Abstract A Monte Carlo simulation tool has been developed, based on the physical models of the Geant4-DNA extension of Geant4, to study the ionisation pattern of charged particles in a multi-target environment. The tool allows to code easily the geometry to build a simulation with multiple targets, since several parameters can be changed interactively and independently via macro commands. In this work a set of nanometric target spheres is embedded in a cylindrical water phantom 20 nm in height and 40 nm in diameter. The targets are randomly distributed in such a way that they do not overlap and are contained within a smaller cylindrical volume 20 nm in diameter and height. The water phantom is irradiated by ions which are shot parallel to the central axis and randomly distributed over the cross section of the inner cylinder. Two different types of simulations are performed. In one, the penumbra of secondary electrons is fully simulated, in the other the transport of secondary electrons is carried out only if they are produced inside one of the targets, and the electron track is terminated when it leaves the sphere of production. First results are presented and discussed. INTRODUCTION It is accepted today that the damage induced in living cells by ionising radiation is strongly correlated to the spatial pattern of inelastic interactions inside some critical cell structures of nanometric size, the most important being the DNA(1). In this respect, nanodosimetry has proven to be able to study specific features of particle track structure at the nanometre scale, which are closely related to the biological effects of ionising radiation. For what concerns the experimental investigation of track structure, different nanodosimeters have successfully studied the ionisation component of particle tracks for ions of different type and energy in a single specific volume of nanometric equivalent size(2–4). In this context, a cluster of ionisations large enough (for instance, two ionisations) would correspond to a high probability of inducing a DNA double strand break (DSB). However, the severity of DNA damage is reasonably related to the probability of multiple DSBs close to each other. Consequently, it is of interest to characterise particle track structure by measuring the number of ionisations produced not only in a single volume, but also within neighbouring nanometric volumes placed within short distances. A Monte Carlo simulation tool has been developed, based on the Geant4-DNA physical models(5, 6) of the Geant4 simulation toolkit, which allows to study the ionisation pattern of charged particles in a multi-target environment. This work describes the rationale and the structure of the simulation tool and presents some preliminary results. MATERIALS AND METHODS A program was developed, based on the physical models of the Geant4-DNA extension of Geant4, which allows to code easily the geometry to simulate a multi-target environment. Sensitive targets of nanometric size are embedded in a cylindrical phantom, either randomly or with a specific spatial distribution. Since in Geant4-DNA the cross-sections are defined for liquid water only, both the targets and the embedding phantom are made of this material. The following geometrical parameters can be changed interactively and independently via macro commands: the diameter and length of both the inner and outer cylinder, the number of sensitive targets and their diameter, and the density of the water material of which the targets are made. The radius of the primary beam and the type and energy of primary particles are set by native Geant4 commands. This work presents first results for a multi-target environment, consisting of a number Nt of nanometre-sized sensitive spherical targets that are randomly distributed in an embedding cylinder, 20 nm in both length and diameter, with the only constraint of no overlapping. Two sphere diameters have been considered in this work, 3 and 1 nm. An outer cylindrical ring with a thickness of 20 nm is also included in the simulation setup, to take into account the contribution of electrons that may re-enter after leaving the inner cylinder. The trajectories of incident ions are parallel to the main axis of the cylinders and randomly distributed over the cross section of the inner one. Primary beams of protons and carbon ions were studied, in an energy range from 1 to 60 MeV and from 0.7 to 400 MeV/u, respectively. For each radiation quality Q (defined by ion type and velocity), two simulations were performed. In one, all secondary electron tracks were simulated until they become non-ionising; in the other the transport of secondary electrons was carried out only if they were produced inside one of the spherical targets, and the electron track was terminated when it left the sphere of production. The number of ionisations within each target at the passage of each primary ion was recorded, and the probability distribution Pν(i)(Dt|Q) of the number ν of ionisations (usually called the ionisation cluster-size distribution) was derived for each target sphere (i) by normalising on the total number of incident particles. This distribution depends on the diameter Dt of the spherical target and in principle also on the position of the sphere (i) within the embedding cylinder. The complementary cumulative distribution functions Fk(i) were also derived for each sphere: Fk(i)(Dt|Q)=∑ν=k∞Pν(i)(Dt|Q) (1) This quantity represents the probability that at the passage of a single ionising particle a cluster of k or more ionisations is formed inside a specific sphere. The mean value of Fk(i) averaged over the Nt targets is indicated as F̅k and derived as follows: F̅k(Dt|Q)=1Nt∑i=1NtFk(i)(Dt|Q) (2) Next, looking at the ensemble of Nt spheres with diameter Dt, let the quantity P̃h(k,Nt,Dt|Q) be the probability that upon the passage of a single ionising particle of quality Q at least k ionisations are produced in h out of a total of Nt spheres, while in the remaining Nt− h targets there are less than k ionisations. The value of k is therefore a threshold which rules the target sensitivity, so that a sphere is defined as ‘hit’ only if more than k ionisations take place within it. The mean value Hk(Nt,Dt|Q) of the distribution P̃h(k,Nt,Dt|Q) was derived as follows: Hk(Nt,Dt|Q)=∑h=0NthP̃h(k,Nt,Dt|Q) (3) In particular, H2(Nt,Dt|Q) represents the mean number of targets in which at least two ionisations take place, when an incident particle of quality Q impinges on the internal cylinder. The ratio Hk(Dt|Q)/Nt is independent of Nt and represents the average single-sphere probability of being hit, which is F̅k(Dt|Q). RESULTS The analysis started with the study of the cumulative distribution Fk(i)(Dt|Q) for each target sphere. The restriction of the ion trajectories to the inner cylinder induces a gradient of scored ionisations, depending on the distance of the target sphere from the central axis, when the full ion track (including the entire penumbra) is simulated. Targets close to the lateral surface lack the contribution of secondary electrons produced by ion trajectories outside the inner cylinder. The magnitude of this effect has been tested on the distributions Fk(i)(Dt|Q) by comparing a target located at the centre of the cylinder and one at the lateral surface. As an example, results are shown in Figure 1 for 3-nm target spheres irradiated by 240-MeV carbon ions. It is clear from Figure 1 that there are only minor differences in the Fk(i) distributions as an effect of decreasing contribution from δ-electrons when the target is located close to the border. Figure 1. View largeDownload slide Fk(i) distributions produced by 240-MeV carbon ions in 3-nm target spheres located at three different positions in the embedding cylinder: one at the centre, one at the lateral border and one at the entrance surface. A zoomed view is also shown in the inset. All secondary electron tracks are simulated. Figure 1. View largeDownload slide Fk(i) distributions produced by 240-MeV carbon ions in 3-nm target spheres located at three different positions in the embedding cylinder: one at the centre, one at the lateral border and one at the entrance surface. A zoomed view is also shown in the inset. All secondary electron tracks are simulated. Figure 1 shows also the Fk(i) distribution in a target sphere located at the entrance surface of the embedding cylinder. It can be seen that the main differences are that F1(i)(Dt|Q) at the surface is ~20% lower than at the centre, whereas the influence on F2(i) and F3(i) decreases to ~10%. These differences are due to the absence of a build-up layer of water before the region of interest where the scoring volumes are located. This absence introduces a gradient of scored ionisations between the top of the cylinder and its centre, because the contribution from electrons ejected from outside the cylinder in the forward direction is not taken into account. The magnitude of this effect depends obviously on the velocity of the primary ion and on the thickness of the cylinder; it increases when the velocity of the ion is lower, due to the higher number of forward-emitted secondary electrons. With the selected geometry and radiation qualities, the influence of this effect, estimated as the relative standard deviation, was always less than 10% for F1(i) and always less than 8% for F2(i) and F3(i), as a result of averaging over the number Nt of targets. Looking at the ensemble of spheres, the mean hit frequency per primary track H2*(Dt|Q) can be introduced by the following equation: H2*(Dt|Q)=H2(Dt|Q)Nt×(DvDt)2 (4) The quantity (DV/Dt)2 represents the ratio of the phantom to the single-target active area. H2*(Dt|Q) was analysed as a function of the linear energy transfer (LET) of particles at the entrance surface. Given the 20 nm thickness of the phantom cylinder, the difference between the particle LET at the entrance and at the exit surface is always less than 0.5%. Figure 2 shows the trend of H2*(Dt|Q) as a function of LET, for the case in which all secondary electron tracks are simulated. Two different sphere diameters are shown, Dt = 3 nm and 1 nm. In both cases, protons and carbon ions of the same LET show different H2*(Dt|Q) values, confirming that LET is not a suitable quantity to describe particle track structure(2) and hence neither the radiation quality. Figure 2. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) as a function of LET, for protons and carbon ions, when all secondary electron tracks are simulated. Figure 2. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) as a function of LET, for protons and carbon ions, when all secondary electron tracks are simulated. The same effect can be observed in Figure 3, when the secondary electrons are simulated only if they are produced inside one of the targets and the electron track is terminated when it leaves the sphere of production. If the data are plotted not as a function of LET but of the mean number of ionisations M1 produced in the individual sphere, the data of Figure 3 take the trend shown in Figure 4. When plotted as a function of M1, the data for protons and carbon ions lay on the same curve, emphasising the fact that M1 is a more suitable candidate than LET to describe particle track structure. Moreover, this curve is almost independent of target size. Figure 3. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) as a function of LET, for protons and carbon ions, when only the secondary electrons produced inside the targets are simulated. Figure 3. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) as a function of LET, for protons and carbon ions, when only the secondary electrons produced inside the targets are simulated. Figure 4. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) as a function of M1, for protons and carbon ions, when only the secondary electrons produced inside the targets are simulated. Figure 4. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) as a function of M1, for protons and carbon ions, when only the secondary electrons produced inside the targets are simulated. It can also be observed in Figures 3 and 4 that the trend of H2*(Dt|Q) as a function of both LET and M1 shows a saturation effect at large LET or M1 values. This saturation effect is similar to that of inactivation cross sections. As a final step it is therefore of interest to compare the trend of H2*(Dt|Q) as a function of LET with inactivation cross sections, in a similar way to that recently proposed in experimental nanodosimetry(8). As an example, inactivation cross sections at 5% survival level, derived from survival curves for V79 cells irradiated by protons and carbon ions(7), are plotted in Figure 5, together with the simulated data already shown in Figure 3, scaled by a calibration factor C = 65 μm2. At first glance, there is a very good correspondence between H2*(Dt=1nm|Q) and V79 cross sections at 5% survival, in good agreement with published results(8). Figure 5. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) scaled by a factor C = 65 μm2, compared to inactivation cross sections at 5% survival level for V79 Chinese hamster cells irradiated by protons (squares) and 12C ions (circles), as a function of LET. Figure 5. View largeDownload slide Mean hit frequency per primary track H2*(Dt|Q) scaled by a factor C = 65 μm2, compared to inactivation cross sections at 5% survival level for V79 Chinese hamster cells irradiated by protons (squares) and 12C ions (circles), as a function of LET. DISCUSSION AND CONCLUSIONS A Monte Carlo simulation tool has been developed, which allows the simulation of particle track structure in a multi-target environment, with spherical targets of nanometric size. Two different types of simulations can be performed for each radiation quality. In one, the penumbra of secondary electrons is fully simulated until the electrons become non-ionising, in the other the transport of secondary electrons is only simulated if they are produced inside one of the targets, and the electron track is terminated when it leaves the sphere of production. The preliminary results which are presented in this work suggest that, when a threshold value k = 2 is considered, the mean hit frequency per primary track H2*(Dt=1nm|Q) plotted as a function of LET reproduces the behaviour of inactivation cross sections at 5% survival level, if only the δ-electrons produced inside the targets are simulated, and their tracks are terminated when they leave the sphere of production. These results can be useful to analyse radiobiological data as a result of multiple lesions to the DNA, produced by incident radiation within short distances. Intuitively, two or more ionisations (k = 2) within 1 nm (the target diameter) induce with high probability a DNA DSB, so that H2 would correspond to the mean number of DSBs in close proximity to one another (separated by less than 20 nm). The study should however be extended to cell lines other than the V79 and also to different end points. Furthermore, the tool can be used as a starting point to design a portable nanodosimeter based on the use of modern nanotechnology, for instance, a set of radiation-sensitive nanoparticles dispersed in a layer of tissue-equivalent material. The experimental determination of the number of ionisations in each of the nanometric volumes would probably be unfeasible; however, this might be unnecessary, since the mean number Hk of volumes being ‘hit’ by radiation contains enough information for a consistent characterisation of the radiation field. In addition, since Hk is defined as a mean value, it can be obtained by normalising the total number of hit targets on the number of incident ions, thus removing the need for single-particle detection. However, the trend of Hk as a function of the incident LET matches that of inactivation cross sections only if the secondary electrons entering the sensitive spheres from outside are not considered for the determination of the number of hit targets. The feasibility of such a detector is far from obvious, and will be the aim of a future experimental study. FUNDING This work is supported by the fifth Scientific Commission of the Italian Istituto Nazionale di Fisica Nucleare (INFN) in the framework of the Project NADIR (NAno Dosimetry of Ionising Radiation). REFERENCES 1 Goodhead , D. T. Initial events in the cellular effects of ionizing radiations: clustered damage in DNA . Int. J. Radiat. Biol. 65 , 7 – 17 ( 1994 ). Google Scholar CrossRef Search ADS PubMed 2 Conte , V. , Colautti , P. , Grosswendt , B. , Moro , D. and De Nardo , L. Track structure of light ions: experiments and simulations . New J. Phys. 14 , 093010 ( 2012 ). Google Scholar CrossRef Search ADS 3 Pszona , S. , Bantsar , A. and Nikjoo , H. Ionization cluster size distribution for alpha particles: experiment, modelling . Radiat. Prot. Dosim. 122 ( 1‒4 ), 28 – 31 ( 2006 ). Google Scholar CrossRef Search ADS 4 Hilgers , G. , Bug , M. U. , Gargioni , E. and Rabus , H. Comparison of measured and Monte Carlo simulated track structure parameters in nanometric volumes . Radiat. Prot. Dosim. 161 , 441 – 444 ( 2014 ). Google Scholar CrossRef Search ADS 5 Bernal , M. A. et al. . Track structure modeling in liquid water: a review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit . Phys. Med. 31 , 861 – 874 ( 2015 ). Google Scholar CrossRef Search ADS PubMed 6 Incerti , S. et al. . Comparison of Geant4 very low energy cross section models with experimental data in water . Med. Phys. 37 , 4692 – 4708 ( 2010 ). Google Scholar CrossRef Search ADS PubMed 7 Friedrich , T. , Scholz , U. , Elsässer , T. , Durante , M. and Scholz , M. Systematic analysis of RBE and related quantities using a database of cell survival experiments with ion beam irradiation . J. Radiat. Res. 54 ( 3 ), 494 ( 2013 ). Google Scholar CrossRef Search ADS PubMed 8 Conte , V. , Selva , A. , Colautti , P. , Hilgers , G. and Rabus , H. Track structure characterization and its link to radiobiology . Radiat. Meas. 106 , 506 – 511 ( 2017 ) http://dx.doi.org/10.1016/j.radmeas.2017.06.010 . Google Scholar CrossRef Search ADS © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: firstname.lastname@example.org This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)
Radiation Protection Dosimetry – Oxford University Press
Published: Aug 1, 2018
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