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

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

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

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

Monte Carlo 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.     

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.     

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.     

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.     

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.     

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.     

Monte Carlo simulation of physicochemical processes of liquid water radiolysis

The paper describes developments of the physicochemical part of a computer code system that estimates DNA strand break induction on plasmid pBR322 DNA. In order to test the reliability of the model, we evaluated the dielectric function and the time-dependent yield of chemical species in the presence of OH radical scavenger or dissolved oxygen. Results agree with measurements on the radiolysis of liquid water. When a hybrid model of a liquid inelastic cross-section and a vapour elastic cross-section is used, energy deposition by vibrational excitations is estimated to be approximately 11% of total energy deposition. Received: 4 March 1996 / Accepted in revised form: 14 November 1996     

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 of electron inelastic interactions in DNA

The cross sections of electron inelastic interaction in DNA are calculated using the dielectric response theory and Penn statistical approximation, with the exchange correction included. An empirical approach to obtain optical energy loss function is given for the organic compounds without available optical data. Comparisons of the calculated data with available experimental and theoretical results have been done to show the reliability of the approach proposed in this work. Using this approach, the total inelastic cross sections for five bases: guanine, adenine, thymine, cytosine and uracil have been calculated in the energy range of E10 keV and compared with those recently obtained with the Deutsch-Märk formalism and the Binary-Encounter-Bethe model, respectively. An equivalent unit of the DNA molecule is constructed according to the contents of A-T and G-C base pairs in DNA, and is divided into five constituents, i.e. sugar-phosphate and four bases. The total inelastic cross sections for the constructed unit of the DNA molecule and its constituents have also been calculated.     

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.     

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.     

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.     

Comparison and assessment of electron cross sections for Monte Carlo track structure codes.

The purpose of this study was to make an intercomparison and assessment of cross sections for electrons in water used in electron track structure codes. This study is intended to shed light on the extent to which the differences between the input data and physical and chemical assumptions influence the outcome in biophysical modeling of radiation effects. Ionization cross sections and spectra of secondary electrons were calculated by various theories. The analyses were carried out for water vapor cross sections, as these are more abundant and readily available. All suitable published experimental total ionization cross sections were fitted by an appropriate function and used for generation of electron tracks. Three sets of compiled data were used for comparison of total excitation cross sections and mean excitation energy. The tracks generated by a Monte Carlo track code, using various combinations of cross sections, were compared in terms of radial distributions of interactions and point kernels. The spectrum of secondary electrons emitted by the ionization process was found to be the factor that has the most influence on these quantities. A different set of cross sections for excitation and elastic scattering did not affect the electron track structure as much as did ionization cross sections. It is concluded that all codes, using different cross sections and in different phase, currently used for biophysical modeling exhibit close similarities for energy deposition in larger size targets while appreciable differences are observed in B-DNA-size targets. We recommend fitted functions to all available suitable experimental data for the total ionization and elastic cross sections. We conclude that most codes produce tracks in reasonable agreement with the macroscopic quantities such as total stopping power and total yield of strand breaks. However, we predict differences in frequencies of clustering in tracks from the different models.     

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.     

The properties of liquid water in electric and magnetic fields

A new model of liquid water is proposed, which involves the liquid-crystalline phase, namely, the presence of linearly ordered chains of water molecules and large clusters of these molecules. The presence of linearly ordered chains and clusters in liquid water makes itself evident after the exposure of water to low-frequency electromagnetic radiation. The kinetics of the linearly ordered chains is described by nonlinear excitations (solitons). A hydrodynamic equation describing the behavior of this model system was derived. On the basis of the model, the dimensions of clusters were determined (approximately 600 A). The calculated values of dielectric permeability in the range of low frequencies appeared to be close to their experimentally obtained values. A tenfold increase in the stationary value of dielectric permeability compared with the known value of the dielectric constant in the frequency range of 10(4)-10(6) Hz was predicted. The frequency dependence of dielectric permeability in this range was studied.     

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

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

Thermalization of subexcitation electrons in solid water

We present the results of our Monte Carlo simulations of the slowing down and thermalization of subexcitation (E less than 7.4 eV) electrons in solid water. The scattering cross sections used in the simulations were obtained in another study from the analysis of electron-impact experiments performed on thin ice films deposited on a metal substrate at 14 K. The procedure by which these cross sections were determined is tested with our simulation code and is shown to be satisfactory. We find an average electron thermalization distance of approximately 13 nm, which is larger than what is usually assumed (2-7 nm) in models describing the diffusion-controlled track reactions which occur after 10(-12) s in irradiated liquid water. As for our calculated average thermalization time, it is of the order of 10(-13) s, in good agreement with experimental observations. To show the progression of the thermalization process, we give the distributions of slowing-down distances and times obtained for different stages of this process. The possibility that the subexcitation electrons undergo a dissociative attachment to water molecules is considered and its consequences on the initial yield of various chemical species are discussed. In particular, this dissociative attachment could provide a new explanation for the origin of the unscavengeable initial yield of molecular hydrogen.     

Track structures and dose distributions from decays of (131)I and (125)I in and around water spheres simulating micrometastases of differentiated thyroid cancer

The disintegration of the radionuclides (131)I and (125)I and the subsequent charged-particle tracks left behind in water (as a model substance for a biological cell) are simulated by the Monte Carlo track structure simulation code PARTRAC, using new inelastic electron scattering cross sections for condensed water. Every photon and electron emitted was followed in detail, event by event, down to 10 eV. From the spatial information on the track structures, absorbed dose distributions per (131)I and (125)I decay were calculated in and around water spheres simulating micrometastases as well as in the tissue surrounding such metastases. These radionuclides were assumed to be distributed uniformly inside spheres of different diameters (0.01, 0.03, 0.1, 0.3, 1.0 and 3.0 mm). The respective electron degradation spectra, the nearest-neighbor distance distributions between inelastic events, and the distance distributions for all activations for both iodine radionuclides were calculated. The absorbed fractions of the initial electron energies, absorbed doses and energy depositions, and single-event distributions, F(1)(epsilon), inside the six water spheres described above and in the surrounding tissue were also calculated. The absorbed doses per decay inside the six water spheres, i.e., the calculated S values (listed from 0.01 to 3.0 mm), were 6.8 x 10(-4), 7.2 x 10(-5), 5.5 x 10(-6), 4.9 x 10(-7), 3.1 x 10(-8) and 1.8 x 10(-9) Gy Bq(-1) s(-1) for (131)I, and 3.4 x 10(-3), 1.7 x 10(-4), 5.1 x 10(-6), 2.0 x 10(-7), 5.6 x 10(-9) and 2.2 x 10(-10) Gy Bq(-1) s(-1) for (125)I. It is concluded that, in the treatment of thyroid cancer, the geometrical track structure properties of (125)I might be superior to those of (131)I in micrometastases with diameters less than 0.1 mm; however, in this medical context, many other factors also have to be considered.