Comparisons of calculations with PARTRAC and NOREC: transport of electrons in liquid water.

Monte Carlo computer models that simulate the detailed, event-by-event transport of electrons in liquid water are valuable for the interpretation and understanding of findings in radiation chemistry and radiation biology. Because of the paucity of experimental data, such efforts must rely on theoretical principles and considerable judgment in their development. Experimental verification of numerical input is possible to only a limited extent. Indirect support for model validity can be gained from a comparison of details between two independently developed computer codes as well as the observable results calculated with them. In this study, we compare the transport properties of electrons in liquid water using two such models, PARTRAC and NOREC. Both use interaction cross sections based on plane-wave Born approximations and a numerical parameterization of the complex dielectric response function for the liquid. The models are described and compared, and their similarities and differences are highlighted. Recent developments in the field are discussed and taken into account. The calculated stopping powers, W values, and slab penetration characteristics are in good agreement with one another and with other independent sources.

Calculation of radiation-induced DNA damage from photons and tritium beta-particles. Part I: Model formulation and basic results.

Radiation-induced damage in nucleosomal DNA was modelled by Monte Carlo means. An atomistic representation of DNA with a first hydration shell was used. DNA single- and double-strand break (SSB and DSB) yields were calculated for 137Cs photons, x-rays and tritium beta-particles. Monte Carlo-generated electron tracks for liquid water were used to model energy deposition. Chemical evolution of a track and interactions between species and DNA following water radiolysis were modelled in an encounter-controlled manner. The effects of varying the scavenging capacity of the environment, the extent of DNA protection by histones and the setting of a threshold for direct energy depositions on DNA break yields were all systematically studied. DSB complexity was assessed in terms of DNA breaks and base damage accompanying a DSB. Model parameters were adjusted to make predictions consistent with experimental data on DSB yields and yield modification by a variety of factors including changing DNA conformation and incorporation of scavengers. An embedded model of nucleosomal DNA by histones was required to explain experimentally observed modification of DSB yield by removal of bound histones. Complex DSB, defined as DSB accompanied by an additional strand breakage, exhibited high association with base damage. It is shown that hydroxyl radical interactions with bases are a major contributor to DSB complexity. On average there were 1.15 and 2.69 OH-base interactions accompanying simple and complex DSB, respectively for 137Cs. Over 80% of complex DSB had at least one OH-base interaction associated with a DNA break.

Calculation of radiation-induced DNA damage from photons and tritium beta-particles. Part II: Tritium RBE and damage complexity.

Yields of DNA single- and double-strand breaks (SSB and DSB) in nucleosomal DNA were calculated for 137Cs, 70 keV photons and tritium beta-particles by Monte Carlo means. Monte Carlo-generated electron tracks for liquid water were used to model energy deposition. Chemical evolution of a track and interactions between species and DNA following water radiolysis were modelled in an encounter-controlled manner. The calculated relative biological effectiveness (RBE) for DSB production for tritium against 137Cs was 1.2 for the total DSB yield. Tritium beta-particles were slightly more efficient compared to 137Cs in producing complex DSB, defined as DSB accompanied by additional strand breaks. The RBE for complex DSB formation was 1.3. Most complex DSB exhibited associated base damage; the extent of the base damage was similar for all the radiation types considered. Correlated DSB conforming to nucleosome periodicity were observed. However, their frequency was low, of the order of 2% of total DSB. For all the DNA damage endpoints considered and their response to variation of the scavenging environment or DNA conformation no difference was observed between 70 keV photons and tritium beta-particles.

Investigation of a Monte Carlo model for chemical reactions.

Monte Carlo computer simulations are in use at a number of laboratories for calculating time-dependent yields, which can be compared with experiments in the radiolysis of water. We report here on calculations to investigate the validity and consistency of the procedures used for simulating chemical reactions in our code, RADLYS. Model calculations were performed of the rate constants themselves. The rates thus determined showed an expected rapid decline over the first few hundred ps and a very gradual decline thereafter out to the termination of the calculations at 4.5 ns. Results are reported for different initial concentrations and numbers of reactive species. Generally, the calculated rate constants are smallest when the initial concentrations of the reactants are largest. It is found that inhomogeneities that quickly develop in the initial random spatial distribution of reactants persist in time as a result of subsequent chemical reactions, and thus conditions may poorly approximate those assumed from diffusion theory. We also investigated the reaction of a single species of one type placed among a large number of randomly distributed species of another type with which it could react. The distribution of survival times of the single species was calculated by using three different combinations of the diffusion constants for the two species, as is sometimes discussed in diffusion theory. The three methods gave virtually identical results.

Product yields from irradiated glycylglycine in oxygen-free solutions: Monte Carlo simulations and comparison with experiments.

The radiation chemistry of photon-irradiated aqueous solutions of biological molecules may be considered under four distinct time regimes: physical transport (< or = 10(-15) s); prechemical conversion of H2O+, H2O*, and subexcitation electrons into free radicals and molecular products (10(-15) s to 10(-12) s); chemical reactions within individual electron tracks (10(-12) s to 10(-6) s); and chemical reactions within overlapping tracks (>10(-6) s). We have previously reported of the use of the Monte Carlo radiation transport/chemistry codes OREC and RADLYS to model the radiolysis of glycylglycine in oxygen-free solution to a time of 1 micros. These simulations successfully predicted the yields of free ammonia, an end product created solely in the reaction of the hydrated electron with the solute within individual tracks. Other measurable products are only partially created during intratrack reactions, and thus one must additionally consider the late, intertrack chemistry of this system. In this paper, we extend our simulations of glycylglycine radiolysis to model for the first time the events which occur during this late chemistry stage. The model considers the product rates of the reactants in bulk solution by using previously available microsecond intratrack yields given by single-track OREC/RADLYS simulations and an x-ray dose rate of 2.80 Gy min(-1) as used in a companion experimental program. These rates are then applied in a series of coupled, differential rate equations that describe the solution chemistry of glycylglycine radiolysis. Product yields are reported as a function of time over a total irradiation period of 10(4) s. Excellent overall agreement is seen between the theoretical predictions and measurements of five radiolysis end products: free ammonia, acetylglycine, diaminosuccinic acid, aspartic acid, and succinic acid. The model also gives the explicit contributions of intratrack and intertrack reactions to the various end products. For example, the model predicts that approximately 56% and 93% of succinic acid and aspartic acid, respectively, are produced during intertrack reactions at a solute concentration of 0.05 M; these contributions drop to 0.07% and 11%, respectively, at 1.2 M.

The cellular environment in computer simulations of radiation-induced damage to DNA.

Radiation-induced DNA single- and double-strand breaks were modeled for 660 keV photon radiation and scavenger capacity mimicking the cellular environment. Atomistic representation of DNA in B form with a first hydration shell was utilized to model direct and indirect damage. Monte Carlo generated electron tracks were used to model energy deposition in matter and to derive initial spatial distributions of species which appear in the medium following radiolysis. Diffusion of species was followed with time, and their reactions with DNA and each other were modeled in an encounter-controlled manner. Three methods to account for hydroxyl radical diffusion in a cellular environment were tested: assumed exponential survival, time-limited modeling and modeling of reactions between hydroxyl radicals and scavengers in an encounter-controlled manner. Although the method based on modeling scavenging in an encounter-controlled manner is more precise, it requires substantially more computer resources than either the exponential or time-limiting method. Scavenger concentrations of 0.5 and 0.15 M were considered using exponential and encounter-controlled methods with reaction rate set at 3x10(9) dm3 mol(-1) s(-1). Diffusion length and strand break yields, predicted by these two methods for the same scavenger molarity, were different by 20%-30%. The method based on limiting time of chemistry follow-up to 10(-9) s leads to DNA damage and radical diffusion estimates similar to 0.5 M scavenger concentration in the other two methods. The difference observed in predictions made by the methods considered could be tolerated in computer simulations of DNA damage.

Modelling DNA damage induced by different energy photons and tritium beta-particles.

PURPOSE: To model the production of single- and double-strand breaks (ssb and dsb) in DNA by ionizing radiations. To compare the predicted effectiveness of different energy photon radiations and tritium beta-particles. MATERIALS AND METHODS: Modelling is carried out by Monte Carlo and includes consideration of direct energy depositions in DNA molecules, the production of species, their diffusion and interactions with each other and DNA. Computer-generated electron tracks in liquid water are used to model energy deposition and to derive the initial positions of chemical species. Atomistic representation of the DNA in B form with a first hydration shell is used. Photon radiations in the energy range 70keV-1MeV and tritium beta-particles are considered. RESULTS: A tentative increase for dsb yield has been predicted for 70 keV photons and tritium compared with 137Cs. This increase is more pronounced for complex dsb. Double-strand breaks are much more prone compared with ssb to combine with additional strand breaks and base damage, which contributes to break complexity. At least half of DNA breaks are hydroxyl radical mediated. CONCLUSIONS: The developed model makes predictions compatible with features of available experimental data. Break complexity has to be addressed in biophysical modelling when the relative effectiveness of radiations in DNA damage is studied. Obtained data strongly argue against the dominance of direct radiation action in DNA damage in the cellular environment predicted by some theoretical studies.

Monte Carlo simulation of diffusion and reaction in water radiolysis--a study of reactant 'jump through' and jump distances.

In Monte Carlo simulations of water radiolysis, the diffusion of reactants can be approximated by "jumping" all species randomly, to represent the passage of a short period of time, and then checking their separations. If, at the end of a jump, two reactant species are within a distance equal to the reaction radius for the pair, they are allowed to react in the model. In principle, the possibility exists that two reactants could "jump through" one another and end up with a separation larger than the reaction radius with no reaction being scored. Ignoring this possibility would thus reduce the rate of reaction below that intended by such a model. By making the jump times and jump distances shorter, any error introduced by 'jump through' is made smaller. This paper reports numerical results of a systematic study of 'jump through' in Monte Carlo simulations of water radiolysis. With a nominal jump time of 3 ps, it is found that more than 40% of the reactions of the hydrated electron with itself and of the H atom with itself occur when reactions during 'jump through' are allowed. For all other reactions, for which the effect is smaller, the contributions of 'jump through' lie in the range 1%-16% of the total. Corrections to computed rate constants for two reactions are evaluated for jump times between 0.1 and 30 ps. It is concluded that jump-through corrections are desirable in such models for jump times that exceed about 1 ps or even less. In a separate study, we find that giving all species of a given type the same size jump in a random direction yields results that are indistinguishable from those when the jump sizes are selected from a Gaussian distribution. In this comparison, the constant jump size is taken to be the root-mean-square jump size from the Gaussian distribution.

Effects of elastic and inelastic scattering in giving electrons tortuous paths in matter.

Heavy charged particles travel in essentially straight lines in matter, while electrons travel in tortuous paths. Frequent multiple elastic Coulomb scattering by atomic nuclei is often cited as the reason for this electron behavior. Heavy charged particles also undergo multiple Coulomb scattering. However, because they are massive, significant deflections occur only in rare, close encounters with nuclei. In contrast to heavy particles, the inelastic interaction of an electron with an atomic electron represents a collision with a particle of equal mass. In principle, therefore, repeated inelastic scattering of an electron can also produce large-angle deflections and thus contribute to the tortuous nature of an electron's track. To investigate the relative importance of elastic and inelastic scattering on determining the appearance of electron tracks, detailed Monte Carlo transport computations have been carried out for monoenergetic pencil beams of electrons normally incident on a water slab with initial energies from 1 keV to 1 MeV. The calculations have been performed with deflections due to (1) inelastic scattering only, (2) elastic scattering only, and (3) both types of scattering. Results are presented to show the spreading of the pencil beams with depth in the slab, the transmission through slabs of different thicknesses, and back-scattering from the slab. The results show that elastic nuclear scattering is indeed the principal physical process that causes electron paths to be tortuous; however, the smaller effect of inelastic electronic scattering is far from negligible.

Radiotoxicity of platinum-195m-labeled trans-platinum (II) in mammalian cells.

The chemotoxicity and radiotoxicity of trans-dichlorodiammineplatinum (II) labeled with 195mPt (trans-195mPt) are investigated to ascertain the potential of radioplatinum coordination complexes as antineoplastic agents. Platinum-195m, with a half-life of about 4 days, is a prolific emitter of low-energy Auger electrons because of the high probability of internal conversion in its isomeric transitions. The kinetics of cellular uptake and retention after incubation and the radiotoxicity of this Auger electron emitter in the form of trans-195mPt is investigated using cells of the Chinese hamster V79 cell line. The cellular uptake of 195mPt reaches a plateau in about 3 to 5 h of incubation and varies nonlinearly with the extracellular concentration of radioactivity. The radioactivity is eliminated from the cells after incubation with an effective half-life of 24 h. Cell survival data, when corrected for the chemical toxicity of nonradiolabeled trans-platinum, give a cell survival curve typical for radiations with high linear energy transfer. At 37% survival, the mean lethal cellular uptake is about 1.0 mBq/cell. Dosimetric considerations, based on subcellular distribution of the radionuclide, yield a value of 4.8 for the relative biological effectiveness when compared with 250 kVp X rays. Theoretical Monte Carlo track-structure calculations indicate that the density of radical species produced in liquid water in the immediate vicinity of a 195mPt decay site is substantially greater than the density of species along the track of a 5.3 MeV alpha particle. This explains qualitatively the efficacy of 195mPt in causing high-LET radiation type biological effects. The extreme radiotoxicity of intranuclearly localized 195mPt, in conjunction with the proclivity of platinum chemotherapy agents to bind to DNA in the cell nucleus, suggests that the combination of chemical effects and the effects of Auger electrons that can be obtained with radioplatinum coordination complexes may have potential in the treatment of cancer.

Monte Carlo track-structure calculations for aqueous solutions containing biomolecules.

Detailed Monte Carlo calculations provide a powerful tool for understanding mechanisms of radiation damage to biological molecules irradiated in aqueous solution. This paper describes the computer codes, OREC and RADLYS, which have been developed for this purpose over a number of years. Some results are given for calculations of the irradiation of pure water. Comparisons are presented between computations for liquid water and water vapor. Detailed calculations of the chemical yields of several products from X-irradiated, oxygen-free glycylglycine solutions have been performed as a function of solute concentration. Excellent agreement is obtained between calculated and measured yields. The Monte Carlo analysis provides a complete mechanistic picture of pathways to observed radiolytic products. This approach, successful with glycylglycine, will be extended to study the irradiation of oligonucleotides in aqueous solution.

Effects of the tissue-air interface in calculations of beta-particle skin dose at a depth of 70 microns.

The effects that the tissue-air interface has on the basal-layer dose at a depth of 70 microns from beta emitters on the skin surface are studied using Monte Carlo calculations. The dose is decreased at small lateral distances from a point source but is increased at large distances.

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.

Radiation damage to a biomolecule: new physical model successfully traces molecular events.

For the first time, a complete computer simulation of physical and chemical reactions at the molecular level has been used to calculate the yield of a chemical species resulting from irradiation of a biological molecule in aqueous solution. Specifically, when a solution of glycylglycine is irradiated anaerobically, an ammonia molecule is released by the action of a hydrated electron, which is produced by irradiation of water. In the computations, Monte Carlo techniques are used to simulate the statistical progression of molecular events as they are assumed to occur. These include the initial physical ionization and excitation of water molecules along a particle track in the liquid; the subsequent formation of free radicals and other species: and the random diffusion and chemical reactions of the species with each other, the solvent, and solute molecules. We have calculated and measured the yield of ammonia from irradiation of glycylglycine with 250 kVp x-rays as a function of glycylglycine concentration between 0.01 and 1.2 M. Excellent agreement is obtained between predicted and measured results. The literal simulation of events, combined with specific experimental measurements, offers a powerful new tool for studying mechanisms of radiation action and damage at the molecular level.

Monte Carlo calculations of free ammonia production in deoxygenated solutions of glycylglycine irradiated by X rays and 60Co gamma rays.

Detailed-history Monte Carlo computer codes were used to simulate the formation, diffusion, and chemical reaction of free-radical species within deoxygenated aqueous solutions of glycylglycine irradiated by 250-kVp X rays and by 60Co gamma rays. In one reaction, hydrated electrons react with the glycylglycine solute to produce unbound, or free, ammonia. This reaction is complete by 10(-6) s within individual electron tracks for glycylglycine concentrations greater than or equal to 0.025 M. For solute concentrations from 0.025 to 1.2 M, calculated G values of free ammonia are in excellent agreement with measured values. In addition, the computer model predicts a statistically significant difference between the G value of free ammonia produced under X irradiation and that produced under 60Co gamma irradiation.

Calculations for beta dosimetry using Monte Carlo code (OREC) for electron transport in water.

A Monte Carlo computer code (OREC) for calculating the detailed transport and energy deposition for primary electrons and all of their secondaries in liquid water has been investigated for use in beta-ray dosimetry. Some modifications have been made in the original code for its application to tissue and tissue-equivalent materials. The code gives reasonably good agreement with beta spectral data and depth-dose curves measured in tissue-equivalent plastics for several calibrated beta sources. The calculations permit a direct evaluation of the skin dose equivalent, i.e., the dose equivalent, Hs (0.07), at a depth of 0.070 mm in tissue. Calculations are presented for monoenergetic electrons, showing the distributions in the maximum depth of penetration and in the total pathlength traveled. Direct comparisons are made between depth-dose curves calculated for 99Tc and 147Pm plaque sources and measurements made with extrapolation chambers. The energy spectrum of beta particles emerging from a thick 99Tc plaque source also is calculated, and the angular distribution is found to be almost independent of the energy. The pulse-height spectrum in a tissue-equivalent plastic scintillator calculated for this source shows good agreement with the measured spectrum. The calculations also provide the Hs(0.07) dose equivalent for the 99Tc source, which is found to be consistent with that inferred independently from the spectral measurements. A calculated curve for converting spectrometer measurements to Hs(0.07) dose equivalent is in good agreement with a semi-empirical curve that was developed independently. It appears that calculations made with the electron transport code for water can provide useful information for beta dosimetry.

A method of obtaining neutron dose and dose equivalent from digital measurements and analysis of recoil-particle tracks.

The feasibility of a digital approach to neutron dosimetry has been investigated. Such an approach uses an ionization detector capable of measuring the numbers of electrons produced within various subvolumes of a chamber gas along a charged-particle track. In addition, a computer algorithm is used to infer absorbed dose, LET, and dose equivalent given this digital track-structure information for each event. This paper describes one detector design capable of providing digital track-structure information and discusses examples of proton and C-ion tracks calculated from a Monte Carlo charged-particle transport code. The associated computer algorithm is presented next with its verification accomplished by running a variety of recoil particles through a simulated detector volume and comparing the resulting average energy deposition and dose equivalent to those unfolded by the algorithm.

A Monte Carlo primer for health physicists.

The basic ideas and principles of Monte Carlo calculations are presented in the form of a "primer" for health physicists. A simple integral with a known answer is evaluated by two different Monte Carlo approaches. Random numbers, which underlie Monte Carlo work, are discussed, and a sample table of random numbers generated by a hand calculator is presented. Monte Carlo calculations of dose and linear energy transfer (LET) from 100-keV neutrons incident on a tissue slab are discussed. The random-number table is used in a hand calculation of the initial sequence of events for a 100-keV neutron entering the slab. Some pitfalls in Monte Carlo work are described. While this primer addresses mainly the "bare bones" of Monte Carlo, a final section briefly describes some of the more sophisticated techniques used in practice to reduce variance and computing time.

Calculation of heavy-ion tracks in liquid water.

Detailed Monte Carlo calculations are presented of proton and alpha-particle tracks in liquid water. The computations treat the interactions of the primary particle and all secondary electrons on a statistical, event-by-event basis to simulate the initial physical changes that accompany the passage of an ion through water. Our methods for obtaining the cross sections needed for such calculations are described. Inelastic scattering probabilities (inverse mean free paths) are derived from a complex dielectric response function constructed for liquid water, based on experimental and theoretical data. Examples of partial cross sections for ionization and excitation by protons are shown. The computation of electron transport and energy loss includes exchange, elastic scattering, and a scheme for the delocalization of energy shared collectively by a large number of electrons in the condensed medium. Several examples of calculated proton and alpha-particle tracks are presented and discussed. The meaning and significance of the concept of a track core are briefly addressed in the light of this work. The present paper treats only the initial, physical changes produced by radiation in water (in approximately 10(-15) s in local regions of a track). The work described here is used in calculations that we have reported in other publications on the later chemical development of charged-particle tracks.

Effects of a bolus and inhomogeneities on pion stopping distributions.

In radiotherapy treatments with negative pion beams, an external bolus is often used to compensate for inhomogeneities within the body in order that the pions will have the proper stopping distribution within a tumor. However, angular beam divergence, multiple Coulomb scattering, and elastic and inelastic nuclear scattering limit the degree to which the pion stopping region can be controlled. We have used the Monte Carlo computer code PION-I to calculate pion stopping distributions for several idealized cases in order to show explicitly the effects of a number of factors on stopping distributions. Calculations have also been made for the same geometrical configurations used in measurements of pion stopping distributions in the biomedical beam at the Los Alamos Meson Physics Facility, and the calculated results are compared with experiment.