Clinical implementation of full Monte Carlo dose calculation in proton beam therapy

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Phys. Med. Biol. 53 (2008) 4825–4853 doi:10.1088/0031-9155/53/17/023

Clinical implementation of full Monte Carlo dosecalculation in proton beam therapy

Harald Paganetti, Hongyu Jiang 1, Katia Parodi2, Roelf Slopsema3

and Martijn Engelsman

Department of Radiation Oncology, Massachusetts General Hospital and Harvard MedicalSchool, Boston, MA 02114, USA

Received 7 March 2008, in final form 3 June 2008Published 13 August 2008Online at stacks.iop.org/PMB/53/4825

AbstractThe goal of this work was to facilitate the clinical use of Monte Carlo protondose calculation to support routine treatment planning and delivery. TheMonte Carlo code Geant4 was used to simulate the treatment head setup,including a time-dependent simulation of modulator wheels (for broad beammodulation) and magnetic field settings (for beam scanning). Any patient-field-specific setup can be modeled according to the treatment control system of thefacility. The code was benchmarked against phantom measurements. Using asimulation of the ionization chamber reading in the treatment head allows theMonte Carlo dose to be specified in absolute units (Gy per ionization chamberreading). Next, the capability of reading CT data information was implementedinto the Monte Carlo code to model patient anatomy. To allow time-efficientdose calculation, the standard Geant4 tracking algorithm was modified. Finally,a software link of the Monte Carlo dose engine to the patient database and thecommercial planning system was established to allow data exchange, thuscompleting the implementation of the proton Monte Carlo dose calculationengine (‘DoC++’). Monte Carlo re-calculated plans are a valuable tool torevisit decisions in the planning process. Identification of clinically significantdifferences between Monte Carlo and pencil-beam-based dose calculationsmay also drive improvements of current pencil-beam methods. As an example,four patients (29 fields in total) with tumors in the head and neck regions wereanalyzed. Differences between the pencil-beam algorithm and Monte Carlowere identified in particular near the end of range, both due to dose degradationand overall differences in range prediction due to bony anatomy in the beampath. Further, the Monte Carlo reports dose-to-tissue as compared to dose-to-water by the planning system. Our implementation is tailored to a specific

1 Present address: University of Southern California, Los Angeles, CA, USA.2 Present address: Heidelberg Ion Therapy Center, Heidelberg, Germany.3 Present address: University of Florida Proton Therapy Institute, Jacksonville, FL, USA.

0031-9155/08/174825+29$30.00 © 2008 Institute of Physics and Engineering in Medicine Printed in the UK 4825

4826 H Paganetti et al

Monte Carlo code and the treatment planning system XiO (ComputerizedMedical Systems Inc.). However, this work describes the general challengesand considerations when implementing proton Monte Carlo dose calculationin a clinical environment. The presented solutions can be easily adopted forother planning systems or other Monte Carlo codes.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Monte Carlo dose calculation is considered to be the most accurate method to compute dosesin radiation therapy. This is because Monte Carlo simulations take into account the physics ofparticle interactions on a particle-by-particle basis using theoretical models or experimentalcross-section data for electromagnetic and nuclear interactions. Further, they consider tissueinhomogeneities by using specific material properties, e.g. elemental composition, electrondensity, mass density or ionization potential. The appropriate position of inhomogeneitiesalong the beam path and its scattering effects are modeled. Secondary particles can betracked, which allows the appropriate consideration of nuclear fragments. It has been shownthat the difference between dose distributions obtained with pencil-beam algorithms andMonte Carlo can be significant for certain treatment areas and beam configurations in photontherapy (Pawlicki and Ma 2001). Dose distributions are usually more conformal in protontherapy (Bussiere and Adams 2003, Suit et al 2003). Consequently, the potential impact ofMonte Carlo dose calculation may be even bigger in particular in the distal part of the beambecause of the sharp dose fall-off. Further, dose deposition in proton beams not only dependson electromagnetic but also on nuclear interactions (non-elastic interactions and multiplescattering).

Full proton Monte Carlo dose calculation, including treatment head simulation and dosecalculation for passive scattering and beam scanning delivery, is currently not commerciallyavailable. Consequently, it is likely that institutions offering proton therapy and interestedin Monte Carlo dose calculation capability will develop their own customized solution.This paper describes the roadmap to a clinical implementation of proton Monte Carlo dosecalculation. It tries to cover all relevant aspects. Some of the details are specific to treatmenttechniques used at Massachusetts General Hospital (MGH), our planning system and ourMonte Carlo code. However, the tasks required and the strategy of approaching them islargely independent of the available hardware and software.

The specific aim was the clinical implementation of a Monte Carlo dose calculation enginethat could be used in parallel to the commercial treatment planning system for both protontherapy techniques, i.e. broad beam modulation (BBM) and pencil-beam scanning (PBS).BBM is usually achieved by modulating a field with pristine Bragg curves using, for example,a rotating wheel. Such a modulator wheel combines variable thickness absorbers in circularrotating tracks that result in a temporal variation of the beam energy (Koehler et al 1975).Treatment fields are shaped to a desired target profile using custom milled apertures. Thedistal part of the dose distribution is shaped using patient-field-specific milled compensators.In contrast, using PBS, protons are deflected magnetically to scan much smaller pencil beamsacross the target volume without the need of aperture or compensator. PBS offers the possibilityof intensity-modulated proton therapy (Lomax 1999).

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4827

2. Methods and materials

2.1. Routine treatment planning

Treatment strategies and treatment options can be different in proton therapy compared tophoton or electron therapy. Sharp distal dose fall-off of proton dose distributions makesit critical to understand the uncertainties when determining the penetration depth requiredto cover a target. Better conformity causes the dose distribution to be more affected byuncertainties in beam delivery, patient setup/immobilization, tissue heterogeneities, organmotion and dose calculation.

The treatment planning program currently used in proton therapy at MGH is XiO(Computerized Medical Systems Inc.). Its dose calculation method is based on a pencil-beam algorithm developed in-house (Hong et al 1996). Based on the philosophy of XiO, atreatment plan results in a set of prescribed SOBP (spread-out Bragg peak) fields, which aresolely characterized by range, R, and modulation width, M. The delivery of the desiredfield, i.e. the translation into machine parameters, is specified outside of the planningprogram within the treatment machine software of the facility (treatment control system(TCS)).

2.2. Proton Monte Carlo dose calculation

Several Monte Carlo codes such as MCNP (Briesmeister 2000), MCNPX (Waters 2002),EGSnrc (Kawrakow 2000), BEAM (Rogers et al 1995), Geant4 (Agostinelli et al 2003),PENELOPE (Salvat et al 2001), PEREGRINE (Hartmann Siantar et al 2001), DPM (Sempauet al 2000) and others are being used in radiation therapy. Monte Carlo methods have beenapplied to verify the results of the approximate dose calculation algorithms implementedin commercial treatment planning tools (e.g. Carlsson et al (1997) and Ma et al (2000)).Further, due to the availability of fast computers, Monte Carlo dose calculation methodshave been implemented in commercial treatment planning systems for photon/electron dosecalculations. Most of these implementations are based on the VMC Monte Carlo code (Fippel1999, Kawrakov and Fippel 2000).

We chose Geant4 because of its open source design and because of its ability to transportall particles relevant to radiation therapy applications, e.g. photons, electrons, protons andions. The code is developed and maintained by the Geant4 collaboration and individualcontributors and is based on C++ object-oriented architecture. It is not a standalone MonteCarlo executable, but a developing tool kit organized into 17 categories of classes. To conductMonte Carlo simulations, the user must provide his/her own code, giving descriptions ofgeometry, materials, particles of interest, physics processes and user actions. The user code iscompiled and linked to the pre-compiled Geant4 class libraries to create the problem-specificexecutable. The toolkit, initially designed for use in high-energy physics, has found itswide applications in brachytherapy (Perez-Calatayud et al 2004, Torres et al 2004), externalphoton/electron (Fix et al 2000, 2001a, 2001b) and external proton (Jiang et al 2005, 2007,Paganetti 1998, Paganetti and Goitein 2000, Paganetti et al 2004a, 2004b, Szymanowski andOelfke 2002, Zacharatou Jarlskog et al 2008) dose calculations. Geant4 has been validatedfor use in medical physics, in particular for proton therapy applications (Carrier et al 2004,Paganetti 2006, Paganetti and Gottschalk 2003, Zacharatou Jarlskog and Paganetti 2008).Our Monte Carlo implementation utilizes a few improvements in efficiency compared to thestandard Geant4 Monte Carlo package (Jiang and Paganetti 2004).

Pre-requisite for accurate Monte Carlo simulations is the correct setup of the physicsinteractions within the Monte Carlo code. Thus, one has to make sure that the Monte

4828 H Paganetti et al

Carlo program applies the appropriate cross sections or models for the energy region underconsideration (relative cross sections may be sufficient). Electromagnetic interactions aswell as nuclear interactions have to be considered. The latter may contribute significantlyto the dose distribution (Laitano et al 1996, Medin and Andreo 1997, Paganetti 2002). Forthis project, all simulations were performed using the Geant4 versions 5.0 and 8.0 (patch01). The setups for the underlying physics (interaction types, cross sections, models)have been previously identified for version 5.0 (Paganetti et al 2004b) and version 8.0(Zacharatou Jarlskog and Paganetti 2008). Note that the versions prior to 8.0 hadshortcomings with respect to light charged particles (electron) tracking, i.e. the codepermitted electrons to reach geometric boundaries in large steps, and underestimated lateraldisplacement near interfaces (Poon et al 2005). These effects are insignificant for proton dosecalculations.

Geant4 calculates material-dependent ionization potentials internally but it also allowsuser defined settings. We achieved a better agreement of our simulations with experimentalresults when setting the ionization potentials based on the ICRU (1984). We include and trackall relevant particles in the simulation: protons, neutrons, helium ions, deuterons, tritons,photons and electrons (the production cut-off was set to 0.05 mm in projected range). Theenergy transferred to recoil nuclei is deposited locally. Electrons and photons are tracked untiltheir energy at the origin is smaller than a CSDA-range of 1 mm, after which the energy isdeposited locally. The maximum step size in the Monte Carlo was chosen to be 1 mm (or thedistance to the next geometrical boundary, whichever is smaller). Exceptions are the areas ofmagnetic fields, range compensator and ionization chambers used for absolute dosimetry. Forthe magnetic fields, the maximum step size is chosen to be 0.5 mm to minimize uncertaintiesdue to the curved particle path in the field, which is broken up into linear chord segments. Forthe range compensator 0.5 mm is used while for the ionization chamber we use 0.1 mm tomeet clinical requirements on uncertainties in absolute dose (±2.5%) for all treatment headsettings.

2.3. Beam at treatment head entrance

The first step in any Monte Carlo dose calculation is to obtain information about the beamat the position where it enters the simulated area, i.e. the treatment head entrance (usuallythe starting point for particle tracking). The variables are beam energy (E), energy spread(�E), beam spot size (σ x, σ y) and beam angular distribution (σ θx, σ θy). Some of these can bemeasured, and others are given by the vendor of the facility (Paganetti et al 2004b). The beamenergy (and spread) and the beam spot size are independent parameters. However, there is acorrelation between the particle position and its angle (as well as a very small correlation withits energy).

For BBM, the double-scattering system washes out these correlations, and angular spreadand beam spot size have only little influence on the dose distribution when varied withinrealistic boundaries (Paganetti et al 2004b). At MGH treatment head entrance, the beamspot size is typically ∼6.5 mm (σ ) and the angular spread is typically ∼3.2 mm mrad (σ ) indouble-scattering mode. The most critical parameter is the energy spread because it influencesthe width of the Bragg peak, the slope of the distal fall-off and the peak-to-plateau ratio. Wetherefore decided to determine this parameter experimentally. Several pristine depth–dosedistributions were measured and compared with simulations. Figure 1 shows the set ofmeasured and simulated pristine peaks done for different beam ranges and for different stepsin the modulator wheels.

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4829

Figure 1. Upper: measured (solid lines) and Monte Carlo simulated (open circles) pristinedepth–dose curves for different settings of modulator wheel and double scattering system. Lower:measured (solid lines) and Monte Carlo simulated (dashed lines) dose as a function of depth forthe distal fall-off regions (±5 mm in depth) in the eight curves given in the upper figure.

The energy spread (�E) was varied to find the best agreement between measured andsimulated peak widths and peak/plateau ratios resulting in

�E = 1.6375 − 5.2 × 10−3E (%). (1)

Once this relationship was determined, it was hard-coded in the Monte Carlo routine and hasnever been changed since then. Depth–dose curves in water are measured daily at our facilityas part of a quality assurance procedure. Analysis of the peak/plateau ratios and the widths ofthe Bragg peaks confirm that the energy spread has not changed since commissioning of thefacility. Note that due to the effects of the beam absorber and beam shaping slits in the energyselection system at the cyclotron exit and due to the magnetic beam steering, the absoluteenergy spread reaches its maximum at around 160 MeV.

For beam scanning, the four input parameters cannot be considered independently becausethere is less scattering material in the beam path than with BBM and because of the magneticfields. A parameterization of the phase space at treatment head entrance is therefore required.In particular, geometrical beam position and angular deviation are correlated. Using the spatialbeam spread (σ ) in x and y, σ x and σ y, and the angular spread distribution (σ θ) in x and y, σ θx

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Figure 2. Example phase space distributions (correlation between position and angle) for onedirection (x or y) for a de-focusing beam (left) and a focusing beam (right).

and σ θy, the phase space (angular and spatial distribution) at treatment head entrance can beparameterized in the x-direction as (similar relation holds for the y-direction)

f (x, θx) = 1√2π

√1 − �2

θxσx

exp

(− (x − θx�θxσx/σθx)

2

2σ 2x (1 − �θx)

).

1√2πσθx

exp

(− θ2

x

2σ 2θx

). (2)

The parameters �θx and �θy describe the correlation between angle and position (0 for BBMdelivery simulation). They are positive for a de-focusing beam and negative for a focusingbeam (typical case for scanned delivery). Example distributions are shown in figure 2.

2.4. Simulation of the treatment heads

Proton therapy treatment heads typically contain many devices with field-specific settings.When starting the simulation, the generic geometry is initialized using parameters providedvia an input file. The Monte Carlo geometry contains all devices and equipment settings neededfor different delivery techniques and only the respective input files differ. All treatment headelements were simulated with high accuracy based on original drawings from the vendor(Paganetti et al 2004b).

Although the settings of the treatment head are patient field specific (except for PBSwhere only the magnetic field is variable), there are only two devices that have to be fabricatedpatient field specific, i.e. the aperture and the compensator. For each of these devices, XiO

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4831

generates files that can be imported directly by a milling machine for fabrication. The MonteCarlo code reads the same files to define their geometrical shapes and virtually fabricates thedevices (Paganetti et al 2004b).

The desired R and M are given by the treatment plan and have to be translated intotreatment head setup and beam setup (Paganetti et al 2004b). At MGH, this is done by theTCS software, which calculates the beam energy and treatment head setting necessary todeliver a specific SOBP. This part of the TCS software was incorporated into the Monte Carlocode.

To simulate BBM delivery, the Monte Carlo simulation changes the rotational positionof the wheel in steps of 0.7◦ (Paganetti 2004). Because our facility uses only a limited setof modulator wheels, the desired M is translated into desired rotation angles where the beamcurrent is turned on and off at the cyclotron (beam source) level (Lu and Kooy 2006). Further,in order to fine-tune the shape of the SOBP depth–dose distribution, the beam current iscontinuously modulated as a function of the rotation angle using up to 24 sets of beam-currentmodulation look-up tables to ensure that each SOBP satisfies its flatness specification. Thesetables were incorporated into the Monte Carlo code.

For the simulation of PBS, the magnetic field settings defined in the TCS (based onprescriptions by the planning system) are translated into magnetic strengths in Tesla as afunction of position in the treatment head geometry (Paganetti et al 2005). The scanningmagnets are currently implemented in the Monte Carlo as perfect dipoles, with straight fieldboundaries and magnetic field lengths based on measurements. To scan a particular patternwithin the patient, the scanning trajectory for a given energy layer is discretized in points.Through the input file, the magnetic field is set for each beam spot for which a pre-definednumber of protons are simulated.

The treatment head simulation code was benchmarked against measurements in variousphantoms (water, lung equivalent4 material, bone equivalent material) showing very goodagreement. For example, measured dose distributions of an SOBP in water can be reproducedwith accuracies within typically ∼1 mm in R and ∼3 mm in M (the accuracy of themeasurements is typically well within ∼0.5 mm in R and 3 mm in M (or 3% in dose forlarge M)). Figure 1 shows an analysis of the distal fall-off for pristine Bragg curves illustratingthat the range agreement is within 1 mm. A set of measured and simulated SOBP fieldsis given in figure 3. All data points, with a few exceptions in the distal part of the depth–dose curve, show an agreement of within 2.5%. The absolute doses are within 1.5% forthe calibration point (typically in the center of the SOBP) when compared with ionizationchamber measurements (Paganetti 2006). An example of an inhomogeneous phantom setupis shown in figure 4. The simulation was based on the manufacturer’s information on materialcharacteristics (density, composition). Comparisons between measured (ionization chamber)and Monte Carlo predicted dose distributions are shown for depth–dose curves and a beamprofile. A small discrepancy can be seen in the penumbra steepness of the profile and in thedistal dose fall-off when going through a lung equivalent material. The latter might be causedby the granularity of the material, while simulating a homogenous mass in the Monte Carlo.The edge scattering effects visible in the beam profile are nicely reproduced by the MonteCarlo. We have further compared the Monte Carlo simulations in plastic phantoms usingin vivo post-irradiation PET imaging (Parodi et al 2007a).

Figure 5 illustrates the simulation of pencil-beam scanning where proton pencils havebeen steered through the treatment head and a scanning pattern was irradiated in a water

4 Note that the term ‘equivalent’ refers to photon attenuation in megavoltage photon beams, not proton energy loss.

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Figure 3. Measured (solid lines) and simulated (open circles) SOBP fields for different settings ofthe modulator wheel and double-scattering system.

phantom. Shown is a distal layer in a field of 20 cm range in water delivering an in-homogenousfield in order to illustrate the scanning pattern.

2.5. Simulation of the patient geometry

The patient geometry is stored in the DICOM format by the CT scanner. The DICOM datastream is imported by XiO and then rewritten in a specific format with one set of four files perCT slice. These files separate the information on the slice contours, the electron density pervoxel and the CT information. For convenience, we generate one binary cube file that containsthe HU information for each voxel. The variable, non-equidistant, slice spacing used in theCT scan is preserved and used also by the Monte Carlo program. We did optimize Geant4 forthe use of CT data by modifying its tracking algorithm (Jiang and Paganetti 2004).

For analytical dose calculation methods, the common practice in photon therapy is to usethe electron density or mass density to characterize the radiation energy loss in tissues. This isvalid if the dominant energy loss process is in interaction with electrons. The approximationbreaks down if nuclear interactions become significant. For protons, instead of electron densityor mass density, relative stopping power has to be used to accurately define water equivalenttissue properties. XiO is capable of handling photon and proton treatments and thus has toincorporate two different methods of CT conversion. For every CT voxel, a lookup table isused to convert HU into electron density (for photon calculations) and into relative stoppingpower (for proton calculations).

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4833

Figure 4. Comparison of the Monte Carlo predicted dose distribution (open circles) with measuredvalues using an ionization chamber (solid lines). The right side depicts the geometry (black: boneequivalent material (thickness: 3 cm); dark gray: lung equivalent material (thickness: 5 cm); lightgray: water). The dashed lines indicate the planes corresponding to the shown dose distributions(depth–dose curves: 1, 2 and 3; profile at 8 cm depth: 4). The gap between the bone and lungmaterial was 6 cm and the gap between the phantom front face and the treatment head aperturewas 8 cm. For the depth–dose curves, a treatment head setup to deliver a pristine field with 14 cmrange was applied. An SOBP (full modulation) was used for the beam profile.

Figure 5. Intensity map arbitrary units for a distal layer of a field with a range of 20 g cm−2 and apre-defined scanning pattern.

Because Monte Carlo dose calculations are not based on water equivalent propertiesbut on the exact material composition, a conversion from HU to human tissues (defined viaelemental composition and weights) must be implemented. The accuracy of Monte Carlo dose

4834 H Paganetti et al

Figure 6. Data flow for Monte Carlo dose calculation.

calculations is affected by the ability to precisely define materials based on HU (Jiang et al2007). We use a conversion method published by Schneider et al (2000), with an extensionto higher HU in order to deal with high-Z materials (e.g. titanium) (Parodi et al 2007a). Inour implementation, the HU space is divided into 27 groups: 1 group for air, 1 group forlung tissue, 7 groups for soft tissues, 15 groups for skeletal tissues and 3 groups for high-Zmaterials. Within each group, the elemental composition and weights are preserved, whereasthe mass density continuously increases as the HU increases (except in the small range of14–23 where a constant density is assigned). Because typically each density defines a separatematerial in the Monte Carlo, one would still have to deal with about 3000 materials, which canbe very inefficient in terms of computer memory or simulation run-time because of frequentchanges in cross sections and other associate tables. Consequently, a method to dynamicallyassign the mass density to the materials during particle transport so that one HU group canshare one material was developed (Jiang and Paganetti 2004).

Table 1 shows the definition of tissue groups, their densities and their elementalcompositions. The density differs for each HU but is given only for the center of the binfor simplicity. Also shown is a density correction factor to normalize the density in the MonteCarlo to mimic the HU versus relative stopping power table of the planning system. This isnecessary to avoid differences in the dose distributions simply due to different HU conversiontables. Note that the Monte Carlo only normalizes the mass density to the planning system. Itdoes not use a stopping power table but considers the appropriate material composition.

Clinicalim

plementation

offullM

onteC

arlodose

calculationin

protonbeam

therapy4835

Table 1. Tissue groups used for patient representation in the Monte Carlo code (material compositions are based on Schneider et al (2000)). Titanium is shown as one example toaccommodate high-Z implants. Other high-Z materials can be added accordingly. The density differs for each HU but is given only for the center of the bin for simplicity. The densitycorrection factor normalizes the density in the Monte Carlo to mimic the HU versus relative stopping power table of the planning system.

(center of HU bin) Material composition weights (%)

Group HU range Density (g cm−3) Density correction H C N O Na Mg P S Cl Ar K Ca Ti

1 [; −951] 0.0270 1.051 75.5 23.2 1.32 [−950; −121] 0.4800 0.977 10.3 10.5 3.1 74.9 0.2 0.2 0.3 0.3 0.23 [−120; −83] 0.9264 0.948 11.6 68.1 0.2 19.8 0.1 0.1 0.14 [−82; −53] 0.9577 0.958 11.3 56.7 0.9 30.8 0.1 0.1 0.15 [−52; −23] 0.9845 0.968 11.0 45.8 1.5 41.1 0.1 0.1 0.2 0.26 [−22; 7] 1.0113 0.976 10.8 35.6 2.2 50.9 0.1 0.2 0.27 [8; 18] 1.0296 0.983 10.6 28.4 2.6 57.8 0.1 0.2 0.2 0.18 [19; 79] 1.0609 0.993 10.3 13.4 3.0 72.3 0.2 0.2 0.2 0.2 0.29 [80; 119] 1.1199 0.971 9.4 20.7 6.2 62.2 0.6 0.6 0.3

10 [120; 199] 1.1117 1.002 9.5 45.5 2.5 35.5 0.1 2.1 0.1 0.1 0.1 4.511 [200; 299] 1.1650 1.005 8.9 42.3 2.7 36.3 0.1 3.0 0.1 0.1 0.1 6.412 [300; 399] 1.2244 1.010 8.2 39.1 2.9 37.2 0.1 3.9 0.1 0.1 0.1 8.313 [400; 499] 1.2834 1.014 7.6 36.1 3.0 38.0 0.1 0.1 4.7 0.2 0.1 0.114 [500; 599] 1.3426 1.018 7.1 33.5 3.2 38.7 0.1 0.1 5.4 0.2 11.715 [600; 699] 1.4018 1.021 6.6 31.0 3.3 39.4 0.1 0.1 6.1 0.2 13.216 [700; 799] 1.4610 1.025 6.1 28.7 3.5 40.0 0.1 0.1 6.7 0.2 14.617 [800; 899] 1.5202 1.030 5.6 26.5 3.6 40.5 0.1 0.2 7.3 0.3 15.918 [900; 999] 1.5794 1.033 5.2 24.6 3.7 41.1 0.1 0.2 7.8 0.3 17.019 [1000; 1099] 1.6386 1.035 4.9 22.7 3.8 41.6 0.1 0.2 8.3 0.3 18.120 [1100; 1199] 1.6978 1.038 4.5 21.0 3.9 42.0 0.1 0.2 8.8 0.3 19.221 [1200; 1299] 1.7570 1.041 4.2 19.4 4.0 42.5 0.1 0.2 9.2 0.3 20.122 [1300; 1399] 1.8162 1.043 3.9 17.9 4.1 42.9 0.1 0.2 9.6 0.3 21.023 [1400; 1499] 1.8754 1.046 3.6 16.5 4.2 43.2 0.1 0.2 10.0 0.3 21.924 [1500; 1599] 1.9346 1.048 3.4 15.5 4.2 43.5 0.1 0.2 10.3 0.3 22.525 [1600; 1999] 2.0826 1.042 3.4 15.5 4.2 43.5 0.1 0.2 10.3 0.3 22.526 [2000; 3060] 2.4655 1.049 3.4 15.5 4.2 43.5 0.1 0.2 10.3 0.3 22.527 [3061;] 4.5400 1.000 100.0

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2.6. Clinical implementation

Figure 6 illustrates the data stream to and from the Monte Carlo program. For each treatmentplan, the planning program provides information about the number of beams, the gantryangles, the patient couch angles, the air gaps between patients and treatment head, the doseper beam, R (distal 90% dose level of the SOBP) and M (distance between the proximal anddistal 90% dose level in a SOBP). In clinical practice, this information is transferred to theTCS, which then determines the appropriate treatment head settings and beam settings. It isdone in a similar way within the Monte Carlo program. The patient geometry (CT data) istransferred from the departmental patient database to the planning system. From there, the CTis imported into the Monte Carlo using a XiO-specific data format. This is then transformedinto a single binary cube (preserving the (variable) slice spacing and the voxel grid size). TheXiO format is used for convenience in order to generate the Monte Carlo input from only onesource. If desired, reading DICOM directly by the Monte Carlo would be straightforward (aDICOM reader for Geant4 has been presented by others (Kimura et al 2004, 2005)).

The Monte Carlo simulation is done in two steps. In the first step protons are trackedthrough the treatment head. The result of this simulation is stored in a phase space file. Thephase space distribution contains particle type, energy, position and angular momentum forparticles that cross a plane at the exit of the treatment head (typically downstream of the rangecompensator). The second step tracks particles through the patient geometry. Separationof dose calculations into phase space calculation and patient dose simulation is a commonpractice when using Monte Carlo in radiation therapy. Typically, this is done in order to reusephase space distributions for different patients and thus save computation time. For BBM,this is impractical because treatment head setups are highly patient field specific even withoutthe patient-field-specific aperture and compensator. Settings of scatterers, modulator wheelsegments and beam energy result in a huge amount of setup possibilities. Further, a separationof phase space calculation and dose calculation avoids a potential overlap of the treatmenthead geometry and the patient CT cube (depending on the size of the air gap). Overlappinggeometries can cause ambiguous situations in the Monte Carlo. Thus, the phase space conceptallows the particles that are ‘stored’ in the phase space file to be started within the CT geometry.

To facilitate the data flow and management, a user interface was developed to extractpatient information from the planning system for Monte Carlo simulations. The user selects aspecific patient, plan and treatment field. The software reads the CT and planning informationfrom the standard XiO generated data files. It then generates the input files for the MonteCarlo code: the CT data; a milling machine file for the aperture; a milling machine file for thecompensator; and an input file containing information about R, M, gantry angle, couch angle,isocenter position in the XiO coordinate system, voxel numbers and slice dimensions in X andY in the CT coordinate system, number of slices and their thickness, the positions of the CTslices in the CT coordinate system, width of the air gap and the prescribed dose.

The Monte Carlo code calculates the dose based on the CT grid, which is then stored ina file having the same format as the imported CT data. This offers the maximum resolutionto analyze dose distributions. Calculation efficiency would be improved if done on a morecourse grid. However, interpolations in the HU space could lead to uncertainties in materialassignments. In the treatment planning code, the calculation grid is a variable set by thetreatment planner. In general, it exceeds the CT grid size and is typically set to 2 × 2 ×2.5 mm3. In order to compare the Monte Carlo results with the ones from the planning system,re-sampling is necessary. This is done after the complete dose calculation on the CT grid isfinished (information on the XiO grid is provided in the input file). Consequently, the MonteCarlo generates two dose cubes, one based on the original CT grid and one based on the

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4837

planning grid. The latter has the appropriate format, including the file header, to potentiallyallow import into the XiO planning system for analysis or comparison with the pencil-beamresults. However, for convenient comparison of the dose cubes from XiO and Monte Carlo,an in-house developed standalone dose analysis toolkit (‘DCA’) is used, which visualizes CT,contours and both dose cubes overlaid on the CT and calculates DVHs.

A dose distribution calculated by XiO is a relative dose distribution and needs to benormalized to, for example, the prescription dose to the target area. For a patient treatmentfield, the proton fluence required to deliver the desired dose is specified in machine monitorunits (MU). At MGH, a proton therapy output factor is defined as the dose delivered to acalibration point in the treatment field divided by the required MU. A MU corresponds to afixed amount of charge collected in one of the segmented transmission ionization chambers(monitor chambers) close to the snout of the treatment heads. Because the treatment headgeometry is not incorporated in XiO, the machine output (absolute dose) is either calculatedseparately or measured prior to treatment (Kooy et al 2003, Kooy et al 2005). The MonteCarlo dose calculation provides dose to tissue by considering the energy deposited in eachvoxel and the material density. Based on a detailed simulation of the ionization chamberreading, the Monte Carlo code simulates absolute dose to the target without any empiricalnormalization factors. Thus, the Monte Carlo generated dose distributions can be specified incGy per MU (Paganetti 2006).

Typically, a statistical accuracy of 2.5% is desired for the target volume. The requirednumber of particle histories depends on the efficiency of the treatment head (determinedby the double scattering system in BBM), the required geometrical resolution, and slightlyon beam range and modulation width but typically does not depend on the field sizedownstream of the patient-field-specific aperture (because at MGH we are treating with fixedfield sizes impinging on the patient aperture). A typical number of proton histories fora given patient field is ∼20–25 million at treatment head entrance if sufficient statisticalaccuracy is requested for a single field based on the treatment planning grid resolution(figure 7). The number per field decreases for a complete treatment plan with typicallybetween 1 and 15 fields. A 2.5% accuracy in the target volume does not guarantee the sameaccuracy in the surrounding tissues. However, while the statistical uncertainty has a biginfluence on the dose–volume histogram (DVH) of the target volume, its impact on the DVHsof organs at risk is typically less, because the significance of the statistical effect depends onthe steepness of the DVH (Jiang et al 2000, Keall et al 2000). Figure 7 shows the influenceof the number of histories on the steepness of the CTV DVH and the shapes of the DVHsfor spinal cord and skin for a single field from a treatment plan for a para-spinal tumor. Theonly way to ensure that the statistical accuracy for each field is sufficient before starting thesimulation is to create a look-up table of required histories as a function of beam and treatmenthead parameters.

All simulations are started by submitting scripts to a LINUX-based computer clusterdedicated to dose calculation with currently 26 machines with either two or four CPUs each.The CPU power is virtually divided into 80 slots. Currently, Monte Carlo dose calculationis still time consuming, i.e. typically ∼6 h per patient (for 2.5% uncertainty in the CTV forall fields combined) when using 20 calculation slots in parallel for a simulation. Most ofthe calculation time (typically ∼90%) is spent tracking particles through the treatment head.Thus, a possible strategy to improve efficiency would be to parameterize the beam at thetreatment head exit (Paganetti 1998). While not straightforward for BBM, this is feasible forbeam scanning techniques. Calculation time per patient for PBS are therefore in the order of∼40 min (or about 13 CPU-hours). Up to now, the Monte Carlo dose calculation engine was

4838 H Paganetti et al

Figure 7. DVH of the CTV (upper), the spinal cord (middle) and the skin (lower) as a function ofthe number of histories for a single field from a treatment plan for a para-spinal tumor. The linesrefer to the use of 2, 6, 10, 14 and 18 million incident protons (numbers increasing for the differentcurve as indicated by the arrows).

considered a research tool with less focus on speed. This will allow us to use the current codeas gold standard when working on improving the Monte Carlo efficiency.

3. Results and discussion

3.1. General considerations

So far, we did apply Monte Carlo dose calculations mainly for breast, nasopharyngeal, para-nasal sinus, para-spinal and lung malignancies for BBM treatments. The purpose of this

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4839

paper is to demonstrate the roadmap of a clinical implementation of proton Monte Carlo dosecalculation. In order to motivate Monte Carlo dose calculation in proton therapy, the followingsections will discuss four cases (29 fields in total) that have been treated at our facility.

Monte Carlo dose calculation is a more accurate technique than analytical algorithmsbecause of the more detailed consideration of particle interactions and deflections in tissue.Other aspects also lead to differences when comparing Monte Carlo results with the resultsfrom the planning system. For example, the planning system does its dose calculation on aplanning grid size, which is larger than the CT grid, while we decided to use the CT grid inthe Monte Carlo (to avoid errors due to material interpolation).

The pencil-beam model characterizes the beam at the patient surface based onmeasurements of pristine depth–dose curves, source size and SAD values. It assumes ahomogenous fluence map through the aperture opening superimposing pristine Bragg curvesto a perfectly flat dose plateau in water. In contrast, the Monte Carlo dose distribution isbased on a proton field generated by a complete model of the treatment head geometry. Slightdifferences can thus be expected.

The pencil-beam algorithm as implemented does not take into account aperture scattering.Aperture scattering is taken into account when assessing the dose to be delivered by measuringor simulating the output factor. Thus, the prescribed doses as determined based on the pencil-beam results are not affected by aperture scattering. However, only the Monte Carlo dosecalculation shows the (typically quite small) scatter contribution to the dose at a low range.

The XiO planning system only specifies relative doses. Thus, the treatment plannerassigns the prescription dose to the CTV (full coverage). The Monte Carlo dose distributionis simulated in absolute values. This is done based on the knowledge of the actual clinicallydelivered monitor units per field and the Monte Carlo simulation of the output factor (dose permonitor unit in water), which determines the number of histories per monitor unit.

Pencil-beam algorithms consider water of various densities to represent human tissues,and hence report water equivalent absorbed dose, or dose-to-water. Monte Carlo simulationscalculate dose-to-tissue. Energy loss depends on elemental composition leading to differencesbetween dose-to-water and dose-to-tissue. For photon beams the difference is approximately1% in soft tissues and can exceed 10% for cortical bone (Siebers et al 2000). Similar effects,though different in magnitude, can be expected in proton beams (Palmans and Verhaegen 2005).Converting dose-to-tissue into dose-to-water, or vice versa, is not necessarily straightforwardfor proton beams due to the involvement of not only ionization, but also multiple Coulombscattering and nuclear interactions with which protons can deposit energy. In the clinicallyused energy range, protons predominantly loose energy via ionization. If the influence fromnuclear interactions is ignored and charged particle equilibrium is assumed, the ratio of dose-to-water and dose-to-tissue is represented by the ratio of the mass stopping powers. For anaccurate conversion, the energy fluence would have to be recorded for each voxel.

There are both pros and cons for using either dose-to-water or dose-to-tissue (Liu andKeall 2002). Clinical dosimetry protocols are based on dose-to-water and so is our clinicalexperience in terms of defining dose constraints and prescribed doses (although for softtissues the difference may be negligible). Further, water is certainly the most importantmaterial to assess radiation action on cells. Nevertheless, the increasing use of Monte Carlodose calculation, which naturally determines dose-to-tissue, may be an argument in favor ofreporting dose-to-tissue in the future.

Because of the different dose standards, the following case studies are based onnormalizing dose-to-tissue from the Monte Carlo system to dose-to-water from the treatmentplanning system at the 50% target dose for each field separately. For the four cases consideredhere, the normalization causes corrections of ∼3%, on average. Because of the dependence

4840 H Paganetti et al

Figure 8. Axial, coronal and sagittal views of dose distributions calculated using the Geant4 MonteCarlo system DoC++. The patient was treated with three fields (columns 1–3) for a para-spinaltumor. The upper row also shows the GTV contour in red.

on density, discrepancies between the planning system and the Monte Carlo will occur, forexample, in bone.

In order to allow comparison with photon treatments in clinical trials, doses in protontherapy have to be corrected for the difference in relative biological effectiveness (RBE). Inproton therapy, an RBE of 1.1 is being used (Paganetti et al 2002) with the notation Gy(RBE)if this factor is included in the reported dose according to a recommendation by the ICRU(2008).

Quality assurance is an important aspect for any dose calculation engine. For the majorityof patient fields for which Monte Carlo dose calculations are done, we currently do measure adepth–dose curve in water which is then compared with a Monte Carlo prediction. In addition,we are performing post-irradiation PET imaging for a small subset of patients, which, webelieve, could serve as a quality assurance procedure for beam delivery, planning system andMonte Carlo dose calculations in the future (Parodi et al 2007b).

3.2. Case study 1: spinal cord

This patient was treated for a spinal cord astrocytoma extending from the medulla to C7. Thetreatment plan consists of three coplanar fields, with each field differing in the gantry angle,the couch angle, R, M, aperture and compensator. The field size parameters are 12.8; 5.5;∼7.8 cm (R; M; average aperture diameter), 12.6; 5.5; ∼7.9 cm and 12.5; 5.5; ∼7.8 cm,respectively. The prescribed dose was 45 Gy(RBE) to the CTV administered in 30 fractions(1.5 Gy(RBE) per fraction), with each field delivering 15 Gy(RBE).

Challenging for the pencil-beam dose calculation might be the fact that the distal fall-offis within bone (possibly causing range degradation) and the fact that the left and right fields

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4841

Figure 9. Axial views of three proton therapy treatment fields as planned for a para-spinal tumor.The calculated dose distributions using the Monte Carlo system are shown in the left column.The treatment plan was executed using XiO (middle column). The right column shows the dosedifference (Monte Carlo minus XiO).

are tangential to bone/tissue interfaces. The Monte Carlo dose calculation is based on a CTwith 176 × 147 × 126 slices with voxel dimensions of 0.932 × 0.932 × 2.5–3.75 mm3 (notethat the slice thickness is variable).

Figure 8 shows the Monte Carlo calculated dose distributions for all three fields in oneCT slice. A comparison with the dose distributions predicted by the planning system is givenin figure 9 for all fields. Small differences (up to ∼4–5%) can be seen in the lateral penumbrafor the posterior–anterior field, where the planning system predicts a slightly sharper fall-off.For the other two fields the difference in the penumbra is much smaller, probably becausethe posterior–anterior field penetrates more bony anatomy. The main differences are in thedistal fall-off, i.e. in the end of range of the beams. These can be attributed to four factors.First, some differences in bone are expected because the Monte Carlo shows dose-to-boneinstead of dose-to-water. Second, there are potential problems of analytical dose calculationmethods to accurately predict dose degradation in the distal fall-off (Urie et al 1986). Third,the Monte Carlo system (based on the simulation of the entire treatment head) even predictsa higher range in a water tank (by ∼1.5 mm) than the planning system for this field. This isa discrepancy of more than 1 mm, which is very rare (based on all the fields simulated so far)but could be caused by discrepancies in the geometry modeling of the treatment head (based

4842 H Paganetti et al

Figure 10. Same patient as shown in figures 8 and 9 with all three beams combined. Upper left:Monte Carlo dose distribution; lower left: pencil-beam dose distribution; upper right: differenceimage (Monte Carlo minus XiO); lower right: gamma index plot (2 mm/2% condition).

on the manufacturer’s specifications) and the actual treatment head. Finally, there might be asmall experimental error when measuring the depth–dose curve. The range difference looksdramatic on the difference image but corresponds to only ∼1.5 mm range discrepancy. Theincreased range causes the large difference in air seen in one of the fields, because the planningsystem had predicted a field just shy of the air volume. Interestingly, there is a significantreduction in range for a small area predicted in the Monte Carlo for parts of the field goingthrough the sphenoid bone. This may be caused by the almost tangential position of thesphenoid sinus relative to the beam.

Figure 10 shows, for one slice, the total dose distribution as the sum of the three treatmentfields as well as the difference image and gamma index plot. Differences between pencil-beam results and Monte Carlo calculations seem to be negligible except for the end of rangeregions. Figure 11 shows the dose–volume histograms for brainstem and GTV consideringthe entire plan. The agreement is quite good, i.e. a Monte Carlo dose calculation would nothave influenced the treatment planning decision. Also shown is the DVH for the odontoid,which is not a critical structure but is used for the patient setup.

3.3. Case study 2: nasopharynx

This patient had a tumor in the right nasopharynx (with involvement of the neck region).Seven proton fields (delivered in 2 Gy(RBE) per fraction; 5 fields used in 15 fractions and2 fields used in 5 fractions) were used for treatment of the primary target and both the rightand the left neck regions. The prescribed dose to the primary target CTV was 60 Gy(RBE),administered by one of the fields. In addition, 60 Gy(RBE) (to the CTV) was delivered to theupper-right and the upper-left neck (2 fields each). Two fields with a dose of 10 Gy(RBE) eachwere used for a boost to the nodes. The patient also received a dose from five photon fieldsto the lower neck region, which was not included in this proton Monte Carlo study. Photon

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4843

Figure 11. Dose–volume histograms (total plan; brainstem, odontoid and GTV) for the patientshown in figures 8–10. Solid lines: Monte Carlo; dashed lines: XiO.

Figure 12. Dose distributions for one field to the left neck and one field to the right neck of anasopharynx patient with the neck involved. The calculated dose distributions using the MonteCarlo system are shown in the left column. The treatment plan was done using XiO (middlecolumn). The right column shows the dose difference.

fields are sometimes used in addition to proton fields because photon beams provide betterskin sparing or because of limited capacity at the proton treatment facility.

Challenging for the pencil-beam dose calculation might be the fact that the neck fieldsare almost tangential to the patient surface, requiring proper modeling of scattering at theair/tissue interface. The Monte Carlo dose calculation is based on a CT with 169 × 155 ×125 slices with voxel dimensions of 0.656 × 0.656 × 1.25–3.75 mm3 (variable slice thickness).

All seven fields were simulated but only two fields are shown as examples in figure 12,one left-posterior field and one right-posterior field with a total prescribed dose of 30 Gy(RBE)each. The field size parameters are 11.4; 8.8; ∼6.2 cm (R; M; average aperture diameter) and11.9; 10.3; ∼7.2 cm, respectively. Again, like in the previous case, there are some differencesin the penumbra region. The penumbra agrees well, within 0.5 mm, for the 60% dose leveland lower. However, closer to the field edge, discrepancies of 1.5 mm (at 95% dose) can befound for one of the fields. Further, there are the expected dose discrepancies for both fieldsin air and in bone.

4844 H Paganetti et al

Figure 13. Spread-out Bragg peak in water for one of the fields shown in figure 12 as assumedby the planning system (line) and as simulated by the Monte Carlo (based on the treatment headgeometry, closed circles).

Figure 14. Same patient as shown in figure 12 with all seven beams combined. Upper left: MonteCarlo dose distribution; lower left: pencil-beam dose distribution; upper right: difference image(Monte Carlo minus XiO); lower right: gamma index plot (2 mm/2% condition).

The differences in range are presumably due to areas where the beam stops in either boneor air, and because the beam travels tangential to the patient surface, presumably causingproblems for the scattering algorithm in the planning system at the patient/air interface. In awater tank, the range predicted by the planning system agrees perfectly with the Monte Carlopredicted range as seen in figure 13 for one of the applied fields.

Figure 14 shows all seven fields combined. For most areas the agreement betweenthe pencil-beam algorithm and the Monte Carlo is quite good (within about 3% variation).

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4845

Figure 15. Dose–volume histograms (GTV, CTV and submandibular glands) for the patient shownin figure 12. Solid lines: Monte Carlo; dashed lines: XiO.

Exceptions are the dose to air and some areas associated with the 60–95% penumbra regionalso seen in the lower field in figure 12. Figure 15 shows the dose–volume histograms for thetarget (GTV and CTV) and the submandibular glands. The Monte Carlo predicts a lower doseto the glands because they are located in an area affected by differences in beam range andbecause the glands are next to the patient’s surface almost tangential to the incoming beam.Note that the reason for a less homogenous dose to the GTV in the Monte Carlo results isnot lack of statistical resolution. The reason, at least in part, lies in the fact that the planningsystem assumes a perfectly flat SOBP in water whereas the Monte Carlo calculation (due tothe simulation of the treatment head) is based on the SOBP actually delivered (which typicallyhas small variations within ±1–2%). This is illustrated nicely in figure 13.

3.4. Case study 3: spinal cord

This was a patient with a chordoma in the spinal meninges. Treatment was done with sixproton fields and three photon fields, delivering 75.6 Gy(RBE). Two fields were administeredin 13 fractions (1 Gy(RBE) per fraction) and four fields were administered in 7 fractions using2 Gy(RBE) per fraction. The Monte Carlo dose calculation is based on a CT with 81 ×69 × 101 slices with voxel dimensions of 0.488 × 0.488 × 2.5 mm3. Out of the proton fields,we only present two fields in figure 16, one right-anterior field and one left-posterior field.The fields were delivered in 1 Gy(RBE) per fraction to a total of 13 Gy(RBE) and 2 Gy(RBE)per fraction to a total of 14 Gy(RBE), respectively. The field size parameters are 14.1; 10.9;∼7.2 cm (R; M; average aperture diameter) and 8.4; 3.1; ∼3.8 cm, respectively. The agreementis very good, except for some small areas in the distal part of the fields, where the MonteCarlo predicts a higher dose. This appears mostly within the distal fall-off of the field inareas where the beam traveled through bone. Figure 17 shows all proton fields combined and

4846 H Paganetti et al

Figure 16. Dose distributions for two single fields for a para-spinal tumor patient. Left: dosedistribution as calculated by Monte Carlo; middle: dose distributions as calculated by the planningsystem; right: difference maps. The upper field shows the CTV contour in red on the planningsystem result. Note that the field in the second row is designed to cover only part of the targetvolume.

Figure 17. Same patient as shown in figure 16 with all six proton fields combined. Upper left:Monte Carlo dose distribution; lower left: pencil-beam dose distribution; upper right: differenceimage (Monte Carlo minus XiO); lower right: gamma index plot (2 mm/2% condition).

figure 18 shows the DVH distributions. Discrepancies can be up to 6%. The significantlyhigher inhomogeneity of the target dose predicted by the Monte Carlo is caused at least in partby the bony anatomy included in the CTV volume contour and by the fact that there were CTartifacts due to metal present in the target volume.

3.5. Case study 4: sphenoid sinus

The fourth case considered was an uncharacteristically complicated case involving 13 protonand 2 photon fields. The high number of fields was chosen to allow conformal treatment of aC-shaped target while protecting several critical structures. Four fields were used to administer76 Gy(RBE) to the primary GTV. In addition, one field ensured 70 Gy(RBE) to be given to

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4847

Figure 18. Dose–volume histograms (CTV, and spinal cord) for the patient shown in figure 17.Solid lines: Monte Carlo; dashed lines: XiO.

Figure 19. Dose distributions four fields for a sphenoid sinus tumor patient. The upper two andthe lower two fields represent a patch field combination with a patch line across the 50% distalfall-off and 50% lateral penumbra. Left: dose distribution as calculated by Monte Carlo; middle:dose distributions as calculated by the planning system; right: difference maps.

the GTV of the node and eight fields to deliver 66 Gy(RBE) to the primary CTV and the upperneck targets. Treatment was done delivering 2 Gy(RBE) per fraction. Three fields were used

4848 H Paganetti et al

Figure 20. Combination of the patch field pairs shown in figure 19. Left: dose distribution ascalculated by Monte Carlo; middle: dose distributions as calculated by the planning system; right:difference maps.

Figure 21. Same patient as shown in figures 19 and 20 with all proton fields combined. Upper left:Monte Carlo dose distribution; lower left: pencil-beam dose distribution; upper right: differenceimage (Monte Carlo minus XiO); lower right: gamma index plot (2 mm/2% condition) includingthe contours for the upper neck CTV (turquoise) and the primary CTV (magenta).

in 12 fractions, three in 11 fractions, two in 8 fractions, one in 6 fractions, two in 5 fractionsand two in 4 fractions. The Monte Carlo dose calculation is based on a CT with 161 × 177 ×111 slices with voxel dimensions of 0.65 × 0.65 × 1.25–3.75 mm3 (variable slice thickness).

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4849

Figure 22. Dose–volume histograms for chiasm, brainstem, right optic nerve, left optic nerve,spinal cord, right temporal lobe, right parotid, left parotid as well as the target structures (CTVnode, CTV upper neck, CTV primary, GTV primary) for the patient shown in figures 19–21. Solidlines: Monte Carlo; dashed lines: XiO.

Because of the C-shaped target, the ‘field patching’ technique (Bussiere and Adams 2003)was used for this patient. In ‘field patching’, a technique unique to proton therapy, two fieldsare combined so that one field treats only part of the target avoiding a nearby critical organwith the lateral penumbra. The second field is used to cover the remaining segment, alsoavoiding the critical organ with the lateral penumbra. The distal fall-off at 50% dose of onefield is hereby matched to the lateral penumbra at 50% dose of the other field at the so-calledpatch line. In these cases, uncertainties in the penumbra and distal fall-off position are crucial.Consequently, patch lines are positioned solely in target structures allowing a slight overshootof the beam to ensure coverage. Further, a single patch combination is only used for threeto five fractions. Nevertheless, field patching is very sensitive to range uncertainties and oneusually treats with two patch field combinations, i.e. four fields, by alternating the fields forrange and penumbra matching as shown in figures 19 and 20.

One might expect uncertainties in the pencil-beam dose calculation particularly in thedistal fall-off region due to range uncertainties as well as dose degradation. Thus, the patch

4850 H Paganetti et al

field technique, positioning the distal fall-off region within the target, might show the mostclinically significant differences between pencil-beam and Monte Carlo.

Out of the proton fields, we present only four fields in figures 19 and 20, where wecombined two right-posterior and two left-posterior fields for illustration. The field sizeparameters are 9.0; 7.3; ∼3.3 cm (R; M; average aperture diameter), 12.5; 10.1; ∼3.1 cm,10.9; 9.6; ∼3.2 cm, and 8.0; 7.3; ∼3.1 cm, respectively.

As for the other cases studied, figure 19 reveals differences mainly in the distal part ofthe fields. This influences the precision of the field patching as seen in figure 20, wherequite significant discrepancies are illustrated across the patch line. However, obviously thedifferences are largely washed out by the alternating patch field use. Figure 21 gives the totaldose distribution over all proton fields. A significant difference of more than 3 Gy is in theregion already visible in the third field in figure 19. This might be due to a high gradient inthe range compensator in this area and could be an indication that uncertainties in such areahave to be addressed by increased compensator smearing. The big discrepancies (hot spots inthe Monte Carlo of up to 6 Gy) appear to be just outside of the upper neck CTV but partlywithin the primary CTV (see figure 21). Thus, in this case, uncertainties in the end of therange region do affect also the target dose.

The differences are reflected in the DVH analysis (figure 22). The dose homogeneity inthe CTV for the node is significantly compromised when looking at the Monte Carlo results,which is presumably a result of the relatively small and superficial target.

4. Conclusion

Proton Monte Carlo dose calculation for treatment planning support can be done accuratelyand efficiently using Geant4 Monte Carlo based software. The presented implementation istailored to the Monte Carlo code Geant4 and the treatment planning system XiO. However,the presented solutions can be easily adopted for other planning systems or other Monte Carlocodes. The described Monte Carlo code ‘DoC++’ is currently in use at the Francis H BurrProton Therapy Center, Massachusetts General Hospital.

The shown comparison between the planning system results and the Monte Carlo resultsis not a pure comparison between Monte Carlo and pencil-beam based dose calculation inpatient anatomy. Discrepancies are caused by different parameterizations of the treatmenthead beam output and differences in the dose metric (dose-to-tissue versus dose-to-water).

The four cases shown as examples reveal that, as expected, there are differences betweenthe Monte Carlo and the pencil-beam dose calculation. While the agreement in the beampenumbra is generally quite good, differences in range can be seen in most cases (netdifferences in range as well as range degradation). These depend on the range compensatorgradient, the amount of bony anatomy in the beam path (large density variations) and theexistence of air–bone–tissue interfaces (in particular if those interfaces are tangential to thebeam). Even small discrepancies in local energy deposition can result in considerable changesin range over the entire beam path through tissue (Jiang et al 2007). The pencil-beamalgorithm is less sensitive to geometrical complexities and frequent density variations, i.e.bone–soft tissue, bone–air or air–soft tissue interfaces. The significance of the discrepanciesdepends on the geometrical position of organs at risk and on applying margins that do reflectdose calculation uncertainties, in particular at the end of the range. For single fields or incases where one would rely on an accurate distal fall-off (if the distal part of the SOBP wouldpoint to a critical structure or if field patching is applied), the discrepancies might have clinicalimplications.

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy 4851

Acknowledgments

We would like to thank Sashidar Kollipara, Tom Madden and Andrew Kaplan for their helpin dealing with converting data formats, providing software for analysis and taking careof computer hardware management. Further, we would like to thank Christina ZacharatouJarlskog for her (separately published) work on the Geant4 physics setup. We would also liketo thank Joseph Perl (SLAC) from the Geant4 collaboration for answering many questions. DrsChan, Liebsch and Loeffler provided the patient data used in this study. Treatment planningwas done by Judy Adams. This work was supported in part by National Institutes of Health(5 P01 CA21239-25).

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