Energy deposition and relative frequency of hits of cylindrical nanovolume in medium irradiated by ions: Monte Carlo simulation of tracks structure

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1 DOI /s ORIGINAL PAPER Energy deposition and relative frequency of hits of cylindrical nanovolume in medium irradiated by ions: Monte Carlo simulation of tracks structure Ianik Plante Francis A. Cucinotta Received: 20 April 2009 / Accepted: 27 October 2009 Ó Springer-Verlag 2009 Abstract Radiation track structure simulations have been used for many years to study the DNA damage caused by heavy ions. These studies are highly relevant for treatment planning of heavy ion radiotherapy and space radiation risk assessment. Measurements of the frequency of d-rays hits, mean specific energy per target hits and per ion, and the frequency of dose distribution in a cylindrical target volume placed at various radial distances from 4 He 2?, 12 C 6? and 16 O 8? tracks have been performed by Schmollack et al. (in Radiat Res 153: , 2000). In the present work, Monte Carlo simulation of radiation tracks has been performed with the RITRACKS and the RETRACKS codes along with a target volume to simulate the experiment of Schmollack et al. The results of these simulations are compared to those of previous deterministic models of the radial dependence of the mean specific energy. Our Monte Carlo simulations are consistent with the experimental data both in the core and in the penumbra of the beam, and are shown to provide a better description of the experimental data than deterministic codes. I. Plante F. A. Cucinotta (&) NASA Johnson Space Center, 2101 NASA Parkway, Houston, TX 77058, USA Francis.A.Cucinotta@nasa.gov I. Plante ianik.plante-1@nasa.gov I. Plante Division of Space Life Sciences, Universities Space Research Association, 3600 Bay Area Boulevard, Houston, TX 77058, USA Introduction The interaction of ionizing radiation with mammalian cells and tissues induces a variety of DNA damage and oxidative stress as a result of energy deposition in biomolecules that could lead to senescence, apoptosis, mutations, genetic instability and carcinogenesis (National Council of Radiation Protection and Measurements 2006). Thus, simulations of the radiation track structure to study the energy deposition in biomolecules and cells by heavy ions have been done by several groups (Goodhead and Nikjoo 1989; Nikjoo et al. 1997; Ballarini et al. 2008; Dingfelder 2006; Cucinotta et al. 2000). These studies are highly relevant to radiotherapy treatment planning by heavy ions (Nikjoo et al. 2008; Elsässer et al. 2008) and space radiation risk assessment (Cucinotta and Durante 2006; Durante and Cucinotta 2008). A very important aspect of the track structure model is the so-called track core, which is a cylindrical region of dense energy deposition along the primary ion path surrounded by a much larger track Penumbra formed by the so-called d-rays, i.e., highenergy electrons that can travel distances up to a few millimeters in biological media (Magee and Chatterjee 1980). Heavy ions radiation tracks can be simulated either with deterministic models, amorphous track codes or Monte Carlo simulations (reviewed in Nikjoo et al. 2006). Numerous experiments (Glass and Roesch 1972; Schmollack et al. 2000; Varma et al. 1975) have been conducted in the past to investigate track characteristics. One relevant experiment is from Schmollack et al. (2000), who have performed measurements of the frequency of d- rays hits, mean specific energy per target hits and per ion, and the frequency of dose distribution in a cylindrical volume placed at various radial distances from 4 He 2?, 12 C 6? and 16 O 8? tracks. Their experiment is based on a

2 technique developed by Rossi and Rosenzweig (1955), which is the use of a proportional counter in a large container filled with a tissue-equivalent gas mixture, to simulate sub-cellular sizes target volumes surrounded by tissue. The target is a radially movable cylinder proportional counter of 5 mm in diameter. By adjusting the density of the gas, the detector dimension is equivalent of the simulated site sizes of 150, 300 and 600 nm. This is to be compared with the size of a small DNA fragment (*2 nm), nucleosome or protein (*10 nm), chromatin fiber (*25 nm) (Goodhead and Nikjoo 1989), and cell nuclei of mammal (*10 lm), yeast (*0.9 lm) and Bacillus subtilis spores (*0.5 lm) (Schmollack et al. 2000). Schmollack et al. then used the amorphous track structure model of Kiefer and Straaten (1986) to analyze their results. This track structure model is very useful to explain such experimental data (Cucinotta et al. 1999). The frequency of hits v(r) and the radial dose D(r) are modeled by vðrþ ¼a v r b v ð1þ and DðrÞ ¼a D r b D ð2þ where the parameters a v, b v, a D and b D are determined by least-square fits of the data corresponding to radial distance greater than the target size. The model is able to reproduce satisfactorily the experimental data obtained by Schmollack et al., except maybe for 4 He 2?. However, it is not able to explain the steep decrease of the mean specific energy per target hit and per ion when the radial distance corresponds to the edge of the cylinder. It also predicts an increase in the mean specific energy per target hit at the vicinity of the penumbra radius, which is not observed experimentally. The model also does not predict the frequency of dose distribution that is measured in the target. In the present work, we have performed Monte Carlo track structure simulations and obtained the frequency of dose distribution, the frequency of hits, the mean energy deposited per target hit and per ion. Monte Carlo track structure simulations The complex succession of events that follows the irradiation of matter is stochastic in nature. Thus, Monte Carlo simulations are well suited to study the track structure and have therefore been used to calculate 3D representations of the electron and ion tracks in matter (Muroya et al. 2006; Plante et al. 2005; Emfietzoglou et al. 2000). These simulations have greatly contributed to our knowledge of radiation dosimetry, radiation chemistry (Autsavapromporn et al. 2007; Meesungnoen and Jay-Gerin 2005; Kreipl et al. 2009a, b) and chromosome damage (Ballarini et al. 2008) by heavy ions. The experiments of Schmollack et al. (2000) are reexamined here by using the Monte Carlo track structure simulation program RITRACKS (Plante and Cucinotta 2008, 2009). The RITRACKS program is used to simulate the so-called physical and physico-chemical stages (Cobut et al. 1998; Jay-Gerin and Ferradini 1999) of the radiolysis of water. The ion is followed on an event-by-event basis, calculating all ionization and excitation events produced and recording the position of the generated radiolytic species and the energy and direction of the secondary electrons. This code uses recently revisited ionization and excitation cross-sections, which take into account the effective charge of the ion (Plante and Cucinotta 2008). Similarly, the produced electrons are followed by the electron track structure code RETRACKS, which also simulates the ionization, electronic excitation, elastic collisions and dissociative attachment events. Electron crosssections have also been reviewed and extended up to 100 MeV (Plante and Cucinotta 2009). Early events such as the possible recombination of an electron with its parent cation, the dissociation of ionized and excited water molecules, plasmon decay and electron thermalization are also included in the RETRACKS code. Both codes have been validated by calculation of relevant dosimetric quantities such as the stopping power and electron penetration range. For example, the radial dose distributions of ions calculated from RITRACKS and RETRACKS are able to reproduce successfully experimental data and calculations from amorphous tracks (Plante and Cucinotta 2008). Figure 1 displays typical radiation track structures in liquid water for 16 O 8? of 21 MeV amu -1 (LET * 168 kev lm -1 ), 12 C 6? of 25 MeV amu -1 (LET * 76 kev lm -1 )and 4 He 2? of 25 MeV amu -1 (LET * 9.5 kev lm -1 ), projected along the z-axis. A cylindrical target of 600 nm of diameter is also shown at this scale to illustrate the experimental conditions. The track core and penumbra are clearly seen on this figure. A large drop in the number of hits to the target is expected when the edge of the cylinder is near the origin, since the energy deposited in the core is outside the cylinder. The radial dose distribution profile of these ions is calculated as in Plante and Cucinotta (2008), by calculating the energy deposited in a differential volume element, dividing the value by the mass of the differential element and thus converting it to the unit J/kg, which corresponds to Gy. The results are shown on Fig. 2. The three ions have the same dose distribution profile, which differs only by a scaling factor that is the charges ratio (Z 1 /Z 2 ) 2. This is not surprising, since the ion cross-section is a function of Z 2 within the plane-wave Born approximation (Dingfelder 2006). In fact, the three curves shown in Fig. 2 are almost

3 Fig. 1 Monte Carlo simulation radiation tracks in liquid water for a 16 O 8? of 21.2 MeV amu -1 (LET * 168 kev lm -1 ), b 12 C 6? of 25 MeV amu -1 (LET * 76 kev lm -1 ), c 4 He 2? of 25 MeV amu -1 (LET * 9.5 kev lm -1 ). The circle represents a 600-nm diameter cylindrical target approximately 38 lm (Plante and Cucinotta 2009), which is larger than the penumbra radius calculated by the model of Kiefer and Straaten (1986), i.e., 14.6 lm. Indeed, this is what is seen in Fig. 2: there is no dose deposited over beyond 30 lm. Because of the stochastic nature of the tracks, this distance is not expected to be found exactly in our simulations. Results and discussion Relative frequency of target hits Fig. 2 Calculation of radial dose distributions for 16 O 8? of 21.2 MeV amu -1 (straight line), 12 C 6? of 25 MeV amu -1 (dashed line) and 4 He 2? of 25 MeV amu -1 (dotted line) indistinguishable, if they are divided by their respective Z 2 factor (not shown). For ions with classical energies, such as those used for this study, the maximum energy transfer to an electron at rest in a collision is 4mMT=ðm þ MÞ 2 ffi 4ðm=MÞT, where m and M are the electron and ion mass and T is the kinetic energy of the ion (Turner 2007). Since the ions have about the same energy per nucleon, the maximum energy that can be transferred in a collision to an electron is similar for all ions studied, about 54 kev. The range of these electrons is The first quantity that was calculated is the frequency of target hits. It is obtained by simulating a given number of ion tracks and counting how many target volumes have energy deposited inside. The number of simulation track histories needed for convergence of the results greatly varies with radial distance. Typically, ,000 histories are needed for convergence. This is similar to the number of ions used by Schmollack et al. (2000) in their experiments. Comparison of the model results to those of experiments measuring the frequency of hits for the ions 4 He 2?, 12 C 6? and 16 O 8? for a 150-nm target are shown in Fig. 3. The uncertainty on the position of the cylinder in the experiment of Schmollack et al. (2000) was about lm; this is included in our code by putting the track at a random radial distance from the origin, sampled from a Gaussian distribution of r = 0.2 lm. The simulation results are in better agreement with experimental results if

4 Fig. 3 Relative frequency of a 150-nm target hits as a function of the radial distance for 16 O 8? of 21.2 MeV amu -1, 12 C 6? of 25 MeV amu -1 and 4 He 2? of 25 MeV amu -1. This calculation (black squares, connected by straight lines); squares; fit of the experimental data: dashed line; model of Kiefer and Straaten (1986): solid line. The calculated data for 12 C 6? has been radially corrected by 30 nm (for details see text) this uncertainty is included. As in the experiment of Schmollack et al. (2000), one hit may contain one or more d- rays generated by the corresponding single passing ion. In general, our results are in good agreement with experimental data, except for 4 He 2? ions and at large radial distances for the other ions. At a radial distance of *75 nm, which corresponds to ion tracks barely touching the edge of the cylinder, the frequency of hits decreases by about one order of magnitude. For 12 C 6? ions, the experimental result for 90 nm does not show a significant reduction that is observed with 4 He 2? and 16 O 8? ions. This suggests that there is a systematic error of about 30 nm on the radial distance for the 12 C 6? experiments. By adding 30 nm to the radial distance, our simulation results are in much better agreement. This operation is also done to other simulation results obtained with 12 C 6? ions. At larger radial distance, the decrease is then approximately linear on this plot, in agreement with the experimental data. The faster decrease in the calculated frequency of target hits may be indicative of a condensed phase effect on the electron cross-sections, since our previously calculated electron penetration ranges are in excellent agreement with the experimental data (Plante and Cucinotta 2009). The largest uncertainty in the electron cross-sections is at low energy; indeed, since much less high-energy electrons are generated by the 4 He 2? ions, this may explain why the results are not as good for 4 He 2? ions. Nevertheless, our simulations clearly indicate the steep decrease near the edge of the target, which is not reproduced by the model of Kiefer and Straaten (1986). The effect of the target size on the frequency of hits is shown on Fig. 4 for 16 O 8? ions. The decrease starts at about 75, 150 and 300 nm, respectively, which is half the diameter of the cylinder. The decrease is not as steep as in the case of 12 C 6? and 4 He 2? ions, because there are much more d-rays in the penumbra (see Fig. 1), so the probability of hits decreases slower. Distribution of energy deposition events The distribution of energy deposition events in a 150-nm target is calculated for 16 O 8? ions at 25, 60, 90, 270, 860 and 1100 nm (Fig. 5) by recording the energy deposition in target volumes for each simulation history in energy bins. Our results are compared with the Schmollack et al. (2000). The agreement is not perfect, but the general trend of our calculated curves follows the experimental data. The positions of the maximum of the peaks are close to the experimental values. The model of Kiefer and Straaten (1986) was not used to obtain the distribution of energy deposition events and may require more calculations to do so. In general, the experimental peaks are larger than the calculated peaks, which may result from an uncertainty on the position of the target, estimated to be about 50 nm. The peak is sharper for the radial distances of 25 and 60 nm, corresponding to a direct hit by the ion. For 90 nm and greater distances, the target is not hit by the track core; as expected, the peaks become broader. There are large statistical fluctuations in the

5 Fig. 4 Relative frequency of target hits by d-rays as a function of the target radial distance for 16 O 8? ions of 21.2 MeV amu -1, for target sizes of 150, 300 and 600 nm, respectively. This calculation: black squares, connected by straight lines; experimental data from Schmollack et al. (2000): open squares; fit of the experimental data: dashed line; model of Kiefer and Straaten (1986): solid line experimental data of Schmollack et al. (2000), which are probably due to rather small dose intervals. Mean specific energy per target hit The mean specific energy per target hit was calculated by scoring the dose deposited in the cylinder and dividing it by the number of target hits. The calculations performed for 4 He 2?, 12 C 6? and 16 O 8? ions on a 150-nm target are shown on Fig. 6. Our data agree very well with experimental data for the 16 O 8? ion and reproduce the steep decrease at about 75 nm, which corresponds to the edge of the cylinder. For the 12 C 6? ion, the 30-nm correction is added to the radial distance. The calculated data for a radial distance[100 nm are in excellent agreement with experimental data. Rather confusing results are obtained for 4 He 2? ions. Our data seems to indicate a decrease in z 1 (r) at about 75 nm, but almost returns to the previous level at about 100 nm. The data for 4 He 2? are not in agreement with the experimental data, but are closer to the predictions of the model of Kiefer and Straaten (1986). A tentative explanation can be tried. When the cylinder is fully located in the penumbra region, the energy deposition events are from secondary electrons and are expected to be more or less constant. In fact, it is instructive to superpose the experimental and the calculated data of the three ions on the same plot (not shown). The energy loss per event is the same for all ions in the penumbra, except for 4 He 2? ions. However, the curve of Kiefer and Straaten (1986) is also in agreement with other ion s data. Thus, we may have some doubt about the validity of the penumbra data for 4 He 2? ions. We also note that the uncertainty on the experimental data is larger for 4 He 2? ions than for 12 C 6? and 16 O 8? ions. In the vicinity of the penumbra radius, the model of Kiefer and Straaten (1986) predicts an increase in z 1 (r) followed by a steep decrease to zero. This behavior is not found experimentally and may be due to simplifications inherent in deterministic calculations, since similar trends were found in a model by Cucinotta et al. for smaller (Cucinotta et al. 1999) and larger volumes (Cucinotta et al. 1998). This effect is more important for larger target volumes, i.e., 300 and 600 nm. We have calculated z 1 (r) for 16 O 8? ions of 21.2 MeV amu -1, for 150-, 300- and 600-nm targets. The results are shown in Fig. 7. The agreement between our calculated values and the experimental data is very good; the steep drop of z 1 (r) near the edge of the cylinder is also well reproduced by our calculations. At large radial distances, energy deposition in the target volume is a very rare event, and our calculations may not be conclusive because of the poor statistics. However, we have found no evidence of the increase in the vicinity of the penumbra radius predicted by deterministic models (Kiefer and Straaten 1986; Cucinotta et al. 1998, 1999). Mean specific energy per ion The mean specific energy per ion was obtained by calculating the dose deposited in a target volume and dividing it by the total number of incident ions. The calculation has been performed once again for 4 He 2?, 12 C 6? and 16 O 8?

6 experimental data. The agreement is excellent for all ions. For 12 C 6? ions, the 30-nm correction is added to the radial distance. Over about 100 nm, the trend is the same as the experimental data and the model of Kiefer and Straaten (1986) for all ions. The calculation has been repeated for 16 O 8? ions on 150-, 300- and 600-nm targets. Results are shown in Fig. 9. The agreement between the results for our calculation and experimental data is very good for the 150-nm target. The calculation of Kiefer and Straaten (1986) is better than ours for the 600-nm target. Since the mean specific energy per target hit calculated for the 16 O 8? ion (Fig. 7) is in excellent agreement with the experimental data, we conclude that our results shown in Fig. 9 are the consequence of the frequency of hits, which are not so good at large radial distances for the 600-nm target. Conclusion Fig. 5 Probability densities of the specific energies z for a 150-nm target at the vicinity of a 25 MeV amu -116 O 8? ion at radial distances 25, 60, 90, 270, 860 and 1100 nm, respectively. This calculation: solid line; Schmollack et al. (2000): dashed line ions on a 150-nm target. Results are shown in Fig. 8. Our calculations are able to reproduce the steep decrease near the edge of the cylinder, in good agreement with We have used our recent Monte Carlo simulation codes of water radiolysis by ions and electrons RITRACKS and RETRACKS, respectively, to reproduce the experiment of Schmollack et al. (2000). A cylindrical target was placed at various radial distances in the vicinity of 4 He 2?, 12 C 6? and 16 O 8? ion tracks. The simulation programs were then used to calculate the frequency of target hits, the dose deposition, and the mean specific energy per target hit and per ion. Schmollack et al. used a tissue-equivalent gas mixture to simulate the target volume surrounded by tissue. The Fig. 6 Mean specific energy per target hit for a 150-nm target in the vicinity of 16 O 8? of 21.2 MeV amu -1, 12 C 6? of 25 MeV amu -1 and 4 He 2? of 25 MeV amu -1. This calculation: black squares, connected by straight lines; squares; fit of the experimental data: dashed line; model of Kiefer and Straaten (1986): solid line. The calculated data for 12 C 6? has been radially corrected by 30 nm (for details see text)

7 Fig. 7 Mean specific energy per target hit for 150-, 300- and 600-nm targets in the vicinity of 16 O 8? of 21.2 MeV amu -1. This calculation: black squares, connected by straight lines; squares; model of Kiefer and Straaten (1986): solid line Fig. 8 Mean specific energy per ion for a 150-nm target in the vicinity of 16 O 8? of 21.2 MeV amu -1, 12 C 6? of 25 MeV amu -1 and 4 He 2? of 25 MeV amu -1. This calculation: black squares, connected by straight lines; squares; fit of the experimental data: dashed line; model of Kiefer and Straaten (1986): solid line. The calculated data for 12 C 6? has been radially corrected by 30 nm (for details see text) experimental conditions were certainly different from the simulation, but it is unclear how this leads to differences between our results and theirs. The faster decrease observed in our calculated frequency of target hits in the penumbra may be indicative of a condensed phase effect on the electron cross-sections. The paper of Schmollack et al. (2000) also indicates an uncertainty on the position of the target of about 50 nm, which affects their results at small radial distances. For 12 C 6? ions and the 150-nm target size, the comparison indicates that the radial distances were overestimated by about 30 nm in the experimental data set. Nevertheless, in general, our calculations are in good agreement with their data. Our simulations were able to reproduce data that could not be calculated by the model of

8 Fig. 9 Mean specific energy per ion for 150-, 300- and 600- nm targets in the vicinity of 16 O 8? of 21.2 MeV amu -1. This calculation: black squares, connected by straight lines; squares; model of Kiefer and Straaten (1986): solid line Kiefer and Straaten (1986). The overall good agreement of our simulations with experimental data provides another validation of our Monte Carlo tracks structures programs RITRACKS and RETRACKS. These studies are of great relevance to understand DNA damage that is caused by heavy ions, which is very important to understand the risk of galactic cosmic rays to which astronauts will be exposed during prolonged exploration missions, and can be applied to larger volumes for microdosimetry applications (Metting et al. 1988; Badhwar and Cucinotta 2000) in our future work. Acknowledgments This work was supported by the NASA Space Radiation Risk Assessment Project. We also thank the referees for their useful comments. References Autsavapromporn N, Meesungnoen J, Plante I, Jay-Gerin J-P (2007) Monte Carlo study of the effects of acidity and LET on the primary free-radical and molecular yields of water radiolysis application to the Fricke Dosimeter. Can J Chem 85: Badhwar GD, Cucinotta FA (2000) A comparison on depth dependence of dose and linear energy transfer spectra in aluminum and polyethylene. Radiat Res 153:1 8 Ballarini F, Alloni D, Facoetti A, Ottolenghi A (2008) Heavy-ion effects: from track structure to DNA and chromosome damage. New J Phys 10: Cobut V, Frongillo Y, Patau JP, Goulet T, Fraser M-J, Jay-Gerin J-P (1998) Monte-Carlo simulation of fast electron and proton tracks in liquid water I. Physical and physicochemical aspects. Radiat Phys chem 51: Cucinotta FA, Durante M (2006) Cancer risk from exposure to galactic cosmic rays: implications for space exploration by human beings. Lancet Oncol 7: Cucinotta FA, Katz R, Wilson JW (1998) Radial distribution of electron spectra from high-energy ions. Radiat Environ Biophys 37: Cucinotta FA, Nikjoo H, Goodhead DT (1999) Application of amorphous track models in radiation biology. Radiat Env Biophys 38:81 92 Cucinotta FA, Nikjoo H, Goodhead DT (2000) Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles. Radiat Res 153: Dingfelder M (2006) Track structure: time evolution from physics to chemistry. Radiat Prot Dosim 122:16 21 Durante M, Cucinotta FA (2008) Heavy ion carcinogenesis and human space exploration. Nat Rev Cancer 8: Elsässer T, Cunrath R, Krämer M, Scholz M (2008) Impact of track structure calculations on biological treatment planning in ion radiotherapy. New J Phys 10: Emfietzoglou D, Papamichael G, Moscovitch M (2000) An event-byevent computer simulation of interaction of energetic charged particles and all their secondary electrons in water. J Phys D Appl Phys 33: Glass WA, Roesch WC (1972) Measurement of ionization distributions in tissue-equivalent gas. Radiat Res 49: Goodhead DT, Nikjoo H (1989) Track structure analysis of ultrasoft X-rays compared to high- and low-let radiations. Int J Radiat Biol 55: Jay-Gerin J-P, Ferradini C (1999) La radiolyse de l eau et des solutions aqueuses: historique et actualité. Can J Chem 77: Kiefer J, Straaten H (1986) A model of ion track structure based on classical collision dynamics. Phys Med Biol 31: Kreipl MS, Friedland W, Paretzke HG (2009a) Time- and spaceresolved Monte-Carlo study of water radiolysis for photon, electron and ion irradiation. Radiat Env Biophys 48:11 20

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