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.     

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.     

A new, vapour-phase mechanism for stomatal responses to humidity and temperature

A new mechanism for stomatal responses to humidity and temperature is proposed. Unlike previously-proposed mechanisms, which rely on liquid water transport to create water potential gradients within the leaf, the new mechanism assumes that water transport to the guard cells is primarily through the vapour phase. Under steady-state conditions, guard cells are assumed to be in near-equilibrium with the water vapour in the air near the bottom of the stomatal pore. As the water potential of this air varies with changing air humidity and leaf temperature, the resultant changes in guard cell water potential produce stomatal movements. A simple, closed-form, mathematical model based on this idea is derived. The new model is parameterized for a previously published set of data and is shown to fit the data as well as or better than existing models. The model contains mathematical elements that are consistent with previously-proposed mechanistic models based on liquid flow as well as empirical models based on relative humidity. As such, it provides a mechanistic explanation for the realm of validity for each of these approaches.     

A comparison of depth dependence of dose and linear energy transfer spectra in aluminum and polyethylene

A set of four tissue-equivalent proportional counters (TEPCs), with their detector heads at the centers of 0 (bare), 3, 7 and 9-inch-diameter aluminum spheres, were flown on Shuttle flight STS-89. Five such detectors at the centers of polyethylene spheres were flown 1 year earlier on STS-81. The results of dose-depth dependence for the two materials convincingly show the merits of using material rich in hydrogen to decrease the radiation exposure to the crew. A comparison of the calculated galactic cosmic radiation (GCR) absorbed dose and dose-equivalent rates using the radiation transport code HZETRN with nuclear fragmentation model NUCFRG2 and the measured GCR absorbed dose rates and dose-equivalent rates shows that they agree within root mean square (rms) error of 12.5 and 8.2%, respectively. However, there are significant depth-dependent differences in the linear energy transfer (LET) spectra. A comparison for trapped protons using the proton transport code BRYNTRN and the AP-8 MIN trapped-proton model shows a systematic bias, with the model underpredicting dose and dose-equivalent rates. These results show the need for improvements in the radiation transport and/or fragmentation models.     

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.     

NOREC,a Monte Carlo code for simulating electron tracks in liquid water

The work reported here was originally motivated by a discussion of Monte Carlo computer codes for electron transport in water given in Report No. 130 by the National Council on Radiation Protection and Measurements (NCRP). It was pointed out (correctly) that a published depth-dose distribution calculated by the Oak Ridge electron transport code, OREC, for 800 keV electrons normally incident on a water slab was apparently in error, possibly due to inadequate treatment of elastic scattering. In this paper we describe the replacement of the original OREC elastic cross sections by current ones from the National Institute of Standards and Technology (NIST). This investigation led also to the critical examination and revision of some other parts of the program, as described here. The revised code, which we have renamed NOREC, represents the first substantial review and modification of the Oak Ridge code in a number of years. We also present some comparisons of results calculated with the old and new versions and discuss their implications with respect to earlier studies. We have also written a version of NOREC in C++ language, which is available to other investigators. This paper provides a record of a response to the NCRP published statement and documentation for the revised code, NOREC.     

Formation of ionization clusters in nanometric structures of propane-based tissue-equivalent gas or liquid water by electrons and alpha-particles

Despite the importance of ionization yield formation in sub-cellular structures a few nanometres in size, with regard to radiation damage our present knowledge in this respect is almost exclusively based on Monte Carlo simulations which in turn are based on cross section sets for water vapour or liquid water. Experimental data, although urgently needed, are still missing because the direct measurement of ionization yields in sub-cellular structures or, at least, in nanometric volumes of liquid water, is not yet possible. The best feasible way to overcome this problem of measurement at present, is the use of highly sophisticated counters filled with gases at low operating pressure to simulate target volumes a few nanometres in diameter at unit density. An indispensable prerequisite of the reliability of such measurements is, however, a check of the equivalence of the ionization yield produced in a specified target gas and the yield to be expected in liquid water or biological material. For this purpose, the ionization yield formation by electrons and alpha-particles in liquid water was simulated using the Monte Carlo method and compared with that produced in propane-based tissue-equivalent gas (composition by volume 55% C3H8, 39.6% CO2, 5.4% N2). After a short summary of the most important physical aspects of ionization cluster formation, new results are presented and discussed from the point of view of radiation physics and radiation biology.     

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.     

Target analysis studies of red cell water and urea transport

Radiation inactivation was used to determine the nature and molecular weight of water and urea transporters in the human red cell. Red cells were frozen to -50 degrees C in a cryoprotectant solution, irradiated with 1.5 MeV electrons, thawed, washed and assayed for osmotic water and urea permeability by stopped-flow light scattering. The freezing and thawing process did not affect the rates of water or urea transport or the inhibitory potency of p-chloromercuribenzenesulfonate (pCMBS) on water transport and of phloretin on urea transport. Red cell urea transport inactivated with radiation (0-4 Mrad) with a single target size of 469 +/- 36 kDa. 40 microM phloretin inhibited urea flux by approx. 50% at each radiation dose, indicating that urea transporters surviving radiation were inhibitable. Water transport did not inactivate with radiation; however, the inhibitory potency of 2.5 mM pCMBS decreased from 86 +/- 1% to 4 +/- 9% over a 0-2 Mrad dose range. These studies suggest that red cell water transport either required one or more low-molecular-weight proteins, or is lipid-mediated, and that the pCMBS-binding site which regulates water flow inactivates with radiation. These results also suggest that red cell urea transport is mediated by a specific, high-molecular-weight protein. These results do not support the hypothesis that a band 3 dimer (190 kDa) mediates red cell osmotic water and urea transport.     

Radiation quality of tritium beta-rays: microdosimetric distributions for nanometer-size targets in a medium containing tritiated water

To elucidate the characteristics of the action of tritium beta-rays, the following parameters are derived: electron slowing down spectra of primary electrons (beta-rays) and delta-rays in a medium containing tritiated water; and frequency distributions for the microdosimetric quantity j (number of effective primary events per track per target), fj, for nanometer-size targets exposed to tritiated water. Features of the radiation quality of tritium beta-rays are discussed by comparing the present results with those for 60Co gamma-rays and 7 MeV electrons. It is concluded that, although tritium beta-rays, 60Co gamma-rays, and 7 MeV electrons are classified as the same low l.e.t. radiation, the radiation quality of tritium beta-rays is considerably different from those of 60Co gamma-rays and 7 MeV electrons, and has specific features such as a high average l.e.t., a small total electron fluence per unit absorbed dose, and a different microdosimetric distribution, fj, for nanometer-size targets.     

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.     

Entropy effects on the ion-diffusion rate in transmembrane protein channels

We treat the transport of univalent cations through pore-like protein channels in biological membranes analytically, using two models (A + B) for the channel and the ion-channel interaction. A Lennard-Jones-type repulsion between the ions and the pore wall is introduced. We also include Van der Waals- and coulomb-type interactions between polar ligands of the pore-forming protein (e.g., carbonyl groups directed towards the axis of the channel) and the migrating particles. In model A, the polar groups are assumed to occur in pairs of dipoles pointing in opposite directions (as in the gramicidin A channel), while in model B the channel is treated as a pore with a radially isotropic charge distribution. In both models the ion-channel interaction leads to the occurrence of periodic potentials, corresponding to quasi-equilibrium and transition state sites of the ion in the pore. The diffusion rate can be calculated employing rate-theoretical concepts on the basis of microscopic parameters. It is demonstrated that the anomaly (inversion of the normal mass effect) for the transport rates of different ions can be related to differences in the activation entropy. The latter quantity is estimated analytically for both models. As a test, we performed numerical calculations with parameters based on the gramicidin A model. The results are in good agreement with experimental data and data from computer simulations. This shows that simple analytic expressions are well suited for predicting trends in the ionic conductivity of protein channels on the basis of microscopic interactions.     

An analytic approach to developing transport threshold models of neoclassical tearing modes in tokamaks

Transport threshold models of neoclassical tearing modes in tokamaks are investigated analytically. An analysis is made of the competition between strong transverse heat transport, on the one hand, and longitudinal heat transport, longitudinal heat convection, longitudinal inertial transport, and rotational transport, on the other hand, which leads to the establishment of the perturbed temperature profile in magnetic islands. It is shown that, in all these cases, the temperature profile can be found analytically by using rigorous solutions to the heat conduction equation in the near and far regions of a chain of magnetic islands and then by matching these solutions. Analytic expressions for the temperature profile are used to calculate the contribution of the bootstrap current to the generalized Rutherford equation for the island width evolution with the aim of constructing particular transport threshold models of neoclassical tearing modes. Four transport threshold models, differing in the underlying competing mechanisms, are analyzed: collisional, convective, inertial, and rotational models. The collisional model constructed analytically is shown to coincide exactly with that calculated numerically; the reason is that the analytical temperature profile turns out to be the same as the numerical profile. The results obtained can be useful in developing the next generation of general threshold models. The first steps toward such models have already been made.     

Intercomparison of dose enhancement ratio and secondary electron spectra for gold nanoparticles irradiated by X-rays calculated using multiple Monte Carlo simulation codes

PurposeTargeted radiation therapy has seen an increased interest in the past decade. In vitro and in vivo experiments showed enhanced radiation doses due to gold nanoparticles (GNPs) to tumors in mice and demonstrated a high potential for clinical application. However, finding a functionalized molecular formulation for actively targeting GNPs in tumor cells is challenging. Furthermore, the enhanced energy deposition by secondary electrons around GNPs, particularly by short-ranged Auger electrons is difficult to measure. Computational models, such as Monte Carlo (MC) radiation transport codes, have been used to estimate the physical quantities and effects of GNPs. However, as these codes differ from one to another, the reliability of physical and dosimetric quantities needs to be established at cellular and molecular levels, so that the subsequent biological effects can be assessed quantitatively.MethodsIn this work, irradiation of single GNPs of 50 nm and 100 nm diameter by X-ray spectra generated by 50 and 100 peak kilovoltages was simulated for a defined geometry setup, by applying multiple MC codes in the EURADOS framework.ResultsThe mean dose enhancement ratio of the first 10 nm-thick water shell around a 100 nm GNP ranges from 400 for 100 kVp X-rays to 600 for 50 kVp X-rays with large uncertainty factors up to 2.3.ConclusionsIt is concluded that the absolute dose enhancement effects have large uncertainties and need an inter-code intercomparison for a high quality assurance; relative properties may be a better measure until more experimental data is available to constrain the models.     

Effect of Resonant Radiation Transport on the Parameters of RF and DC Discharges in a He-Ar-Xe Mixture

A study is made of the effect of the transport of Xe 147-nm resonant radiation on the parameters of a low-temperature plasma of DC and RF discharges in gas mixtures used as the working medium in lasers based on infrared transitions in xenon. RF discharges are treated in the planar geometry typical of slab lasers. DC discharges in tubes are treated in cylindrical geometry. The trapping of resonant radiation is described using different approximate models: the decay time approximation for a plasma slab (the Holstein approximation) and the effective lifetime approximation (the Biberman approximation). The transport equation for resonant radiation is solved numerically. The effect of the radiation transport on both the current-voltage characteristics of a discharge and the spatial distribution of the excited Xe atoms is investigated. The current-voltage characteristics calculated for a DC discharge with allowance for the resonant radiation transport agree well with the experimental characteristics. It is found that, for an RF discharge, the effective lifetime approximation overestimates the density of the excited Xe atoms near the electrodes by several times and underestimates this density at the midplane of the discharge gap.     

Estimation of the electron density and radiative energy losses in a calcium plasma source based on an electron cyclotron resonance discharge

The parameters of a calcium plasma source based on an electron cyclotron resonance (ECR) discharge were calculated. The analysis was performed as applied to an ion cyclotron resonance system designed for separation of calcium isotopes. The plasma electrons in the source were heated by gyrotron microwave radiation in the zone of the inhomogeneous magnetic field. It was assumed that, in such a combined trap, the energy of the extraordinary microwave propagating from the high-field side was initially transferred to a small group of resonance electrons. As a result, two electron components with different transverse temperatures—the hot resonance component and the cold nonresonance component—were created in the plasma. The longitudinal temperatures of both components were assumed to be equal. The entire discharge space was divided into a narrow ECR zone, where resonance electrons acquired transverse energy, and the region of the discharge itself, where the gas was ionized. The transverse energy of resonance electrons was calculated by solving the equations for electron motion in an inhomogeneous magnetic field. Using the law of energy conservation and the balance condition for the number of hot electrons entering the discharge zone and cooled due to ionization and elastic collisions, the density of hot electrons was estimated and the dependence of the longitudinal temperature T _e∥ of the main (cold) electron component on the energy fraction β lost for radiation was obtained.     

Absorbed fractions for electrons and beta particles in sensitive regions of human respiratory tract

The absorbed fractions (AF) of electrons in sensitive layers of human respiratory tract were calculated in this paper. For that purpose the source code for simulation package PENELOPE, based on Monte Carlo method, was developed. The human respiratory tract was modeled according to ICRP66 publication, where AF of electrons was calculated using EGS4 simulation software. Some approximations used in ICRP66 were corrected in this work, and new values of AF for radon progeny are given. Minimal energy (EABS) that electron can have during transport through material is 1 keV in ICRP66, while it is set as low as 100 eV in the presented work. Lowering value of EABS gives more accurate results for AF when initial energy of electrons is below 50 keV. To represent tissue, water is used in ICRP66, while in this work epithelia tissue is used.