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.     

Influence of radiation quality on the yield of DNA strand breaks in SV40 DNA irradiated in solution.

Using highly energetic particles to irradiate plasmid DNA in aerobic aqueous solution, we have compiled an extensive database on how yields of DNA single- and double-strand breaks (SSBs and DSBs) vary with radiation quality. This study was performed in a low-scavenging buffer system and covers a wide range of ion species (helium to uranium) and LETs (5 to 16,000 keV/microm). For LETs up to around 40 keV/microm for SSBs and 400 keV/microm for DSBs, the total energy deposition determines cross section. At higher LET, cross sections level off and individual plateaus for particles of different atomic numbers are observed. For each ion species this is more pronounced and occurs at lower LET for SSBs than for DSBs, leading to an increase in the DSB:SSB ratio from 1:70 for X rays to 1:6 at 500 keV/microm. At this LET, the influence of track structure becomes evident, with high local concentrations of ionization events favoring the formation of DSBs and also intratrack recombination reactions. For lower-energy ions, a saturation in production of measurable DSBs is apparent, due to correlated lesion induction within densely ionizing particle tracks. For very heavy low-energy ions, both SSB and DSB cross sections decrease with particle velocity at nearly constant LET, forming individual hooked curves when plotted as a function of LET.     

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.     

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.     

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.     

Biophysical modeling of fragment length distributions of DNA plasmids after X and heavy-ion irradiation analyzed by atomic force microscopy

The investigation of fragment length distributions of plasmid DNA gives insight into the influence of localized energy distribution on the induction of DNA damage, particularly the clustering of double-strand breaks. We present an approach that determines the fragment length distributions of plasmid DNA after heavy-ion irradiation by using the Local Effect Model. We find a good agreement of our simulations with experimental fragment distributions derived from atomic force microscopy (AFM) studies by including experimental constraints typical for AFM. Our calculations reveal that by comparing the fragmentation in terms of fluence, we can uniquely distinguish the effect of different radiation qualities. For very high-LET irradiation using nickel or uranium ions, no difference between their fragment distributions can be expected for the same dose level. However, for carbon ions with an intermediate LET, the fragmentation pattern differs from the distribution for very high-LET particles. The results of the model calculations can be used to determine the optimal experimental parameters for a demonstration of the influence of track structure on primary radiation damage. Additionally, we compare the results of our model for two different plasmid geometries.     

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.     

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.     

Responses to accelerated heavy ions of spores ofBacillus subtilis of different repair capacity

Summary Inactivation, mutagenesis of histidine reversion and the involvement of DNA repair were studied in spores ofBacillus subtilis irradiated with heavy ions at LBL, Berkeley and GSI, Darmstadt. Five groups of ions (from boron to uranium) were used with residual energies from 0.2 MeV/u up to 18.6 MeV/u; in addition, carbon ions were used with a residual energy of 120 MeV/u. Action cross sections of both inactivation and mutagenesis show a similar dependence on ion mass and energy: for lighter ions (Z 10), the lethal response is nearly energy independent (Z = 10) or decreasing with energy (Z 6); these light ions, up to 18.6 MeV/u, induce hardly any mutations. For heavier ions (Z 26), the lethal as well as the mutagenic responses increase with ion mass and energy up to a maximum or saturation. The efficiency of DNA repair to improve survival and the mutagenic efficiency per lethal event, both, increase with ion energy up to a saturation value which, depending on strain and endpoint, either roughly coincides with the X-ray value or is smaller than that after X-ray treatment. For repair based on recombination events, the increase in the survival effects with ion energy is more pronounced than for that based on repair replication. At energies of 1 MeV/u or below, neither DNA repair nor mutation induction appear to be significant. The results support previous suggestions on the importance of the radial distribution of the energy around the ion track in biological action cross section and the evidence that the entire core of the spore represents the sensitive site in responses to heavy ions.     

Radial secondary electron dose profiles and biological effects in light-ion beams based on analytical and Monte Carlo calculations using distorted wave cross sections

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for (1)H(+), (4)He(2+) and (6)Li(3+) ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r(2) is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV (1)H(+), 2 MeV (4)He(2+) and 3 MeV (6)Li(3+) are almost the same, with about 30% more delta electrons in the sub keV range from (4)He(2+)and (6)Li(3+) compared to (1)H(+). A similar behavior is also seen for 1 MeV (1)H(+), 4 MeV (4)He(2+) and 6 MeV (6)Li(3+), all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.     

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.     

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     

Initial yields of DNA double-strand breaks and DNA Fragmentation patterns depend on linear energy transfer in tobacco BY-2 protoplasts irradiated with helium, carbon and neon ions

The ability of ion beams to kill or mutate plant cells is known to depend on the linear energy transfer (LET) of the ions, although the mechanism of damage is poorly understood. In this study, DNA double-strand breaks (DSBs) were quantified by a DNA fragment-size analysis in tobacco protoplasts irradiated with high-LET ions. Tobacco BY-2 protoplasts, as a model of single plant cells, were irradiated with helium, carbon and neon ions having different LETs and with gamma rays. After irradiation, DNA fragments were separated into sizes between 1600 and 6.6 kbp by pulsed-field gel electrophoresis. Information on DNA fragmentation was obtained by staining the gels with SYBR Green I. Initial DSB yields were found to depend on LET, and the highest relative biological effectiveness (about 1.6) was obtained at 124 and 241 keV/microm carbon ions. High-LET carbon and neon ions induced short DNA fragments more efficiently than gamma rays. These results partially explain the large biological effects caused by high-LET ions in plants.     

The relative biological effectiveness of densely ionizing heavy-ion radiation for inducing ocular cataracts in wild type versus mice heterozygous for the ATM gene

The accelerated appearance of ocular cataracts at younger ages has been recorded in both astronauts and airline pilots, and is usually attributed to high-energy heavy ions in galactic cosmic ray radiation. We have previously shown that high-LET 1-GeV/nucleon ⁵⁶Fe ions are significantly more effective than X-rays in producing cataracts in mice. We have also shown that mice haploinsufficient for ATM develop cataracts earlier than wild-type animals, when exposed to either low-LET X-rays or high-LET ⁵⁶Fe ions. In this paper we derive quantitative estimates for the relative biological effectiveness (RBE) of high energy ⁵⁶Fe ions compared with X-rays, both for wild type and for mice haploinsufficient for ATM. There is a clear trend toward higher RBE’s in haploinsufficient animals, both for low- and high-grade cataracts. Haploinsufficiency for ATM results in an enhanced sensitivity to X-rays compared with the wild type, and this enhancement appears even larger after exposure to high-LET heavy ions.Dedicated to the memory of Professor Basil V. Worgul, who passed away in January 2006, much missed by all his colleagues.     

Mutation induction in spores ofBacillus subtilis by accelerated very heavy ions

Summary Mutation induction (resistance to sodium azide) in spores ofBacillus subtilis was investigated after irradiation with heavy ions from Neon to Uranium with specific particle energies between 0.17 and 18.6 MeV/u. A strong dependence of the mutation induction cross section on particle charge and energy was observed. From the results it was concluded that mutation induction in bacterial spores by very heavy ions is mainly caused by secondary electrons.     

Description of light ion production cross sections and fluxes on the Mars surface using the QMSFRG model

The atmosphere of Mars significantly attenuates the heavy ion component of the primary galactic cosmic rays (GCR), however, increases the fluence of secondary light ions (neutrons, and hydrogen and helium isotopes) because of particle production processes. We describe results of the quantum multiple scattering fragmentation (QMSFRG) model for the production of light nuclei through the distinct mechanisms of nuclear abrasion and ablation, coalescence, and cluster knockout. The QMSFRG model is shown to be in excellent agreement with available experimental data for nuclear fragmentation cross sections. We use the QMSFRG model and the space radiation transport code, HZETRN to make predictions of the light particle environment on the Martian surface at solar minimum and near maximum. The radiation assessment detector (RAD) experiment will be launched in 2009 as part of the Mars Science Laboratory (MSL). We make predictions of the expected results for time dependent count-rates to be observed by the RAD experiment. Finally, we consider sensitivity assessments of the impact of the Martian atmospheric composition on particle fluxes at the surface.     

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.     

Heavy ion effects on yeast: inhibition of ribosomal RNA synthesis

Diploid wild-type yeast cells were exposed to beams of heavy ions covering a wide range of linear energy transfer (LET) (43-13,700 keV/microns). Synthesis of ribosomal RNA (rRNA) was assessed as a functional measure of damage produced by particle radiation. An exponential decrease of relative rRNA synthesis with particle fluence was demonstrated in all cases. The inactivation cross sections derived were found to increase with LET over the entire range of LET studied. The corresponding values for relative biological effectiveness were slightly less than unity. Maximum cross sections measured were close to 1 micron 2, implying that some larger structure within the yeast nucleus (e.g., the nucleolus) might represent the target for an impairment of synthetic activity by very heavy ions rather than the genes coding for rRNA. Where tested, an oxygen effect for rRNA synthesis could not be demonstrated.     

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.