International Journal of Radiation Biology, January–February 2012; 88(1–2): 189–194© 2012 Informa UK, Ltd.ISSN 0955-3002 print / ISSN 1362-3095 onlineDOI: 10.3109/09553002.2011.624572

A Monte Carlo evaluation of carbon and lithium ions dose distributions in water

Reza Taleei1, Martha Hultqvist2, Irena Gudowska2 & Hooshang Nikjoo1

1Radiation Biophysics Group, Department of Oncology-Pathology, Karolinska Institute, Stockholm, and 2Medical Radiation Physics, Department of Physics, Stockholm University, Stockholm, Sweden

Correspondence: Reza Taleei, Radiation Biophysics Group, Department of Oncology-Pathology, Karolinska Institute, PO Box 260, SE-171 76 Stockholm, Sweden. Tel: 46 8 517 748 72. Fax: 46 8 343 525. E-mail: Reza.Taleei@ki.se

(Received 24 February 2011; revised 5 September 2011; accepted 7 September 2011)

Introduction

Radiotherapy with low linear energy transfer (LET) radia-tions like photons and electrons has shown promising results to cure cancer in the past half century. Many efforts have been made to maximize the tumour control probability (TCP) while minimizing the normal tissue complication probability (NTCP) (Niemierko et al. 1992). Among the important developments in this area are novel methods like conformal radiotherapy, intensity modulated radiotherapy (IMRT), Image guided radiotherapy (IGRT) (Bucci et al. 2005), and more recently the use of particles such as proton and carbon ions (Tsujii et al. 2008, Combs et al. 2010). Therefore, due to the possibil-ity of achieving a dose distribution that is highly conformed to the tumour volume while surrounding normal tissues are spared, radiotherapy with light ions or so-called hadron therapy has gained interest worldwide. The favourable dose distribution is enabled by the inverse depth dose profile of ions which ends with a sharp Bragg peak, and by the small lateral scattering of the ions. For ions heavier than protons, an additional advantage is the increased relative biological effectiveness (RBE) as compared to conventional photons and electrons, and protons.

The Monte Carlo method has been proved to be accurate and promising for the calculations of dose distributions both in the tumour and normal tissue. The general purpose Monte Carlo codes, SHIELD-HIT10 (Heavy Ion Transport) (Gudowska et al. 2004, Geithner et al. 2006, Sobolevsky 2010) and FLUKA 2008.3d.1 (FLUKtuierende KAskade) (Ferrari et al. 2005, Battistoni et al. 2007), are capable of performing heavy ion transport in heterogeneous complex geometries. SHIELD-HIT has been used in several studies of relevance to radiotherapy with light ions, e.g., in the evaluation of secondary organ absorbed doses from irradiation with pri-mary beams of protons up to oxygen ions (Hultqvist and Gudowska 2010), and studies of the production of clinically useful positron emitter beams during carbon ion decelera-tion (Lazzeroni and Brahme 2011). Similarly, the FLUKA code

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AbstractPurpose: To compare dose distributions on the central- and off-axis for 12C and 7Li ion beams simulated by the codes SHIELD-HIT (Heavy Ion Transport) and FLUKA (FLUKtuierende KAskade), and compare with experimental data for 300 MeV/u 12C and 185 MeV/u 7Li ion beams.Materials and methods: The general purpose Monte Carlo codes, SHIELD-HIT10 and FLUKA 2008.3d.1 were used for the ion dose distribution calculations. SHIELD-HIT transports hadrons and atomic nuclei of arbitrary charge and mass number in an energy range from 1 keV/u up to 1 GeV/u. Similarly, FLUKA transports charged hadrons in an energy range from 100 keV up to 20 TeV. Neutrons are transported down to thermal energies in both codes. Inelastic nuclear interactions are modelled in SHIELD-HIT by the Many Stage Dynamical Model (MSDM), whereas in FLUKA the Pre-Equilibrium Approach to Nuclear Thermalisation (PEANUT) package which includes a Generalized Intra-Nuclear Cascade model was used.Results: The dose distributions in water irradiated with 300 MeV/u 12C and 185 MeV/u 7Li ion beams were simulated with the two codes. Studies were performed of the energy deposition both on the central axis and at lateral distances up to 10 cm off-axis. The dose distributions calculated by SHIELD-HIT and FLUKA were compared with published experimental data. The dose mean lineal energy y–D, frequency mean lineal energy y–F , dose mean specific energy z–D , and frequency mean specific energy z–F were calculated with the ion track-structure code PITS99 (Positive Ion Track Structure 99), coupled with the electron code KURBUC for the primary and secondary ions average energies at 1 mm before the Bragg peak.Conclusion: The Monte Carlo codes show good agreement with experimental results for off-axis dose distributions. The disagreements in the Bragg peak region for the central-axis dose distributions imply that further improvements especially in the nuclear interaction models are required to increase the accuracy of the codes.

Keywords: Dose distributions, Monte Carlo, carbon and lithium ions

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190 R. Taleei et al.

has been used in radiotherapy studies such as calculations of physical and biological doses for hadron therapy (Battistoni et al. 2008). Several papers have reported comparisons of simulated and measured dose distributions for 12C beams on the central axis with FLUKA (Mairani et al. 2010, Parodi et al. 2010) and SHIELD-HIT (Gudowska et al. 2004, Geithner et al. 2006).

In this work, the capability of SHIELD-HIT and FLUKA to reproduce the measured energy deposition in water by 12C and 7Li ion beams reported by Martino et al. (2010) at GSI (Gesellschaft für Schwerionenforschung) was investigated. The calculations were performed both on the central-axis and off-axis. In addition, the microdosimetric parameters of the ions’ average energies close to the Bragg peak maximum were calculated using the Monte Carlo track structure codes PITS99 (Positive Ion Track Structure 99) (Wilson and Nikjoo 1999), for the ion transport, and KURBUC (Uehara et al. 1999) for the delta electrons transport.

Materials and methods

Experimental set-up and simulation geometryDose distributions in water from irradiation with 300 MeV/u 12C and 185 MeV/u 7Li beams were measured by Martino et al. (2010) with a tissue equivalent proportional counter (TEPC) detector (outer shell diameter ∼ 2 cm). The water phantom was a 30 30 30 cm3 cube including a 2 cm Para-Methoxymethamphetamine (PMMA) wall, and before reaching the phantom the ions impinged on a 100 mm alu-minium window, a 1 mm thick scintillation detector, and a 13.5 mm thick ionization chamber (Figure 1). The beams had ∼ 2–3 mm spot diameter at the entrance of the phantom.

In the simulations with SHIELD-HIT and FLUKA, the energy deposition was scored directly in water, i.e., without simulating the TEPC. The water phantom, including the

PMMA wall was simulated, as well as the aluminium win-dow. However, the scintillation detector and ionization chamber were not considered in the simulations. The scor-ing volumes in water were cylinders of 9 mm diameter and 1 mm height. The energies of the simulated ions were adjusted to have a good agreement between the calculated and mea-sured position of the Bragg peak maximum (306 MeV/u 12C and 186 MeV/u 7Li). The beam energy Gaussian full width at half maximum (FWHM) was 1%, and the spot diameter was 3 mm at the aluminium window. In order to investigate the dif-ferences between the codes in dose calculations prior to the experimental setting simulations, the central axis depth dose in a simple cylindrical water phantom with 10 cm radius and 1 mm depth resolution were simulated for monoenergetic 12C and 7Li ions.

Simulation parameters

Settings used in the simulations with the SHIELD-HIT codeIn the simulations with the code SHIELD-HIT10, charged particles were transported down to 25 keV/u using stopping power data from ICRU49 (International Commission on Radiation Units and Measurements [ICRU] 1993) and ICRU73 (ICRU 2005), while neutrons were transported down to ther-mal energies. Energy straggling of the charged particles was described by the Vavilov model and multiple scattering was modelled according to the theory by Molière. The Many Stage Dynamical Model (MSDM) (Botvina et al. 1997, Dementyev and Sobolevsky 1999) was used for the modelling of inelastic nuclear interactions.

Settings used in the simulations with FLUKAIn the simulations with the code FLUKA, the hadron ther-apy settings for the standard code were used. The FLUKA

Figure 1. Experimental and simulation geometry. The detector positions in the water phantom are presented with red spots. The ion beams impinged on the aluminium window, scintillation detector (SC) and ionization chamber (IC) before entering the water phantom.

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C and Li ions dose distributions 191

code transports charged hadrons by multiple-Coulomb scattering down to 100 keV and neutrons down to thermal energies. The FLUKA code uses a parameterized stopping power developed from ICRU, e.g., for proton and a particles which shows within 1% agreement with ICRU49 stopping powers (ICRU 1993, Parodi and Squarcia 2001). The FLUKA code has an energy straggling model similar to the Blunck-Leisegang energy loss straggling model and multiple scat-tering based on the Molière theory. The inelastic nuclear interactions in FLUKA are modelled by the Pre-Equilibrium Approach to Nuclear Thermalisation (PEANUT) pack-age which includes a Generalized Intra-Nuclear Cascade model (Ballarini et al. 2007). The hadronic interactions governed by Boltzmann master equation (BME) up to 100 MeV/u (not yet included in the standard version), and relativistic quantum molecular dynamics (RQMD) model from 100 MeV/u to 5 GeV/u could be used for simulations with FULKA. However, in the standard FLUKA version that we have used in our simulations, the BME model is not used. Therefore no nuclear interaction below 100 MeV/u was considered. Interactions below 100 MeV/u influence both the fragmentation tail and the lateral distribution, so results with BME could be rather different from the results presented in this paper.

Microdosimetry calculationsThe average energies of the primary and secondary ions were calculated in the simple cylinder water phantom with the code SHIELD-HIT at 1 mm before the Bragg peak (17.1 cm and 17.6 cm for 7Li and 12C ions, respectively). The microdo-simetric parameters dose mean lineal energy y–

D, frequency mean lineal energy y–

F, dose mean specific energy z–D, and

frequency mean specific energy z–F were calculated with the

track-structure code PITS99, for the primary ion simulation, coupled with the KURBUC code for the delta electrons simu-lation. The details of microdosimetric calculations have been published elsewhere (Lillhok et al. 2007, Hultqvist et al. 2010, Nikjoo and Lindborg 2010).

Results

In order to compare the codes SHIELD-HIT and FLUKA, dose calculations were made on the central axis in a simple cylindrical water phantom (10 cm radius and 30 cm length) divided into slabs of 1 mm height. The number of simulated primary particles was 1 million. Figure 2 illustrates the calcu-lated depth dose in the cylindrical water phantom. The 12C and 7Li ions doses simulated with the FLUKA code are pre-sented in crosses with dashed line, and diamonds with solid

0 5 10 15 200

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16.5 17.0 17.50

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Figure 2. Depth dose in a simple cylindrical water phantom with 10 cm radius for (a) 300 MeV/u 12C and (b) 185 MeV/u 7Li ion beams simulated by FLUKA and SHIELD-HIT. In order to clarify the differences, the Bragg peak region has been magnified.

Figure 3. Central-axis and off-axis depth dose in water (experimental set up in Figure 1) for (a) 306 MeV/u 12C and (b) 186 MeV/u 7Li ions simulated by FLUKA, SHIELD-HIT, and experimental results. The error bars represent the standard deviation of the mean for the simulations with 1106 primary particles (The simulation data are provided in a tabulated format in the Supplementary material, available online).

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of the experimental setup with the FLUKA code in crosses, and with the SHIELD-HIT code in diamonds together with the experimental data in circles for the 12C and 7Li ion beams, respectively. It was expected from the first simula-tions in the cylindrical phantom that the simulated central axis dose show differences with the measured dose in the Bragg peak and beyond where the simulations overesti-mate the experimental results. In comparison to the 7Li results, the 12C simulation is in a better agreement with the experimental data.

Microdosimetric spectra and parameters help to under-stand the details of energy deposition for the primary and secondary ions separately. Figure 4 illustrates the absolute frequency of deposition of events of energy E per target and per unit dose in cylindrical volumes of 30 nm length and diameter in water irradiated with mean energies of primary and secondary ions.

Table I lists the ions and their mean energies at 1 mm before the Bragg peak. The corresponding linear energy transfer (LET) (Watt 1996), average stopping power, dose mean lineal energy y–

D, frequency mean lineal energy y–F,

line illustrate the doses simulated by the code SHIELD-HIT. The results show fairly good agreement between the codes (within 10%) in energy deposition in the region before the Bragg peak (up to 16.5 cm). But there are larger differences in the Bragg peak and beyond, probably due to differences in the modelling of nuclear fragmentation and stopping pow-ers used in the codes. The discrepancies for 7Li are larger than for 12C.

In order to simulate the experimental set up (Figure 1), several beam energies and scoring sizes were investigated to achieve the best agreement with the measured central axis dose distribution. The optimum central dose distribu-tion for 12C ion beam was achieved with 306 MeV/u 1% Gaussian FWHM for both codes. The optimum central dose distribution for 7Li ion beam was achieved with 186 MeV/u 1% Gaussian FWHM. The optimum setting for the simulations of both ion beams were achieved with the cylindrical scoring volume of 4.5 mm radius and 1 mm height. The spot size radius at the aluminium window was set to 1.5 mm. Figures 3a and 3b show the dose in central- and off-axis (1, 2, 5, 10 cm from centre) for the simulation

Figure 4. Frequencies of energy deposition in a cylindrical volume (30 nm height by 30 nm diameter) in water irradiated with 12C and 7Li ions. The left ordinate gives the absolute frequency (f E) of deposition events greater than the energy E (eV) in the target volume when randomly positioned, and uniformly irradiated with 1Gy of the given radiation. The right ordinate is the corresponding average number of events in such targets in a typical mammalian cell. The frequency of hits of any size is given by f( E) 1/Z–F and the number of events corresponding to the frequency f( E), is obtained from n [f( E)/f( 0)]M, where M is the number of genetic targets per genome. There are about 1.6 106 elements of chromatin fibers per genome.

Table I. Microdosimetry parameters for primary and secondary ions in 7Li and 12C beams.

Primary beam FragmentsAverage energy

(MeV/u)LET (keV/mm)

(Watt 1996)

Average stopping power

(keV/mm)y–D

(keV/mm)y–F

(keV/mm)z–D

(cGy)z–F

(cGy)

C-12 18 101.76 103.0 75.53 20.42 1.14E 06 3.09E 05P 106 0.68 0.60 10.31 2.67 1.56E 05 4.04E 04

He-4 117 2.65 2.30 11.05 3.54 1.67E 05 5.35E 04Li-7 114 6.02 5.70 14.21 5.36 2.15E 05 8.09E 04Be-9 63 16.39 15.20 19.79 9.33 2.99E 05 1.41E 05B-11 53 29.47 28.30 27.46 12.58 4.15E 05 1.90E 05

Li-7 13 34.11 33.40 31.72 14.49 4.79E 05 2.19E 05P 48.5 1.21 1.20 10.80 3.01 1.63E 05 4.54E 04

He-4 30 7.68 7.30 14.92 6.22 2.25E 05 9.39E 04

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C and Li ions dose distributions 193

dose mean specific energy z–D, and frequency mean specific

energy z–F of the ions are listed in Table I. The lighter the frag-

ments, the higher the mean energy, and the lower the y–D.

Discussion and conclusion

In comparison to the experimental results, both codes show good agreement in off-axis doses. While the size of the scoring volume had a minor influence on the calcu-lated dose delivery off-axis, it had a major influence on the dose in the central axis. Both codes overestimate the central-axis dose after the Bragg peak. The 12C dose dis-tribution is in better agreement in comparison with the 7Li dose distribution for both codes, which could partly be due to the fact that there are more experimental data available for benchmarking of 12C. Differences between the results of the codes before and after the Bragg peak are mainly attributed to the different nuclear interaction models employed in the codes. Although additional test simulations with SHIELD-HIT showed that the scintillation detector does not have a significant effect on the off-axis doses (data not shown), it is recommended to consider the monitoring devices in the simulations if the geometry and the positions of these devices are accurately known. Since several secondary particles like neutrons, protons, helium ions, and heavier ions are generated and followed by the Monte Carlo codes, the accuracy of the interaction models is of great importance to calculate the dose distribution. Although the Monte Carlo codes show good agreement with experimental results, further improvements espe-cially in the nuclear interaction models are required to increase the accuracy of the codes.

The microdosimetry calculations have been included in the work to analyze the spectrum of the energy depositions. Such calculations provide a wealth of information on details of energy deposition events at microscopic volumes (Nikjoo and Lindborg 2010). It can be seen from Figure 4 that for a dose of 1 Gy of low LET radiation, which causes nearly 50% killing of most mammalian cells, a considerable number of chromatin segments have received substantial amounts of energy. For example, for energy deposition of E 200 eV in the volume of the 30 30 nm cylinder, this energy deposition corresponds to roughly on average to ∼ 20 atomic interactions and nearly 10 of these being ionizations and the remainder excitations. Substantial molecular damage may arise from such energy deposition in the DNA. Since the frequency of energy depositions, the average lineal and specific energies have been calculated for the average energies of the ions at 1 mm before the Bragg peak, the same calculations for the whole energy spectrum of the ions at different depth and lateral distances will be required to calculate more accurate microdosimetric parameters.

Acknowledgements

We would like to thank Giovanna Martino for providing experimental data in electronic format. The work of the Radi-ation Biophysics Group was partially supported by SSM - The Swedish Radiation Safety Authority.

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

ReferencesBallarini F, Battistoni G, Brugger M, Campanella M, Carboni M,

Cerutti F, Empl A, Fasso A, Ferrari A, Gadioli E, Garzelli MV, Lantz M, Mairani A, Mostacci A, Muraro S, et al. 2007. The physics of the FLUKA code: Recent developments. Advances in Space Research 40: 1339–1349.

Battistoni G, Muraro S, Sala PR, Cerutti F, Ferrari A, Roesler S, Fasso A, Ranft J. 2007. The FLUKA code: Description and benchmarking. Proceedings of the Hadronic Shower Simulation Workshop 2006 (Fermilab 6–8 September 2006). AIP Conference Proceedings 896:31–49.

Battistoni G, Broggi F, Brugger M, Campanella M, Carboni M, Cerutti F, Colleoni P, D’Ambrosio C, Empl A, Fasso A, Ferrari A, Gadioli E, Lantz M, Lee K, Lukasik G, et al. 2008. The FLUKA code and its use in hadron therapy. Nuovo Cimento Della Societa Italiana Di Fisica C-Geophysics and Space Physics 31:69–75.

Botvina AS, Dementyev AV, Smirnova ON, Sobolevsky NM, Toneev VD. 1997. MSDM-multi-stage dynamical model. In: Michel R, Nagel P, editors. International Codes and Model Intercomparison for Inter-mediate Energy Activation Yields NSC/DOC(97)-1, NEA/P&T No 14. Paris: OECD. pp 307–312.

Bucci MK, Bevan A, Roach M. 2005. Advances in radiation therapy: Conventional to 3D, to IMRT, to 4D, and beyond. CA: A Cancer Journal for Clinicians 55:117–134.

Combs SE, Jakel O, Haberer T, Debus J. 2010. Particle therapy at the Heidelberg Ion Therapy Center (HIT) – integrated research-driven university-hospital-based radiation oncology service in Heidelberg, Germany. Radiotherapy and Oncology 95:41–44.

Dementyev AV, Sobolevsky NM. 1999. SHIELD-universal Monte Carlo hadron transport code: Scope and applications. Radiation Measure-ments 30:553–557.

Ferrari A, Sala PR, Fasso A, Ranft J. 2005. FLUKA: A multi-particle transport code, CERN-2005-10, INFN/TC_05/11, SLAC-R-773.

Geithner O, Andreo P, Sobolevsky N, Hartmann G, Jakel O. 2006. Calcu-lation of stopping power ratios for carbon ion dosimetry. Physics in Medicine and Biology 51:2279–2292.

Gudowska I, Sobolevsky N, Andreo P, Belkic D, Brahme A. 2004. Ion beam transport in tissue-like media using the Monte Carlo code SHIELD-HIT. Physics in Medicine and Biology 49:1933–1958.

Hultqvist M, Gudowska I. 2010. Secondary absorbed doses from light ion irradiation in anthropomorphic phantoms representing an adult male and a 10 year old child. Physics in Medicine and Biology 55:6633–6653.

Hultqvist M, Lillhok JE, Lindborg L, Gudowska I, Nikjoo H. 2010. Nanodosimetry in a 12C ion beam using Monte Carlo simulations. Radiation Measurements 45:1238–1241.

International Commission on Radiation Units and Measurements (ICRU). 1993. Report 49. Stopping powers and ranges for protons and alpha particles. Bethesda, MD: ICRU.

International Commission on Radiation Units and Measurements (ICRU). 2005. Report 73. Stopping of ions heavier than helium. Bethesda, MD: ICRU.

Lazzeroni M, Brahme A. 2011. Production of clinically useful positron emitter beams during carbon ion deceleration. Physics in Medicine and Biology 56:1585–1600.

Lillhok JE, Grindborg JE, Lindborg L, Gudowska I, Carlsson GA, Soderberg J, Kopec M, Medin J. 2007. Nanodosimetry in a clini-cal neutron therapy beam using the variance-covariance method and Monte Carlo simulations. Physics in Medicine and Biology 52: 4953–4966.

Mairani A, Brons S, Cerutti F, Fasso A, Ferrari A, Kramer M, Parodi K, Scholz M, Sommerer F. 2010. The FLUKA Monte Carlo code cou-pled with the local effect model for biological calculations in car-bon ion therapy. Physics in Medicine and Biology 55:4273–4289.

Martino G, Durante M, Schardt D. 2010. Microdosimetry measure-ments characterizing the radiation fields of 300 MeV/u (12)C and 185 MeV/u (7)Li pencil beams stopping in water. Physics in Medi-cine and Biology 55:3441–3449.

Niemierko A, Urie M, Goitein M. 1992. Optimization of 3D radiation-therapy with both physical and biological end-points and constraints. International Journal of Radiation Oncology Biology Physics 23:99–108.

Int J

Rad

iat B

iol D

ownl

oade

d fr

om in

form

ahea

lthca

re.c

om b

y M

emor

ial U

nive

rsity

of

New

foun

dlan

d on

09/

20/1

3Fo

r pe

rson

al u

se o

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194 R. Taleei et al.

Tsujii H, Kamada T, Baba M, Tsuji H, Kato H, Kato S, Yamada S, Yasuda S, Yanagi T, Kato H, Hara R, Yamamoto N, Mizoe J. 2008. Clinical advantages of carbon-ion radiotherapy. New Journal of Physics 10:075009–075024.

Uehara S, Nikjoo H, Goodhead DT. 1999. Comparison and assessment of electron cross sections for Monte Carlo track structure codes. Radiation Research 152:202–213.

Watt DE. 1996. Quantities for dosimetry of ionizing radiations in liquid water. 8th ed. London: Taylor & Francis.

Wilson WE, Nikjoo H. 1999. A Monte Carlo code for positive ion track simulation. Radiation and Environmental Biophysics 38: 97–104.

Nikjoo H, Lindborg L. 2010. RBE of low energy electrons and photons. Physics in Medicine and Biology 55:R65–109.

Parodi K, Squarcia S. 2001. Improvement of low-energy stopping power algorithms in the FLUKA simulation program. Nuclear Instruments & Methods in Physics Research Section a – Accelerators. Spectrom-eters Detectors and Associated Equipment 456:352–368.

Parodi K, Mairani A, Brons S, Naumann J, Kramer M, Sommerer F, Haberer T. 2010. The influence of lateral beam profile modifications in scanned proton and carbon ion therapy: A Monte Carlo study. Physics in Medicine and Biology 55:5169–5187.

Sobolevsky N. 2010. SHIELD_HIT Multipurpose Hadron Transport Code, updated 12.01.11: http://www.inr.ru/shield/

Supplementary Material

Simulation data

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