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Medical Dosimetry, Vol. 36, No. 4, pp. 347-350, 2011Copyright © 2011 American Association of Medical Dosimetrists

doi:10.1016/j.meddos.2010.09.001

DOSE CALCULATION ACCURACY OF THE MONTE CARLOALGORITHM FOR CYBERKNIFE COMPARED WITH OTHER

COMMERCIALLY AVAILABLE DOSE CALCULATION ALGORITHMS

SUBHASH SHARMA, PH.D., JOSEPH OTT, M.S., JAMONE WILLIAMS, M.S., andDANNY DICKOW, M.S.

Parkview Comprehensive Cancer Center, Fort Wayne, IN

(Received 1 July 2010; accepted 8 September 2010)

Abstract—Monte Carlo dose calculation algorithms have the potential for greater accuracy than traditionalmodel-based algorithms. This enhanced accuracy is particularly evident in regions of lateral scatter disequilib-rium, which can develop during treatments incorporating small field sizes and low-density tissue. A heteroge-neous slab phantom was used to evaluate the accuracy of several commercially available dose calculationalgorithms, including Monte Carlo dose calculation for CyberKnife, Analytical Anisotropic Algorithm and PencilBeam convolution for the Eclipse planning system, and convolution-superposition for the Xio planning system.The phantom accommodated slabs of varying density; comparisons between planned and measured dosedistributions were accomplished with radiochromic film. The Monte Carlo algorithm provided the most accuratecomparison between planned and measured dose distributions. In each phantom irradiation, the Monte Carlopredictions resulted in gamma analysis comparisons >97%, using acceptance criteria of 3% dose and 3-mmdistance to agreement. In general, the gamma analysis comparisons for the other algorithms were <95%. TheMonte Carlo dose calculation algorithm for CyberKnife provides more accurate dose distribution calculations inregions of lateral electron disequilibrium than commercially available model-based algorithms. This is primarilybecause of the ability of Monte Carlo algorithms to implicitly account for tissue heterogeneities, density scalingfunctions; and/or effective depth correction factors are not required. © 2011 American Association of MedicalDosimetrists.

Printed in the USA. All rights reserved0958-3947/11/$–see front matter

Key Words: Cyberknife, Monte Carlo, Heterogeneity corrections, Dose calculation.

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INTRODUCTION

A Monte Carlo dose calculation algorithm has recentlybecome commercially available for CyberKnife (Ac-curay, Inc., Sunnyvale, CA) treatment planning. Numer-ous studies have shown that Monte Carlo dose calcula-tion algorithms are more accurate than traditionalcorrection-based algorithms or convolution algorithms atpredicting dose distributions delivered to heterogeneousvolumes.1–4 The accuracy of Monte Carlo algorithmstem from their inherent ability to model individual par-icle interactions in tissue. Heterogeneities are implicitlyncluded in Monte Carlo algorithms via the calculation ofarticle interaction probabilities and subsequent doseeposition. Previous studies have shown that conven-ional algorithms tend to overestimate the dose deliveredo low-density heterogeneous volumes; the level of over-stimation is field size– and energy-dependent.2–4 This isecause of the failure of conventional algorithms todequately account for lateral scatter disequilibrium thatrises for small field sizes, low-density tissue, and in-reased beam energy.5 Because of their robust nature,

Monte Carlo algorithms have the potential to providemore accurate results in heterogeneous volumes.

Reprint requests to Joseph Ott, M.S., Parkview ComprehensiveCancer Center, 11141 Parkview Plaza Drive, Suite 110, Fort Wayne,

IN 46845. E-mail address: joseph.ott@parkview.com.

347

The goal of this study was to extend previouslypublished work, which compared the accuracy of theCyberKnife Monte Carlo and ray-tracing dose calcula-tion algorithms at predicting dose delivered to heteroge-neous tissues.4 We evaluated the accuracy of variousommercially available treatment planning algorithmsrom multiple vendors, including the Multiplan Montearlo algorithm version 2.1 (Accuray, Inc., Sunnyvale,A), Xio Convolution-Superposition (CS) algorithmersion 4.3.1 (CMS), Eclipse analytical anisotropic al-orithm (AAA), and Eclipse pencil beam convolutionlgorithm (PBC) version 8.1 (Varian Medical Systems,alo Alto, CA), in predicting dose delivered to targets in

he presence of heterogeneities.Tissue heterogeneities are accounted for very dif-

erently in each of the treatment planning algorithms.he PBC algorithm utilizes the Batho Power Law orquivalent tissue-air-ratio correction method.6 In either

case, the dose distribution is first calculated assuming awater-equivalent (homogeneous) medium. The homoge-neous distribution is then multiplied point-by-point, by acorrection factor calculated using the selected method.The AAA algorithm was developed, in part, to achieveimproved dose calculation accuracy in heterogeneousmedia compared with the PBC algorithm.7 It incorporates

the convolution/superposition principle with density-scaled

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primary energy deposition functions and polyenergetic scat-ter kernels, which is similar to the calculation method of theCS algorithm from Xio.

The Multiplan Monte Carlo algorithm uses a dual-source model derived from a set of clinically measuredbeam data (percent depth dose, profiles, etc.).8 Practi-ally speaking, 12 independent Monte Carlo models areenerated, one for each of the 12 fixed collimators usedor CyberKnife treatments. Tissue heterogeneity effectsn the dose distribution are implicitly included in thealculation, density scaling, and/or use of correction fac-ors are not required.

METHODS AND MATERIALS

The Radiological Physics Center (RPC) anthropo-orphic thorax phantom was used to validate the accu-

acy of the CyberKnife Monte Carlo dose calculationlgorithm. The RPC thorax phantom is designed to sim-late the treatment of a solitary left lung mass.9 Dosim-

etry inserts allow comparisons between planned and de-livered dose distributions; thermoluminescent dosimetrycapsules are used for absolute dose comparisons, andradiochromic film is used for relative dosimetry.

Measurements to compare the treatment planningalgorithms were conducted using a modified StandardImaging Baby Blue (BB) Phantom. The Standard Imag-ing BB phantom is constructed of a polystyrene basematerial that simulates unit density soft tissue. Balsawood and a standard imaging lung slab were used inconjunction with the BB phantom to simulate separateheterogeneous environments. A GE LightSpeed com-puted tomography (CT) simulator was used to imageeach of the phantom configurations. The CT numbers(measured at 120 kVp) for the lung slab and wood were–730 � 5 HU and –590 � 30 HU, respectively. Thehantom setup with the lung slab, as well as a sagittal CTlice through the center of the phantom, are shown inig. 1. To avoid electron streaming along central axis

hrough the gap between the lung and polystyrene slabs,

Fig. 1. Photograph and midplane sagittal CT slice of the B

he anterior fields were positioned 1 cm inferior from theenter of the phantom, as shown in the sagittal CT slice.

For each algorithm and phantom combination, airect comparison was made between the measured andredicted dose distributions. Dose distribution compari-ons were based on MD-55 gafchromic film measure-ents. Film scanning was accomplished with a flatbed

canner that uses a white light source. To maximize theensitivity of the film, only the signal from the redhannel was used in the comparisons.

Single anterior beam treatment plans were createdor each phantom using the various algorithms. A dose ofpproximately 2000 cGy was prescribed to the plane ofhe film for each plan; this placed the point of measure-ent toward the center of our calibration curve forD-55 film (Fig. 2). The depth of the film plane was 6

m from the anterior surface of the phantom. As shownn Fig. 1, an ion chamber, placed below the film plane,as used as a second check of the delivered dose. AAA,BC, and Xio CS single-beam plans were generated andelivered using a 4 � 4-cm2, 6-MV anterior photon

beam from a Varian Clinac iX linear accelerator. ACyberknife G4 was used to deliver the single beamMonte Carlo plan using a 30-mm circular cone collima-

Fig. 2. Calibration curve for gafchromic MD-55 film.

B phantom with the lung-equivalent slab in place.

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Monte Carlo algorithm for cyberknife ● S. SHARMA et al. 349

tor. As such, dose calculation algorithms from multiplevendors were tested with the same phantom, under sim-ilar lateral scatter conditions.

Analysis was conducted using MapCheck version4.01 (Sun Nuclear Corporation, Melbourne, FL). Thesoftware allowed for comparison of relative planned anddelivered dose distributions using gamma analysis (3%,3 mm). Gamma analysis is a quantitative tool that incor-porates both dose and distance to agreement measure-ments to determine the level of conformity between 2dose distributions. In addition, profile comparisonsthrough the center of the film were also analyzed.

Fig. 3. Representative gamma analysis plots and profiles

Table 1. Gamma analy

Xio CMS (%) Eclipse PB

omogeneous phantom 93.6 91.hantom—lung insert 90.3 93.hantom—Wood insert 94.6 92.

alues in the table correspond to the gamma pass rate using criteria o

(B) algorithms. The profiles correspond to the ve

RESULTS AND DISCUSSION

For each phantom irradiation, the MultiPlan MonteCarlo algorithm provided a more accurate comparison be-tween planned and delivered dose distributions than the Xioconvolution-Superposition, PBC, and AAA algorithms. Ta-ble 1 contains a summary of these comparisons. In eachcase, the Monte Carlo predictions resulted in a gammaanalysis comparison �97%, indicating that �97% of theixels within the irradiated film plane met or exceeded the%, 3-mm dose and distance criteria. In general, the gammanalysis comparisons for the other algorithms were �95%.

lung phantom insert for the Monte Carlo (A) and AAA

lts for each algorithm

Eclipse AAA (%) Multiplan�Monte Carlo (%)

97.1 97.492.1 99.994.4 99.9

lative dose and 3 mm distance-to-agreement.

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rtical green line shown in the gamma plot.

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Representative gamma analysis plots and profilesfor the lung insert phantom are shown in Fig. 3A for theMonte Carlo algorithm and Fig. 3B for AAA. The MonteCarlo algorithm most accurately predicts the increasedtransmission and scatter perturbation through the low-density lung insert, as indicated by the rise on the rightside of the profile. In addition, the Monte Carlo algo-rithm also accurately predicts the shape and gradientthroughout the entire profile. Of particular interest is thebroadening of the profile caused by the presence of thelow-density material, which is illustrated by the discrep-ancy in the penumbra width on the right side of theprofile for the AAA algorithm.10 The penumbra pre-dicted by the Monte Carlo algorithm conforms very wellto the measured penumbra.

Based on the type of heterogeneity correction usedby each of the algorithms (correction-based calculationsfor PBC and polyenergetic scatter kernel convolution forAAA and Xio CS) one would expect the AAA and XioCS models to fare better under these experimental con-ditions than the PBC algorithm. In general, this trend isobserved in the film comparisons, with the exception ofthe phantom with the lung insert. This observation couldbe a result of the convolution-based algorithms overes-timating the impact of the low-density lung insert on thescattered component of the dose. At very small fieldsizes, the dose distribution may be influenced more bythe increased transmission of primary radiation throughthe lung insert. In addition, the MD-55 film used in thesemeasurements is documented to have a uniformity un-certainty in the range of 3–5%, which could partiallyaccount for discrepancies in the film comparisons.11

CONCLUSION

In this study, the Monte Carlo algorithm fared theest at predicting the dose distribution delivered in all 3xperimental setups (homogeneous phantom, lung slabhantom, wood phantom). The ability of Monte Carlolgorithms to implicitly account for tissue heterogene-

ties results in accurate predictions of primary photon

ttenuation as well as lateral photon and electron scatter,factors that greatly influence dose distributions deliv-

red to heterogeneous volumes. In general, the AAAlgorithm was more accurate than PBC; however, in thease of the lung slab insert, PBC actually fared slightlyetter than AAA. Based on the results from the other 2hantoms, this discrepancy could be a result of the doc-mented 3–5% uncertainty in uniformity of MD-55 ra-iochromic films.

The authors thank Mu Young Lee, Ph.D., and Miroslav Nikolic, Ph.D.,of Accuray, Inc.

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