Track Structure Model Research Articles

A simple track structure model of ion beam radiotherapy

A simple radiotherapy ion beam calculation based on the cellular track structure model, using in vitro cell survival parameters fitted from recent experimental data, is presented. The calculation represents a single-fraction ion exposure (roughly corresponding to a 2 Gy fraction of megavolt X rays) and exploits concepts used in clinical radiotherapy, such as entrance, or 'skin' ion dose. The depth distribution of cells surviving their irradiation by a beam of 385 MeV amu(-1) carbon ions is calculated over the range of the stopping ions, as a sequence of track-segments, in the continuous slowing-down approximation. An interpretation of the 'clinical relative biological effectiveness' concept is suggested.

On the relationship between dose-, energy- and LET-response of thermoluminescent detectors

Measurements of the response of thermoluminescent (TL) detectors after gamma ray doses high enough to observe signal saturation provide input to microdosimetric models which relate this gamma-ray response with the energy response after low doses of photons (gamma rays and low-energy X rays) and after high-LET irradiation. To measure their gamma ray response up to saturation, LiF:Mg,Ti (MTS-7 and MTT), LiF:Mg,Cu,P (MCP-7), CaSO4:Dy (KCD) and Al2O3:C detectors were irradiated with 60Co gamma rays over the range 1-5000 Gy. The X-ray photon energy response and TL efficiency (relative to gamma rays) after doses of beta rays and alpha particles, were also measured, for CaSO4:Dy and for Al2O3:C. Microdosimetric and track structure modelling was then applied to the experimental data. In a manner similar to LiF:Mg,Cu,P, the experimentally observed under response of alpha-Al2O3:C to X rays <100 keV, compared with cross-section calculations, is explained as a microdosimetric effect caused by the saturation of response of this detector without prior supralinearity (saturation of traps along the tracks). The enhanced X-ray photon energy response of CaSO4:Dy is related to the supralinearity observed in this material after high gamma ray doses, similarly to that in LiF:Mg,Ti. The discussed model approaches support the general rule relating dose-, energy- and ionisation density-responses in TL detectors: if their gamma ray response is sublinear prior to saturation, the measured photon energy response is lower, and if it is supralinear, it may be higher than that expected from the calculation of the interaction cross sections alone. Since similar rules have been found to apply to other solid-state detector systems, microdosimetry may offer a valuable contribution to solid-state dosimetry even prior to mechanistic explanations of physical phenomena in different TL detectors.

Chromatin loops are responsible for higher counts of small DNA fragments induced by high-LET radiation, while chromosomal domains do not affect the fragment sizes

Purpose: To apply a polymer model of DNA damage induced by high-LET (linear energy transfer) radiation and determine the influence of chromosomal domains and loops on fragment length distribution.Materials and methods: The yields of DSB (double-strand breaks) induced by high-LET radiation were calculated using a track structure model along with a polymer model of DNA packed in the cell nucleus. The cell nucleus was constructed to include the chromosomal domains and chromatin loops. The latter were generated by the random walk method.Results and conclusions: We present data for DSB yields per track per cell, DNA fragment sizes, the radial distribution of DSB with respect to the track center, and the distribution of 0, 1, 2, and more DSB from a single particle. Calculations were carried out for a range of particles including He (40 keV/μm), N (225 keV/μm), and Fe ions (150 keV/μm). Situations relevant to PFGE (pulsed-field gel electrophoresis) and microbeam experiments with direct irradiation of the cell nucleus were simulated to demonstrate the applicability of the model. Data show that chromosomal domains do not have a significant influence on fragment-size distribution, while the presence of DNA loops increases the frequencies of smaller fragments by nearly 30% for fragment sizes in the range from 2 kbp (bp = base pair) to 20 kbp.

A Numerical Study into the Reconstruction of Impact Forces on Railway Track-like Structures

This article presents the development of a process by which an impact experienced by a track-like structure can be reconstructed based on its vibration response. The process is essentially based on an inverse analysis technique, while a cepstral analysis technique is also used to improve waveform reconstructions. Firstly, a finite element (FE) model of a simple track structure was generated and calibrated to a real laboratory model to show that it was able to simulate impact events. The rail geometry was then replaced with a simple rectangular beam in order to allow simulation of a rolling wheel by means of a moving mean load. The simple beam geometry was necessary because the rail geometry carried an excessive computational cost when incorporating a moving mean load. This is a legitimate substitution because the inverse analysis technique is geometrically independent. It was found that the acceleration response of the track structure due to the dynamic impact was largely unaffected by the moving mean loading condition. It was also found that the inverse analysis technique shows potential for reconstructing input forces, but in some instances the reconstructed waveform has ambiguous peaks and excessive signal pollution around the force waveform. The cepstral analysis was then found to be useful in sufficiently ‘smoothing’ the transfer function spectrum such that an improved waveform reconstruction could be obtained. An error analysis showed that the regular transfer function as obtained by the inverse analysis technique when ‘smoothed’ by cepstral analysis gave a lower order of error. It was found that to provide sufficient coverage of a full crib of rail, three calibration points were required for the transfer function, with four accelerometers to pick up the track responses along the crib.

Cellular parameters and RBE-LET dependences for modelling heavy-ion radiotherapy

Sets of four parameters (m, E0, sigma0 and kappa) of the cellular track structure model of Katz have been fitted to recently published data concerning human melanoma (AA) and mammalian (V79) cells exposed to a variety of lighter ions and to mixed ion-Co60 and ion-ion irradiation. Using these parameters, model predictions of V79 survival were verified against experimental data. RBE-LET dependences were calculated and compared with experimental data obtained for V79 cells after exposure to 3He, 12C and 20Ne ion beams. The presented track-segment approach used in track structure calculations, while satisfactory for heavier ions, may be of limited value for predicting the RBE-LET dependence of proton and helium radiotherapy beams in regions close to the distal range of these particles. We discuss the predictive capability of this model and propose standards in reporting cellular radiobiology data for application in modelling heavy ion beam radiotherapy.

Experimental and mathematical analysis of a multi-layer system of railway track

Based on experimental measurement of a model of a multi-layer non-linear system with inserted geosynthetic layers of the permanent way structure, a new design method will be designed for dimensioning the sleeper subgrade structure using classical and geosynthetic materials or sub-ballast vibration-damping matting. The results of measurements on a track structure model in a 1:1 scale performed in a testing box will be verified by means of a numerical model. A two-dimensional solution will be subsequently verified by means of a spatial model. Numerical modelling will serve for transferring the values measured on the experimental model into a current railway track structure.

Microdosimetric modelling of the relative efficiency of thermoluminescent materials

Thermoluminescence (TL) dosimetry relies on evaluating the dose absorbed in the TL detector by measuring the light output by the detector, i.e. by the TL glow-curve analysis. However, the absolute efficiency of the TL light emission per unit dose of ionizing radiation absorbed in the detector is known to depend on the energy and quality (ionization density) of this radiation. Moreover, as the TL light is absorbed in the detector itself, the spatial distribution of energy deposition events inside the detector also needs to be considered. It is convenient to describe the response of the detector (TL output per unit dose) relative to that after a dose of sparsely ionizing reference radiation, such as 137Csγ-rays, via relative efficiency, ηiγ, defined as the TL light signal emitted by the TL detector per unit imparted energy of radiation of the type i, normalized to the signal per unit imparted energy of this reference radiation. Microdosimetric models have provided an insight as to the variation of ηiγ, with the energy and ionization density, related to the spatial distribution of ionizations and excitations produced by the ionizing radiation in the detector, as well as some experimental factors related to the TL light transport within the detector. To study the variation of ηiγ with LET in LiF:Mg, Ti detectors irradiated by heavy charged particles (high-LET radiation), the most successful approach was the track structure model, based on the radial distribution of dose (RDD) around the ion tracks. For low-LET radiation (photons, electrons) the microdosimetric model has been successfully applied to predict ηiγ for LiF:Mg,Ti, LiF:Mg,Cu,P, and CaF2:Tm TL detectors, to explain the discrepancy between the measured and predicted photon-energy response of these detectors.

Cellular parameters for track structure modeling of radiation hazard in space

Based on irradiation with 45 MeV/u N and B ions and with Co-60 γ rays, cellular parameters of Katz's track structure model have been fitted for the survival of V79-379A Chinese hamster lung fibroblasts. Cellular parameters representing neoplastic transformations in C3H10T/1/2 cells after their irradiation with heavy ion beams, taken from earlier work, were also used to model the radiation hazard in deep space, following the system for evaluating, summing and reporting occupational exposures proposed in 1967 by a subcommittee of NCRP. We have performed model calculations of the number of transformations in surviving cells, after a given fluence of heavy charged particles of initial energy 500 MeV/u, penetrating thick layers of cells. We take the product of cell transformation and survival probabilities, calculated along the path lengths of charged particles using cellular survival and transformation parameters, to represent a quantity proportional to the “radiation risk factor” discussed in the NCRP document. The “synergistic” effect of simultaneous charged particle transfers is accounted for by the “track overlap” mode inherent in the model of Katz.

The Parameter-Free Track Structure Model of Scholz and Kraft for Heavy-Ion Cross Sections

The "parameter-free", "local effects" theory of Scholz and Kraft is an extension to mammalian cells of the theory of RBE for dry enzymes and viruses of Butts and Katz. Its claim for parameter freedom has been challenged elsewhere. Here we examine its conceptual base and find errors in its use of the physical concept of cross section and its neglect of the radiobiological relationship between target size and radiosensitivity in evaluating the radiation damage to "point targets".

A track structure model for simulation of strand breaks in plasmid DNA after heavy ion irradiation.

We present a track structure model based on the local dose deposited around heavy ion tracks to explain the cross sections for single-strand and double-strand break induction in plasmid DNA in different aqueous buffers. The model is based only on measurable quantities, namely the effect distribution for inducing strand breaks after x-ray irradiation as a function of dose, and the radial dose distribution of the heavy ion track. The effect of indirect DNA damage mediated by free radicals produced in the water surrounding the DNA is accounted for by allowing the radial dose distribution to be smeared in space by an effective target size corresponding to the squared sum of the geometrical extension of the plasmid molecule and the mean free drift path of the radicals in the buffer solution. Our calculations reproduce well the measured cross sections for single-strand and double-strand break induction in SV40 plasmid DNA in various buffer solutions both as a function of the LET and of the specific energy of the heavy ion.

Dose–effect modifying factors in radiation protection—a 1967 NationalCommission on Radiation Protection document revisited

In 1967 Subcommittee M-4 of the National Commission on Radiation Protectionproposed a system for evaluating, summing and reporting occupational exposures.It appears that some 30 years later these concepts could be implemented in asystem of radiation protection based on Katz’s cellular track structure model,which is able to quantify and predict the response of systems relevant to radiationprotection, such as survival or oncogenic transformations in cell cultures,enzymes, bacteria or whole organisms. As a consequence of this approach, anm-power-law(with mranging between 2 and 3.5) dependence of effect, or radiation risk, after doses ofstandard Co-60 radiation, would follow.

Limits imposed by ionizing radiation on the long-term survival of trapped bacterial spores: beta radiation

Purpose : A model is presented for determining the survival time TF of a fraction F of a population of bacterial spores trapped within a fluid inclusion and subject to genetic damage from beta radiation. Methods : The limiting factor to survival is the production of double-strand breaks (DSB) in the DNA resulting from singletrack cleaving and from the cumulative effects of single-strand breaks (SSB) induced by the presence of ionizing radiation in the environment. The model considers the probability that radicals and ions formed by the passage of high-energy particles will interact with a DNA molecule and induce damage. Results : The survival time T for a fraction F of a trapped population is a weak function F of both F and the length L in base pairs of the genome. For irradiation due to a beta source trapped with the spores within the inclusion, the survival time is also inversely proportional to the concentration of the radionuclide, the dominant factor in limiting survival time. Conclusions : The predictions of the model are consistent with measured DSB formation rates, the observed survival of trapped spores over time periods as long as 250Ma, and track structure models which address low physical dose rates.

Simulation of Exon Deletion Mutations Induced by Low-LET Radiation at theHPRTLocus

Friedland, W., Li, W. B., Jacob, P. and Paretzke, H. G. Simulation of Exon Deletion Mutations Induced by Low-LET Radiation at the HPRT Locus. Radiat. Res. 155, 703-715 (2001). The induction of HPRT mutants with exon deletions after irradiation with photons was simulated using the biophysical radiation track structure model PARTRAC. The exon-intron structure of the human HPRT gene was incorporated into the chromatin fiber model in PARTRAC. After gamma and X irradiation, simulated double-stranded DNA fragments that overlapped with exons were assumed to result in exon deletion mutations with a probability that depended on the genomic or the geometric distance between the breakpoints. The consequences of different assumptions about this probability of deletion formation were evaluated on the basis of the resulting fractions of total, terminal and intragenic deletions. Agreement with corresponding measurements was obtained assuming a constant probability of deletion formation for fragments smaller than about 0.1 Mbp, and a probability of deletion formation decreasing with increasing geometric or genomic distance between the end points for larger fragments. For these two assumptions, yields of mutants with exon deletions, size distributions of deletions, patterns of deleted exons, and patterns of deleted STS marker sites surrounding the gene were calculated and compared with experimental data. The yields, size distributions and exon deletion patterns were grossly consistent, whereas larger deviations were found for the STS marker deletion patterns in this comparison.

An ion-track structure model based on experimental measurements and its application to calculate radiolysis yields

An ion track structure model proposed previously on the basis of classical binary collision theory and experimental measurements of ionization distribution around ion path using low-pressure gas has been applied to calculate the radiolysis yields for heavy ion bombarded Fricke solution and solid alanine dosimeter. The calculation results are compared satisfactorily with reported experimental G-values.

A polymer, random walk model for the size-distribution of large DNA fragments after high linear energy transfer radiation.

DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to < 0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.

Analysis of MIR-18 results for physical and biological dosimetry: radiation shielding effectiveness in LEO

We compare models of radiation transport and biological response to physical and biological dosimetry results from astronauts on the Mir space station. Transport models are shown to be in good agreement with physical measurements and indicate that the ratio of equivalent dose from the Galactic Cosmic Rays (GCR) to protons is about 3/2:1 and that this ratio will increase for exposures to internal organs. Two biological response models are used to compare to the Mir biodosimetry for chromosome aberration in lymphocyte cells; a track-structure model and the linear-quadratic model with linear energy transfer (LET) dependent weighting coefficients. These models are fit to in vitro data for aberration formation in human lymphocytes by photons and charged particles. Both models are found to be in reasonable agreement with data for aberrations in lymphocytes of Mir crew members: however there are differences between the use of LET dependent weighting factors and track structure models for assigning radiation quality factors. The major difference in the models is the increased effectiveness predicted by the track model for low charge and energy ions with LET near 10 keV/μm. The results of our calculations indicate that aluminum shielding, although providing important mitigation of the effects of trapped radiation, provides no protective effect from the galactic cosmic rays (GCR) in low-earth orbit (LEO) using either equivalent dose or the number of chromosome aberrations as a measure until about 100 g/cm 2 of material is used.

Stochastic radial dose distributions and track structure theory.

Measured single-event distributions of the specific energy deposited in cylindrical volumes with simulated diameters down to 150 nm for (4)He and (12)C ions with energies of 25 MeV/nucleon and (16)O ions with 21 MeV/nucleon and radial distances up to 12 microm are presented. The mean specific energy per ion <z(r)>, the mean specific energy per target hit z(1)(r), and the relative frequency of target hits nu(r) as a function of radial distance are evaluated and compared with the corresponding quantities of the track structure model of Kiefer and Straaten (Phys. Med. Biol. 31, 1201-1209, 1986). Though there are some discrepancies in the absolute values, the radial dependence of <z(r)>, z(1)(r) and v(r) for (12)C and (16)O ions is reproduced satisfactorily. The model fails to describe the data for (4)He ions. A more detailed comparison of the radial shape of the mean specific energies calculated from the experimental data from the present work and data from the literature reveals a significant projectile charge dependence which is not included in track structure models.

A method for radioprobing DNA structures using Auger electrons

Purpose : To present a new method for radioprobing a DNA triple helix structure by Auger electrons emitted in the decay of 125 I using theoretical/computational approaches. Materials and methods : A Monte Carlo track structure method was used to simulate the damage to a triplex resulting from Auger electrons emitted in the decay of an incorporated 125 I atom in plasmid DNA. Comparison of the theoretical frequency distributions of single-strand breaks induced on the Pu and Py strands with the experimental data and a knowledge of the distances from the strand breaks to the iodine provide information on the structures otherwise difficult to obtain with X-ray crystallography. Results : In comparing theoretical frequency distributions of singlestrand breaks with the experimental data it is found that the results are very sensitive to the conformation of the triplex model used. It is found that the best fit to the experimental data results from using a hybrid triplex model, in which the base-step geometry is A-like, while the sugar puckers adopt the B-like C2'- endo conformation. Conclusions : The approach and technique presented here represent a valuable new addition to the methods available for DNA structure determination since they provide information on medium-range structure otherwize difficult to obtain in the absence of X-ray crystallography. It is concluded that currently accepted models for triplex structure are not optimal, and a modified structure is proposed that fits the radioprobing results better, while maintaining agreement with the fibre diffraction and NMR data. Although the method has proved to be very useful for scoring alternative trial solutions, further studies combining experimental data from multiple iodine positions with track structure modelling are required for directing structural optimization.

The general relation between tissue response to x-radiation (α/β-values) and the relative biological effectiveness (RBE) of protons: Prediction by the Katz track-structure model

Purpose : Experimental data suggest that the relative biological effectiveness (RBE) of protons compared to x-rays may be determined by the α / β -ratio of the x-ray survival curve. The data are referring to the centre of a spread-out Bragg peak (SOBP) formed to deliver a homogeneous dose to the tumour by modulating the proton energy. In an effort to explore the basis for this observation, calculations were performed to investigate the response of different biological targets through a range of proton energies and doses. Materials and methods : To describe the x-ray survival curve, the parameters of the linear-quadratic equation, α and β, as well as those of the multi-target/single-hit equation, n and D 0, were considered. These parameters were varied to investigate the RBE using the Katz track-structure model. Known cell line characterizations, as well as different hypothetical cells assuming different α / β -ratios but similar target size parameters in the framework of the track-structure theory, were considered. Results : The RBE was found to increase with increasing α / β when the parameter n was varied, but to decrease with increasing α / β when D 0 was varied. This held when all other radiosensitivity parameters were assumed to stay constant. Thus, the RBE cannot be predicted by the α / β -ratio alone. Conclusions : Although there is no direct correlation between the proton RBE and the parameters describing the x-ray survival curve, the track-structure model predicts a tendency for late-responding tissues (low α / β) to have higher RBE values than early-responding tissues (high α / β) . These calculations reinforce the experimental findings, but also strongly suggest that there are circumstances in which the tendency for RBE to increase with increasing α / β does not occur, or even could be reversed.

The link between physics and chemistry in track modelling.

The physical structure of a radiation track provides the initial conditions for the modelling of radiation chemistry. These initial conditions are not perfectly understood, because there are important gaps between what is provided by a typical track structure model and what is required to start the chemical model. This paper addresses the links between the physics and chemistry of tracks, with the intention of identifying those problems that need to be solved in order to obtain an accurate picture of the initial conditions for the purposes of modelling chemistry. These problems include the reasons for the increased yield of ionisation relative to homolytic bond breaking in comparison with the gas phase. A second area of great importance is the physical behaviour of low-energy electrons in condensed matter (including thermolisation and solvation). Many of these processes are not well understood, but they can have profound effects on the transient chemistry in the track. Several phenomena are discussed, including the short distance between adjacent energy loss events, the molecular nature of the underlying medium, dissociative attachment resonances and the ability of low-energy electrons to excite optically forbidden molecular states. Each of these phenomena has the potential to modify the transient chemistry substantially and must therefore be properly characterised before the physical model of the track can be considered to be complete.