A Monte Carlo code for the simulation of heavy-ion tracks in water

TILDA, a new Monte Carlo track structure code for ions in gaseous water that is valid for both high-LET (approximately 10(4) keV/microm) and low-LET ions, is presented. It is specially designed for a comparison of the patterns of energy deposited by a large range of ions. Low-LET ions are described in a perturbative frame, whereas heavy ions with a very high stopping power are treated using the Lindhard local density approximation and the Russek and Meli statistical method. Ionization cross sections singly differential with energy compare well with the experiment. As an illustration of the non-perturbative interaction of high-LET ions, a comparison between the ion tracks of light and heavy ions with the same specific energy is presented (1.4 MeV/nucleon helium and uranium ions). The mean energy for ejected electrons was found to be approximately four times larger for uranium than for helium, leading to a much larger track radius in the first case. For electrons, except for the excitation cross sections that are deduced from experimental fits, cross sections are derived analytically. For any orientation of the target molecule, the code calculates multiple differential cross sections as a function of the ejection and scattering angles and of the energy transfer. The corresponding singly differential and total ionization cross sections are in good agreement with experimental data. The angular distribution of secondary electrons is shown to depend strongly on the orientation of the water molecule.     

Comparison of microdosimetric simulations using PENELOPE and PITS for a 25 keV electron microbeam in water

The calculations presented compared the performances of two Monte Carlo codes used for the estimation of microdosimetric quantities: Positive Ion Track Structure code (PITS) and a main user code based on the PENetration and Energy Loss of Positrons and Electrons code (PENELOPE-2000). Event-by-event track structure codes like PITS are believed to be superior for microdosimetric applications, and they are written for this purpose. PITS tracks electrons in water down to 10 eV. PENELOPE is one of the few general-purpose codes that can simulate random electron-photon showers in any material for energies from 100 eV to 1 GeV. The model used in the comparison is a water cylinder with an internal scoring geometry made of spheres 1 microm in diameter where the scoring quantities are calculated. The source is a 25 keV electron pencil beam impinging normally on the sphere surface. This work shows only the lineal energy y and spectra graphical presentation as a function of y since for microdosimetry and biology applications, and for discussion of radiation quality in general, these results are more appropriate. The computed PENELOPE results are in agreement with those obtained with the PITS code and published previously in this journal. This paper demonstrates PENELOPE's usefulness at low energies and for small geometries. What is still needed are experimental results to confirm these analyses.     

Energy deposition spectra ofΠ − calculated from pion nucleus interaction data

Summary Distributions of absorbed dose in linear energy transfer (LET) and in lineal energy (y) are calculated for beams of negatively charged pions in a water phantom. The calculation is based on a comprehensive set of experimental data. The production of-ray electrons by fast particles is taken into account semiempirically. The results are compared with experimentally obtained spectra of ionization yields. The equivalence of data derived from pion nucleus interaction and taken from microdosimetry is clearly revealed. The distribution of absorbed dose is given in a sequence of contributions from the various secondary particles, i.e., the socalled star particles emitted following a nuclear capture process or the recoil nuclei from pion scatterings. This unique feature of calculated spectra will be useful for a characterization of the beam quality in view of the existing dependence of biological effects on track structure properties.     

Ionization and charge-transfer: basic data for track structure calculations

It is widely accepted that an understanding of the detailed structure of charged particle tracks is essential for interpreting the mechanistic consequences of energy deposition by high linear energy transfer (LET) radiation. The spatial relationship of events along the path of a charged particle, including excitation, ionization, and charge-transfer, govern subsequent chemical, biochemical, and biological reactions that can lead to adverse biologic effects. The determination of spatial patterns of ionization and excitation relies on a broad range of cross-section data relating the interactions of charged particles to the molecular constituents of the absorbing medium. It is important that these data be absolute in magnitude, comprehensive in scope, and reliable if accurate assessment of track structure parameters is to be achieved. Great strides have been made in the development of this database, understanding the underlying theory, and developing analytic models, particularly for interactions involving electrons and protons with atoms and molecules. The database is less comprehensive for interactions involving heavier charged particles, especially those that carry bound electrons, and for interactions in condensed phase media. Although there has been considerable progress in understanding the physical mechanisms for interactions involving fast heavy ions and atomic targets during the past few years, we still lack sufficient understanding to confidently predict cross-sections for these ions with biologically relevant material. In addition, little is known of the interaction cross-sections for heavy charged particles as they near the end of their track, i.e., for low velocity ions where collision theory is less well developed and where the particle's net charge fluctuates owing to electron capture and loss processes. This presentation focuses on the current status of ionization and charge-transfer data. Compilations, reviews, Internet sources, theoretical models, and recent data applicable to track structure calculations are discussed.     

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.     

Microdosimetric structure of heavy ion tracks in tissue

Summary Energy dissipation in tracks of high energy heavy ions in tissue shows a lateral spread of several to many microns depending on the energy of the primary particle. Complete dosimetric characterization, therefore, requires in addition to the Linear Energy Transfer (LET) information on the radial energy distribution. The theory of track structure distinguishes two regions: core and penumbra. The core is a narrow central zone with a radius in tissue far below 1 micron where energy deposition occurs mainly in processes of excitation and electron plasma oscillation. According to the Equipartition Principle, half of the total energy dissipation accrues in this manner. The penumbra is a peripheral zone enveloping the core where energy deposition occurs mainly in ionization events by energetic secondary electrons released by the primary particle in the center of the core traveling at rather high speed thus spreading laterally. The extension of the penumbra depends in a complex manner on the maximum transferable energy to electrons which in turn depends on the speed of the primary particle. Local energy density in the penumbra decreases with the square of increasing radius. It therefore amounts only to a very small fraction of the core density already a few microns away from the center. In general terms, track structure can be described as exhibiting a core of enormous energy density with lateral dimensions remaining entirely on the submicroscopic level surrounded by a penumbra where energy density drops precipitously to very small levels. The relationships are illustrated with micrographs of different sections of a heavy particle track in nuclear emulsion and their counterpart graphical plots.     

DNA complex lesions induced by protons and ⋅-particles: track structure characteristics determining linear energy transfer and particle type dependence

The yield of DNA double-strand breaks (dsb) and DNA complex lesions induced by protons and α-particles of various energies was simulated using a Monte Carlo track structure code (MOCA15) and a simple model of the DNA molecule. DNA breaks of different complexity were analysed. The linear energy transfer (LET) and particle-type dependence of lesions of higher complexity seems to confirm the importance of clustered damage in DNA as a relevant step leading to biological endpoints such as cell inactivation. The detailed structure of proton and α-particle tracks was analysed to identify the main characteristics possibly responsible for such a dependence. The role of the primary ion and of its secondary electrons in inducing dsb and complex lesions is described, showing that the relative contribution of secondary electron tracks alone in inducing clustered lesions is almost negligible at high LET, but tends to dominate below ≈10 keV/μm. This is consistent with the observed similar effectiveness of low-LET fast particle radiation and sparsely ionizing radiation such as x-rays. The dependence on LET and particle type is mainly due to energy deposition events of the primary ion together with short range electrons surrounding the ion track; the yield of complex lesions due to secondary electron tracks alone is substantially LET independent. The radial distributions of the energy contributing to the induction of complex lesions were analyzed and compared with the radial distributions of energy deposition of the full tracks. The results suggest that the stochastic behaviour (i.e. cluster properties) of the energy deposition pattern within a radius of a few nanometers around the ion track plays a relevant role in determining the biological radiation effectiveness. Received: 20 December 1996 / Accepted in revised form: 5 March 1997     

Modeling of chromosome aberration response functions induced by particle beams with different LET

This study is based on our already published experimental data (Kowalska et al. in Radiat Environ Biophys 58:99–108, 2019) and is devoted to modeling of chromosome aberrations in human lymphocytes induced by 22.1 MeV/u 11B ions, 199 MeV/u 12C ions, 150 MeV and spread-out Bragg peak (SOBP) proton beams as well as by 60Co γ rays. The curvature of the dose–effect curves determined by the linear-quadratic model was considered in the frame of a simple analytical approach taking into account increase in the irradiation dose due to overlapping interaction regions of ion tracks. The model enabled to estimate effective interaction radius which could be compared with the physical expectations. The results were also compared to the Amorphous Track Structure Model of Katz which allows to get some additional information about the ion track structure. The analysis showed that the curvature of the experimental dose–effect curves mainly results from highly efficient repair processes of the DNA damage.     

Analysis of low-energy electron track structure in liquid water

An implementation is presented of interaction cross sections for non-relativistic electron track structure simulations. The model, incorporating liquid-phase cross sections for inelastic interactions and improved algorithms for elastic scattering, is applied to Monte Carlo simulation of the track structure of low-energy electrons. Benchmark distributions and mean values are presented for several measures of penetration distances that characterize the general physical extent of the track structure. The results indicate that, except for the last approximately 500 eV of energy loss, electron tracks have a quasi-linear character; this suggests that a major part of an electron track may be reasonably described by a lineal-energy-like characterization.     

Methodological Issues in Modern Track Analysis

Track analysis is the core of panbiogeographic analysis. In this work, we reflect on the formalization of track analysis, its methodological issues, and interpretations by using new software developments and from a contemporary evolutionary biogeographical viewpoint. From a geometric perspective, we analyze the meaning of a minimal spanning tree, considering that Prim’s algorithm is the most commonly used to draw individual tracks. We then show the existing methodologies (graphs, PAE, combined method, AE) and software packages (Trazos2004, Croizat, Martitracks, fossil) used to perform track analysis. Finally, we illustrate a track analysis using Nearctic mammals as an example. Based on our review, connectivity matrix analysis may be the best way to associate individual tracks into generalized tracks because it compares the minimal spanning tree topologies. However, it is the most demanding of all methods, since it requires a high spatial congruence among species, and therefore more algorithmic development.     

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.     

Mathematical simulation of proton tracks in water vapor and their microdosimetric analysis

Summary The spatial pattern of primary physical events was calculated for protons in water vapor by means of a Monte Carlo program. Two different cross section data sets were used to cover the proton energy range from 0.2 to 15 MeV. From the spatial pattern of primary energy deposition, proximity functions were derived and from these the dose mean lineal energy was calculated. The contributions of different track components to for spherical target volumes of 1–100 nm were analysed. The results are compared with the LET approximation and with analytical calculations of based on expectation values of the radial energy deposition around the proton path (radial dose profiles). Finally the associated volume of proton tracks was calculated using the so called linear approximation, and energy deposition distributions were derived. These were compared with distributions calculated by means of restricted-LET.Dedicated to Prof. W. Jacobi on the occasion of his 60th birthday     

The probabilities of one- and multi-track events for modeling radiation-induced cell kill

In view of the clinical importance of hypofractionated radiotherapy, track models which are based on multi-hit events are currently reinvestigated. These models are often criticized, because it is believed that the probability of multi-track hits is negligible. In this work, the probabilities for one- and multi-track events are determined for different biological targets. The obtained probabilities can be used with nano-dosimetric cluster size distributions to obtain the parameters of track models. We quantitatively determined the probabilities for one- and multi-track events for 100, 500 and 1000 keV electrons, respectively. It is assumed that the single tracks are statistically independent and follow a Poisson distribution. Three different biological targets were investigated: (1) a DNA strand (2 nm scale); (2) two adjacent chromatin fibers (60 nm); and (3) fiber loops (300 nm). It was shown that the probabilities for one- and multi-track events are increasing with energy, size of the sensitive target structure, and dose. For a 2 × 2 × 2 nm³ target, one-track events are around 10,000 times more frequent than multi-track events. If the size of the sensitive structure is increased to 100–300 nm, the probabilities for one- and multi-track events are of the same order of magnitude. It was shown that target theories can play a role for describing radiation-induced cell death if the targets are of the size of two adjacent chromatin fibers or fiber loops. The obtained probabilities can be used together with the nano-dosimetric cluster size distributions to determine model parameters for target theories.     

Kinetic partitioning during folding of the p53 DNA binding domain

The DNA-binding domain (DBD) of wild-type p53 loses DNA binding activity spontaneously at 37 degrees C in vitro, despite being thermodynamically stable at this temperature. We test the hypothesis that this property is due to kinetic misfolding of DBD. Interrupted folding experiments and chevron analysis show that native molecules are formed via four tracks (a-d) under strongly native conditions. Folding half-lives of tracks a-d are 7.8 seconds, 50 seconds, 5.3 minutes and more than five hours, respectively, in 0.3M urea (10 degrees C). Approximately equal fractions of molecules fold through each track in zero denaturant, but above 2.0M urea approximately 90% fold via track c. A kinetic mechanism consisting of two parallel folding channels (fast and slow) is proposed. Each channel populates an on-pathway intermediate that can misfold to form an aggregation-prone, dead-end species. Track a represents direct folding through the fast channel. Track b proceeds through the fast channel but via the off-pathway state. Track c corresponds to folding via the slow channel, primarily through the off-pathway state. Track d proceeds by way of an even slower, uncharacterized route. We postulate that activity loss is caused by partitioning to the slower tracks, and that structural unfolding limits this process. In support of this view, tumorigenic hot-spot mutants G245S, R249S and R282Q accelerate unfolding rates but have no affect on folding kinetics. We suggest that these and other destabilizing mutants facilitate loss of p53 function by causing DBD to cycle unusually rapidly between folded and unfolded states. A significant fraction of DBD molecules become effectively trapped in a non-functional state with each unfolding-folding cycle.     

DNA strand breaks induced by low-energy heavy ions

The DNA unwinding method was used to estimate DNA breakage in Chinese hamster cells exposed to heavy ions with LET in the range of 750-5000 keV/micron. Comparison of the primary induced unwinding rate per dose unit for ions with various track diameters but similar LET showed a pronounced influence on the track diameter. Low-energy ions, producing thin tracks with diameters (penumbra) in the submicrometer region, were almost two orders of magnitude less efficient than more energetic ions producing tracks with diameters of several micrometers and about three orders of magnitude less efficient than X-rays. For the thin tracks, clustering of breaks was indicated by comparison of the DNA unwinding rates in two different alkaline solutions. The results indicate that the unwinding rate cannot be used as a good measurement for DNA breaks in this case. The residual unwinding remaining after 4 h of repair at 37 degrees C correlated well with the ability of the various ions to produce cell-killing.     

Basic aspects of photon transport through matter with respect to track structure formation

After a short summary of the most important physical aspects of photon interaction with matter and of the main elements of photon transport simulation, some basic features of photon tracks in liquid water are discussed. These include the statistical distribution of the number of photon interactions caused during the complete photon slow-down, the corresponding mean value, the distance distribution of photon interactions, and the spectral distribution of secondary electrons or, which is the same, the spectral distribution of the start energy of secondary electron tracks. The latter distribution can easily be interpreted in terms of the track entity concept of Mozumder and Magee, which, therefore, proves to be the most natural concept of track structure analysis in the case of photon irradiation. Received: 20 September 1998 / Accepted in revised form: 30 April 1999     

The relative biological effectiveness of 670 MeV/A neon as a function of depth in water for a tissue model

Linear energy transfer (LET infinity) spectra of identified charge fragments and primaries, produced by nuclear interactions of 670 MeV/A neon in water, were measured along the unmodulated Bragg curve of the neon beam. The relative biological effectiveness (RBE) values for spermatogonial cell killing, as reported on the basis of weight loss assay of mouse testes irradiated with beams of approximately constant single LET infinity, were summed over the particle LET infinity spectra to obtain an effective RBE for each charged-particle species, as a function of water absorber thickness. The resultant values of effective RBE were combined to obtain an effective RBE for the mixed radiation field. The RBE calculated in this way was compared with experimental RBEs obtained for spermatogonial cell killing in the mixed radiation field produced by neon ions traversing a thick water absorber. Discrepancies of 10-40% were observed between the calculated RBE and the RBE measured in the mixed radiation field. Part of this discrepancy can be attributed to undetected low-Z fragments, whose contribution is not included in the calculation, leading to an overestimated value for the calculated RBE. On the other hand, calculated values 10% greater than the measured RBE are explained as track structure effects due to the higher radial ionization density near neon tracks relative to the ionization density near the silicon tracks used to fit the RBE vs LET infinity data.