Analysis of low-energy electron track structure in liquid water

An implementation is presented of interaction cross sections for non-relativistic electron track structure simulations. The model, incorporating liquid-phase cross sections for inelastic interactions and improved algorithms for elastic scattering, is applied to Monte Carlo simulation of the track structure of low-energy electrons. Benchmark distributions and mean values are presented for several measures of penetration distances that characterize the general physical extent of the track structure. The results indicate that, except for the last approximately 500 eV of energy loss, electron tracks have a quasi-linear character; this suggests that a major part of an electron track may be reasonably described by a lineal-energy-like characterization.     

A Monte Carlo code for the simulation of heavy-ion tracks in water

TILDA, a new Monte Carlo track structure code for ions in gaseous water that is valid for both high-LET (approximately 10(4) keV/microm) and low-LET ions, is presented. It is specially designed for a comparison of the patterns of energy deposited by a large range of ions. Low-LET ions are described in a perturbative frame, whereas heavy ions with a very high stopping power are treated using the Lindhard local density approximation and the Russek and Meli statistical method. Ionization cross sections singly differential with energy compare well with the experiment. As an illustration of the non-perturbative interaction of high-LET ions, a comparison between the ion tracks of light and heavy ions with the same specific energy is presented (1.4 MeV/nucleon helium and uranium ions). The mean energy for ejected electrons was found to be approximately four times larger for uranium than for helium, leading to a much larger track radius in the first case. For electrons, except for the excitation cross sections that are deduced from experimental fits, cross sections are derived analytically. For any orientation of the target molecule, the code calculates multiple differential cross sections as a function of the ejection and scattering angles and of the energy transfer. The corresponding singly differential and total ionization cross sections are in good agreement with experimental data. The angular distribution of secondary electrons is shown to depend strongly on the orientation of the water molecule.     

Calculations of heavy-ion track structure

A Monte Carlo model is presented to study details of the energy deposition inside tracks of heavy charged particles in water vapor. The input data for most of the calculations based on the binary encounter approximation are double-differential cross sections for electron emission after heavy-ion impact. The paths of the liberated electrons are simulated, taking into account elastic scattering, ionization, and excitation. Each basic interaction of an electron or heavy ion is treated individually. Radial dose distributions and specific energy deposition are calculated for projectiles from protons to uranium in the energy range from one to several hundred megaelectron volts per unified atomic mass unit. Good agreement with measurements in tissue-equivalent gas and propane is obtained for light and medium-heavy projectiles, whereas for heavy projectiles such as uranium, deviations around a factor of 2–3 are observed.     

Cross section calculations for electron scattering from DNA and RNA bases

Differential and integral cross sections for elastic electron collisions with uracil, cytosine, guanine, adenine and thymine have been calculated using the independent atom method with a static-polarization model potential for incident energies ranging from 50 to 4000 eV. Total cross sections for single electron-impact ionization of selected DNA and RNA bases have also been calculated with the binary-encounter-Bethe model from the ionization threshold up to 5000 eV. Cross sections within the investigated energy range, can be related to the molecular symmetry, the number of target electrons and molecular size; elastic and ionization processes are most efficient for guanine and adenine molecules, while the lowest cross sections were obtained for the uracil molecule. The ionization cross sections for cytosine, thymine, adenine and guanine are compared with those recently obtained with a semi-classical and binary-encounter-Bethe formalisms. No theoretical and experimental data for elastic electron scattering from DNA and RNA bases are available, but comparisons with calculations for molecules of similar size and geometry allows the validity of the theoretical approach to be verified.     

Calculation on spectrum of direct DNA damage induced by low-energy electrons including dissociative electron attachment

In this work, direct DNA damage induced by low-energy electrons (sub-keV) is simulated using a Monte Carlo method. The characteristics of the present simulation are to consider the new mechanism of DNA damage due to dissociative electron attachment (DEA) and to allow determining damage to specific bases (i.e., adenine, thymine, guanine, or cytosine). The electron track structure in liquid water is generated, based on the dielectric response model for describing electron inelastic scattering and on a free-parameter theoretical model and the NIST database for calculating electron elastic scattering. Ionization cross sections of DNA bases are used to generate base radicals, and available DEA cross sections of DNA components are applied for determining DNA-strand breaks and base damage induced by sub-ionization electrons. The electron elastic scattering from DNA components is simulated using cross sections from different theoretical calculations. The resulting yields of various strand breaks and base damage in cellular environment are given. Especially, the contributions of sub-ionization electrons to various strand breaks and base damage are quantitatively presented, and the correlation between complex clustered DNA damage and the corresponding damaged bases is explored. This work shows that the contribution of sub-ionization electrons to strand breaks is substantial, up to about 40–70%, and this contribution is mainly focused on single-strand break. In addition, the base damage induced by sub-ionization electrons contributes to about 20–40% of the total base damage, and there is an evident correlation between single-strand break and damaged base pair A–T.     

Differential and integral W-values for ionization in gaseous water under electron and proton irradiation: consistency of inelastic collision cross sections.

Differential and integral W-values for ionization in gaseous water for electron and proton irradiation have been analyzed from the theoretical point of view for consistency between ionization and total inelastic collision cross sections. For low-energy electrons, which are ubiquitous for all primary radiations, the experimental or compiled cross sections from different sources are sometimes not consistent with one another. A practical, self-consistent procedure is outlined in such cases. The high-energy asymptotic W-values for differential and integral ionization are calculated to be 33.7 and 34.7 eV, respectively, for electron irradiation and 34.6 and 32.5 eV, respectively, for proton irradiation. The computed variations of the W-values with energy are generally in good agreement with experiment. Integral primary W-values due only to the interactions between the incident particle and the water vapor are calculated to be 43.5 and 45.0 eV for electrons and protons, respectively, in the high-energy asymptotic limit.     

Ionization yields in hydrocarbons under electron irradiation

Ionization yields and W-values in several hydrocarbon gases under electron irradiation have been calculated using Inokuti's solution of the Fowler equation, i.e., incorporating a linear dependence of ionization yield on source electron energy. Collision stopping powers of hydrocarbons were evaluated using the Bethe formula with mean excitation energies determined using the additivity rule with modification based on molecular bond strengths. Contributions to the collision stopping powers from discrete level excitations were estimated by multiplying collision stopping powers by the excitation fractions constructed from atomic calculations. Average energy transfers for ionizing collisions producing subionization electrons were calculated using differential ionization cross sections proposed by Khare and co-workers. The calculated W-values are in good agreement with those recommended by ICRU.     

Cross sections for low-energy (10-50 eV) electron damage to DNA

We report direct measurements of the formation of single-, double- and multiple strand breaks in pure plasmid DNA as a function of exposure to 10-50 eV electrons. The effective cross sections to produce these different types of DNA strand breaks were determined and were found to range from approximately 10(-17) to 3 x 10(-15) cm(2). The total effective cross section and the effective range for destruction of supercoiled DNA extend from 3.4 to 4.4 x 10(-15) cm(2) and 12 to 14 nm, respectively, over the range 10-50 eV. The variation of the effective cross sections with electron energy is discussed in terms of the electron's inelastic mean free path, penetration depth, and dissociation mechanisms, including resonant electron capture; the latter is found to dominate the effective cross sections for single- and double-strand breaks at 10 eV. The most striking observations are that (1) supercoiled DNA is approximately one order of magnitude more sensitive to the formation of double-strand breaks by low-energy electrons than is relaxed circular DNA, and (2) the dependence of the effective cross sections on the incident electron energy is unrelated to the corresponding ionization cross sections. This finding suggests that the traditional notion that radiobiological damage is related to the number of ionization events would not apply at very low energies.     

Microdosimetric structure of heavy ion tracks in tissue

Summary Energy dissipation in tracks of high energy heavy ions in tissue shows a lateral spread of several to many microns depending on the energy of the primary particle. Complete dosimetric characterization, therefore, requires in addition to the Linear Energy Transfer (LET) information on the radial energy distribution. The theory of track structure distinguishes two regions: core and penumbra. The core is a narrow central zone with a radius in tissue far below 1 micron where energy deposition occurs mainly in processes of excitation and electron plasma oscillation. According to the Equipartition Principle, half of the total energy dissipation accrues in this manner. The penumbra is a peripheral zone enveloping the core where energy deposition occurs mainly in ionization events by energetic secondary electrons released by the primary particle in the center of the core traveling at rather high speed thus spreading laterally. The extension of the penumbra depends in a complex manner on the maximum transferable energy to electrons which in turn depends on the speed of the primary particle. Local energy density in the penumbra decreases with the square of increasing radius. It therefore amounts only to a very small fraction of the core density already a few microns away from the center. In general terms, track structure can be described as exhibiting a core of enormous energy density with lateral dimensions remaining entirely on the submicroscopic level surrounded by a penumbra where energy density drops precipitously to very small levels. The relationships are illustrated with micrographs of different sections of a heavy particle track in nuclear emulsion and their counterpart graphical plots.     

The role of atomic inner shell relaxations for photon-induced DNA damage

The influence of relaxations of atoms making up the DNA and atoms attached to it on radiation-induced cellular DNA damage by photons was studied by very detailed Monte Carlo track structure calculations, as an unusually high importance of inner shell ionizations for biological action was suspected from reports in the literature. For our calculations cross sections for photons and electrons for inner shell orbitals were newly derived and integrated into the biophysical track structure simulation programme PARTRAC. Both the local energy deposition in a small sphere around the interacting relaxed atom, and the number of relaxations per Gy and Gbp were calculated for several target geometries and many monoenergetic photon irradiations. Elements with the highest order number yielded the largest local energy deposition after interaction. The atomic relaxation after ionization of the L1 shell was found to be more biologically efficient than that of the K shell for high Z atoms. Generally, the number of inner shell relaxations produced by photon irradiation was small in comparison to the total number of double strand breaks generated by such radiation. Furthermore, the energy dependence of the total number of photon-induced and electron-induced relaxations at the DNA atoms does not agree with observed RBE values for different biological endpoints. This suggests that the influence of inner shell relaxations of DNA atoms on radiation-induced DNA damage is in general rather small.     

Monte Carlo transport of swift protons and light ions in water: The influence of excitation cross sections,relativistic effects,and Auger electron emission in w-values

PurposeTo develop a particle transport code to compute w-values and stopping power of swift ions in liquid water and gases of interest for reference dosimetry in hadrontherapy. To analyze the relevance of inelastic and post-collisional processes considered.MethodsThe Monte Carlo code MDM was extended to the case of swift ion impact on liquid water (MDM-Ion). Relativistic corrections in the inelastic cross sections and the post-collisional Auger emission were considered. The effects of introducing different electronic excitation cross sections were also studied.ResultsThe stopping power of swift ions on liquid water, calculated with MDM-Ion, are in excellent agreement with recommended data. The w-values show a strong dependence on the electronic excitation cross sections and on the Auger electron emission. Comparisons with other Monte Carlo codes show the relevance of both the processes considered and of the cross sections employed. W and w-values for swift electron, proton, and carbon ions calculated with the MDM and MDM-Ion codes are in very close agreement with each other and with the 20.8 eV experimental value.ConclusionWe found that w-values in liquid water are independent of ion charge and energy, as assumed in reference dosimetry for hadrontherapy from sparse experimental results for electron and ion impact on gases. Excitation cross sections and Auger emission included in Monte Carlo codes are critical in w-values calculations. The computation of this physical parameter should be used as a benchmark for micro-dosimetry investigations, to assess the reliability of the cross sections employed.     

Comparison of microdosimetric simulations using PENELOPE and PITS for a 25 keV electron microbeam in water

The calculations presented compared the performances of two Monte Carlo codes used for the estimation of microdosimetric quantities: Positive Ion Track Structure code (PITS) and a main user code based on the PENetration and Energy Loss of Positrons and Electrons code (PENELOPE-2000). Event-by-event track structure codes like PITS are believed to be superior for microdosimetric applications, and they are written for this purpose. PITS tracks electrons in water down to 10 eV. PENELOPE is one of the few general-purpose codes that can simulate random electron-photon showers in any material for energies from 100 eV to 1 GeV. The model used in the comparison is a water cylinder with an internal scoring geometry made of spheres 1 microm in diameter where the scoring quantities are calculated. The source is a 25 keV electron pencil beam impinging normally on the sphere surface. This work shows only the lineal energy y and spectra graphical presentation as a function of y since for microdosimetry and biology applications, and for discussion of radiation quality in general, these results are more appropriate. The computed PENELOPE results are in agreement with those obtained with the PITS code and published previously in this journal. This paper demonstrates PENELOPE's usefulness at low energies and for small geometries. What is still needed are experimental results to confirm these analyses.     

LET,track structure and models

Summary Swift heavy ions when penetrating through matter strip off those electrons having a smaller orbital velocity than the ion velocity. The remaining electrons screen the nuclear charge yielding an effective charge. The effective charge of the ions interacts predominately with the target electrons causing excitation and ionizations of the target atoms. Using the Bethe Bloch formula for the energy loss combined with the Barkas formula for effective charge, the energy loss values as well as unrestricted and restricted linear transfer can be calculated within a few percent of accurancy. From the primary energy loss only a small fraction of 10% or less is transformed into excitation. The major part of the energy loss is used for the ionization of the target atoms and the emission of the corresponding electrons with a high kinetic energy. These electrons form the track around the trajectory of the primary ion in which two thirds of the primary energy is deposited by collisions of primary, secondary and later generations of electrons with the target molecules. In the electron diffusion process the energy is transported from the center of the track into the halo. The radial dose decreases with the square of the radial distance from the center. The diameter of the track is determined by the maximum range of the emitted electrons, i.e. by the maximum energy electrons. All ions having the same velocity i.e. the same specific energy produce electrons of the same energy and therefore tracks of the same diameters independent of the effective charge. But the dose inside the track increases with the square of the effective charge. Track structure models using this continuous dose distributions produce a better agreement with the experiment than models based on microdosimetry. The critical volume as used in microdosimetry is too large compared to the size of the DNA as critical structure inside the biological objects. Track structure models yield better results because the gross-structure of the track i.e. its lateral extension and the thin down toward the end of the track is included in these calculations. In a recent refinement the repair capacity of the cell has been included in a track structure model by using the complete shouldered x-ray survival curve as a template for the local damage produced by the particle tracks. This improved model yields presently the best agreement with the experiment.Invited paper given on the fourth workshop on Heavy Charged Particles in Biology and Medicine GSI, Darmstadt, FRG, September 23–25, 1991     

Ionization and charge-transfer: basic data for track structure calculations

It is widely accepted that an understanding of the detailed structure of charged particle tracks is essential for interpreting the mechanistic consequences of energy deposition by high linear energy transfer (LET) radiation. The spatial relationship of events along the path of a charged particle, including excitation, ionization, and charge-transfer, govern subsequent chemical, biochemical, and biological reactions that can lead to adverse biologic effects. The determination of spatial patterns of ionization and excitation relies on a broad range of cross-section data relating the interactions of charged particles to the molecular constituents of the absorbing medium. It is important that these data be absolute in magnitude, comprehensive in scope, and reliable if accurate assessment of track structure parameters is to be achieved. Great strides have been made in the development of this database, understanding the underlying theory, and developing analytic models, particularly for interactions involving electrons and protons with atoms and molecules. The database is less comprehensive for interactions involving heavier charged particles, especially those that carry bound electrons, and for interactions in condensed phase media. Although there has been considerable progress in understanding the physical mechanisms for interactions involving fast heavy ions and atomic targets during the past few years, we still lack sufficient understanding to confidently predict cross-sections for these ions with biologically relevant material. In addition, little is known of the interaction cross-sections for heavy charged particles as they near the end of their track, i.e., for low velocity ions where collision theory is less well developed and where the particle's net charge fluctuates owing to electron capture and loss processes. This presentation focuses on the current status of ionization and charge-transfer data. Compilations, reviews, Internet sources, theoretical models, and recent data applicable to track structure calculations are discussed.     

Cross sections for low-energy (1-100 eV) electron elastic and inelastic scattering in amorphous ice

We report the integral cross sections per scatterer (i.e. elastic collision, phonon excitations, vibrational excitations, electronic excitations and ionization) for 1-100 eV electron scattering in an amorphous film of ice condensed at a temperature of 14 K. The integral cross sections are determined relative to the total from a two-stream multiple-scattering analysis of the electron energy distribution backscattered from the film. Their energy dependence is obtained from both the analysis of the elastic electron reflectivity as a function of the film thickness and the vibrational electron energy-loss spectra measured for several incident energies and large film thickness. The magnitude and various features found in the energy dependence of the cross sections are discussed, whenever possible, by comparison with data and with scattering mechanisms available in the gas phase. Microcospic effects, which are implicitly included in cross sections determined in this way, are discussed in terms of interference and coherent multiple-scattering contributions among the scattering sites as well as interactions of the scattering sites with their neighbors in the condensed phase.     

A track structure model for simulation of strand breaks in plasmid DNA after heavy ion irradiation

We present a track structure model based on the local dose deposited around heavy ion tracks to explain the cross sections for single-strand and double-strand break induction in plasmid DNA in different aqueous buffers. The model is based only on measurable quantities, namely the effect distribution for inducing strand breaks after x-ray irradiation as a function of dose, and the radial dose distribution of the heavy ion track. The effect of indirect DNA damage mediated by free radicals produced in the water surrounding the DNA is accounted for by allowing the radial dose distribution to be smeared in space by an effective target size corresponding to the squared sum of the geometrical extension of the plasmid molecule and the mean free drift path of the radicals in the buffer solution. Our calculations reproduce well the measured cross sections for single-strand and double-strand break induction in SV40 plasmid DNA in various buffer solutions both as a function of the LET and of the specific energy of the heavy ion.     

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.     

Analysis of Data on the Cross Sections for Electron-Impact Ionization and Excitation of Electronic States of Atomic Hydrogen (Review)

A review is given of experimental and theoretical data on the cross sections for ionization, excitation, and deexcitation of atomic hydrogen. The set of the cross sections required to calculate the electron energy distribution function and find the level-to-level rate coefficients needed to solve balance equations for the densities of neutral and charged particles in hydrogen plasma is determined.     

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.     

Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles

This paper develops a deterministic model of frequency distributions for energy imparted (total energy deposition) in small volumes similar to DNA molecules from high-energy ions of interest for space radiation protection and cancer therapy. Frequency distributions for energy imparted are useful for considering radiation quality and for modeling biological damage produced by ionizing radiation. For high-energy ions, secondary electron (delta-ray) tracks originating from a primary ion track make dominant contributions to energy deposition events in small volumes. Our method uses the distribution of electrons produced about an ion's path and incorporates results from Monte Carlo simulation of electron tracks to predict frequency distributions for ions, including their dependence on radial distance. The contribution from primary ion events is treated using an impact parameter formalism of spatially restricted linear energy transfer (LET) and energy-transfer straggling. We validate our model by comparing it directly to results from Monte Carlo simulations for proton and alpha-particle tracks. We show for the first time frequency distributions of energy imparted in DNA structures by several high-energy ions such as cosmic-ray iron ions. Our comparison with results from Monte Carlo simulations at low energies indicates the accuracy of the method.