiments. We demonstrate the utility of these studies for low dose radiation biology calculating that in E. coli, the median rate at which the radiation background induces double strand breaks is 2.8 × 10-8 DSB day-1, significantly less than the mutation rate per generation measured in E. coli, which is on the order of 10-3.

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

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