Spatial distributions of inelastic events produced by electrons in gaseous and liquid water

The spatial distributions of ionizations and other inelastic events in charged-particle tracks are important quantities that influence the final outcome of radiation interaction. Calculations of such distributions are presented for the tracks of electrons in the energy range 100 eV to 10 keV in liquid water and water vapor, and the results are compared. The distributions include the frequency of nearest-neighbor distances for all inelastic events, the mean nearest-neighbor distances for ionizations and for all inelastic events as a function of electron energy, the frequency of distances between all ionizations and all inelastic events, and the farthest distances between all inelastic events in electron tracks. The physical differences between liquid water and water vapor are discussed in terms of the respective inverse mean free paths, the collision spectra, and the nonlocalization of energy losses that are likely to occur in the liquid.     

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 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.     

Energy loss of hydrogen- and helium-ion beams in DNA: calculations based on a realistic energy-loss function of the target

We have calculated the electronic energy loss of proton and α-particle beams in dry DNA using the dielectric formalism. The electronic response of DNA is described by the MELF-GOS model, in which the outer electron excitations of the target are accounted for by a linear combination of Mermin-type energy-loss functions that accurately matches the available experimental data for DNA obtained from optical measurements, whereas the inner-shell electron excitations are modeled by the generalized oscillator strengths of the constituent atoms. Using this procedure we have calculated the stopping power and the energy-loss straggling of DNA for hydrogen- and helium-ion beams at incident energies ranging from 10 keV/nucleon to 10 MeV/nucleon. The mean excitation energy of dry DNA is found to be I = 81.5 eV. Our present results are compared with available calculations for liquid water showing noticeable differences between these important biological materials. We have also evaluated the electron excitation probability of DNA as a function of the transferred energy by the swift projectile as well as the average energy of the target electronic excitations as a function of the projectile energy. Our results show that projectiles with energy ?100 keV/nucleon (i.e., around the stopping-power maximum) are more suitable for producing low-energy secondary electrons in DNA, which could be very effective for the biological damage of malignant cells.     

Low-energy electron penetration range in liquid water

Monte Carlo simulations of electron tracks in liquid water are performed to calculate the energy dependence of the electron penetration range at initial electron energies between 0.2 eV and 150 keV, including the subexcitation electron region (<7.3 eV). Our calculated electron penetration distances are compared with available experimental data and earlier calculations as well as with the results of simulations using newly reported amorphous ice electron scattering cross sections in the range approximately 1-100 eV.     

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.     

Calculation of the proximity function of electrons

A new semianalytical method to calculate the proximity function for electrons is proposed. An integral equation for the proximity function that can be solved by using information on the spatial dose distributions is obtained. The proximity function for electrons in the energy range from 10 eV to 10 keV is calculated by solving the equation numerically, using a set of electron collision cross sections for water vapor. The results are in good agreement with those obtained using the Monte Carlo method. The proposed method can be used for electrons of high energies much more efficiently than the Monte Carlo method.     

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.     

On the eptihermal neutron energy limit for Accelerator-Based Boron Neutron Capture Therapy (AB-BNCT): Study and impact of new energy limits

Background and purpose: Accelerator-Based Boron Neutron Capture Therapy is a radiotherapy based on compact accelerator neutron sources requiring an epithermal neutron field for tumour irradiations. Neutrons of 10 keV are considered as the maximum optimised energy to treat deep-seated tumours. We investigated, by means of Monte Carlo simulations, the epithermal range from 10 eV to 10 keV in order to optimise the maximum epithermal neutron energy as a function of the tumour depth.Methods: A Snyder head phantom was simulated and mono-energetic neutrons with 4 different incident energies were used: 10 eV, 100 eV, 1 keV and 10 keV. ¹⁰B capture rates and absorbed dose composition on every tissue were calculated to describe and compare the effects of lowering the maximum epithermal energy. The Therapeutic Gain (TG) was estimated considering the whole brain volume.Results: For tumours seated at 4 cm depth, 10 eV, 100 eV and 1 keV neutrons provided respectively 54%, 36% and 18% increase on the TG compared to 10 keV neutrons. Neutrons with energies between 10 eV and 1 keV provided higher TG than 10 keV neutrons for tumours seated up to 6.4 cm depth inside the head. The size of the tumour does not change these results.Conclusions: Using lower epithermal energy neutrons for AB-BNCT tumour irradiation could improve treatment efficacy, delivering more therapeutic dose while reducing the dose in healthy tissues. This could lead to new Beam Shape Assembly designs in order to optimise the BNCT irradiation.     

Benefits and Limitations of Low-kV Macromolecular Imaging of Frozen-Hydrated Biological Samples

Object contrast is one of the most important parameters of macromolecular imaging. Low-voltage transmission electron microscopy has shown an increased atom contrast for carbon materials, indicating that amplitude contrast contributions increase at a higher rate than phase contrast and inelastic scattering. Here, we studied image contrast using ice-embedded tobacco mosaic virus particles as test samples at 20–80 keV electron energy. The particles showed the expected increase in contrast for lower energies, but at the same time the 2.3-nm-resolution measure decayed more rapidly. We found a pronounced signal loss below 60 keV, and therefore we conclude that increased inelastic scattering counteracts increased amplitude contrast. This model also implies that as long as the amplitude contrast does not increase with resolution, beam damage and multiple scattering will always win over increased contrast at the lowest energies. Therefore, we cannot expect that low-energy imaging of conventionally prepared samples would provide better data than state-of-the-art 200–300 keV imaging.     

Monte Carlo simulation of strand-break induction on plasmid DNA in aqueous solution by monoenergetic electrons

The radiation-induced process of strand breaks on pBR322 plasmid DNA in aqueous solution for different energy electrons was studied by Monte Carlo simulation. Assumptions of induction mechanisms of single- and double-strand breaks (SSBs and DSBs) used in the simulation are that SSB is induced by OH or H reaction with DNA and that DSB is induced by two SSBs on the opposite strands within 10 bp. Dose-response relationships of SSBs and DSBs were demonstrated for monoenergetic electrons of 100 eV, 10 keV, 1 keV and 1 MeV, and the yields of SSB and DSB were calculated. The dose-response relationships of SSBs and DSBs can be fitted by linear and linear-quadratic functions, respectively. The ratio of quadratic to linear components of DSB induction changes due to the electron energy. A high contribution of the linear component is observed for 1 keV electrons in the dose range below 160 Gy. The yields of SSBs and DSBs for all examined electron energies lie well within the experimental data when the probability of strand-break induction by OH and H is assumed to be around 0.1-0.2. The yield of SSBs has a minimum at 1 keV, while the yield of DSBs has a maximum at 1 keV in the examined energies. The strand breaks are formed most densely for 1 keV electrons.     

Comparison of simple perturbation-theory estimates for the liquid–solid and the liquid–vapor interfacial free energies of Lennard-Jones systems

The most naive perturbation method to estimate interfacial free energies is based on the assumption that the interface between coexisting phases is infinitely sharp. Although this approximation does not yield particularly accurate estimates for the liquid–vapor surface tension, we find that it works surprisingly well for the interface between a dense liquid and a solid. As an illustration we estimate the liquid–solid interfacial free energy of a Lennard-Jones system with truncated and shifted interactions and compare the results with numerical data that have been reported in the literature. We find that the agreement between theory and simulation is excellent. In contrast, if we apply the same procedure to estimate the variation of the liquid–vapor surface tension, for different variants of the Lennard-Jones potential (truncated/shifted/force-shifted), we find that the agreement with the available simulation data is, at best, fair. The present method makes it possible to obtain quick and easy estimate of the effect on the surface free energy of different potential-truncation schemes used in computer simulations.     

Comparative microdosimetry of photoelectrons and Compton electrons: an analysis in terms of generalized proximity functions

A current discussion on mammography screening is focused on claims of high relative biological effectiveness (RBE) of mammography X rays compared to conventional 200 kV X rays. An earlier assessment in terms of the electron spectra of these radiations has led to the conclusion that the RBE is bound to be less than 2, regardless of specific model assumptions and the microdosimetric properties of electrons. The present study extends this result in terms of the microdosimetric proximity function, t(x), for electrons, which is essentially the spatial auto-correlation function of energy within particle tracks. If pairs of DNA lesions, e.g. chromosome breaks or deletions, bring about the observed damage, the value t(x) determines for a specified radiation the relative frequency of pairs of lesions a distance x apart. The effectiveness of the radiation is thus proportional to an average of the values of t(x) over the distances, x, for which lesions can combine. The analysis suggests that 15 keV electrons can have a low-dose relative biological effectiveness (RBE(M)) of 1.6 relative to 40 keV electrons if the interaction distances do not exceed about 1 micro m. An extension of the concept, the reduced proximity function, t(delta)(x), permits the inclusion of models with an energy threshold, such as delta = 100 eV, 500 eV or 2 keV, for the formation of each of the DNA lesions. This makes it possible to assess the potential impact of the Auger electrons which accompany most photoelectrons, but only a minority of the Compton electrons. It is found that the Auger electrons could make photoelectrons substantially more effective than Compton electrons at energies below 10 keV but not at energies above 15 keV. The conclusions obtained for the RBE of 15 keV electrons relative to 40 keV electrons will be roughly representative of the RBE of mammography X rays relative to conventional 200 kV X rays.     

Effect of multiple ionization on the yield of H2O2 produced in the radiolysis of aqueous 0.4 M H2SO4 solutions by high-LET 12C6+ and 20Ne9+ ions

Monte Carlo track structure simulations were performed to investigate the effect of multiple ionization of water on the primary (or "escape") (at approximately 10(-6) s) yield of hydrogen peroxide (G(H2O2)) produced in the radiolysis of deaerated 0.4 M H2SO4 solutions by 12C6+ and 20Ne9+ ions at high linear energy transfer (LET) up to approximately 900 keV/microm. It was found that, upon incorporating the mechanisms of double, triple and quadruple ionizations of water in the calculations, a quantitative agreement between theory and experiment can be obtained. The curve for G(H2O2) as a function of LET reaches a well-defined maximum of approximately 1.4 molecules/100 eV at approximately 180-200 keV/microm, in very good accord with the available experimental data. Our results also show that, for the highest LET values considered in this study, the H2O2 escape yields obtained in 0.4 M sulfuric acid solutions are about 45% greater in magnitude than those found in neutral water. Contrary to a recent assumption suggesting that the limiting value of G(H2O2) at infinite LET should be approximately 1 molecule/100 eV, somewhat similar for neutral and acidic water, our simulations show a clear decrease in the primary H2O2 yields with increasing LET at high LET, indicating that the question of the limiting value of G(H2O2) at very high LET for both neutral and acidic liquid water is still open.     

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.     

Monte Carlo simulation of the spatial distribution of energy deposition for an electron microbeam

Dosimetry calculations characterizing the spatial variation of the energy deposited by the slowing and stopping of energetic electrons are reported and compared with experimental measurements from an electron microbeam facility. The computations involve event-by-event, detailed-histories Monte Carlo simulations of low-energy electrons interacting in water vapor. Simulations of electron tracks with starting energies from 30 to 80 keV are used to determine energy deposition distributions in thin cylindrical rings as a function of penetration and radial distance from a beam source. Experimental measurements of the spatial distribution of an electron microbeam in air show general agreement with the density-scaled simulation results for water vapor at these energies, yielding increased confidence in the predictions of Monte Carlo track-structure simulations for applications of the microbeam as a single-cell irradiator.     

Structural prediction of peptides bound to MHC class I

An ab initio structure prediction approach adapted to the peptide-major histocompatibility complex (MHC) class I system is presented. Based on structure comparisons of a large set of peptide-MHC class I complexes, a molecular dynamics protocol is proposed using simulated annealing (SA) cycles to sample the conformational space of the peptide in its fixed MHC environment. A set of 14 peptide-human leukocyte antigen (HLA) A0201 and 27 peptide-non-HLA A0201 complexes for which X-ray structures are available is used to test the accuracy of the prediction method. For each complex, 1000 peptide conformers are obtained from the SA sampling. A graph theory clustering algorithm based on heavy atom root-mean-square deviation (RMSD) values is applied to the sampled conformers. The clusters are ranked using cluster size, mean effective or conformational free energies, with solvation free energies computed using Generalized Born MV 2 (GB-MV2) and Poisson-Boltzmann (PB) continuum models. The final conformation is chosen as the center of the best-ranked cluster. With conformational free energies, the overall prediction success is 83% using a 1.00 Angstroms crystal RMSD criterion for main-chain atoms, and 76% using a 1.50 Angstroms RMSD criterion for heavy atoms. The prediction success is even higher for the set of 14 peptide-HLA A0201 complexes: 100% of the peptides have main-chain RMSD values < or =1.00 Angstroms and 93% of the peptides have heavy atom RMSD values < or =1.50 Angstroms. This structure prediction method can be applied to complexes of natural or modified antigenic peptides in their MHC environment with the aim to perform rational structure-based optimizations of tumor vaccines.     

Monte Carlo determination of a nanoDot OSLD response using quality index for diagnostic kilovoltage X-ray beams

PurposeThis study aims to investigate the energy response of an optically stimulated luminescent dosimeter known as nanoDot for diagnostic kilovoltage X-ray beams via Monte Carlo calculations.MethodsThe nanoDot response is calculated as a function of X-ray beam quality in free air and on a water phantom surface using Monte Carlo simulations. The X-ray fluence spectra are classified using the quality index (QI), which is defined as the ratio of the effective energy to the maximum energy of the photons. The response is calculated for X-ray fluence spectra with QIs of 0.4, 0.5, and 0.6 with tube voltages of 50–137.6 kVp and monoenergetic photon beams. The surface dose estimated using the calculated response is verified by comparing it with that measured using an ionization chamber.ResultsThe nanoDot response in free air for monoenergetic photon beams (QI = 1.0) varies significantly at photon energies below 100 keV and reaches a factor of 3.6 at 25–30 keV. The response differs by up to approximately 6% between QIs of 0.4 and 0.6 for the same half-value layer (HVL). The response at the phantom surface decreases slightly owing to the backscatter effect, and it is almost independent of the field size. The agreement between the surface dose estimated using the nanoDot and that measured using the ionization chamber for assessing X-ray beam qualities is less than 2%.ConclusionsThe nanoDot response is indicated as a function of HVL for the specified QIs, and it enables the direct surface dose measurement.