INSTITUTE OF PHYSICS PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 49 (2004) 1933–1958 PII: S0031-9155(04)70415-7

Ion beam transport in tissue-like media using theMonte Carlo code SHIELD-HIT

Irena Gudowska1, Nikolai Sobolevsky2, Pedro Andreo1, Dževad Belkic1

and Anders Brahme1

1 Division of Medical Radiation Physics, Karolinska Institutet and Stockholm University,PO Box 260, S-171 76 Stockholm, Sweden2 Department of Neutron Research, Institute for Nuclear Research of the Russian Academyof Sciences, 117312 Moscow, Russia

Received 14 October 2003Published 29 April 2004Online at stacks.iop.org/PMB/49/1933DOI: 10.1088/0031-9155/49/10/008

AbstractThe development of the Monte Carlo code SHIELD-HIT (heavy ion transport)for the simulation of the transport of protons and heavier ions in tissue-likemedia is described. The code SHIELD-HIT, a spin-off of SHIELD (availableas RSICC CCC-667), extends the transport of hadron cascades from standardtargets to that of ions in arbitrary tissue-like materials, taking into accountionization energy-loss straggling and multiple Coulomb scattering effects. Theconsistency of the results obtained with SHIELD-HIT has been verified againstexperimental data and other existing Monte Carlo codes (PTRAN, PETRA),as well as with deterministic models for ion transport, comparing depthdistributions of energy deposition by protons, 12C and 20Ne ions impingingon water. The SHIELD-HIT code yields distributions consistent with a propertreatment of nuclear inelastic collisions. Energy depositions up to and wellbeyond the Bragg peak due to nuclear fragmentations are well predicted.Satisfactory agreement is also found with experimental determinations of thenumber of fragments of a given type, as a function of depth in water, producedby 12C and 14N ions of 670 MeV u−1, although less favourable agreement isobserved for heavier projectiles such as 16O ions of the same energy. Thecalculated neutron spectra differential in energy and angle produced in a mimicof a Martian rock by irradiation with 12C ions of 290 MeV u−1 also showsgood agreement with experimental data. It is concluded that a careful analysisof stopping power data for different tissues is necessary for radiation therapyapplications, since an incorrect estimation of the position of the Bragg peakmight lead to a significant deviation from the prescribed dose in small targetvolumes. The results presented in this study indicate the usefulness of theSHIELD-HIT code for Monte Carlo simulations in the field of light ion radiationtherapy.

0031-9155/04/101933+26$30.00 © 2004 IOP Publishing Ltd Printed in the UK 1933

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1. Introduction

Investigations into the advantages of ‘heavy charged particles’ as compared to electrons,photons and neutrons for radiation therapy were initiated in the early 1950s, with the Bevalacaccelerator complex at the Lawrence Berkeley Laboratory LBL (now LBNL) in Berkeley(Chu et al 1993, Castro 1994, Raju 1996) pioneering the utilization of light (Z < 10) andheavy ions (neon and argon). The rationale for the use of ions instead of conventionalradiation therapy beams is at least twofold. First, the energy deposition increases along thepenetration depth of the beam ending with a sharp maximum (called the Bragg peak) at the endof the particle range. Moreover, the reduced range straggling and multiple Coulomb scatteringprocesses due to large particle mass result in a very narrow beam penumbra. Second, theintense ionization density along the particle path and particularly at the end of its range, resultsin an increased cell killing and augmented radiobiological effect largely superior to that ofconventional radiation therapy beams, especially for radio-resistant or hypoxic tumours (Chu1999, Kraft 2000a, Tsujii et al 2002).

Because of the lower equipment cost compared to other light ions, the use of protons inradiation therapy has become customary and currently the total number of patients treated withthis modality is more than thirty thousand (Particles 2001). However, the relative biologicaleffectiveness (RBE) of protons is only about 8–15% higher than that of photons or electrons,and much less (about 3 times lower) than that of light ions (1 < Z < 10). Heavy ions suchas neon and argon (first tested in Berkeley) have the highest linear energy transfer (LET) andtheir RBE is, therefore, elevated also in the beam entrance and the plateau regions, wherehealthy normal tissues are usually located. In addition, due to the large penetration of thefragmentation products released by the incident ions, the tail of the dose distribution beyondthe Bragg peak may be too high for sparing normal tissue close to the tumour.

The above-listed limitations motivated an increased interest worldwide in the use oflighter ions which resulted in the construction of the first clinical research facility, HIMAC,in Chiba, near Tokyo (Kanai et al 1999). HIMAC initiated the treatment of patients mainlywith carbon ions in 1994 (Kanai et al 1999) and thus far more than 1500 patients have beentreated by this facility. More recently, the advantageous results from Chiba with carbon beamsled to the design of a dedicated clinical facility in Hyogo, Japan (Itano et al 1995, Hyogo IonBeam Medical Center). The GSI heavy ion physics research facility in Darmstadt, Germany,initiated clinical treatments with carbon ions in 1997 (Kraft 2000b). This facility has usedcertain advanced 3D (three-dimensional) beam scanning techniques and positron emissiontomography (PET) imaging to monitor the dose delivery by visualizing all positron emitters(10C, 11C, 13N, 15O, . . . ) produced in the nuclear reactions of the incident carbon ions withtissue (Pawelke et al 1997). The promising results at GSI for an extended group of tumours(skull base, chordomas and chondrosarcomas; Debus et al (2000)) have motivated the plansfor construction of a dedicated clinical installation in Heidelberg, which should be ready by2006 (Eickhoff et al 1998, Bar et al 2001). Plans for building additional facilities for radiationtherapy with light ions have followed in Europe, and feasibility studies have been conductedfor other facilities in Italy (CNAO; Amaldi (2001)), Austria (MED-AUSTRON 1998), France(ETOILE 2002), and Sweden (Brahme et al 2001).

In order to evaluate the dose delivered to tissue and to estimate biological effects in lightion radiation therapy, accurate knowledge of the physics of ion interaction with matter isnecessary. Increased knowledge about the cross sections (differential in energy and angle)of different nuclear and atomic processes with light and heavy ions in tissue-like materials isrequired. The light and heavy ion transport problem is very complex and, therefore, there is aneed for extensive experimental and theoretical studies to develop accurate transport methods.

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This work describes the development of the Monte Carlo code SHIELD-HIT (heavy iontransport) for the transport of protons and heavier ions in the tissue-like matter of interest forlight ion therapy. Simulations of the transport of proton and heavier ions in various substanceshave been performed for projectiles with energies up to 700 MeV u−1. Spatial distributionsof the energy deposition, due to the primary beam particles and their secondaries generatedby nuclear interactions, have been computed for narrow pencil beams impinging on a waterphantom, up to depths well beyond the Bragg peak. The production of secondary particlesof different LET, as well as the track-length fluence differential in energy of all transportedparticles inside and outside a phantom, have also been computed. The results determined withSHIELD-HIT are shown to be consistent both with the available experimental data, with otherexisting Monte Carlo codes and with deterministic methods for ion transport in matter.

2. Status of Monte Carlo codes for ion transport

Several Monte Carlo (MC) computer codes exist, or are in the stage of development, forsimulation of the transport of light and heavy ions in matter. They are designed mainly forapplications in high-energy particle physics. A major drawback of the majority of the codesavailable for application in the field of radiation therapy is that their cut-off energies (thelowest possible energy handled by the code) are too close to the incident energies of interestin radiation therapy (about 500 MeV u−1).

The two major codes for simulation of hadronic cascades (neutrons, protons, pions),HETC (Armstrong and Chandler 1972) and SHIELD (Sobolevsky 1970) have been developedin the early 1970s in the US (Oak Ridge) and the former USSR (Dubna), respectively.They were applicable up to energies of about 30 GeV and SHIELD was later extendedto energies of the order of TeV (Dementyev and Sobolevsky 1997). The original HETCcode was based on Bertini’s model of intranuclear cascades (Bertini 1969), while SHIELDused the Dubna cascade-evaporation model of nuclear reactions (Barashenkov and Toneev1972). These two codes have evolved considerably, and while SHIELD has kept its originalname throughout, various spin-offs of HETC have emerged under the names of HERMES(Cloth et al 1988), LAHET (Prael and Lichtenstein 1989), MCNPX (Hughes et al 1997,MCNPX), NMTC/JAERI (Takada et al 1998) and PHITS (Iwase et al 2002). The HETCfamily of codes includes many components of basic physics via nuclear cross sections andit mainly concentrates on the transport of individual particles/ions at energies up to about10 GeV. A modern version of SHIELD (see below) can simulate the transport of hadronsand nuclei with energies in the range from TeV down to a few MeV, and to thermal energiesin the case of neutrons. This latter version of SHIELD has been benchmarked extensively(Dementyev and Sobolevsky 1999, Sobolevsky 2001), and its results were found to be in goodagreement with the available experimental data for various phenomena studied.

Since the mid-1970s another Monte Carlo code called MARS (Mokhov 1995, MARS)has been developed at the Institute of High Energy Physics, Russia, and the Fermi NationalAccelerator Laboratory, USA. A hadronic part of the current version MARS14 can simulatedetailed hadronic cascades in an arbitrary 3D geometry of shielding, in accelerator anddetector components for beam energies ranging from 1 MeV up to 100 TeV. In spite of thelatest important developments, especially concerning the implementation of modern particleevent generators of hadron–nucleus and nucleus–nucleus interactions, and their satisfactoryvalidation with experimental data (mainly for interactions at very high energies), this codeis still unsuitable for ion therapy purposes. This is because the transport of heavy chargedsecondaries (d, t, α and others) produced in hadronic cascades cannot be followed and theirenergy is deposited locally.

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Two Monte Carlo codes widely used in the European nuclear physics community havebeen FLUKA (Fasso et al 1997, Ferrari and Sala 1997) and GEANT3 (Brun et al 1978), bothdeveloped by various groups in the mid-1970s under the framework of CERN. The FLUKAcode is a self-sufficient hadron transport code, whereas GEANT3 is a package that can usedifferent generators of hadron–nucleus interactions adopted from other codes. FLUKA cansimulate the interactions and transport of different radiation types using the condensed-historyapproach, in particular, hadron–hadron and hadron–nucleus interactions in the energy range0–100 TeV, or nucleus–nucleus interactions in the range 5 GeV u−1 to 10 TeV u−1 (Fasso et al2001). FLUKA has frequently been used for proton transport for radiation therapy purposes(Agosteo et al 1998, Biaggi et al 1999). However, the version of FLUKA for light and heavyion transport at energies below 5 GeV u−1 is still under development (Andersen et al 2002).By applying the improved version of the relativistic quantum molecular dynamics (RQMD)model in the energy range 0.1–5 GeV u−1, satisfactory agreement between FLUKA andexperimental results has been obtained. Nevertheless, further developments, particularly fornucleus–nucleus interactions at energies below 5 GeV u−1 using a new self-consistent QMDmodel, are still in the planning stage. In the energy range below 100 MeV u−1 the Boltzmannmaster equation (BME) model will be adopted in FLUKA. These developments will allow afull Monte Carlo transport also for nuclei such as carbon ions in tissue-like media.

The first version of GEANT was purely electromagnetic, the hadron–nucleus (hA)generator GHEISHA was implemented in the GEANT3 package in 1980 and the FLUKAhA generator was included in 1985. GEANT3 has certain drawbacks regarding the simplicityof its approximations for nuclear fragmentation processes, but it has become a very useful toolin particle research after some modifications. However, a subsequent drastic change in thecode development strategy has made GEANT3 ‘officially unsupported’, so that the renewedefforts are now concentrated in developing an entirely new version, GEANT, completelyreprogrammed using object-oriented technology in C++. The GEANT4 code (Agostinelliet al 2003) is still in the development stage, especially for hadron and nuclei interactions inthe medium energy range.

A relatively new code, MCNPX (Hughes et al 1997, MCNPX), has been releasedby Los Alamos National Laboratories, USA. It combines the capabilities of LAHET(Prael and Lichtenstein 1989) and MCNP4B codes (Briesmeister 1997). MCNPX includes acombination of new models for hadron interactions with the models of previous codes likeLAHET and FLUKA87. The capabilities of MCNPX for light ion transport in radiationtherapy are still in the development phase and, at present, this code does not include thetransport of ions with A > 4.

For many years researchers in the field of nuclear physics, mainly for industrialapplications, have based their calculations on a ‘classic’ Monte Carlo code TRIM developedat the IBM Research Laboratories. However, this code, as well as its new versionsSRIM2000/2003 (SRIM) are rather simple and their strength lies in the calculation of ionstopping powers. It does not include nuclear collision models or delta-electron production,and a comparison of its results with experimental dose distributions of carbon ions revealsdeficiencies that make it inappropriate for medical applications. For example, the differencein the integrated energy under the depth dose distributions obtained from SRIM2000 and fromGSI experiments (Sihver et al 1998) for the carbon beam of 330 MeV u−1 is about 20%.Moreover, there have been several versions of TRIM or SRIM released during the last fewyears, which include considerable changes in the numerical values of stopping powers, makingit necessary to indicate the version number of the code being used.

In the field of Monte Carlo codes specific for the simulation of protons with energies ofinterest in radiation therapy, PTRAN (Berger 1993a) was the first code developed and has been

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widely used for treatment planning applications (Berger 1993b, 1993c, Carlsson et al 1997). Itincludes ICRU 49 stopping power data (ICRU-49 1993) and nuclear inelastic energy losses, butsecondary protons generated (or other secondary particles) are assumed to deposit their energyat the site of production and no hadron cascade is thus generated. It does not include eitherthe production or the transport of secondary electrons. The code PETRA (Medin and Andreo1997) includes the production and transport of secondary and higher order protons generatedin nonelastic nuclear interactions as well as secondary electrons generated in single proton–electron collisions. PETRA has been used to calculate the proton stopping power ratiosfor ionization chambers employed in the recent international protocol for the dosimetry ofradiation therapy beams (Andreo et al 2000). At the Loma Linda University Medical Center(LLUMC), Los Angeles, the LAHET Monte Carlo code was used to simulate the transport ofthe proton beam for the purpose of the LLUMC proton therapy facility. Simulations of theproton phase space for different operating modes at this facility were performed using a versionof this code, which includes calculation of proton energy straggling via the Landau–Vavilovmethod. On the other hand, in order to calculate proton dose distributions in the patient,the PEREGRINE Monte Carlo transport code (Hartmann Siantar et al 1995) developed atthe Lawrence Livermore National Laboratory (LLNL), USA, was applied. However, thePEREGRINE transport code requires certain pre-calculated particle source files, which for theLLUMC facility were taken from the LAHET simulated proton phase space.

3. Deterministic methods for ion transport in matter

Heavy ion transport in complex media has also been treated using a deterministic approachdeveloped at the NASA Langley Research Center. This line of research, which started about20 years ago, has yielded a family of radiation transport codes mainly dedicated to solvingengineering problems in radiation-shielding analysis for space missions (Wilson et al 1984,1995a, 2002). One of these deterministic codes is the high-charge-and-energy transport codeHZETRN, based on the one-dimensional formulation of the Boltzmann transport equation witha straight-ahead approximation (Wilson et al 1995b). In this code, nuclear fragmentation iscalculated using a semi-empirical abrasion–ablation fragmentation model. Using simplifyingapproximations, the radiation field in and around shielding materials can be provided bythis code with an acceptable accuracy for space research. However, its flexibility forapplication in radiation therapy is insufficient. Moreover, limited access to the NASA radiationtransport codes for users outside the space research community makes them unsuitable forimplementation in radiation therapy.

In some research centres, deterministic methods for ion transport in tissue-like media havebeen developed as a part of the physics program of heavy ion therapy projects (Sihver et al1998, Kramer et al 2000) or for prediction of radiation doses to astronauts on long-term spacemissions (Wilson et al 1984, 1995a). In general, these methods, which are based on one-dimensional transport theory, evaluate nuclear fragmentation processes using semi-empiricalreaction cross sections. These simple approaches exhibit certain deficiencies. For example,the model by Wilson et al (1995a) does not reproduce accurately the experimental dosedistributions (the differences are of the order of 20% for a 20Ne beam of 670 MeV u−1),whereas the model of Sihver et al shows good agreement with measured depth dose data anddose average LET distributions in water, but it fails to correctly reproduce the production oflight secondaries such as n, p, d, t and α particles.

For proton therapy applications, different analytical approaches have been developed usinga pencil kernel algorithm based on a generalization of the Fermi–Eyges formalism and Molieretheory for multiple scattering (Russell et al 2000, Carlsson et al 1997) or by implementing a

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Gaussian distribution of scattering angles according to the generalized Highlands formula asdescribed by Gottschalk (Gottschalk et al 1993, Scheib and Pedroni 1992, Hong et al 1996).In these models, energy-loss straggling effects are described using a Gaussian approximation.Generally, heterogeneous media are not taken into account in these algorithms, except inthe method developed by Hong et al (1996) where the effects of external inhomogeneitiesupstream of the patient are correctly included. In the majority of the deterministic calculationsfor proton beam transport, nuclear inelastic interactions are not taken into account and only ina few cases they are included via some simplified scaling procedures.

In clinical practice at heavy ion therapy centres such as LBL (Chen et al 1979), in operationfrom the early 1950s until 1993, and the facilities operating at the National Institute ofRadiological Sciences (NIRS), Chiba (Endo et al 1996) and GSI, Darmstadt (Kramer et al2000, Jakel et al 2001), radiation therapy treatment planning systems have been developed forthe specific particle and beam designs. Whereas the pioneering LBL planning system used asolution applicable to various heavy projectiles, the systems now operating at the ion therapyfacilities of NIRS and GSI are limited to carbon projectiles only. These treatment systemsare based on a numerical one-dimensional approach for ion transport and absorbed dosecalculations, including a semi-empirical evaluation of the contribution from fragmentationprocesses.

4. The SHIELD and SHIELD-HIT Monte Carlo codes

The SHIELD Monte Carlo code (Sobolevsky 1970, Barashenkov et al 1972a, 1972b,Dementyev and Sobolevsky 1999) simulates the interactions of hadrons and atomic nucleiof arbitrary charge and mass number (Z,A) with complex extended targets in an energyrange from 1 TeV u−1 down to 1 MeV u−1 or to thermal energies in the case of neutrons.SHIELD is used for solving the same type of problems as other well-known Monte Carlo codessuch as LAHET, HERMES, FLUKA, GEANT or MCNPX. Nuclear reactions in SHIELD aresimulated using the so-called Russian nuclear models (see chapter 4.1) where all stages ofhadron–nucleus and nucleus–nucleus inelastic interactions are described. The code is availablefrom RSICC as package CCC-667.

The so-called SHIELD-HIT (heavy ion transport) code extends the original SHIELD tothe simulation of heavy ion transport in the context of radiation therapy. The developmentsincluded in this version stem from a cooperative research project between the Division ofMedical Radiation Physics, Karolinska Institutet, Stockholm University (Stockholm) and theInstitute for Nuclear Research (INR) of the Russian Academy of Science (RAS), Moscow.Since the developments included in SHIELD-HIT were driven by applications to ion radiationtherapy, the most essential improvements of the present version refer to the inclusion of thefluctuations of ionization energy losses (using Gaussian or Vavilov straggling distributions)and multiple Coulomb scattering (using a two-dimensional Gaussian distribution, the so-calledFermi distribution) of heavy charged particles. These processes play a very important rolewhen accurate particle paths and dose distributions are calculated for patient treatments usingion beams.

In its default output, spatial distributions of the energy deposition due to ionizationlosses of heavy charged particles, like primary particles, nuclear fragments, recoil nucleiand charged secondary particles from neutron interactions, are scored. The production andtransport of electrons (delta-rays) are not included in the present version of SHIELD-HIT. Anaccurate track-length algorithm for the evaluation of the fluence differential in energy, bothof the primary ions and their secondaries, including higher order generations of all particles,at selected regions (zones) in the simulated geometry has been implemented. The default

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particle-number-counter fluence estimator has been kept for comparison. SHIELD-HIT alsocalculates the energy spectra of the secondary neutrons produced inside the absorber and thedecelerated spectra of neutrons transported through the absorber. In addition, the spectradifferential both in energy and angle can also be scored for neutrons and charged particlesleaving the irradiated object, thus providing very useful data for radiation protection aspects ofheavy ion beam irradiation. An interesting output of the code is the calculation of the spatialdistribution of radionuclides generated during ion transport in the medium, in particular thedistribution of positron emitters, which is of interest for monitoring the dose delivered to atarget using PET.

A Combinatorial Geometry package (Emmet 1975, Dementyev 1994) is included inSHIELD-HIT, which allows simulation of complicated geometries and therefore realisticdescriptions of experimental set-ups. This latter package provides the material descriptionof complex targets (up to 16 materials) each containing up to 8 atomic elements. Suchcomplexity is sufficient for the majority of tasks but, if required, more elaborate set-ups couldreadily be implemented. The spatial distribution of the radiation source can be simulated invarious ways, e.g. as a pencil beam, as a beam with the initial divergence simulated by aGaussian distribution with variances σ x and σ y, as a broad parallel beam, etc. The energyof the source can be described as a mono-energetic beam, as a beam with a given Gaussianenergy spread of width σ E or as a particle spectrum. These features provide an excellenttool for performing realistic transport simulations, from the radiation source via the beamdelivery system, including range modulators, collimators, beam monitoring devices, all theway through the patient. Simultaneously, most radiation protection problems around iontherapy facilities can be studied.

The SHIELD-HIT code is currently under further development and, as such, at the presentstage it is not available to the general user.

4.1. Physical models for nuclear interactions with matter

SHIELD and SHIELD-HIT include the models for a detailed description of various stages ofelastic and inelastic nuclear interactions of hadrons/nuclei with matter, while simultaneouslykeeping track of the generation and transport of all the types of secondary particles down tothe cut-off energy for the simulation process.

The capabilities of any Monte Carlo hadron transport code depend critically upon themodel used to describe inelastic nuclear interactions. SHIELD treats these processes using themany stage dynamical model (MSDM) developed at the Joint Institute of Nuclear Research(Dubna) and at INR-RAS, Moscow (Botvina et al 1997, Dementyev and Sobolevsky 1997).SHIELD has been tested on a large variety of hadron–nucleus and nucleus–nucleus collisionsfor energies in the range from about 15 MeV to a few hundred GeV. In figure 1 the reactioncross sections for proton collisions with Be, C and O nuclei used by SHIELD/SHIELD-HITare compared with the experimental data published in the Atomic Data and Nuclear Data Tables(Bauhoff 1986) and with the evaluations from ICRU Report 63 (ICRU-63 2000). The MSDMassumes that an inelastic nuclear interaction proceeds through the following subsequentstages: fast cascade, coalescence, pre-equilibrium decay of residual nuclei and, finally,equilibrated de-excitation of a nucleus. The fast cascade stage of nuclear reactions reducesthe projectile–target interaction to a series of binary collisions between nuclear constituentsand/or produced hadrons. Below 1 GeV, this stage is modelled using the Dubna cascademodel (Toneev and Gudima 1983), whereas above 10 GeV the independent quark–gluonstring model (QGSM) (Amelin et al 1990a) is used. In the intermediate region, 1–10 GeV,an extension of the QGSM (Amelin et al 1990b) is employed. At the end of the cascade

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stage, nucleons which are close to each other in the momentum space can coalesce to formcomplex particles such as 2H, 3H, 3He nuclei and α particles (Toneev and Gudima 1983).Evolution of the excited residual nucleus towards equilibrium is described in terms of thepre-equilibrium model based on a Monte Carlo solution of the corresponding master equation(Gudima et al 1983). At this stage, nucleons and lightest nuclei can be emitted during theequilibration process. Further equilibrated de-excitation of the residual nucleus is included

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through several mechanisms. For light nuclei (A < 16) a modified model of the Fermi break-up(Botvina et al 1987) is used. Medium and heavy nuclei under moderate excitation (E∗/A <

2 MeV) suffer successive particle evaporation, including competition of evaporation andfission of heavy nuclei (Botvina et al 1987, Adeev et al 1993). Highly excited nuclei (E∗/A >

2 MeV) can be disintegrated into several excited fragments according to the statistical modelof multifragmentation (SMM) (Botvina et al 1990) with a subsequent emission of particlesfrom the fragments.

4.2. Physical models for atomic interactions

The ionization energy loss of heavy charged particles is calculated in SHIELD-HITusing the standard Bethe–Bloch equation, as given in the ‘Review of particle physics’(Particle Data Group 2002) which is the default in the code. As is well known, this expressionis adequate for high energies only. For protons and alpha particles, where the internationalrecommended values for stopping powers exist, the data from ICRU Report 49 (ICRU-491993) can be selected for a number of materials of dosimetric and clinical interest. Theimplementation of such data brings the results from SHIELD-HIT, notably the position of theBragg peak and, therefore, the particle range, in close agreement with results produced withother modern Monte Carlo codes for the transport of these particles. An updated computerprogram for the calculation of stopping powers (MSTAR), mostly based on a large compilationof experimental data, has recently been developed by Paul and Schinner (2001, 2002) whoseplanned implementation in SHIELD-HIT is expected to improve its basic data at lower energies(cf Paul and Schinner (2003)).

The physical models for energy straggling and multiple Coulomb scattering of heavycharged particles implemented in the SHIELD-HIT code are well known and have been adoptedfrom the well-documented studies. Fluctuations in the particle energy loss can be sampledaccording to either Vavilov (1957) or Gaussian (Rossi 1952, Remizovich et al 1988) stragglingdistributions. In the former case, the subroutine VAVRAN and accompanying routines from theCERN library (Mathlib) are used in their original forms. Multiple Coulomb scattering effectsare simulated on the basis of a two-dimensional Gaussian model (Rossi 1952, Remizovich et al1988) and the Fermi distribution, which yields the correlated angular deviations and transversaldisplacements of a particle. The Moliere multiple scattering distribution will be implementedin a future version.

The energy and the range of a projectile, or of a secondary charged particle and nuclearfragments, the direction of motion at the end of the range, as well as the coordinates of theendpoint of the range, are computed taking into account both energy straggling and multiplescattering effects. The range of a particle is divided into multiple steps such that the averageenergy loss at each step is relatively small. Then, for each step, the endpoint energy, directionof motion and transversal displacement are sampled. As a result, the endpoint of the rangecan be related to the particle energy as well as to a geometric zone of the medium and thesediffer from calculations which exclude straggling and multiple scattering. In order to performa detailed study of the influence of various physical processes on the general features of iontransport, one can switch off straggling, multiple scattering and nuclear interactions in anydesired combination.

In addition to physical algorithms, a few ‘purely technical’ modifications have beenimplemented in SHIELD-HIT for a more accurate computation of the range–energy andoptical depth–energy dependence of charged particles. As incident energies in ion therapy arebelow 1 GeV u−1, the energy grid for these quantities has been narrowed down from 1 TeV u−1

to 10 GeV u−1, while keeping the same array dimensions. Furthermore, interpolation in the

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Figure 2. Depth distribution of energy deposition along the central axis of a cylindrical waterphantom irradiated with a 200 MeV proton beam calculated with the Monte Carlo codes PTRAN—excluding nuclear interactions (Carlsson et al 1997), PETRA—including nuclear interactions(Medin and Andreo 1997) and SHIELD-HIT. The dotted and short-dashed curves for protonsin water obtained by SHIELD-HIT correspond to Bethe–Bloch’s stopping powers (with Iw =69 eV) and to ICRU-49 stopping powers (with Iw = 75 eV), respectively. The values of theintegrated energies under the distributions are also given in the plot.

data tables has been changed from linear to a quadratic interpolation algorithm which allowshigher accuracy in the computation of ranges and energies, consistent with the requirementsof medical physics.

As is clear from the above brief exposition, SHIELD-HIT includes the state-of-the-artmodels from nuclear physics. On the other hand, the atomic physics modelling is quiterudimentary, since it is based on the simple Bethe–Bloch formula for ionization. This wasinherited from SHIELD, which was primarily concerned with nuclear physics. Our nextimprovement of the current version of SHIELD-HIT is focused on the introduction of thestate-of-the-art ionization models from atomic physics. This will not slow down the SHIELD-HIT simulations, since the more sophisticated atomic physics models shall be applied only topre-compute ionization cross sections. Such cross sections will then be readily accessible toSHIELD-HIT as modules for a direct sampling.

5. Results and discussion

Using SHIELD-HIT we can carry out simulations of interactions between tissue-like mediaand projectiles ranging from proton (1H) to neon (20Ne) ions at incident energies in the interval10–670 MeV u−1. Various distributions of the energy deposition and particle spectra in themedium obtained with SHIELD-HIT have been compared with experimental data and withthe results obtained using other well-documented Monte Carlo codes and numerical methodsdeveloped by other authors. A representative sample of these studies is presented below.

Depth–energy deposition distributions in water for 200 MeV protons are shown in figure 2for simulations using three different Monte Carlo codes: SHIELD-HIT, PTRAN (Carlsson et al1997) and PETRA (Medin and Andreo 1997). The last two codes have been thoroughlyvalidated against experimental data in the context of proton radiation therapy. The PTRAN

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Figure 3. Depth–energy depositions in water, normalized to the integral under the curve, calculatedwith the SHIELD-HIT code (full line) and experimental data (full squares) from the TRIUMFmedical beam-line (Oelfke et al 1996) for a proton beam of 110 MeV. SHIELD-HIT simulationused ICRU-49 stopping power data and an initial energy of the proton beam of 111.3 MeV u−1.

code does not take into account nuclear reactions, whereas PETRA includes energy losses dueto inelastic nuclear interactions that may generate up to three secondary protons. The shapesof the computed distributions are similar for the three codes and the difference in the integratedenergy under the curves is less than 1%. The lack of nuclear interactions in PTRAN can beseen clearly at shallow depths. Of special interest are the results obtained with SHIELD-HITusing two different sets of proton stopping powers. It can be observed that the position ofthe Bragg peak obtained with the default stopping powers, using the standard Bethe–Blochequation (Particle Data Group 2002) with a mean excitation energy for water Iw = 69 eV isshifted for about 4–5 mm towards smaller depths compared with the results from PETRA andPTRAN. On the other hand, the use of stopping powers from ICRU-49, in which Iw = 75 eVis recommended, brings the peak and ranges of all the codes into excellent agreement. Theremaining differences relative to PTRAN are caused by the lack of nuclear interactions inthis latter code. The success of this comparison led us to implement in SHIELD-HIT theICRU-49 stopping powers for alpha particles which, together with protons, are the only typesof particles for which an international standardized set of stopping power data have thus farbeen produced.

In figure 3 the depth distribution of the energy deposition in water calculated by SHIELD-HIT is compared with the measurement from the TRIUMF medical beam-line 2C, Vancouver(Oelfke et al 1996) for a proton beam of 110 MeV. The calculations with SHIELD-HIT werecarried out for a pencil beam transported through a cylindrical water phantom (R = 10 cm,L = 30 cm). Our simulations using the stopping power data from ICRU-49 and a primaryproton beam of 110 MeV resulted in the Bragg peak position shifting towards lower depthsby 2 mm from the position determined by the experiment. In order to match exactly theexperimental distribution, a proton energy of 111.3 MeV was used in the calculations, giving anearly perfect agreement between the compared dose profiles. The difference in the integratedenergy under the calculated and experimental curves is found to be about 4%. In the work byOelfke et al (1996), there is no information about the measurement procedure of the energy

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Figure 4. Comparison of the SHIELD-HIT calculations with the measurements at HIMAC (Kanai2000) and GSI (Sihver et al 1998, Kramer et al 2000) for the distribution of energy deposition(normalized to the integral under the curves) as a function of depth along the axis of a waterphantom irradiated with 12C ion beams of 195, 290 and 330 MeV u−1. SHIELD-HIT simulationis done with Iw = 75 eV.

deposition or about the beam properties in front of the absorber. The calculated profile withthe beam energy adjustment of 1.3 MeV (amounting to a difference of 1.2% relative to theenergy used in the experiment) correctly reproduces the Bragg peak region. This indicatesthat a real initial energy in front of the water absorber was slightly different from the originallyclaimed value of 110 MeV (Oelfke et al 1996).

Depth–energy deposition distributions in water for 12C ions calculated withSHIELD-HIT are compared in figure 4 with the experimental data from HIMAC for a290 MeV u−1 beam (Kanai 2000) and from GSI for 195 MeV u−1 (Kramer et al 2000) and330 MeV u−1 (Sihver et al 1998). The standard Bethe–Bloch equation with a mean excitationenergy for water Iw = 75 eV (cf ICRU-37 and ICRU-49) was used for the SHIELD-HITcalculations of the stopping powers of carbon in water. The agreement between the MonteCarlo distributions and the GSI and HIMAC measurements (normalized to the value of theintegral under the curve) is satisfactory over the entire depth range except at the Bragg peakmaximum. It is clearly seen that SHIELD-HIT reproduces well the contribution to the energydeposition due to the secondary fragments at depths beyond the Bragg peak for all the above-discussed experimental data. The differences of the calculated and the measured integral ofthe total energy deposition for these distributions are less than 3%. However, all the calculateddistributions show small differences of about 1–2 mm in the projectile maximum range.

Detailed SHIELD-HIT calculations for different ion beams were performed to analysethe change of the position and the shape of the Bragg peak using different values of themean excitation energy Iw for water and by varying the initial energy of the incident beamand its energy spread. In these calculations the depth resolution in the Bragg peak regionwas chosen as 0.1 mm in order to match the sub-millimetre precision of the measured Braggpeak position (Kramer et al 2000). Here the experimental data from GSI (Jakel 2002) wereused for comparison. Figure 5(a) shows the variation of the Monte Carlo calculated depth–energy deposition in the Bragg peak region for a carbon beam of 400 MeV u−1 using Iw

values for water of 75 eV (ICRU-37 and ICRU-49), 77 eV (Kramer et al 2000) and 79.8 eV

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(Bichsel and Hiraoka 1992). The shift of the position of the calculated Bragg peak for carbonions with an initial energy of 403 MeV u−1 and Iw = 75 eV is also included. When theenergy spread of the primary beam is modelled with a Gaussian distribution of a given width,σ (E), the Monte Carlo calculated Bragg peaks are broader and shallower, as can be seen infigure 5(b). The production of the secondary particles beyond the Bragg peak is reproducedperfectly, similar to the results presented in figure 4 for carbon beams of lower energiesproduced at GSI.

Since the physical beam transport model used at GSI for carbon beams (Kramer et al2000) matches exactly their experimental data, the results presented in figure 5 also allows acomparison with the numerical approach implemented in the dose planning system at GSI.

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The measured position of the Bragg peak for carbon ions of 400 MeV u−1 is reasonably wellmatched by the SHIELD-HIT results for a carbon beam with an initial energy of 403 MeV u−1,Iw = 75 eV and σ (E) = 0. In spite of the fact that the total integral of the energy depositionfor a 400 MeV u−1 carbon beam calculated over the entire depth range differs by less than 3%from the experimental results, none of the above-applied approaches allows reproduction ofthe shape and the height of the experimental Bragg peak.

Contrary to these latter evaluations, the comparison of the SHIELD-HIT calculationswith the experimental data by Matsufuji et al 2003, presented in figure 6, shows a nearlyperfect agreement regarding the shape and the height of the Bragg peak. In the experimentof Matsufuji et al, the depth distribution of the energy deposition of a carbon beam of279.2 MeV u−1 produced at HIMAC was measured in the PMMA absorber. It is worthwhileto note that in the paper by Matsufuji et al the primary carbon beam was said to have the energyof 290 MeV u−1 (see their figure presenting the results of the energy deposition), whereas intheir table showing the properties of the incident beam, initial energy in front of the absorberof 279.23 MeV u−1 was given.

The results in figure 6 are presented as a function of the PMMA depth given as a water-equivalent thickness. In the experiment of Matsufuji et al the depth resolution of the detector(a parallel-plate ionization chamber) was 0.5 mm (water-equivalent thickness) and the depthresolution of the SHIELD-HIT calculations was 0.1 mm. The difference in the integratedenergy under the calculated and experimental curves shown in figure 6 is about 4%.

In order to understand the quite remarkable differences in the shape of the Bragg peakpresented in figure 5 and compared with the GSI experiment, sensitivity tests of SHIELD-HITcalculations for different depth resolutions were carried out. Both SHIELD-HIT calculationswith the resolution of 1.0 mm and 0.1 mm give exactly the same position of the Bragg peakfor a carbon beam of 279.2 MeV u−1 and the difference in the integrated energy under theBragg peaks is less than 0.7%. Also, both calculations show that the difference between thecalculated and the measured heights of the Bragg peak is about 7%, which is significantlysmaller than the difference of 25% for the results presented in figure 5. The difference in

Ion beam transport in tissue-like media using MC code SHIELD-HIT 1947

the detector resolution of 0.1 mm and 0.5 mm in the experiments at GSI (Jakel 2002) andat HIMAC (Matsufuji et al 2003) respectively could influence somewhat the shape of themeasured Bragg peak. This observation requires further investigation.

The SHIELD-HIT distribution presented in figure 6 matches exactly the position of theexperimental Bragg peak maximum. This agreement was obtained by a horizontal shift ofthe calculated profile by 4.2 mm towards the lower depths. There are several possible reasonsfor the observed mismatch of the Bragg peak position, which could be as follows: (a) theexperimental position of the Bragg peak was determined with an accuracy ±3 mm (see the endof the next paragraph), (b) the uncertainty of the initial energy of the carbon beam, (c) thedifference between stopping power used in SHIELD-HIT and the tables (Salamon 1980) usedin the experimental procedure.

One should also point out that in the experiment of Matsufuji et al the residual energyof the primary carbon beam, which was determined after passing any layer of the PMMAabsorber, was deduced by the procedure using the stopping power data of Salamon. Such aprocedure has an influence on the uncertainty of the determined residual energy of the primarybeam and, hence, also on the Bragg peak position. The uncertainty of the stopping power usedin the work by Matsufuji et al was estimated as ±2% at the maximum.

Similar problems related to an accurate matching of the calculated depth dose distributionswith the experimental data have been reported in a number of previous publications(Oelfke et al 1996, Sihver et al 1998, Kramer et al 2000). The main reason for these problemsis insufficiently accurate knowledge about the initial energy of the beam and its energydistribution when impinging on the absorber. In the paper of Matsufuji et al (2003) a detailedanalysis of the properties of the incident beam used for the measurement has been presented.These authors also gave the initial beam energy and the beam energies at the positions inthe beam-line after passing different materials/detectors. This type of information, althoughextremely important for accurate calculations by means of MC or deterministic methods, israrely supplied in the literature.

The calculated range as well as the energy loss of particles and, hence, the positionof the Bragg peak are also significantly influenced by the accuracy of the applied stoppingpower tables. A comprehensive discussion on the reliability assessment of the availablestopping power tables for light and heavy ions, or of the programs for stopping powercomputations has been presented by several authors (Tai et al 1997, Sihver et al 1998,Geissel et al 2002, Paul and Schinner 2003). There are significant differences (up to 10%)between the experimental and calculated values, as well as among different models forevaluation of stopping power data depending on the particle type and energy range.

Even the experimental results of the dose distributions depend upon the accuracy of theused stopping power tables whenever the residual energy of the primary beam after passingthrough the absorber is deduced by fitting to the calculated depth–dose profile (Matsufuji et al2003). A similar dependence also takes place in the cases when the calculations of the ‘water-equivalent thickness’ of the materials in the beam-line are performed (Sihver et al 1998).

The energy or depth scaling procedures of the calculated as well as measured depth dosedistributions are reported by Sihver et al (1998), Oelfke et al (1996) and Kramer et al (2000).In the work of Sihver et al the measured curves were always normalized in the horizontaldirections in order to match the calculated ones. In the same work, a good agreement betweenthe theoretical and the measured heights of the Bragg peak was achieved by performing thecalculations for the Gaussian energy distribution with σ (E) being about 0.15% of the incidentbeam energy. A similar procedure was used by Oelfke et al who approximated the energyspectra of the proton beam by a Gaussian distribution, with a width fitted to the experimentaldata in order to reproduce the measured depth profiles. In the work of Kramer et al a very

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Figure 7. Comparison of the SHIELD-HIT calculations with the GSI experiment and the modelcalculations of Sihver et al (1998) for the depth distribution of the energy deposition in the waterphantom irradiated with a 270 MeV u−1 12C ion beam. The results are normalized to the entranceenergy deposition. The total energy deposition and the contributions from the primary 12C beamand from secondaries of all generations are plotted separately.

good agreement between the calculated and experimental distributions was achieved throughthe adjustment of the energy loss table by using the mean ionization energy I = 77 eV forwater.

Accurate modelling of energy straggling, multiple scattering and nuclear collisions is ofmajor importance for the determination of dose distributions in a treatment planning system.Improper evaluation of nuclear interactions, particularly for projectiles like carbon ions, canlead to a serious overestimation or underestimation of the calculated dose, especially whenthe heterogeneity is taken into account. High accuracy of the physical dose in the Bragg peakregion is also of special importance for the correct consideration of the relative biologicalefficiency.

The contribution from various generations of particles in a hadron cascade to the depth–energy deposition distribution is of special interest. Figure 7 shows Monte Carlo computeddistributions for 270 MeV u−1 12C ions in water, where results are normalized to the entranceenergy deposition. The contributions from the primary 12C beam and from the secondaries ofall generations are presented separately. Experimental data from GSI (Sihver et al 1998) andcalculations from a model by Sihver et al 1998 for the total energy deposition distribution,also included in the figure, agree very well with the SHIELD-HIT distribution. Nevertheless,some discrepancies between the two calculations can be observed for the contribution fromthe primary beam and the contributing secondary nuclear fragments.

In a recent experiment by Schall et al (1996), the number of secondary fragments with agiven charge Z was measured as a function of depth in water irradiated by ion beams in theenergy range between 200 and 670 MeV u−1. Several projectiles from 10B to 20Ne were used.Figure 8 shows a comparison of these experimental data with the results obtained by meansof SHIELD-HIT, where the number of fragments with Z = 5 determined for 12C, 14N and 16Oprojectiles having the energy of 670 MeV u−1 are plotted. The agreement between the twosets of data is quite satisfactory for the 12C and 14N projectiles, where discrepancies are lessthan 15%. However, for the 16O projectile, the Monte Carlo results differ from the measuredboron production by about 25%. The SHIELD-HIT calculations of the depth distribution of

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heavier secondaries, e.g. Z = 6 and Z = 7, for 14N and 16O projectiles with energies of about670 MeV u−1 (not included in the plot to avoid clutter), show even higher discrepancies, upto 35%, compared with the experimental data. These differences seem to indicate certainweakness of the nuclear model implemented in SHIELD-HIT for the production of heaviersecondaries (Z � 6). This point deserves further study.

Note that the discrepancies between SHIELD-HIT and the experiment discussed abovecohere with the common situation encountered in the previously published data. An extensivecompilation of experimental data presented in Schopper (1991–1999) shows significantdiscrepancies for a large set of experiments. Disagreement among measurements rangesfrom 30% (most common) through 50% (frequent) up to a factor of 2 or 3 (occasional). Insome cases differences even up to an order of magnitude could be observed.

Comparisons of the models with the experimental data also show a large variation ofdiscrepancies in the range from about 5% to 400% (see tables I and II in the paper by Sihveret al (1993) and table 3 in the paper by Sihver et al (1998)). However, one should keep inmind that most of the models discussed in the paper by Sihver et al (1998) are semi-empiricalwith many-parameter formulae fitted to these specific experimental data. By comparison, theSHIELD-HIT code evaluates secondary particle production for any target, any projectile andfor a very wide energy range. The availability of a more complete set of experimental data forproduction of heavier secondary particles would allow a further improvement of the nuclearmodels implemented in SHIELD-HIT.

Figure 9 shows the integrated track-length fluence of different secondary fragments(neutrons, protons, 2H, 4He and 11B ions) as a function of depth in water irradiated witha pencil beam of 391 MeV u−1 12C ions. SHIELD-HIT calculations were performed for tworegions of a cylindrical water phantom (R = 10 cm, L = 30 cm), a central axis region with aradius of 0.4 cm and the outer region. The values shown in figure 9 have been obtained from thetrack-length fluence calculations differential in energy, �E(z), implemented in SHIELD-HITfor the detailed evaluation of dosimetry quantities and LET distributions. As another example,figure 10 shows the track-length fluences differential in energy for protons, neutrons and 4He

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particles produced by 12C ions of 391 MeV u−1 at a depth of 25.9 cm, close to the Braggpeak maximum. The same geometry has been used for the results shown in figures 9 and 10.It can be seen that there is a difference of approximately one order of magnitude in thefluence of secondary protons, neutrons and alpha particles compared with that of the rest ofthe secondary particles. This type of calculation also provides interesting information aboutenergy distributions of secondary particles outside the irradiated volume.

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Figure 11. Comparison of SHIELD-HIT Monte Carlo calculations with the experimental datafrom the HIMAC experiment (Heilbronn 2002) for the production of secondary neutrons in aMarsbar target irradiated by a 12C beam with an energy of 290 MeV u−1. The neutron spectradifferential in energy are compared with the experimental results for the angles 30◦ (a) and 60◦ (b).

Figure 11 compares the SHIELD-HIT calculations with the measured data (Heilbronn2002) for production of secondary neutrons in a Marsbar target, material used in space radiationresearch to simulate a Martian rock, irradiated by a carbon beam of 290 MeV u−1. The Marsbartarget consists of 85% simulated Martian regolith and 15% polyethylene, thus containing sevenelements (H, C, O, Mg, Si, Ca, Fe) of different atomic densities. In the experiment, the Marsbartarget was irradiated by a 290 MeV u−1 12C beam at the HIMAC medical facility in Chiba,Japan (Heilbronn 2002); the experimental details are described elsewhere (Iwata et al 2001).For the SHIELD-HIT calculations, the target geometry and composition, as well as the shapeof the initial carbon beam, were carefully simulated. The calculated spectra differential in

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energy for neutrons leaving the target are compared with the experimental results for scatteringangles of 30◦ and 60◦ in figures 11(a) and 11(b), respectively. The statistical uncertainties ofthe calculated values are less than 10%, whereas the uncertainties of the experimental datavary with the neutron energy and are in the range 5–35%. It should be pointed out that there isa strong dependence of the experimental uncertainties on the width of the experimental energybin. The discrepancies between the SHIELD-HIT results and the experimental data are lessthan 30% in the neutron energy range 60–200 MeV, whereas at the ‘tails’ of the spectra, largerdiscrepancies are observed.

Validation of the SHIELD-HIT calculations of the energy deposition in water has alsobeen done for projectiles heavier than carbon. The results presented in figure 12 show thedepth distribution of the energy deposition in water (normalized to the dose at a depth of7.5 cm) for a 20Ne beam of 670 MeV u−1 calculated with SHIELD-HIT, and for experimentsat LBL (Wilson et al 1984) and GSI (Sihver et al 1998). The measured distribution of Sihveret al (1998) was adjusted in the horizontal direction in order to match the position of themaximum of the Bragg peak given by the LBL experiment. The experimental position of theBragg peak agrees with a SHIELD-HIT calculation using neon ions of energy 667 MeV u−1

and employing Iw = 75 eV. The shape of the measured energy deposition shown in figure 12is satisfactorily reproduced by the SHIELD-HIT calculations with a difference in the integratedenergy under the curves of about 2%. Some discrepancies between calculated and measureddepth distributions of the energy deposition for a 20Ne beam are observed in the regionbehind the Bragg peak, indicating larger uncertainties in the SHIELD-HIT calculations of thefragmentation processes for ions heavier than carbon.

One of the important potential applications of the SHIELD-HIT code is related toin situ monitoring of ion dose delivery to a patient using the calculated distribution of PETisotopes (Enghardt et al 1999a, 1999b). Figure 13 shows the SHIELD-HIT calculated depth

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distribution of the production rate of positron emitters for a 20Ne beam of 406 MeV u−1

transported through a PMMA phantom. The Monte Carlo calculation is compared to theexperimental distribution (Enghardt et al 1992) measured at GSI using a pulsed beam and a5 min PET scan with a resolution of 7.3 mm (FWHM). Since no convolution of the calculateddistribution with the positron detector resolution has been performed, the SHIELD-HIT resultsshow a sharper and more peaked depth profile of positron emitters in the Bragg peak region.The number of the calculated positron emitters produced by the 20Ne beam in the region behindthe Bragg peak is overestimated by SHIELD-HIT compared to the experiment, consistentwith the results presented in figure 12 for the same depth region. More Monte Carlo studiesand comparison with the experimental distributions of the PET emitters in the tissue arerequired, taking into account the PET detector spatial resolution, its efficiency and the timecourse of the beam irradiation.

6. Conclusions

A Monte Carlo code termed SHIELD-HIT (heavy ion transport) for simulation of transport ofprotons and heavier ions in tissue-like media has been developed. The SHIELD-HIT code is aspin-off of the general purpose code SHIELD (available as RSICC CCC-667) and extends thetransport of hadron cascades from certain standard targets to that of ions in arbitrary tissue-like materials, taking into account ionization energy-loss straggling (Gaussian or Vavilov)and multiple Coulomb scattering (Gaussian) effects. SHIELD-HIT describes inelastic nuclearreactions using the many stage dynamical model developed at JINR, Dubna and at INR-RAS,Moscow.

The consistency of the results obtained with SHIELD-HIT has been demonstratedcomparing depth distributions of energy depositions by protons, 12C and 20Ne ions impingingon water with experimental data, with other existing Monte Carlo codes (PTRAN, PETRA)

1954 I Gudowska et al

and with deterministic models for ion transport used in radiation therapy with carbon ions.SHIELD-HIT yields distributions consistent with a proper treatment of nuclear inelasticcollisions. Energy depositions up to and well beyond the Bragg peak due to nuclearfragmentations are well predicted. Satisfactory agreement is also found with experimentaldeterminations of the number of fragments of a given type, as a function of depth in water,produced by 12C and 14N ions of 670 MeV u−1. Somewhat less favourable agreement isobserved for heavier projectiles such as 16O at the same energy. The calculated neutronspectra differential in energy and angle produced in a Marsbar target (a mimic of a Martianrock of interest for space radiation research) by irradiation with 12C ions of 290 MeV u−1 alsoshows good agreement with the available experimental data.

It is concluded that a careful analysis of stopping power data is necessary for radiationtherapy applications. This is because an incorrect estimation of the position of the Braggpeak might lead to a significant deviation from the prescribed dose in small target volumes,thus jeopardizing the potential advantages of light ions, sharp dose distributions. Accuratedetermination of the physical dose in the Bragg peak region is of special importance for acorrect consideration of the relative biological efficiency.

The results reported in the present work provide the arguments, which support the useof the SHIELD-HIT code for Monte Carlo simulations in the field of ion beams in radiationoncology. The code produces spatial distributions of the energy deposited by primary andall generations of secondary particles, track-length fluence calculations, LET-distributions,etc. It is very well suited as a tool for the characterization of an initial ion beam and forthe design of complicated beam-lines with scattering foils, energy moderators, etc, as well asfor the optimization of collimator design used at a final treatment beam set-up. One of itspotentially important applications concerns the in vivo monitoring of ion beam dose deliveryto the patient, using calculated distributions of PET isotopes. Distributions obtained withSHIELD-HIT can provide invaluable information for the development of other algorithms forphysically and biologically optimized ion therapy treatment planning.

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