A New Standard DNA Damage (SDD) Data Format

Our understanding of radiation-induced cellular damage has greatly improved over the past few decades. Despite this progress, there are still many obstacles to fully understand how radiation interacts with biologically relevant cellular components, such as DNA, to cause observable end points such as cell killing. Damage in DNA is identified as a major route of cell killing. One hurdle when modeling biological effects is the difficulty in directly comparing results generated by members of different research groups. Multiple Monte Carlo codes have been developed to simulate damage induction at the DNA scale, while at the same time various groups have developed models that describe DNA repair processes with varying levels of detail. These repair models are intrinsically linked to the damage model employed in their development, making it difficult to disentangle systematic effects in either part of the modeling chain. These modeling chains typically consist of track-structure Monte Carlo simulations of the physical interactions creating direct damages to DNA, followed by simulations of the production and initial reactions of chemical species causing so-called "indirect" damages. After the induction of DNA damage, DNA repair models combine the simulated damage patterns with biological models to determine the biological consequences of the damage. To date, the effect of the environment, such as molecular oxygen (normoxic vs. hypoxic), has been poorly considered. We propose a new standard DNA damage (SDD) data format to unify the interface between the simulation of damage induction in DNA and the biological modeling of DNA repair processes, and introduce the effect of the environment (molecular oxygen or other compounds) as a flexible parameter. Such a standard greatly facilitates inter-model comparisons, providing an ideal environment to tease out model assumptions and identify persistent, underlying mechanisms. Through inter-model comparisons, this unified standard has the potential to greatly advance our understanding of the underlying mechanisms of radiation-induced DNA damage and the resulting observable biological effects when radiation parameters and/or environmental conditions change.

Comprehensive track-structure based evaluation of DNA damage by light ions from radiotherapy-relevant energies down to stopping

Track structures and resulting DNA damage in human cells have been simulated for hydrogen, helium, carbon, nitrogen, oxygen and neon ions with 0.25–256 MeV/u energy. The needed ion interaction cross sections have been scaled from those of hydrogen; Barkas scaling formula has been refined, extending its applicability down to about 10 keV/u, and validated against established stopping power data. Linear energy transfer (LET) has been scored from energy deposits in a cell nucleus; for very low-energy ions, it has been defined locally within thin slabs. The simulations show that protons and helium ions induce more DNA damage than heavier ions do at the same LET. With increasing LET, less DNA strand breaks are formed per unit dose, but due to their clustering the yields of double-strand breaks (DSB) increase, up to saturation around 300 keV/μm. Also individual DSB tend to cluster; DSB clusters peak around 500 keV/μm, while DSB multiplicities per cluster steadily increase with LET. Remarkably similar to patterns known from cell survival studies, LET-dependencies with pronounced maxima around 100–200 keV/μm occur on nanometre scale for sites that contain one or more DSB, and on micrometre scale for megabasepair-sized DNA fragments.

Cross-section scaling for track structure simulations of low-energy ions in liquid water

Radiation damage by low-energy ions significantly contributes to the high biological efficiency of ion beams in distal Bragg peak regions as well as to the energy-dependent efficiency of neutron irradiation. To enable assessing biological effects of ions at energies <1 MeV u(-1) with track-structure based models, a Barkas-like scaling procedure is developed that provides ion cross sections in liquid water based on those for hydrogen ions. The resulting stopping power and range for carbon ions agree with the ICRU 73 database and other low-energy stopping power data. The method represents the basis for extending PARTRAC simulations of light ion track structures and biological effects down to the keV u(-1) range.

Cross sections for track structure codes: volume versus surface transport

Cross-section calculations and transport models for Monte Carlo track structure codes are discussed as well as the simulation of secondary electron emission yields from thin metal foils. Inelastic cross sections for volume (bulk) and surface transport of electrons in copper are presented and implemented into PARTRAC. Simulations for the volume and surface excitation model are presented and analysed.

Electron emission from condensed phase material induced by fast protons

Monte Carlo track simulation has become an important tool in radiobiology. Monte Carlo transport codes commonly rely on elastic and inelastic electron scattering cross sections determined using theoretical methods supplemented with gas-phase data; experimental condensed phase data are often unavailable or infeasible. The largest uncertainties in the theoretical methods exist for low-energy electrons, which are important for simulating electron track ends. To test the reliability of these codes to deal with low-energy electron transport, yields of low-energy secondary electrons ejected from thin foils have been measured following passage of fast protons. Fast ions, where interaction cross sections are well known, provide the initial spectrum of low-energy electrons that subsequently undergo elastic and inelastic scattering in the material before exiting the foil surface and being detected. These data, measured as a function of the energy and angle of the emerging electrons, can provide tests of the physics of electron transport. Initial measurements from amorphous solid water frozen to a copper substrate indicated substantial disagreement with MC simulation, although questions remained because of target charging. More recent studies, using different freezing techniques, do not exhibit charging, but confirm the disagreement seen earlier between theory and experiment. One now has additional data on the absolute differential electron yields from copper, aluminum and gold, as well as for thin films of frozen hydrocarbons. Representative data are presented.

Simulation of secondary electron yields from thin metal foils after fast proton impact

Differential and total inelastic cross sections are derived for the interaction between fast protons and Cu. The calculations are done under the non-relativistic plane-wave first-Born approximation and the dielectric theory. A semi-empirical optical oscillator strength density function and a simple linear-momentum dispersion algorithm are used to construct the energy loss function or Bethe surface of the medium. A transport model using these inelastic cross sections is implemented in the Monte Carlo code PARTRAC to simulate the spectra of secondary electron emissions from this homogeneous and isotropic thin copper foil target. Comparisons with experimental results show general agreement for impact energies >50 eV up to non-relativistic values. The model, however, overestimates the secondary electron yields at lower energies.

Electron emission from amorphous solid water induced by passage of energetic protons and fluorine ions

Absolute doubly differential electron emission yields were measured from thin films of amorphous solid water (ASW) after the transmission of 6 MeV protons and 19 MeV (1 MeV/nucleon) fluorine ions. The ASW films were frozen on thin (1-microm) copper foils cooled to approximately 50 K. Electrons emitted from the films were detected as a function of angle in both the forward and backward direction and as a function of the film thickness. Electron energies were determined by measuring the ejected electron time of flight, a technique that optimizes the accuracy of measuring low-energy electron yields, where the effects of molecular environment on electron transport are expected to be most evident. Relative electron emission yields were normalized to an absolute scale by comparison of the integrated total yields for proton-induced electron emission from the copper substrate to values published previously. The absolute doubly differential yields from ASW are presented along with integrated values, providing single differential and total electron emission yields. These data may provide benchmark tests of Monte Carlo track structure codes commonly used for assessing the effects of radiation quality on biological effectiveness.

Comparisons of calculations with PARTRAC and NOREC: transport of electrons in liquid water

Monte Carlo computer models that simulate the detailed, event-by-event transport of electrons in liquid water are valuable for the interpretation and understanding of findings in radiation chemistry and radiation biology. Because of the paucity of experimental data, such efforts must rely on theoretical principles and considerable judgment in their development. Experimental verification of numerical input is possible to only a limited extent. Indirect support for model validity can be gained from a comparison of details between two independently developed computer codes as well as the observable results calculated with them. In this study, we compare the transport properties of electrons in liquid water using two such models, PARTRAC and NOREC. Both use interaction cross sections based on plane-wave Born approximations and a numerical parameterization of the complex dielectric response function for the liquid. The models are described and compared, and their similarities and differences are highlighted. Recent developments in the field are discussed and taken into account. The calculated stopping powers, W values, and slab penetration characteristics are in good agreement with one another and with other independent sources.

Monte Carlo modelling of energy deposition in trabecular bone

This study includes the design and testing of a program that creates quadric-based geometric models of the trabecular region, designed specifically for use with the 2005 version of the Monte Carlo radiation transport code PENELOPE. Our model was tested, by comparison with published data, in two aspects: the distributions of path lengths throughout the geometry and absorbed fraction values from the monoenergetic emission of electrons from within our geometry. In both comparisons, our results show a close agreement with published methods.

Heavy ion track structure simulations in liquid water at relativistic energies

Interaction cross sections for bare heavy charged (HZE) particles are obtained from proton interaction cross sections by scaling laws. Proton interaction cross sections are calculated within the (relativistic) plane wave Born approximation and the modelled dielectric response function of liquid water. Relativistic polarisation effects (Fermi density effect) are discussed. The interaction model is implemented into the biophysical track structure simulation code PARTRAC.

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.

Cross section calculations in condensed media: charged particles in liquid water

Ionisation cross sections for charged particles are deduced within the framework of the relativistic plane wave first Born approximation and the classical electromagnetic theory. The macroscopic dielectric response function is related to the atomic generalised oscillator strength. Interaction cross sections for proton impact on liquid water are presented and discussed. A semi-empirical model for the angular distribution of secondary electrons produced by proton impact on liquid water, which is based on the Bethe approach, is presented.

Simulation of DNA damage after proton and low LET irradiation

A module for proton track structure simulation in liquid water was implemented in the biophysical model PARTRAC. Simulated tracks of energy deposition events from the radiation under investigation were superimposed on a higher-order DNA target model describing the whole genome inside a human cell. The parameters controlling DNA damage from direct and indirect effects were adapted to agree with yields and pathway contributions derived from gamma ray irradiation experiments. Single and double strand break (DSB) induction was simulated for irradiations by protons, photons and electrons over a wide range of initial energies. The relative biological effectiveness for DSB induction after proton irradiation was found to rise from 1.2 at 5 keV.micron-1 to about 2.5 at 70 keV.micron-1. About half of this growth resulted from an increased production of DSB clusters associated with small (< 10 kbp) fragments.

Stochastic aspects and uncertainties in the prechemical and chemical stages of electron tracks in liquid water: a quantitative analysis based on Monte Carlo simulations

A new physical module for the biophysical simulation code PARTRAC has recently been developed, based on newly derived electron inelastic-scattering cross-sections in liquid water. In the present work, two modules of PARTRAC describing the production, diffusion and interaction of chemical species were developed with the specific purpose of quantifying the role of the uncertainties in the parameters controlling the early stages of liquid water radiolysis. A set of values for such parameters was identified, and time-dependent yields and frequency distributions of chemical species produced by electrons of different energies were calculated. The calculated yields were in good agreement with available data and simulations, thus confirming the reliability of the code. As the primary-electron energy decreases down to 1 keV, the *OH decay kinetics were found to get faster, reflecting variations in the spatial distribution of the initial energy depositions. In agreement with analogous works, an opposite trend was found for energies of a few hundred eV, due to the very small number of species involved. The spreading effects shown at long times by *OH frequency distributions following 1 keV irradiation were found to be essentially due to stochastic aspects of the chemical stage, whereas for 1 MeV tracks the physical and pre-chemical stages also were found to play a significant role. Relevant differences in the calculated e(aq) -yields were found by coupling the physics of PARTRAC with descriptions of the pre-chemical and chemical stages adopted in different models. This indicates a strict interrelation of the various stages, and thus a strong dependence of the parameter values on the assumptions made for the preceding and subsequent stages of the process. Although equally acceptable results can be obtained starting from different assumptions, it is necessary to keep control of such uncertainties, since they can significantly influence the modeling of radical attack on DNA and, more generally, radiobiological damage estimation. This study confirms the need for new, independently derived data on specific steps of water radiolysis, to be included in comprehensive biophysical simulation codes.

The Bethe surface of liquid water

The Bethe surface of liquid water, which was previously calculated by using a semiempirical model, is compared with recently available data from IXS experiments (inelastic x-ray scattering; Compton scattering of high energy photons) in liquid water. No alarming discrepancy is found for a global view of the Bethe surface, in part because the two sets of data have been constrained by the Bethe sum rule. The shape of the Bethe ridge given by the new data is broader than that obtained through the impulse approximation. The extrapolation to the optical limit (viz., at zero momentum transfer) is shown, and the reliability of these data is discussed in detail.