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.     

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

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

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.     

On pathlength and energy straggling of megavoltage electrons slowing down

Purposeto elucidate the effects of multiple scattering and energy-loss straggling on electron beams slowing down in materials.MethodsEGSnrc Monte Carlo simulations are done using a purpose-written user-code.ResultsPlots are presented of the primary electron’s energy as a function of pathlength for 20 MeV electrons incident on water and tantalum as are plots of the overall distribution of pathlengths as the 20 MeV electrons slow down under various Monte Carlo scenarios in water and tantalum. The distributions range from 1 % to 135 % of the CSDA range in water and from 1 % to 186 % in tantalum. The effects of energy-loss straggling on energy spectra at depth and electron fluence at depth are also presented.ConclusionsThe role of energy-loss straggling and multiple scattering are shown to play a significant role in the range straggling which determines the dose fall-off region in electron beam dose vs depth curves and a significant role in the energy distributions as a function of depth.     

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.     

Simulation of electron-beam irradiation of skin tissue model

Monte Carlo simulation of electrons stopping in liquid water was used to model the penetration and quality of electron-beam irradiation incident on the full-thickness EpiDerm? skin model (EpiDermFT? MatTek, Ashland, VA). This 3D tissue model has a fully developed basement membrane separating an epidermal layer of keratinocytes in various stages of differentiation from a dermal layer of fibroblasts embedded in collagen. The simulations were motivated by a desire to selectively expose the epidermal layer to low-linear energy transfer (LET) radiation in the presence of a nonirradiated dermal layer. The variable-energy electron microbeam at the Pacific Northwest National Laboratory (PNNL) was used as a model of device characteristics and irradiation geometry. At the highest beam energy available (90 keV), we estimate that no more than a few percent of the beam energy will be deposited in the dermal layer. Energy deposition spectra were calculated for 10-μm-thick layers near the 10th, 50th and 90th percentiles of penetration by the 90 keV electron beam. Bimodal spectra showed an increasing component of "stoppers" with increasing depth, which increases the probability of large energy deposition events. Nevertheless, screening by tissue above the layer of interest is the main factor determining energy deposited at a given depth.     

Microdosimetry of electron microbeams

Track structures of 25, 50 and 80 keV primary electrons, simulated by the detailed-history Monte Carlo method, were analyzed for the frequency distributions of energy deposited in spheres with a diameter of 1 microm, placed in a cylindrically symmetrical array around the projected initial direction of the primary electron. The frequency mean of specific energy, the dose mean of lineal energy, and the parameters of lognormal functions fit to the dose distributions were calculated as a function of beam penetration and radial distance from the projected beam axis. Given these data, the stochastics of dose and radiation quality for micrometer-scale sites targeted by a medium-energy electron microbeam can be predicted as a function of the site's location relative to the beam entry point.     

Fundamental parameters of a relativistic runaway electron avalanche in air

A relativistic runaway electron avalanche in air is simulated numerically by the Monte Carlo method with allowance for a large number of elementary processes involving electrons, positrons, and photons. The characteristic time scale of the avalanche amplification is calculated as a function of the overvoltage δ relative to the minimum value of the drag force between the electrons and the atomic particles of the medium. The dynamics of the formation of the electron energy distribution is investigated. The steady-state mean electron energy depends weakly on δ. Over a wide range of δ values, there exists a universal electron energy distribution, which is essentially independent of δ. The angular distributions of electrons integrated over energies, as well as the angular distributions for different energy groups, are calculated. Analytic approximations for the energy and angular distributions are obtained.     

A B3LYP and MP2(full) theoretical investigation into cooperativity effects,aromaticity and thermodynamic properties in the Na+⋯benzonitrile⋯H2O ternary complex

In this work the growth of a graphene monolayer on copper substrate, as typically achieved via chemical vapor deposition of propene (C₃H₆), was investigated by first-principles and kinetic Monte Carlo calculations. A comparison between calculated C1s core-level binding energies and electron spectroscopy measurements showed that graphene nucleates from isolated carbon atoms adsorbed on surface defects or sub-superficial layers upon hydrocarbon fragmentation. In this respect, ab initio nudged elastic band simulations yield the energetic barriers characterizing the diffusion of elemental carbon on the Cu(111) surface and atomic carbon uptake by the growing graphene film. Our calculations highlight a strong interaction between the growing film edges and the copper substrate, indicative of the importance of the grain boundaries in the epitaxy process. Furthermore, we used activation energies to compute the reaction rates for the different mechanisms occurring at the carbon–copper interface via harmonic transition state theory. Finally, we simulated the long-time system growth evolution through a kinetic Monte Carlo approach for different temperatures and coverage. Our ab initio and Monte Carlo simulations of the out-of-equilibrium system point towards a growth model strikingly different from that of standard film growth. Graphene growth on copper turns out to be a catalytic, thermally-activated process that nucleates from carbon monomers, proceeds by adsorption of carbon atoms, and is not self-limiting. Furthermore, graphene growth seems to be more effective at carbon supersaturation of the surface—a clear fingerprint of a large activation barrier for C attachment. Our growth model and computational results are in good agreement with recent X-ray photoelectron spectroscopy experimental measurements.     

Dynamics of an Electron Bunch Accelerated by a Wakefield

The energy characteristics of an electron bunch accelerated by a wakefield are largely determined by the initial bunch dimensions. Present-day injectors are still incapable of ensuring the initial spatial parameters of the bunches required for their acceleration without increasing the energy spread of the bunch electrons. In connection with this, the possibility is studied of improving the energy characteristics of an accelerated bunch by precompressing it in the longitudinal direction in the stage of trapping by a wakefield. Analytic formulas are derived that describe the one-dimensional dynamics of the spatial and energy characteristics of a short (much shorter than the wakefield wavelength) electron bunch in both the trapping and acceleration stages. The analytical results obtained are shown to agree fairly well with the results from one-dimensional and three-dimensional simulations, provided that the electrons are injected into the region that is optimum for acceleration. The possibility is discussed of forming compressed bunches so as to ensure the high quality of the bunch in the course of its acceleration to high energies.     

Determination of initial electron parameters by means of Monte Carlo simulations for the Siemens Artiste Linac 6 MV photon beam

AimIn this study, we investigated initial electron parameters of Siemens Artiste Linac with 6 MV photon beam using the Monte Carlo method.BackgroundIt is essential to define all the characteristics of initial electrons hitting the target, i.e. mean energy and full width of half maximum (FWHM) of the spatial distribution intensity, which is needed to run Monte Carlo simulations. The Monte Carlo is the most accurate method for simulation of radiotherapy treatments.Materials and methodsLinac head geometry was modeled using the BEAMnrc code. The phase space files were used as input file to DOSXYZnrc simulation to determine the dose distribution in a water phantom. We obtained percent depth dose curves and the lateral dose profile. All the results were obtained at 100 cm of SSD and for a 10 × 10 cm² field.ResultsWe concluded that there existed a good conformity between Monte Carlo simulation and measurement data when we used electron mean energy of 6.3 MeV and 0.30 cm FWHM value as initial parameters. We observed that FWHM values had very little effect on PDD and we found that the electron mean energy and FWHM values affected the lateral dose profile. However, these effects are between tolerance values.ConclusionsThe initial parameters especially depend on components of a linac head. The phase space file which was obtained from Monte Carlo Simulation for a linac can be used as calculation of scattering, MLC leakage, to compare dose distribution on patients and in various studies.     

Simulation of the passage of fast electrons and the early stage of water radiolysis by the Monte Carlo method

A numerical computer simulation of the processes of the interaction of electrons with liquid water and vapor was performed, beginning with the absorption of the energy of ionizing radiation and including the chemical changes in the medium. The specific features of the liquid phase compared with the gaseous phase were taken into account. Among them are the decrease of the ionization potential and collective excitations of the plasmon type. The mass stopping powers and ranges of electrons in liquid water and vapor were calculated. Within the frames of the stochastic model the kinetics of water radiolysis in the picosecond range of radiolysis was calculated by the Monte Carlo method. The mechanism of water radiolysis was found with the electron-ion recombination and the reactions of quasi-free and solvated electrons taken into account.     

Equilibria for the adsorption of antibiotics onto neutral polymeric sorbents: Experimental and modeling studies

The objective of this work was to study the equilibria for adsorption of three antibiotics (penicillin V, tetracycline, and cephalosporin C) from water onto commercially available neutral polymeric sorbents. The pH was observed to be an important factor in adsorption as our results suggest that the neutral forms of penicillin V and cephalosporin C are preferentially adsorbed onto the neutral sorbents. Also, sorbent surface chemistry was observed to be important for adsorption, as the antibiotics adsorbed more favorably (both in terms of affinities and enthalpies) onto the aromatic sorbent as compared to the aliphatic ester sorbent. In addition to these thermodynamic measurements, molecular modeling studies and Monte Carlo simulations suggest that adsorption onto aromatic sorbents may involve specific interactions between the planar regions of the antibiotic molecules and the phenyl rings of the aromatic sorbent. The interaction energies predicted from Monte Carlo simulations were observed to provide qualitative agreement with experimentally determined adsorption affinities. (c) 1995 John Wiley & Sons, Inc.     

Monte Carlo simulation and measurement of radiation leakage from applicators used in external electron radiotherapy

External electron radiotherapy is performed using a cone or applicator to collimate the beam. However, because of a trade-off between collimation and scattering/bremsstrahlung X-ray production, applicators generate a small amount of secondary radiation (leakage). We investigate the peripheral dose outside the radiation field of a Varian-type applicator. The dose and fluence outside the radiation field were analyzed in a detailed Monte Carlo simulation. The differences between the calculation results and data measured in a water phantom in an ionization chamber were less than ±1% in regions more than 3 mm below the surface of the phantom and at the depth of dose maximum. The calculated fluence was analyzed inside and outside the radiation field on a plane just above the water phantom surface. Changing the electron energy affected the off-axis fluence distribution outside the radiation field; however, the size of the applicator had little effect on this distribution. For each energy, the distributions outside the radiation field were similar to the dose distribution at shallow depths in the water phantom. The effect of secondary electrons generation by photon transmission through the alloy making up the lowest scraper was largest in the region from the field edge to directly below the cutout and at higher beam energies. The results of the Monte Carlo simulation confirm that the peripheral dose outside the field is significantly affected by radiation scattered or transmitted from the applicator, and the effect increases with the electron energy.     

Benchmark of penelope for low and medium energy X-rays

The Monte Carlo code penelope is benchmarked for X-ray beams with energies between 30 and 300 keV. The results of different simulations performed with penelope are compared with those obtained with a semi-empirical computational model and with experimental measurements. Half-value layer indexes obtained from the attenuation curves for Al and Cu and depth dose curves in water have been considered for this comparison. A good agreement is reached on what guarantees the feasibility of the code.     

Comparison between an event-by-event Monte Carlo code,NOREC, and ETRAN for electron scaled point kernels between 20 keV and 1 MeV

An event-by-event Monte Carlo code called NOREC, a substantially improved version of the Oak Ridge electron transport code (OREC), was released in 2003, after a number of modifications to OREC. In spite of some earlier work, the characteristics of the code have not been clearly shown so far, especially for a wide range of electron energies. Therefore, NOREC was used in this study to generate one of the popular dosimetric quantities, the scaled point kernel, for a number of electron energies between 0.02 and 1.0 MeV. Calculated kernels were compared with the most well-known published kernels based on a condensed history Monte Carlo code, ETRAN, to show not only general agreement between the codes for the electron energy range considered but also possible differences between an event-by-event code and a condensed history code. There was general agreement between the kernels within about 5% up to 0.7 r/r ₀ for 100 keV and 1 MeV electrons. Note that r/r ₀ denotes the scaled distance, where r is the radial distance from the source to the dose point and r ₀ is the continuous slowing down approximation (CSDA) range of a mono-energetic electron. For the same range of scaled distances, the discrepancies for 20 and 500 keV electrons were up to 6 and 12%, respectively. Especially, there was more pronounced disagreement for 500 keV electrons than for 20 keV electrons. The degree of disagreement for 500 keV electrons decreased when NOREC results were compared with published EGS4/PRESTA results, producing similar agreement to other electron energies.     

Condensed-history Monte Carlo simulation of the dosimetric distribution of electron microbeam

To evaluate the dose distributions of an electron microbeam and to help optimization of its design, the condensed-history (CH) Monte Carlo simulation algorithm implemented in the Geant4 toolkit was selected as an alternative to the conventionally used analog algorithm. Compared to the analog algorithm, the CH algorithm is cheaper and less limited by the lack of cross-sections. And, with a properly chosen production cut for secondaries, its accuracy for the problems of microdosimetry is satisfactory. In this work, calculations of the single-event (imparted energy ɛ) size distribution f ₁(ɛ) is described, for compartments in the Orlando electron micro beam. The results agree well with those obtained by use of the analog algorithm and reported in the literature. It is shown that substituting tissue with water in HeLa cells, and replacing Mylar with water of the same mass stopping power in the substrate, makes little difference. Additionally, the neighbor-to-target ratio of average event size R _NT has been calculated as a function of the incident energy of the electrons. Comparison with analog results reported in the literature suggests that the average event size in neighbors, and hence the neighbor-to-target ratio, is sensitive to the selection of the energy threshold. Finally, the effect of finite beam radius on the event size distribution and the neighbor-to-target ratio has also been studied. All results presented suggest the condensed-history technique to provide an efficient and valuable alternative tool in the design of electron microbeams.     

Study of dental prostheses influence in radiation therapy

Dental prostheses made of high density material contribute to modify dose distribution in head and neck cancer treatment. Our objective is to quantify dose perturbation due to high density inhomogeneity with experimental measurements and Monte Carlo simulations.Firstly, measurements were carried in a phantom representing a human jaw with thermoluminescent detectors (GR200A) and EBT2 Gafchromic films in the vicinity of three samples: a healthy tooth, a tooth with amalgam and a Ni–Cr crown, irradiated in clinical configuration. Secondly, Monte Carlo simulations (BEAMnrc code) were assessed in an identical configuration.Experimental measurements and simulation results confirm the two well-known phenomena: firstly the passage from a low density medium to a high density medium induces backscattered electrons causing a dose increase at the interface, and secondly, the passage from a high density medium to a low density medium creates a dose decrease near the interface. So, the results show a 1.4% and 23.8% backscatter dose rise and attenuation after sample of 26.7% and 10.9% respectively for tooth with amalgam and crown compared to the healthy tooth.Although a tooth with amalgam has a density of about 12–13, the changes generated are not significant. However, the results for crown (density of 8) are very significant and the discordance observed may be due to calculation point size difference 0.8 mm and 0.25 mm respectively for TLD and Monte Carlo. The use of Monte Carlo simulations and experimental measurements provides objective evidence to evaluate treatment planning system results with metal dental prostheses.     

Computational binding studies of human pp60c-src SH2 domain with a series of nonpeptide, phosphophenyl-containing ligands

Monte Carlo/free energy perturbation (MC/FEP) simulations were performed on a series of nonpeptide ligands of the human pp60c-src SH2 domain in order to calculate relative free energies of binding for each compound and to understand the structural requirements for high affinity binding. The amido compound, exhibiting the highest experimental affinity, takes advantage of an interaction with a previously unobserved structural water.     

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.