Review Article A Review on the Use of Grid-Based Boltzmann...

Hindawi Publishing CorporationBioMed Research InternationalVolume 2013 Article ID 692874 10 pageshttpdxdoiorg1011552013692874

Review ArticleA Review on the Use of Grid-Based Boltzmann EquationSolvers for Dose Calculation in External Photon BeamTreatment Planning

Monica W K Kan12 Peter K N Yu2 and Lucullus H T Leung1

1 Department of Oncology Princess Margaret Hospital Hong Kong2Department of Physics and Materials Science City University of Hong Kong Tat Chee Avenue Kowloon Tong Hong Kong

Correspondence should be addressed to Monica W K Kan kanwkmhaorghk

Received 2 May 2013 Accepted 22 July 2013

Academic Editor Maria F Chan

Copyright copy 2013 Monica W K Kan et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Deterministic linear Boltzmann transport equation (D-LBTE) solvers have recently been developed and one of the latest availablesoftware codes Acuros XB has been implemented in a commercial treatment planning system for radiotherapy photon beamdose calculation One of the major limitations of most commercially available model-based algorithms for photon dose calculationis the ability to account for the effect of electron transport This induces some errors in patient dose calculations especially nearheterogeneous interfaces between low andhigh densitymedia such as tissuelung interfacesD-LBTE solvers have a high potential ofproducing accurate dose distributions in and near heterogeneous media in the human body Extensive previous investigations haveproved that D-LBTE solvers were able to produce comparable dose calculation accuracy asMonte Carlo methods with a reasonablespeed good enough for clinical use The current paper reviews the dosimetric evaluations of D-LBTE solvers for external beamphoton radiotherapyThis content summarizes and discusses dosimetric validations for D-LBTE solvers in both homogeneous andheterogeneous media under different circumstances and also the clinical impact on various diseases due to the conversion of dosecalculation from a conventional convolutionsuperposition algorithm to a recently released D-LBTE solver

1 Introduction

Highly conformal photon dose distributions in various treat-ment sites can be achieved using different techniques ofmultileaf collimator-based intensity modulated radiotherapyincluding static intensity modulated radiotherapy (IMRT)and volumetric modulated arc therapy (VMAT) Radio-therapy using intensity modulated techniques improves thepossibility to escalate the target dose and minimize dosesto critical organs when compared to three-dimensional con-formal radiotherapy [1ndash11] The use of IMRT or VMAT inpatients usually involves many small field segments some ofwhich might pass through regions of low and high densitymedia such as lung air and bone depending on the locationof the tumor and the surrounding normal tissues One issuethat affects the dose calculation accuracy in highly conformalplanning is the ability of the algorithm to correctly accountfor the effects of radiation transport with the presence ofheterogeneous medium

Correction-based algorithms implemented in commer-cially available clinical treatment planning system include thepencil beam algorithm (PBC) collapsed cone convolutionalgorithm (CCC) and the analytical anisotropic algorithm(AAA) For PBC it assumes that any collimated photon beamincident on the patient is composed of a large number ofinfinitely narrow pencil beams of photons The total dose iscalculated by superposition of pencil beam dose kernels ateach point in space around the incident beam derived fromMonte Carlo simulations The effects of tissue variations andpatient contour are usuallymodeled based on equivalent pathlength methods or the modified Batho correction method[12ndash14] More advanced superpositionconvolution methodssuch as AAA and CCC are able to incorporate electronand secondary photon transport in an approximate way fordose calculations in a heterogeneousmediumThesemethodsuse the superposition of the Monte Carlo derived dosekernels of both primary and scatter components to obtain

2 BioMed Research International

doses in voxels of the irradiated volume To account for thepresence of inhomogeneities simple density scaling of thekernels is applied so that the secondary electron transportis only modeled macroscopically Both AAA and CCC wereproved to produce inaccurate dose distribution inmedia withcomplex heterogeneities in certain circumstances [14ndash18]

The Monte Carlo (MC) methods have been consid-ered the most accurate methods for radiotherapy treatmentplanning dose calculation They are statistical simulationmethods based on random samplingThey solve the radiationtransport problem stochastically by simulating the tracks of asufficiently large number of individual particles using the ran-dom number generated probability distribution governingthe individual physical processes They are therefore capableof accurately computing the radiation dose in media underalmost all circumstances [19 20] However the computationtime required may still limit the use of MC methods forcomplex intensity modulated techniques in the clinical envi-ronment

The desire to develop a fast alternative dose calculationmethod with comparable accuracy to MC methods hasled to the exploration of deterministic solutions to thecoupled system of linear Boltzmann transport equations(LBTE) [21ndash26] It was first demonstrated using the prototypesoftware Attila which was a general purpose grid-basedBoltzmann solver code It was followed by Acuros developedby Transpire Inc (Gig HarborWA USA) specially designedfor radiotherapy dose calculations Recently a version ofdeterministic LBTE solver namely Acuros XB (AXB) hasbeen developed and implemented in the Eclipse treatmentplanning system (Varian Medical Systems Palo Alto CAUSA) The LBTE is the governing equation that describesthe macroscopic behavior of ionizing particles as they travelthrough and interact with matter The electron angular flu-ence is first obtained by solving the LBTE and then the dosecan be generated by using the macroscopic electron energydeposition cross-sections and the density of the materialsWith sufficient refinement without using any approximationthat is if an MC algorithm simulates an infinite numberof particles and a deterministic LBTE (D-LBTE) solverdiscretizes the variables such as space and energy intoinfinitely small grids both approaches will converge on thesame solutionThe achievable accuracy of both approaches isequivalent and is limited only by uncertainties in the particleinteraction data and uncertainties related to the transportedradiation fields Extensive efforts have been made by severalinvestigators to validate the accuracy of D-LBTE solvers indifferent circumstances by comparison against MC and byexperimental verification against measurements Performedvalidations ranged from using a simple geometric phantomwith simple fields to a complex humanoid phantom withmultiple intensity modulated fields Most studies reportedthat D-LBTE solvers were capable of producing comparableaccuracy as MC methods and either equivalent or betteraccuracy than superpositionconvolution algorithms [22ndash35] Dosimetric impact on different media of various clinicalsites due to the conversion of the currently used model-based algorithms to the newly implemented D-LBTE solverswas also investigated by several authors [32 36ndash38] This

paper summarizes and discusses the findings of the mostrecent dosimetric evaluation for D-LBTE solvers in varioustreatment sites

2 The Deterministic LBTE Solvers

More detailed description of the D-LBTE solvers can befound in the literature [21ndash26] Only a summary is reportedhere

The time-independent three-dimensional (3D) systemof the coupled LBTE is solved to determine the energydeposition of photon and electron transport

Ω sdot

997888

nablaΦ

120574+ 120590

120574Φ

120574= 119902

120574120574+ 119902

120574

(1)

Ω sdot

997888

nablaΦ

119890+ 120590

119890Φ

119890minus

120597

120597119864

(119878119877Φ119890) = 119902

119890119890+ 119902

120574119890+ 119902

119890

997888

119903 isin 119881

Ω isin 4120587 119864 gt 0

(2)

whereΦ120574 andΦ119890 are the photon and electron angular fluencerespectively 120590120574 and 120590119890 are the macroscopic photon andelectron total interaction cross-sections for all materials involume 119881 and energies respectively 119902120574120574 119902120574119890 and 119902119890119890 rep-resent the photon scattering source generated from photoninteraction electron scattering source generated fromphotoninteraction and electron scattering source generated fromelectron interactions everywhere in 119881 for all angles andenergies respectively 119902120574 and 119902119890 represent the external photonand electron source from the treatment head respectively997888

119903 is the spatial position vector 119864 is the energy Ω is theunit vector denoting particle direction and 997888nabla is referredto as the ldquostreaming operatorrdquo which may be interpreted asthe number of particles flowing into a volume 119889119881 minusthe number of particles flowing out of 119889119881 for particlestravelling in a direction 119889Ω about Ω with energy 119864 about119889119864 The second terms on the left-hand side of (1) and (2)are the ldquocollision operatorsrdquo which may be thought of as thenumber of particles removed from the volume by absorptionor scattering Equation (2) is the Boltzmann Fokker-Planktransport equation which is solved for the electron transportThe third term on the left-hand side of (2) representsthe continuous slowing down operator where 119878119877 is therestricted plus collisional radiative stopping power Equations(1) and (2) are usually solved through discretization in spaceangle and energy Energy discretization is achieved withthe standard multigroup method Space discretization canbe achieved with a variably sized Cartesian adaptive meshrefinement technique (used by AXB) or by using a high-orderGalerkin-based linear discontinuous finite-element methodto solve the multigroup discrete ordinates equations onfully unstructured tetrahedral elements (used by Attila) Forthe former technique the mesh is limited to refinementin factors of 2 or smaller in any direction This allowsfor the use of finer resolution in higher dose and highdose gradient regions Angle discretization for fluences andscattering sources is achieved with the standard ordinatesmethod where the quadrature order is adaptive by the energygroupThe photon angular fluence of (1) is the summation of

BioMed Research International 3

uncollided (primary photon without interaction withmatter)and collided fluence components (photons produced or scat-tered by photon interactions in the patient) where the latteris discretized using a linear discontinuous finite-elementmethod providing a linear solution variation throughouteach element with discontinuities permitted across elementfaces After solving the electron angular fluence the dose inany grid voxel 119894 is calculated as follows

119863119894 = int

1

0

119889119864int

4120587

119889

Ω(120590

119890

ED (997888

119903 119864))

120588 (

997888

119903 )

Φ

119890(

997888

119903 119864

Ω) (3)

where120590119890ED is themacroscopic energy deposition cross-sectionand 120588 is the material density of the local voxel

Similar to the MC methods D-LBTE solvers also useenergy cut-offs for electrons and photons A particle isassumed to deposit all of its energy locally below the cut-offenergy For example AXB uses an electron cut-off energy of500 keV and a photon cut-off energy of 10 keV Assumptionssimilar to those used in some MC methods are also appliedto (1) and (2) of D-LBTE solvers It is assumed that bothsecondary charged particles produced by pair productionare electrons not one electron plus one positron It is alsoassumed that photons produce electrons but electrons donot produce photons The energy from photons produced bythe electrons is assumed to be deposited locally For (2) it isassumed that the Fokker-Planck operator is used for ldquosoftrdquointeractions leading to small-energy losses Catastrophicinteractions leading to large energy losses are representedwith the standard Boltzmann scattering

Both MC methods and D-LBTE solvers produce errorsMC methods produce stochastic errors when an insufficientnumber of particle histories is followed LBTE solvers pro-duce systematic errors due to finite discretization resolutionin space angle and energy Better accuracy always requireslonger computation time In addition the achievable accu-racy of MC and D-LBTE solver is limited by uncertainties inparticle interaction data patient geometry and compositionof the radiation field being modeled

Similar to some MC methods two options of dosereporting modes that is dose-to-water 119863119908 and dose-to-medium 119863119898 are usually provided in D-LBTE solvers Bothoptions calculate dose considering the elemental compositionof each material in which particles are transported Thedifference between them is mainly in the postprocessing stepin which 119863119908 is obtained by rescaling 119863119898 using the stoppingpower ratio of water to medium

3 Validation in Homogeneous Water

It is important to validate a new dose calculation algorithmin basic geometrical conditions such as that in homoge-neous water before going ahead for more complicated onesThe information regarding the accuracy in simple cases isimportant to identify the sources of errors or uncertaintiesin more complicated geometries Fogliata et al performeda comprehensive assessment of AXB in Eclipse to modelphoton beams of low and high energy in homogeneous water

with simple geometries [26] They also included ldquoflatteningfilter freerdquo (FFF) beams from the Varian TrueBeam machineThe use of an FFF beam significantly increases the doserate and therefore reduces the delivery time of a treatmentmachine Due to the removal of flattening filter the physicalaspects of FFF beams are different from those of conventionalflattened ones including forward peaked intensity profilesin the middle instead of uniform flat profiles across thefields steeper dose fall-off of percentage depth doses in theexponential region less variation of off-axis beam hardeninglower mean energy less photon head scatter and higher sur-face dose For conventional flattened beams the performanceof AXB was determined by comparison of calculated dataagainst measured data in water for open and wedged fieldsFor FFF beams the verification tests were performed for openfields onlyThe overall accuracy was found to be within 1 foropen beams and 2 for mechanical wedges

Testing the performance of AXB using open fields inhomogeneous water was also performed by several otherinvestigators [27 28 32] Doses calculated using AXB werecompared to measuredgolden beam data data calculatedusing AAA and CCC as well as MC simulated data usingdifferent field sizes for different energy beamsOutput factorspercentage depth doses (PDD) and lateral dose profiles atvarious depths were examined In general the agreementbetween the calculated data generated by the various modelsand the measuredgolden beam data were found to bebetter than or close to 2 with slightly larger discrepanciesfound in the build-up and penumbra regions The calculatedpenumbral widths were usually found to be slightly smallerthan the measured ones

In homogeneous water comparable performance wasfound between AXB and AAACCC This was expected asmost commercially available correction-based algorithmsand radiation transport algorithmswere capable of accuratelypredicting the photon beamdose distribution in homogenouswater The discrepancies between calculated data and mea-sured data were mostly limited by the precision and spatialresolution of the beam measurement devices used especiallyin regions of high dose gradient For example the use of ionchamber with finite size for measuring dose profiles wouldbroaden the penumbra width

4 Verification with InhomogeneousSimple Geometric Phantom UsingSingle Open Fields

Several investigations have been performed to examine theaccuracy of several different D-LBTE solvers for predictingthe dose distribution in heterogeneous simple geometricphantoms using single fields of different photon energies[22 25 27ndash31] The media of interest included soft tissuenormal lung light lung air bone aluminium stainless steeland titanium alloy Most of the verifications were performedby benchmarking against the dose distributions calculatedby MC methods Table 1 summarizes the methods phantomgeometries beam configurations and comparison resultsbetween MC and D-LBTE solvers of some previous inves-tigations In general good agreement was found between


Table 1 A summary describing information of some previous investigations for the accuracy of D-LBTE solvers in predicting the doses inheterogeneous simple geometric phantoms using single open fields

Publishedinvestigations

Gifford et al 2006[22]

Vassiliev et al 2010[25]

Bush et al 2011[27] Han et al 2011 [28] Kan et al 2012

[30]

Lloyd andAnsbacher 2013[31]

Beam energy 18MV 6 and 18MV 6 and 18MV 6 and 18MV 6MV 6 and 18MV

Field sizes 15 times 15 cm225 times 25 cm2

50 times 50 cm2

100 times 100 cm2

40 times 40 cm2

100 times 100 cm2

150 times 100 cm2

25 times 25 cm2

50 times 50 cm2

100 times 100 cm2

20 times 20 cm2

30 times 30 cm2

50 times 50 cm2100 times 100 cm2

Phantom(s)geometry

One multilayerphantomwater (0ndash3 cm)aluminium Al(3ndash5 cm)lung (5ndash12 cm)water (12ndash30 cm)

One multilayerphantomwater (0ndash3 cm)bone (3ndash5 cm)lung (5ndash12 cm)water (12ndash30 cm)

Two phantoms(i) one with asingle insert ofnormal lunglight lung or airin water(ii) a bonelungphantom withseveraldisk-shapedbony structures


300 times 300 times

300 cm3 ofwatercontaining 50 times50 times 300 cm3 ofair

200 times 200 times

200 cm3 of musclecube containing20 times 20 times 180 cm3

of stainless steel ortitanium alloy

Monte carlosimulation

EGS4Presta03 statisticaluncertaintyresolution05 times 05 times 02 cm3

voxels

DOSXYZnrclt01 statisticaluncertaintyresolution02 times 02 times 02 cm3

voxels 01 cmlaterally inpenumbra region

DOSXYZnrcsim1 statisticaluncertainty inmedia except upto 45 in airresolution025 times 025 times

025 cm3 voxels


voxels for mostvolume01 times 01 times 02 cm3

near waterboneand bonelunginterfaces

EGS4Presta20 statisticaluncertaintyresolution110 of fielddimensions with02mm binthickness

DOSXYZnrcsim1 statisticaluncertaintyresolution02 times 02 times 02 cm3

voxels

D-LBTE solver Attila code Acuros(Transpire Inc)

AXB of version10 AXB of version 10 AXB of version

10 AXB of version 11

Dosedistributionexamined

PDD PDD and lateralprofiles

PDD and lateralprofiles

PDD lateralprofiles and 3Dgamma evaluation


DifferencebetweenD-LBTE solverand MonteCarlosimulation

Averagediscrepancy is14 with 22maximumdiscrepancyobserved atwaterAl interface

For 6MV maxdiscrepancy lt15 with DTA lt07mm in thebuild-up regionFor 18MV maxdiscrepancy lt 23with DTA lt03mm in thebuild-up region

Discrepancieswere within 2in lung 3 inlight lung up to45 in air 18in bone withslightly largerdiscrepancy (upto 5) atinterfaces

For 6MV averagediscrepancy of 11in PDD and 16in dose profilesFor 18MV averagediscrepancy of16 in PDD and30 and doseprofiles

Discrepanciesare mostlywithin 2 withslightly higherdiscrepancy (upto 6) at theairtissueinterface in thesecondarybuild-up region

In general goodagreement betweenAXB and MC withan average gammaagreement with a21mm criteria of913 to 968

D-LBTE solvers and MC with discrepancies of better thanor equal to 2 in most cases Verification using AXB ofversion 10 showed that therewere slightly larger discrepanciesof up to about 4 to 6 found in the presence of very lowdensity media such as light lung or air especially atnear theinterface in the secondary build-up region when small fieldswere used [27 30] The accuracy of D-LBTE solvers dependson the material assignment and the level of sampling thestructure voxels to the calculation grid Fogliata et al showedthat the version 11 of AXB gave better agreement with MCwhen predicting doses in the presence of air than the version100 of AXB which was due to the inclusion of air material

assignment (airmaterial was not included in version 100) andthe provision of better resampling process of the structurevoxels to the calculation grid [29]

Some of these studies also compared the accuracy of AXBwith AAA [29ndash31] one of which performed the comparisonwith CCC as well [28] All of them observed considerablylarger differences between AAA and MC than those betweenAXB and MC in the presence of lung air and very highdensity objects especially near the interfaces It was found thatAXB could improve the dose prediction accuracy over bothAAA and CCC in the presence of heterogeneities It shouldalso be noted that the depth dose profile data presented


by Han et al showed that CCC produced slightly betteragreement withMC thanAAA in both lung and bone regions[28]

5 Verification Using Multiple Clinical SetupFields with Humanoid Geometry

51 Verification by Comparison with Monte Carlo SimulationSome investigations were performed to examine the accuracyof D-LBTE solvers by comparison against MC methodsfor clinical setup fields [24 25] One study compared thedose distributions from one prostate and one head-and-neck clinical treatment plans calculated by Attila to thosecalculated by MC using the DOSXYZnrc program Bothplans were generated using the CT image data set of thereal patients using multiple coplanar open fields 3D gammaevaluation showed that 981 and 985 of the voxels passedthe 33mm criterion for the prostate case and the head andneck case respectively

Another study compared the dose distributions from atangential breast treatment plan calculated by Acuros (Tran-spire Inc) to those calculated by MC using the DOSXYZnrcprogram The plan was generated on an anthropomorphicphantom with two tangential fields using a field-in-fieldtechnique Field shapes were defined by amultileaf collimatorusing both 6 and 18 MV beams The 3D gamma evaluationshowed that the dose agreement was up to 987 for the21mm criterion and reached 999 for the 22mm cri-terion The differences were mostly found in the air externalto the patient and in the lateral penumbra on the inside edgeof the fields

In general both studies showed excellent agreementbetween D-LBTE solvers and MC in all regions includingthose near heterogeneity and with the use of small fieldsThese studies indicated that D-LBTE solvers were ableto produce similar accuracy as MC methods for compli-cated geometries However the achievable accuracy of MCapproach was also limited by uncertainties of the parti-cle interaction data the geometry and composition of thefield being modeled and other approximations made inradiation transport Comprehensive validations of D-LBTEsolvers should also cover comparisons against experimentalmeasurements Treatment plans with more complex inten-sity modulated fields such as IMRT and VMAT were notincluded in these studies

52 Verification by Comparison against Measurements Ver-ifications of AXB against measurements using IMRT andVMAT plans for various diseases were reported [30 32ndash35]Humanoid phantoms used include the Radiological PhysicsCenter (RPC) phantoms the anthropomorphic phantom (theRANDO phantom The Phantom Laboratory Salem NYUSA) and the CIRS Thorax Phantom (CIRS VA USA)Table 2 summarizes some of the details including methodsand results of each verification study Regarding verificationusing thermoluminescence dosimeters (TLDs) all the calcu-lated data matched with the measured data are within 5with an average discrepancy of about 2 to 3 The positions

of measurement included those inside the heterogeneousmedium and nearat the interfaces

For the gamma analysis using EBT films the passing rateof the 33mm criterion met the recommendation (shouldbe gt90) set by TG 119 for the studies performed in thenasopharyngeal region and the lung where heterogeneitiesexist However the one performed using the RPC head andneck phantom where only tissue equivalent material wasinvolved could only produce a passing rate of 88 for the53mm criterion [33] The inferior results reported mightbe due to the larger uncertainty of the film registrationmethod during analysis

All experimental validations listed also compared theaccuracy between AXB andAAAThe accuracy of both whencompared to TLDmeasurement was quite comparable exceptfor the investigation using intensity modulated stereotacticradiotherapy (IMSRT) in locally persistent nasopharyngealFor the IMSRT cases AXB demonstrated better accuracynear airtissue interfaces when compared with AAA Thismight be due to the very small field segments used inIMSRT cases with the presence of air cavities For validationsperformed with films the accuracy of AXB was in generalshown to be slightly better than that ofAAAWhen comparedto TLD films could measure a much larger number ofpoints in a single measurement and provided better spatialresolution This might be the reason why films could betterdistinguish between the accuracies of AAA and AXB evenwhen the difference was small

6 Dose in Medium against Dose in Water

For external photon beam radiation therapy planning theinput data used for most conventional correctionmodel-based dose algorithms are dose distributions and beamparameters measured in water They usually report patientdose in terms of the absorbed dose to water (119863119908) usingvariable electron density On the other hand LBTE solverscalculate the energy deposition considering radiation parti-cle transport in different media and therefore report dosedirectly to patient medium (119863119898) According to the recom-mendation from the American Association of Physicists inMedicine (AAPM) Task Group 105 MC results should allowconversion between 119863119898 and 119863119908 based on the Bragg-Graycavity theory either during or after the MC simulationThis recommendation also applies to all other deterministicalgorithms that are able to report 119863119898 accurately for planevaluation [39] 119863119898 calculated by LBTE solvers can beconverted to119863119908 using the Bragg-Gray cavity theory by

119863119908 = 119863119898(

119878

120588

)

119908

119898

(4)

where (119878120588)119908119898

is the unrestricted water to medium masscollision stopping power ratio averaged over the energyspectra of primary electrons at the point of interest Ithas been recently debated whether the 119863119898 dose inherentlypredicted by MC methods needs to be converted to 119863119908There are certain arguments between using 119863119898 and 119863119908 forradiotherapy treatment planning in the clinical environment


Table 2 A summary of information on some previous experimental validations for the accuracy of D-LBTE solvers in predicting the dosesin heterogeneous humanoid phantoms using multiple clinical setup fields

Publishedinvestigations Han et al 2012 [33] Kan et al 2013 [34] Kan et al 2012 [30] Han et al 2013 [35] Hoffmann et al

2012 [32]

Disease of interest Oropharyngealtumor

Nasopharyngealcarcinoma

Locally persistentnasopharyngealcarcinoma

Lung cancer Tumor inmediastinum

Media involved Water equivalentmaterials

Tissue air andbone

Tissue air andbone Tissue and lung Tissue lung and

bone

Treatment techniqueused IMRT VMAT IMRT VMAT IMSRT IMRT VMAT

A total of 11different plansincluding opposingfields multiplefields IMRT andVMAT

Phantom used RPC head andneck phantom

Anthropomorphicphantom(RANDO)


RPC thoraxphantom

CIRSThoraxphantom

Measurement device TLD and EBT film TLD and EBT film TLD TLD and EBT film EBT film

LBTE solverAXB version 11using both119863

119898and

119863

119908

AXB version 10using both119863

119898and

119863

119908

AXB version 10using119863

119898only


119898and

119863

119908


119898only

Observed results

For TLD deviationwithin 5For gammaanalysis with film88 passed53mm criterionfor both119863

119898and

119863

119908

For TLD deviationwithin 5 with anaverage of 18For gammaanalysis with film91 passed33mm criterionfor119863

119898and 99 for

119863

119908

For TLDdeviation within3

For TLD deviationwithin 44For gammaanalysis with filmsim97 passed33mm criterionfor119863

119898and 98 for

119863

119908

For gammaanalysis with film982 passed the33mm criterionfor 6MV and995 for 15MV

Those supporting the use of 119863119908 argued that (1) therapeuticand normal tissue tolerance doses determined from clinicaltrials were based on 119863119908 as photon dose measurements andcalculations were historically reported in terms of 119863119908 (2)calibration of treatment machines were performed accordingto recognized dosimetry protocols in terms of the absorbeddose to water and (3) tumor cells embedded within anymedium such as bone were more water-like than medium-like Those supporting the use of119863119898 argued that (1) the doseto the tissues of interest was the quantity inherently computedby radiation transport dose algorithms and therefore wasmore clinical relevant and (2) the conversion of 119863119898 backto 119863119908 might induce additional uncertainty to the finalcalculated dose

Several studies proved that the difference between using119863119908 and 119863119898 for predicting photon dose distribution mainlyoccurred in higher density materials such as the corticalbone The dose discrepancy could be up to 15 due to thelarge difference between the stopping powers of water andthese higher-density materials For soft tissues and lungthe dose discrepancy was only about 1 to 2 [33 35 40]An investigation by Dogan et al based on the MC methodfound that converting 119863119898 to 119863119908 in IMRT treatment plansintroduced a discrepancy in target and critical structure of upto 58 for head and neck cases and up to 80 for prostatecases when bony structures were involved [41] Kan et al

also observed that AXB using119863119908 calculated up to 4 highermean doses for the bony structure in planning target volume(PTV) when compared to 119863119898 in IMRT and VMAT plans ofNPC cases [34] Figure 1 shows the difference in dose volumehistograms (DVHs) between119863119898 and119863119908 for different organsat risk (OAR) and PTV components (both bone and softtissues) They were generated by AXB using both 119863119898 and119863119908 for a typical VMAT plan of an NPC case It can be seenfrom the DVH curves that larger dose differences were foundbetween 119863119898 and 119863119908 in organs with bony structures such asmandible than those with soft tissue such as parotids

Previous studies usingMonteCarlo andAXB calculationsproved that conventional model based algorithms predicteddose distributions in bone that were closer to 119863119898 distribu-tions than to 119863119908 distributions [34 42] It is therefore betterto use 119863119898 for consistency with previous radiation therapyexperience

7 Dosimetric Impact in Clinical Cases

Various studies were performed to assess the dosimetricimpact of using AXB instead of AAA for dose calculations indifferent clinical cases including lung cancer breast cancerand nasopharyngeal carcinomas [36ndash38] AXB calculationsfor these investigations were all performed using the 119863119898option so that the capability of the algorithm to distinguish


0

20

40

60

80

100

120

0 20 40 60 80Dose (Gy)

Rela

tive v

olum

e (

)

Mandible Dm

Mandible Dw

Parotid Dm

Parotid Dw

Spinal cord Dm

Spinal cord Dw

PTV in tissue Dm

PTV in tissue Dw

PTV in bone Dm

PTV in bone Dw

Figure 1 DVH curves for different OAR and PTV componentsgenerated by AXB with both 119863

119898and 119863

119908calculation options for a

typical VMAT plan of an NPC patient

between different elemental compositions in the human bodycould be assessed The grid resolution for dose calculationselected was 25mm In order to evaluate the dose differencesbetween the two algorithms due to the issue of tissueheterogeneity the PTV were divided into components ofdifferent densities and compositions during dose analysis

71 Lung Cancer Theclinical dosimetric impact for advancednon-small-cell lung cancer was assessed using three differ-ent techniques three-dimensional conformal radiotherapyIMRT and RapidArc (the name of the VMAT system fromVarian Medical Systems Inc Palo Alto CA USA) at both 6and 15MV [36] The PTVs were split into two componentsnamely PTV in soft tissue and PTV in lung The doseprescription was 66Gy at 2Gy per fraction to themean targetdose for each planning technique The results demonstratedthat AXB predicted up to 17 and 12 lower mean targetdoses in soft tissue for 6MV and 15MV beams respectivelyand up to 12 higher and 20 lower mean target doses inlung for 6MV and 15MV beams respectively In generalAAA overestimated the doses to most PTV componentsexcept for PTV in lung when using IMRT at 6MV wherethe opposite trend was observed AXB predicted up to 3lower mean doses to OAR The observed trend was similarfor different treatment techniques

72 Breast Cancer The dosimetric impact for breast cancerwas assessed using the opposing tangential field settingtechnique at 6MV [37] Doses in organs were analyzedusing patient datasets scanned under two different breathingconditions free breathing (FB representing higher lung

density) and deep inspiration (DI representing lower lungdensity) The target breast was split into components inmuscle and in adipose tissue It was observed that AAApredicted 16higher doses for themuscle thanAXB (version11) The difference in doses predicted by both algorithms tothe adipose tissue was negligible AAA was found to predictup to 05 and 15higher doses than using version 11 of AXBin the lung region within the tangential field for FB and DIrespectively The authors comparing between versions 10 and11 of AXB found negligible differences in the predicted dosesfor tissue and normal lung However they observed that forthe lower density lung in the condition of DI version 11 ofAXB predicted an average of 13 higher dose than version10This was mainly due to themore accurate dose calculationof version 11 for very low density lung achieved by includingthe low density air in the material list

73 Nasopharyngeal Carcinomas The dosimetric impact forNPC was assessed using IMRT and RapidArc at 6MV due tothe use of AXB version 10 compared to AAA [38] The PTVswith multiple prescriptions were separated into componentsin bone air and tissue AAA was found to predict about 1higher mean doses to the PTVs in tissue 2 higher dosesto the PTVs in bone and 1 lower doses to the PTVs inair AAA also predicted up to 3 higher doses to most serialorgans It should be noted that AAA predicted up to 4higher minimum doses to the PTVs in bone where the grosstumor volume was located

On the whole the various investigations for differenttreatment sites listed above demonstrated that in generalAAA predicted higher doses to PTV and OAR when com-pared with AXB The overestimation by AAA was mostlywithin 2 in soft tissues such as muscle and lung and couldbe up to 4 in bone

8 Discussions

Various studies showed that D-LBTE solvers were able toproduce satisfactory dose calculation accuracy in the pres-ence of heterogeneous media even at and near interfacesof different material densities [22ndash35] They were provedto produce equivalent accuracy to MC methods and betteraccuracy than convolutionsuperposition algorithms Theseresults are expected as D-LBTEmethods model the radiationtransport process in a similar manner as MC methodsThere is still room for improvement in the latest versionof clinically available AXB regarding accuracy in physicalmaterial assignment and calculation speed For example oneof the limitations of AXB is the restrictedmaterial assignmentrange If the CT dataset of a high density object containsHU values corresponding to a mass density greater than30 gcm3 it is required to contain all voxels in a contouredstructure with manual assignment of mass density Thatmeans the mass density of the high density object must beknown for accurate dose calculations The validation of AXBby Lloyd and Ansbacher proved that it was able to predict theback-scatter and lateral-scatter dose perturbations accuratelyadjacent to very higher density objects (with density in


the range from 40 to 80 gcm3) [31] However in realitythis would be difficult for real patient planning due to themisinterpretation of HU values of high density implantsintroduced by shadow artifacts in CT images

When compared to MC methods the use of D-LBTEsolvers might result in relatively shorter calculation time asexplicit modeling of a large number of particle interactionsis not required Previous studies observed that the earlier D-LBTE code Attila performed dose calculations faster thanthe general purpose of MC method such as EGS4 or theEGSnrc by an order of magnitude for both external beamand brachytherapy planning [22 24] Acuros which wasoptimized for use in radiotherapy planning was reported toperform roughly an order of magnitude faster than Attila forvarious clinical cases [25] Furthermore the latest version ofD-LBTE method AXB was reported to produce 3 to 4 timesfaster speed for VMAT planning compared to AAA [36]Theabove evidence indicates that D-LBTE methods can be a fastand accurate alternative toMCmethods However it is in factdifficult to perform direct comparison of the speed betweenMC and D-LBTE solvers as it depends on the hardwareand the efficiency of the coding used The computationtime of D-LBTE solvers might be further reduced in thefuture by implementation on graphical processing units andadditional refinements On the other hand fast MC codeshave been developed to improve the speed of dose calculationfor clinical use Examples include the Voxel-based MonteCarlo (VMC VMC++) Macro Monte Carlo Dose PlanningMethod (DPM) and MCDOSE [43ndash50] Continuous devel-opment ofmore efficientMCcodes in the futuremay competewith currently commercial available D-LBTE methods interms of both accuracy and speed

Although D-LBTE solvers were proved to be moreaccurate than convolutionsuperposition algorithms signif-icant differences were mainly confined to certain extremeconditions These mainly include doses near heterogeneousinterfaces when using single or multiple small fields Up to 8to 10 higher doses near interfaces were predicted by AAAcompared with AXB when stereotactic small fields were usedin the presence of air cavity [30] Smaller differences werefound when using IMRT and VMAT setup fields Severalexperimental verifications showed comparable dose accuracybetween AXB and AAA in soft tissues within complexheterogeneous geometries for clinical intensity modulatedfields [33ndash35] The studies assessing the dosimetric impact ofusing AXB on various clinical sites also showed only about1 to 2 lower means doses in all soft tissues predicted byAXB compared to AAA [36ndash38] Slightly larger differences ofabout 4 were found in bony structures due to the fact thatAXB reported dose tomediumas default whileAAA reporteddose to water as default Most of these comparison studieswere confined between AAA and AXB as both of them areimplemented in the same treatment planning system Com-parison between AXB with other convolutionsuperpositionmethods such asCCC for various clinical sites is not reportedFrom the single field study performed by Han et al [28] insimple heterogeneous geometry it can be predicted that CCCmay produce a closer dose distribution to AXB than AAAfor clinical multiple setup fields It is because CCC predicts

more accurate doses near heterogeneous interfaces thanAAAfor single fields and like AXB it reports dose to medium asdefault

Most dosimetric studies mentioned above indicated thatAAA slightly overestimated the doses to target volumescompared to AXB If D-LBTE methods are used instead ofmodel-based algorithms for treatment planning it is verylikely that more doses will be given to the target volumesprovided that the prescribed doses by oncologists remainunchanged Whether such conversion will bring actual clin-ical impact to the patients such as improvement in tumorcontrol probability for various clinical sites requires furtherinvestigation

9 Conclusions

On the whole grid-based D-LBTE solvers were evaluatedby extensive investigations to be accurate and valuable dosecalculation methods for photon beam radiotherapy treat-ments involving heterogeneous materials They were provedto produce doses in good agreement with MC methodsand measurements in different clinical sites using techniquesranging from relatively simple to very complex intensitymodulated treatment The use of D-LBTE solvers is highlyrecommended for cases with heterogeneities However usersmust be aware of the dosimetric impact on various treatmentsites due to the conversion from using model-based algo-rithms to D-LBTE solvers

References

[1] M K M Kam R M C Chau J Suen P H K Choi and P ML Teo ldquoIntensity-modulated radiotherapy in nasopharyngealcarcinoma dosimetric advantage over conventional plans andfeasibility of dose escalationrdquo International Journal of RadiationOncology Biology Physics vol 56 no 1 pp 145ndash157 2003

[2] W F A R Verbakel J P Cuijpers D Hoffmans M BiekerB J Slotman and S Senan ldquoVolumetric intensity-modulatedarc therapy vs conventional IMRT in head-and-neck cancera comparative planning and dosimetric studyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 74 no 1 pp252ndash259 2009

[3] E Vanetti A Clivio G Nicolini et al ldquoVolumetric modulatedarc radiotherapy for carcinomas of the oro-pharynx hypo-pharynx and larynx a treatment planning comparison withfixed field IMRTrdquo Radiotherapy and Oncology vol 92 no 1 pp111ndash117 2009

[4] P Doornaert W F A R Verbakel M Bieker B J Slotmanand S Senan ldquoRapidArc planning and delivery in patients withlocally advanced head-and-neck cancer undergoing chemora-diotherapyrdquo International Journal of Radiation Oncology BiologyPhysics vol 79 no 2 pp 429ndash435 2011

[5] R A Popple J B Fiveash I A Brezovich and J A BonnerldquoRapidArc radiation therapy first year experience at the Uni-versity of Alabama at Birminghamrdquo International Journal ofRadiation Oncology Biology Physics vol 77 no 3 pp 932ndash9412010

[6] M J Zelefsky Z Fuks L Happersett et al ldquoClinical experiencewith intensity modulated radiation therapy (IMRT) in prostate


cancerrdquo Radiotherapy and Oncology vol 55 no 3 pp 241ndash2492000

[7] F A Vicini M Sharpe L Kestin et al ldquoOptimizing breast can-cer treatment efficacy with intensity-modulated radiotherapyrdquoInternational Journal of Radiation Oncology Biology Physics vol54 no 5 pp 1336ndash1344 2002

[8] C C Popescu I A Olivotto W A Beckham et al ldquoVolu-metric modulated arc therapy improves dosimetry and reducestreatment time compared to conventional intensity-modulaedradiotherapy for locoregional radiotherapy of left-sided breastcancer and internal mammary nodesrdquo International Journal ofRadiation Oncology Biology Physics vol 76 no 1 pp 287ndash2952010

[9] P Zhang L Happersett M Hunt A Jackson M Zelefsky andG Mageras ldquoVolumetric modulated arc therapy planning andevaluation for prostate cancer casesrdquo International Journal ofRadiationOncology Biology Physics vol 76 no 5 pp 1456ndash14622010

[10] I S Grills D Yan A A Martinez F A Vicini J W Wong andL L Kestin ldquoPotential for reduced toxicity and dose escalationin the treatment of inoperable non-small-cell lung cancer acomparison of intensity-modulated radiation therapy (IMRT)3D conformal radiation and elective nodal irradiationrdquo Inter-national Journal of Radiation Oncology Biology Physics vol 57no 3 pp 875ndash890 2003

[11] S D McGrath M M Matuszak D Yan L L Kestin A AMartinez and I S Grills ldquoVolumetric modulated arc therapyfor delivery of hypofractionated stereotactic lung radiotherapya dosimetric and treatment efficiency analysisrdquo Radiotherapyand Oncology vol 95 no 2 pp 153ndash157 2010

[12] A Ahnesjo M Saxner and A Trepp ldquoA pencil beammodel forphoton dose calculationrdquoMedical Physics vol 19 no 2 pp 263ndash273 1992

[13] A Fogliata E Vanetti D Albers et al ldquoOn the dosimetricbehaviour of photon dose calculation algorithms in the pres-ence of simple geometric heterogeneities comparison withMonte Carlo calculationsrdquo Physics in Medicine and Biology vol52 no 5 pp 1363ndash1385 2007

[14] W Ulmer J Pyyry and W Kaissl ldquoA 3D photon superposi-tionconvolution algorithm and its foundation on results ofMonte Carlo calculationsrdquo Physics in Medicine and Biology vol50 no 8 pp 1767ndash1790 2005

[15] A Gray L D Oliver and P N Johnston ldquoThe accuracy of thepencil beam convolution and anisotropic analytical algorithmsin predicting the dose effects due to attenuation from immobi-lization devices and large air gapsrdquoMedical Physics vol 36 no7 pp 3181ndash3191 2009

[16] L Tillikainen H Helminen T Torsti et al ldquoA 3D pencil-beam-based superposition algorithm for photon dose calculation inheterogeneous mediardquo Physics in Medicine and Biology vol 53no 14 pp 3821ndash3839 2008

[17] C Martens N Reynaert C de Wagter et al ldquoUnderdosageof the upper-airway mucosa for small fields as used inintensity-modulated radiation therapy a comparison betweenradiochromic film measurements Monte Carlo simulationsand collapsed cone convolution calculationsrdquo Medical Physicsvol 29 no 7 pp 1528ndash1535 2002

[18] M W K Kan J Y C Cheung L H T Leung B M FLau and P K N Yu ldquoThe accuracy of dose calculations byanisotropic analytical algorithms for stereotactic radiotherapyin nasopharyngeal carcinomardquo Physics in Medicine and Biologyvol 56 no 2 pp 397ndash413 2011

[19] P Andreo ldquoMonte Carlo techniques in medical radiationphysicsrdquo Physics in Medicine and Biology vol 36 no 7 pp 861ndash920 1991

[20] D W O Rogers B A Faddegon G X Ding C-M Ma JWe and T R Mackie ldquoBEAM a Monte Carlo code to simulateradiotherapy treatment unitsrdquoMedical Physics vol 22 no 5 pp503ndash524 1995

[21] T A Wareing J M McGhee J E Morel and S D Pautz ldquoDis-continuous finite element SN methods on three-dimensionalunstructured gridsrdquo Nuclear Science and Engineering vol 138no 3 pp 256ndash268 2001

[22] K A Gifford J L Horton Jr T A Wareing G Faillaand F Mourtada ldquoComparison of a finite-element multigroupdiscrete-ordinates code with Monte Carlo for radiotherapycalculationsrdquo Physics in Medicine and Biology vol 51 no 9 pp2253ndash2265 2006

[23] K A Gifford M J Price J L Horton Jr T A Wareingand F Mourtada ldquoOptimization of deterministic transportparameters for the calculation of the dose distribution arounda high dose-rate 192Ir brachytherapy sourcerdquo Medical Physicsvol 35 no 6 pp 2279ndash2285 2008

[24] O N Vassiliev T A Wareing I M Davis et al ldquoFea-sibility of a multigroup deterministic solution method forthree-dimensional radiotherapy dose calculationsrdquo Interna-tional Journal of Radiation Oncology Biology Physics vol 72 no1 pp 220ndash227 2008

[25] O N Vassiliev T A Wareing J McGhee G Failla M RSalehpour and F Mourtada ldquoValidation of a new grid-basedBoltzmann equation solver for dose calculation in radiotherapywith photon beamsrdquo Physics inMedicine and Biology vol 55 no3 pp 581ndash598 2010

[26] A Fogliata G Nicolini A Clivio E Vanetti PMancosu and LCozzi ldquoDosimetric validation of the Acuros XB advanced dosecalculation algorithm fundamental characterization in waterrdquoPhysics in Medicine and Biology vol 56 no 6 pp 1879ndash19042011

[27] K Bush I M Gagne S Zavgorodni W Ansbacher and WBeckham ldquoDosimetric validation of Acuros XB with MonteCarlo methods for photon dose calculationsrdquo Medical Physicsvol 38 no 4 pp 2208ndash2221 2011

[28] T Han J K Mikell M Salehpour and F Mourtada ldquoDosimet-ric comparison of Acuros XB deterministic radiation transportmethod withMonte Carlo andmodel-based convolutionmeth-ods in heterogeneous mediardquoMedical Physics vol 38 no 5 pp2651ndash2664 2011

[29] A Fogliata G Nicolini A Clivio E Vanetti and L CozzildquoDosimetric evaluation of Acuros XB Advanced Dose Calcu-lation algorithm in heterogeneous mediardquo Radiation Oncologyvol 6 no 1 article 82 2011

[30] W K Kan L Leung and P Yu ldquoVerification and dosimet-ric impact of Acuros XB algorithm on intensity modulatedstereotactic radiotherapy for locally persistent nasopharyngealcarcinomardquoMedical Physics vol 39 no 8 pp 4705ndash4714 2012

[31] S A M Lloyd and W Ansbacher ldquoEvaluation of an analyticlinear Boltzmann transport equation solver for high densityinhomogeneitiesrdquo Medical Physics vol 40 no 1 Article ID011707 2013

[32] L Hoffmann M-B K Joslashrgensen L P Muren and J B BPetersen ldquoClinical validation of the Acuros XB photon dosecalculation algorithm a grid-based Boltzmann equation solverrdquoActa Oncologica vol 51 no 3 pp 376ndash385 2012


[33] T Han F Mourtada K Kisling et al ldquoExperimental validationof deterministic Acuros XB algorithm for IMRT and VMATdose calculations with the Radiological Physics Centerrsquos headand neck phantomrdquo Medical Physics vol 39 no 4 pp 2193ndash2202 2012

[34] W K Kan L Leung W K So et al ldquoExperimental verificationof the Acuros XB and AAA dose calculation adjacent toheterogeneousmedia for IMRT and RapidArc of nasopharygealcarcinomardquo Medical Physics vol 40 no 3 Article ID 0317142013

[35] T Han D Followill J Mikell et al ldquoDosimetric impact ofAcuros XB deterministic radiation transport algorithm forheterogeneous dose calculation in lung cancerrdquoMedical Physicsvol 40 no 5 Article ID 051710 2013

[36] A Fogliata G Nicolini A Clivio E Vanetti and L CozzildquoCritical appraisal of Acuros XB and anisotropic analyticalgorithm dose calculation in advanced non-small-cell lungcancer treatmentsrdquo International Journal of Radiation OncologyBiology Physics vol 83 no 5 pp 1587ndash1595 2012

[37] A Fogliata G Nicolini A Clivio E Vanetti and L Cozzi ldquoOnthe dosimetric impact of inhomogeneity management in theAcuros XB algorithm for breast treatmentrdquoRadiation Oncologyvol 6 no 1 article 103 2011

[38] M K L Leung and P Yu ldquoDosimetric impact of using AcurosXB algorithm for intensity modulated radiation therapy andRapidArc planning in nasopharyngeal carcinomasrdquo Interna-tional Journal of Radiation Oncology ldquoBiologyrdquo Physics vol 85no 1 pp 73ndash80 2013

[39] I J Chetty B Curran J E Cygler et al ldquoReport of theAAPM Task Group No 105 issues associated with clinicalimplementation of Monte Carlo-based photon and electronexternal beam treatment planningrdquoMedical Physics vol 34 no12 pp 4818ndash4853 2007

[40] J V Siebers P J Keall A ENahum andRMohan ldquoConvertingabsorbed dose to medium to absorbed dose to water forMonte Carlo based photon beam dose calculationsrdquo Physics inMedicine and Biology vol 45 no 4 pp 983ndash995 2000

[41] N Dogan J V Siebers and P J Keall ldquoClinical comparison ofhead and neck and prostate IMRT plans using absorbed dose tomedium and absorbed dose to waterrdquo Physics in Medicine andBiology vol 51 no 19 pp 4967ndash4980 2006

[42] C-M Ma and J Li ldquoDose specification for radiation therapydose to water or dose to mediumrdquo Physics in Medicine andBiology vol 56 no 10 pp 3073ndash3089 2011

[43] I Kawrakow M Fippel and K Friedrich ldquo3D electron dosecalculation using aVoxel basedMonteCarlo algorithm (VMC)rdquoMedical Physics vol 23 no 4 pp 445ndash457 1996

[44] I KawrakowandM Fippel ldquoInvestigation of variance reductiontechniques for Monte Carlo photon dose calculation usingXVMCrdquoPhysics inMedicine and Biology vol 45 no 8 pp 2163ndash2183 2000

[45] H Neuenschwander and E J Born ldquoA macro Monte Carlomethod for electron beam dose calculationsrdquo Physics inMedicine and Biology vol 37 no 1 pp 107ndash125 1992

[46] H Neuenschwander T R Mackie and P J ReckwerdtldquoMMCmdasha high-performance Monte Carlo code for electronbeam treatment planningrdquo Physics in Medicine and Biology vol40 no 4 pp 543ndash574 1995

[47] J Sempau S J Wilderman and A F Bielajew ldquoDPM a fastaccurate Monte Carlo code optimized for photon and electronradiotherapy treatment planning dose calculationsrdquo Physics inMedicine and Biology vol 45 no 8 pp 2263ndash2291 2000

[48] C Ma J S Li T Pawlicki et al ldquoMCDOSEmdasha Monte Carlodose calculation tool for radiation therapy treatment planningrdquoPhysics in Medicine and Biology vol 47 no 10 pp 1671ndash16892002

[49] J Gardner J Siebers and I Kawrakow ldquoDose calculationvalidation of VMC++ for photon beamsrdquo Medical Physics vol34 no 5 pp 1809ndash1818 2007

[50] K Jabbari ldquoReview of fast Monte Carlo codes for dose cal-culation in radiation therapy treatment planningrdquo Journal ofMedical Signals amp Sensors vol 1 no 1 pp 73ndash86 2011

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


doses in voxels of the irradiated volume To account for thepresence of inhomogeneities simple density scaling of thekernels is applied so that the secondary electron transportis only modeled macroscopically Both AAA and CCC wereproved to produce inaccurate dose distribution inmedia withcomplex heterogeneities in certain circumstances [14ndash18]

The Monte Carlo (MC) methods have been consid-ered the most accurate methods for radiotherapy treatmentplanning dose calculation They are statistical simulationmethods based on random samplingThey solve the radiationtransport problem stochastically by simulating the tracks of asufficiently large number of individual particles using the ran-dom number generated probability distribution governingthe individual physical processes They are therefore capableof accurately computing the radiation dose in media underalmost all circumstances [19 20] However the computationtime required may still limit the use of MC methods forcomplex intensity modulated techniques in the clinical envi-ronment

The desire to develop a fast alternative dose calculationmethod with comparable accuracy to MC methods hasled to the exploration of deterministic solutions to thecoupled system of linear Boltzmann transport equations(LBTE) [21ndash26] It was first demonstrated using the prototypesoftware Attila which was a general purpose grid-basedBoltzmann solver code It was followed by Acuros developedby Transpire Inc (Gig HarborWA USA) specially designedfor radiotherapy dose calculations Recently a version ofdeterministic LBTE solver namely Acuros XB (AXB) hasbeen developed and implemented in the Eclipse treatmentplanning system (Varian Medical Systems Palo Alto CAUSA) The LBTE is the governing equation that describesthe macroscopic behavior of ionizing particles as they travelthrough and interact with matter The electron angular flu-ence is first obtained by solving the LBTE and then the dosecan be generated by using the macroscopic electron energydeposition cross-sections and the density of the materialsWith sufficient refinement without using any approximationthat is if an MC algorithm simulates an infinite numberof particles and a deterministic LBTE (D-LBTE) solverdiscretizes the variables such as space and energy intoinfinitely small grids both approaches will converge on thesame solutionThe achievable accuracy of both approaches isequivalent and is limited only by uncertainties in the particleinteraction data and uncertainties related to the transportedradiation fields Extensive efforts have been made by severalinvestigators to validate the accuracy of D-LBTE solvers indifferent circumstances by comparison against MC and byexperimental verification against measurements Performedvalidations ranged from using a simple geometric phantomwith simple fields to a complex humanoid phantom withmultiple intensity modulated fields Most studies reportedthat D-LBTE solvers were capable of producing comparableaccuracy as MC methods and either equivalent or betteraccuracy than superpositionconvolution algorithms [22ndash35] Dosimetric impact on different media of various clinicalsites due to the conversion of the currently used model-based algorithms to the newly implemented D-LBTE solverswas also investigated by several authors [32 36ndash38] This

paper summarizes and discusses the findings of the mostrecent dosimetric evaluation for D-LBTE solvers in varioustreatment sites

2 The Deterministic LBTE Solvers

More detailed description of the D-LBTE solvers can befound in the literature [21ndash26] Only a summary is reportedhere

The time-independent three-dimensional (3D) systemof the coupled LBTE is solved to determine the energydeposition of photon and electron transport

Ω sdot

997888

nablaΦ

120574+ 120590

120574Φ

120574= 119902

120574120574+ 119902

120574

(1)

Ω sdot

997888

nablaΦ

119890+ 120590

119890Φ

119890minus

120597

120597119864

(119878119877Φ119890) = 119902

119890119890+ 119902

120574119890+ 119902

119890

997888

119903 isin 119881

Ω isin 4120587 119864 gt 0

(2)

whereΦ120574 andΦ119890 are the photon and electron angular fluencerespectively 120590120574 and 120590119890 are the macroscopic photon andelectron total interaction cross-sections for all materials involume 119881 and energies respectively 119902120574120574 119902120574119890 and 119902119890119890 rep-resent the photon scattering source generated from photoninteraction electron scattering source generated fromphotoninteraction and electron scattering source generated fromelectron interactions everywhere in 119881 for all angles andenergies respectively 119902120574 and 119902119890 represent the external photonand electron source from the treatment head respectively997888

119903 is the spatial position vector 119864 is the energy Ω is theunit vector denoting particle direction and 997888nabla is referredto as the ldquostreaming operatorrdquo which may be interpreted asthe number of particles flowing into a volume 119889119881 minusthe number of particles flowing out of 119889119881 for particlestravelling in a direction 119889Ω about Ω with energy 119864 about119889119864 The second terms on the left-hand side of (1) and (2)are the ldquocollision operatorsrdquo which may be thought of as thenumber of particles removed from the volume by absorptionor scattering Equation (2) is the Boltzmann Fokker-Planktransport equation which is solved for the electron transportThe third term on the left-hand side of (2) representsthe continuous slowing down operator where 119878119877 is therestricted plus collisional radiative stopping power Equations(1) and (2) are usually solved through discretization in spaceangle and energy Energy discretization is achieved withthe standard multigroup method Space discretization canbe achieved with a variably sized Cartesian adaptive meshrefinement technique (used by AXB) or by using a high-orderGalerkin-based linear discontinuous finite-element methodto solve the multigroup discrete ordinates equations onfully unstructured tetrahedral elements (used by Attila) Forthe former technique the mesh is limited to refinementin factors of 2 or smaller in any direction This allowsfor the use of finer resolution in higher dose and highdose gradient regions Angle discretization for fluences andscattering sources is achieved with the standard ordinatesmethod where the quadrature order is adaptive by the energygroupThe photon angular fluence of (1) is the summation of



119863119894 = int

1

0

119889119864int

4120587

119889

Ω(120590

119890

ED (997888

119903 119864))

120588 (

997888

119903 )

Φ

119890(

997888

119903 119864

Ω) (3)


















[30]




50 times 50 cm2

100 times 100 cm2

40 times 40 cm2

100 times 100 cm2

150 times 100 cm2

25 times 25 cm2

50 times 50 cm2

100 times 100 cm2

20 times 20 cm2

30 times 30 cm2


Phantom(s)geometry





300 times 300 times


200 times 200 times





voxels




025 cm3 voxels






voxels































119863119908 = 119863119898(

119878

120588

)

119908

119898

(4)

where (119878120588)119908119898





2012 [32]






Tissue air andbone


bone






RPC thoraxphantom

CIRSThoraxphantom



119898and

119863

119908


119898and

119863

119908


119898only


119898and

119863

119908


119898only

Observed results


119898and

119863

119908


119898and 99 for

119863

119908



119898and 98 for

119863

119908









0

20

40

60

80

100

120

0 20 40 60 80Dose (Gy)

Rela

tive v

olum

e (

)

Mandible Dm

Mandible Dw

Parotid Dm

Parotid Dw

Spinal cord Dm

Spinal cord Dw

PTV in tissue Dm

PTV in tissue Dw

PTV in bone Dm

PTV in bone Dw


119898and 119863









8 Discussions








9 Conclusions


References



























































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















119863119894 = int

1

0

119889119864int

4120587

119889

Ω(120590

119890

ED (997888

119903 119864))

120588 (

997888

119903 )

Φ

119890(

997888

119903 119864

Ω) (3)


















[30]




50 times 50 cm2

100 times 100 cm2

40 times 40 cm2

100 times 100 cm2

150 times 100 cm2

25 times 25 cm2

50 times 50 cm2

100 times 100 cm2

20 times 20 cm2

30 times 30 cm2


Phantom(s)geometry





300 times 300 times


200 times 200 times





voxels




025 cm3 voxels






voxels































119863119908 = 119863119898(

119878

120588

)

119908

119898

(4)

where (119878120588)119908119898





2012 [32]






Tissue air andbone


bone






RPC thoraxphantom

CIRSThoraxphantom



119898and

119863

119908


119898and

119863

119908


119898only


119898and

119863

119908


119898only

Observed results


119898and

119863

119908


119898and 99 for

119863

119908



119898and 98 for

119863

119908









0

20

40

60

80

100

120

0 20 40 60 80Dose (Gy)

Rela

tive v

olum

e (

)

Mandible Dm

Mandible Dw

Parotid Dm

Parotid Dw

Spinal cord Dm

Spinal cord Dw

PTV in tissue Dm

PTV in tissue Dw

PTV in bone Dm

PTV in bone Dw


119898and 119863









8 Discussions








9 Conclusions


References



























































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















[30]




50 times 50 cm2

100 times 100 cm2

40 times 40 cm2

100 times 100 cm2

150 times 100 cm2

25 times 25 cm2

50 times 50 cm2

100 times 100 cm2

20 times 20 cm2

30 times 30 cm2


Phantom(s)geometry





300 times 300 times


200 times 200 times





voxels




025 cm3 voxels






voxels































119863119908 = 119863119898(

119878

120588

)

119908

119898

(4)

where (119878120588)119908119898





2012 [32]






Tissue air andbone


bone






RPC thoraxphantom

CIRSThoraxphantom



119898and

119863

119908


119898and

119863

119908


119898only


119898and

119863

119908


119898only

Observed results


119898and

119863

119908


119898and 99 for

119863

119908



119898and 98 for

119863

119908









0

20

40

60

80

100

120

0 20 40 60 80Dose (Gy)

Rela

tive v

olum

e (

)

Mandible Dm

Mandible Dw

Parotid Dm

Parotid Dw

Spinal cord Dm

Spinal cord Dw

PTV in tissue Dm

PTV in tissue Dw

PTV in bone Dm

PTV in bone Dw


119898and 119863









8 Discussions








9 Conclusions


References



























































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




























119863119908 = 119863119898(

119878

120588

)

119908

119898

(4)

where (119878120588)119908119898





2012 [32]






Tissue air andbone


bone






RPC thoraxphantom

CIRSThoraxphantom



119898and

119863

119908


119898and

119863

119908


119898only


119898and

119863

119908


119898only

Observed results


119898and

119863

119908


119898and 99 for

119863

119908



119898and 98 for

119863

119908









0

20

40

60

80

100

120

0 20 40 60 80Dose (Gy)

Rela

tive v

olum

e (

)

Mandible Dm

Mandible Dw

Parotid Dm

Parotid Dw

Spinal cord Dm

Spinal cord Dw

PTV in tissue Dm

PTV in tissue Dw

PTV in bone Dm

PTV in bone Dw


119898and 119863









8 Discussions








9 Conclusions


References



























































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















2012 [32]






Tissue air andbone


bone






RPC thoraxphantom

CIRSThoraxphantom



119898and

119863

119908


119898and

119863

119908


119898only


119898and

119863

119908


119898only

Observed results


119898and

119863

119908


119898and 99 for

119863

119908



119898and 98 for

119863

119908









0

20

40

60

80

100

120

0 20 40 60 80Dose (Gy)

Rela

tive v

olum

e (

)

Mandible Dm

Mandible Dw

Parotid Dm

Parotid Dw

Spinal cord Dm

Spinal cord Dw

PTV in tissue Dm

PTV in tissue Dw

PTV in bone Dm

PTV in bone Dw


119898and 119863









8 Discussions








9 Conclusions


References



























































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















0

20

40

60

80

100

120

0 20 40 60 80Dose (Gy)

Rela

tive v

olum

e (

)

Mandible Dm

Mandible Dw

Parotid Dm

Parotid Dw

Spinal cord Dm

Spinal cord Dw

PTV in tissue Dm

PTV in tissue Dw

PTV in bone Dm

PTV in bone Dw


119898and 119863









8 Discussions








9 Conclusions


References



























































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















9 Conclusions


References



























































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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