A Monte Carlo simulation of Auger cascades

The energy imparted to biological tissue after the decay of incorporated Auger emitters stems from two sources: (a) energy deposition by the Auger and Coster-Kronig electrons and (b) the charge potential which remains on the multiple ionized atom after the end of the cascade. For the numerical assessment of both the kinetic energy of the released electrons and the charge potential, a new and--for purposes of microdosimetry--precise method is presented. Based on relativistic Dirac-Fock calculations and a rigorous bookkeeping, this method provides a perfect energy balance of the considered atomic system when applied to Monte Carlo simulations of Auger cascades. By comparing the results for charge distribution for krypton and iodine with experimental data and the electron spectrum of 125I with theoretical data, it can be shown that the approach followed in this work is reasonable and appropriate for the determination of the energy deposited by incorporated Auger emitters in small volumes of condensed matter. The total energy deposited by 125I in a volume of 20-nm diameter is 2.03 keV which is made up by multiple ionization (1.07 keV) and energy deposition by the emitted Auger electrons (0.96 keV).     

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.     

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.     

How electron interference can be used in probing the surface of minute bioobjects and in fast reading of polynucleotides

A method is proposed for examining the surface of small biological objects such as macromolecules and their complexes. Based on interference of low-energy electrons, it allows constructing analogs of optical holograms but with a resolution on the order of interatomic distances. A set of such holograms obtained at different electron energies can provide sufficient information for identifying the surface groups of the object. Thus the method can be used for fast reading of e.g. polynucleotide sequences.     

Modeling of Coulomb collisions in a kinetic description of the electron cyclotron resonance plasma heating

The electron distribution function is modeled numerically with allowance for Coulomb collisions and quasilinear effects under cyclotron resonance conditions by solving a two-dimensional kinetic equation containing the quasilinear diffusion operator and the Coulomb collision operator in the Landau form. Two simplified model collision integrals that make it possible to describe electron heating by microwave radiation are considered. The first model collision operator is obtained by introducing the parametric time dependence of the temperature of the background Maxwellian electrons into the linear collision integral. It is shown that the heating of the bulk electrons can be described in a noncontradictory way if the temperature dynamics of the background electrons is calculated from the equation of energy balance, which is governed by the amount of the microwave power absorbed by the resonant electrons with the distribution function modified due to quasilinear effects. This conclusion is confirmed in a more rigorous fashion by comparing the solutions obtained using the first model Coulomb collision integral with those obtained using the second model integral, namely, the nonlinear operator derived by averaging the distribution function of the scattering electrons over pitch angles. The time-dependent linear collision integral is used to obtain analytic solutions describing quasi-steady electron heating with allowance for the quasilinear degradation of microwave power absorption.     

Thermal effects of a short light pulse on biological tissues. II. Light and heat fields

A set of heat conduction equations for a two-component medium simulating biological tissues were formulated. Their solutions were obtained, and the spatial distribution of light and temperature over tissue depth at different times after irradiation by a short light pulse was studied. The local absorption of light by blood vessels and the influence of this effect on the optical parameters of the medium, a more intense heating of blood as compared with its surrounding tissue, heat exchange between them, and heat transfer at the interface with different environments were accounted for. The solutions are expressed via characteristic times of the respective thermal processes to enable one to easily and vividly analyze the features of tissue heating and the influence of optical and thermal parameters on the temperature distributions of the components. The calculations are illustrated by examples.     

Tunable hydroxyapatite wettability: Effect on adhesion of biological molecules

Surface wettability modifications of biocompatible materials and wettability patterning are attractive methods for directed biological cells immobilization for tissue engineering, drug delivery, gene transfer, etc. Hydroxyapatite is known as an implantable biomimetic material and a substrate for effective adhesion of biological cells of various origins. Here we report the use of a low-energy electron irradiation to achieve tunable wettability of the hydroxyapatite in a wide range of contact angles, from 10° to 100°, with accuracy of ±3°. The incident electrons generate electron/hole pairs resulting in significant variation of the surface potential of the hydroxyapatite semiconductor and give rise to pronounced wettability modification. Tailoring the gradually varied wettability state in the hydroxyapatite nanoceramics enabled the differential binding of biological materials with different surface properties, such as bovine serum albumin (BSA) and deoxyribonucleic acid (DNA).     

Effect of low-energy electron irradiation on DNA damage by Fe3+ ion

We investigated the combined effects of low-energy electron irradiation and Fe(3+) ion on DNA damage. We used lyophilized pBR322 plasmid DNA films with various concentrations (0 ~ 7 mM) of Fe(3+) ions and irradiation with monochromatic, low-energy 3 or 5 eV electrons for these studies. DNA-Fe(3+) films were recovered and analyzed by agarose gel electrophoresis to identify and compare the effects of Fe(3+) ions and/or low-energy electrons alone or in combination on DNA damage. In nonirradiated DNA-Fe(3+) films, there was little DNA damage observed (less than 10% of the total DNA loaded on the gel appeared damaged) for Fe(3+) ion up to 7 mM concentration. In irradiated DNA films without Fe(3+) ions, there was also very little DNA damage observed (less than 3% of the total DNA loaded on the gel appeared damaged). However, when DNA-Fe(3+) films, were irradiated with low-energy electrons, DNA damage was significantly increased compared to the sum of the damage caused both by either Fe(3+) ion or low-energy electrons irradiation alone. We proposed that both DEA and/or electron transfer processes might play a role in the enhanced DNA damage when DNA-Fe(3+) films were irradiated by low-energy electrons.     

Electron distribution function in a two-temperature plasma with cold ions

By modeling the dynamics of a large ensemble of particles, it is shown that slow electrons in a two-temperature plasma are in equilibrium with the electron component rather than with cold ions. The result of cooling by a cold ion component is that the number of the low-energy electrons only slightly exceeds that in the equilibrium Maxwellian distribution.     

Experimental and theoretical study of the near IR emission of xenon excited by a fast electron beam

Emission of xenon excited by a 120-keV electron beam at gas pressures of 100, 200, 500, and 760 Torr nm was studied experimentally and theoretically. More than 30 spectral lines were identified in the wavelength range of 750–1000 nm. A self-consistent kinetic model is developed to calculate the emission intensity of xenon atoms in the near IR range. The model includes balance equations for the number densities of electrons, ions and excimer molecules; equations for the populations of electron levels; and the Boltzmann equation for the low-energy part of the electron energy distribution function with a source of slow electrons. Excitation and ionization rates of xenon by the beam electrons and the energy spectrum of slow electrons are calculated by the Monte Carlo method. It is shown that, under these conditions, the main mechanism of xenon atom excitation is dissociative recombination of Xe₃ ⁺ ions.     

Estimated yield of double-strand breaks from internal exposure to tritium

Internal exposure to tritium may result in DNA lesions. Of those, DNA double-strand breaks (DSBs) are believed to be important. However, experimental and computational data of DSBs induction by tritium are very limited. In this study, microdosimetric characteristics of uniformly distributed tritium were determined in dimensions of critical significance in DNA DSBs. Those characteristics were used to identify other particles comparable to tritium in terms of microscopic energy deposition. The yield of DSBs could be strongly dependent on biological systems and cellular environments. After reviewing theoretically predicted and experimentally determined DSB yields available in the literature for low-energy electrons and high-energy protons of comparable microdosimetric characteristics to tritium in the dimensions relevant to DSBs, it is estimated that the average DSB yields of 2.7 × 10(-11), 0.93 × 10(-11), 2.4 × 10(-11) and 1.6 × 10(-11) DSBs Gy(-1) Da(-1) could be reasonable estimates for tritium in plasmid DNAs, yeast cells, Chinese hamster V79 cells and human fibroblasts, respectively. If a biological system is not specified, the DSB yield from tritium exposure can be estimated as (2.3 ± 0.7) × 10(-11) DSBs Gy(-1) Da(-1), which is a simple average over experimentally determined yields of DSBs for low-energy electrons in various biological systems without considerations of variations caused by different techniques used and obvious differences among different biological systems where the DSB yield was measured.     

Absolute and effective cross-sections for low-energy electron-scattering processes within condensed matter

Within the last two decades, a number of experimental techniques have been developed to measure mean free paths and absolute and effective cross-sections for various processes related to the interaction of low-energy electrons with condensed matter. In all of the experiments, a monochromatic electron beam impinges on a thin multilayer film composed of atoms and/or molecules condensed on a metal or semiconductor substrate held at cryogenic temperatures in an ultra-high-vacuum system. Depending on the apparatus, cross-sections are obtained from low-energy electron transmission (LEET), high-resolution electron energy loss (HREEL), x-ray photoelectron (XPS) spectroscopy, electron-stimulated desorption (ESD) of neutral and ions, or a combination of these techniques. Quasi-elastic and inelastic mean free paths have been extracted from LEET data. This method has also served to generate absolute cross-sections for electron trapping and fragment production from the dissociation of transient molecular anions. In amorphous ice, a complete set of absolute cross-sections for all inelastic losses by 1–20 eV electrons has been obtained from HREEL data. Effective cross-sections for neutral and ionic radical formation were generated by desorption and XPS experiments. These various methods are briefly described in this article, and the corresponding cross-sections in the range 0–20 eV summarized. Received: 10 September 1998 / Accepted: 22 October 1998     

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

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

Electron transport in xanthine oxidase. A model for other biological electron transport chains.

Part of the catalytic function of xanthine oxidase (XO) involves the transfer of two electrons from a substrate to a molybdenum ion on the enzyme followed by equilibration of these electrons among other electron resting sites on the enzyme. The electrons are removed from the enzyme at a flavin by oxygen to form hydrogen peroxide. This paper considers mechanisms which allow the electrons to equilibrate between the different resting sites on the enzyme. The mechanisms are chosen to be consistent with known properties of the enzyme (relative reduction potentials, electron transfer rates, and the estimated separation of these resting sites). Tunneling appears to be a good candidate to account for most of the electron transport. It is shown that the XO electron transport system is similar in many respects to sections of mitochondrial electron transport chains and can serve as a nice model for parts of these more complicated biological electron transport systems.     

Role of secondary electrons and metastable atoms in the electron-beam activation of argon-silane mixtures

The energy and spatial degradation of the primary beam electrons and the production of high-energy secondary electrons in ionizing collisions are analyzed by solving the Boltzmann integral equation for the electron distribution function. The effect of the primary and secondary electrons on the direct ionization of an Ar-SiH₄ mixture, the production of metastable argon atoms, and the dissociation of monosilane molecules is investigated over a wide range of the beam electron energies, argon pressures, and monosilane concentrations. The influence of metastable Ar* atoms on the dissociation of SiH₄ is studied by using the balance equation for metastable argon atoms and the equation for the ambipolar diffusion of ions and low-energy secondary (plasma) electrons in the beam plasma. It is shown that the main contribution to the activation of an Ar-SiH₄ mixture in an electron-beam plasma is provided by secondary electrons with energies higher than the excitation threshold for argon and the dissociation threshold for monosilane, whereas the contribution from metastable argon atoms, though potentially being comparable with that from secondary electrons, is less than in gas-discharge plasmas.     

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.     

The Use of ToF-SIMS for Analysis of Bioorganic Samples

The technique for the preparation of biological tissue sections developed for Electron Probe Microanalysis has been adapted for ToF-SIMS analysis of mouse GV stage oocytes. GV-oocyte sample preparation involves the following steps: plunge freezing, freeze drying, impregnation in an embedding medium, and section cutting. Molecule-specific images of the distribution of molecules in a single oocyte have been obtained with the described technique and ToF-SIMS analysis. The ToF-SIMS analysis data show that the efficient lateral image resolution is approximately 1 μm. Hence, ToF-SIMS enables us to study the distribution of chemical substances in relation to the morphological data obtained by scanning electron microscopy or conventional light microscopy.     

Electron and photon spectra for three gadolinium-based cancer therapy approaches

Some recent neutron capture therapy research has focused on using compounds containing the element gadolinium, which produces internal conversion and Auger cascade electrons. The low-energy, short-range Auger electrons are absorbed locally and increase cell killing dramatically as the gadolinium compounds are introduced into the cell nucleus and bind to the DNA. Detailed electron and photon spectra are needed for biophysical modeling and Monte Carlo calculations of damage to DNA. This paper presents calculated electron and photon spectra for three cases: thermal neutron absorption by (157)Gd, the beta-particle decay of (159)Gd, and the K-shell photoelectric event in gadolinium. The Monte Carlo sampling of atomic and nuclear transitions for each of the three cases was used to calculate a large number of representative decays. The sampled decays were used to determine average emissions and energy deposited in small spheres of tissue. The kinetic energy nuclear recoil from gamma-ray and electron emissions was calculated and found to be more than 10 eV for 26% of all (157)Gd neutron capture reactions.     

The Auger electron dosimetry of indium-111 in mammalian cells in vitro

Most of the radionuclides used in the formulation of radiopharmaceuticals emit Auger electrons when they undergo radioactive decay. The release of these low-energy electrons at extracellular sites produces little direct damage to intracellular structures. However, many radiopharmaceuticals, or their metabolites, can be transported into the cell where the Auger electrons have the potential to damage nearby intracellular macromolecules, including DNA. In this preliminary study, chromosome damage, expressed as 60Co equivalent doses, and the effects on cell division following treatment with intracellular and extracellular 111In were measured in Chinese hamster V79 cells. The chromosome aberration yield in cells irradiated by intracellular 111In indicated that damage was induced at a rate of 7.2 X 10(-4) Gy/decay for levels of activity up to 0.075 Bq/cell and 4.5 X 10(4) and 2.9 X 10(4) Gy/decay for intermediate (0.204 Bq/cell) and high (0.389 Bq/cell) levels, respectively. Extracellular 111In-chloride produced damage at a rate of about 6.1 X 10(-12) Gy/decay. As little as 4.4 mBq/cell (about 4.4 X 10(3) Bq/ml of culture) of intracellular 111In was able to affect cell division, whereas extracellular 111In at 1.150 MBq/ml of culture had little effect. These data indicate that the Medical Internal Radiation Dose and International Committee on Radiation Units methods for organ dosimetry may underestimate the potential of intracellular Auger electron emitters to produce radiation damage.     

Enhanced values of the RBE and H ratio for cytogenetic effects induced by secondary electrons from an X-irradiated gold gurface

The low-energy secondary electrons emerging from the entrance surface of an X-irradiated gold foil increase the dose to cells in contact with or at micrometer distances from this surface (Radiat. Res. 150, 92-100, 1998). We examined the effect of the spectrum of these low-energy electrons on the RBE for cytogenetic effects and showed that this RBE was increased. A monolayer of surface-attached human T lymphocytes was exposed to 60 kV X rays in the absence or presence of a gold foil positioned immediately behind the cell layer or separated from it by a Mylar foil 0.9 or 2 microm thick. The enhancement of dose in the cell nuclei caused by the photoelectrons and Auger electrons emerging from the entrance surface of the gold foil was measured by TSEE dosimetry. Dose enhancement factors of 55.7, 46.6 and 37.5 were obtained with 0, 0.9 and 2 microm of Mylar inserted between the gold surface and the cell layer. This large enhancement results from the photoelectric effect in the gold foil, as shown by the accompanying Monte Carlo calculations of the secondary electron spectra at the gold surface. Auger electrons from the gold foil generally were not able to penetrate into the cell nuclei except for that fraction of the cells that had a very thin (< 0.7 microm) layer of cytoplasm and membranes between gold surface and cell nucleus. The dose-yield curves for dicentric chromosomes plus centric rings and for acentric fragments obtained after exposures without or with the gold foil were linear-quadratic. The coefficient alpha, the slope of the linear yield component, was increased in the presence of the gold foil and showed RBE values ranging from 1.7 to 2.2 compared to exposures in absence of the gold foil. The ratio of the yield of interstitial deletions and dicentrics (H ratio) was significantly increased from about 0.17 in the absence of the gold foil to about 0.22 in the presence of the gold foil. The increases in the RBE and the H ratio are interpreted in microdosimetric terms: The preferred occurrence of electron track ends in the vicinity of the gold surface causes an increase in the dose-mean restricted linear energy transfer in cell nuclei exposed to the photoelectrons and Auger electrons.