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Specific Absorbed Fraction of Spherical Tumors Varying Tissue Composition, Radius, and Electron Energy

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Title:
Specific Absorbed Fraction of Spherical Tumors Varying Tissue Composition, Radius, and Electron Energy
Creator:
Mitchell, Timothy
Publication Date:
Language:
English

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Subjects / Keywords:
Bones ( jstor )
Composite particles ( jstor )
Dosage ( jstor )
Electron energy ( jstor )
Electrons ( jstor )
Particle density ( jstor )
Photons ( jstor )
Radius of a sphere ( jstor )
Soft tissue neoplasms ( jstor )
Tumors ( jstor )
Monte Carlo method
Tumors
Genre:
Undergraduate Honors Thesis

Notes

Abstract:
Monte Carlo N-Particle was used to determine the specific absorbed fraction for spherical tumors in 100% soft tissue, 75% soft tissue-25% bone, 50% soft tissue-50% bone, 25% soft tissue-75% bone, and 100% bone elemental compositions listed in the Oak Ridge National Laboratory's technical report ORNL TM-8381. In addition, the specific absorbed fractions for soft tissue from ORNL TM-8381 were compared with the soft tissue from ICRU Report No. 44. The spherical tumor had radii of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, and 2.5 cm and each tumor was surrounded by 3 m of soft tissue to account for electron backscatter and additional dose due to Bremstrahlung photon emissions. A monoenergetic electron source at 21 different energies, ranging between 10 keV and 4 MeV, had an insignificantly smaller radius than the radius of the tumor and was placed in the center of the tumor. For each Monte Carlo N-Particle input file, energy deposition tallies were placed in the tumor to count the total number of electrons and secondary photons deposited in the tumor. Lastly, 10 million particles were simulated to achieve relative errors below 3%. Correlations were found between absorbed fraction and tumor composition, tumor size, and electron energy. The comparison of soft tissues from ORNL's TM-8381 and ICRU 44 yielded very similar results. ( en )
General Note:
Awarded Bachelor of Science in Nuclear Engineering; Graduated August 14, 2012 magna cum laude. Major: Nuclear Engineering
General Note:
Advisor(s): Wesley Bolch
General Note:
College/School: College of Engineering

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University of Florida
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Copyright Timothy Mitchell. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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SpecificAbsorbedFractionofSphericalTumorsVarying TissueComposition,Radius,andElectronEnergy TimothyMitchell 4000SW37thBoulevard Gainesville,Florida32608 271-1898 hizskedo@u.edu

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Abstract MonteCarloN-Particlewasusedtodeterminethespecicabsorbedfractionfor sphericaltumorsin100%softtissue,75%softtissue-25%bone,50%softtissue-50%bone, 25%softtissue-75%bone,and100%boneelementalcompositionslistedintheOakRidge NationalLaboratory'stechnicalreportORNLTM-8381.Inaddition,thespecicabsorbed fractionsforsofttissuefromORNLTM-8381werecomparedwiththesofttissuefromICRU ReportNo.44.Thesphericaltumorhadradiiof0.5cm,1.0cm,1.5cm,2.0cm,and2.5cm andeachtumorwassurroundedby3mofsofttissuetoaccountforelectronbackscatterand additionaldoseduetoBremstrahlungphotonemissions.Amonoenergeticelectronsource at21dierentenergies,rangingbetween10keVand4MeV,hadaninsignicantlysmaller radiusthantheradiusofthetumorandwasplacedinthecenterofthetumor.Foreach MonteCarloN-Particleinputle,energydepositiontallieswereplacedinthetumorto countthetotalnumberofelectronsandsecondaryphotonsdepositedinthetumor.Lastly, 10millionparticlesweresimulatedtoachieverelativeerrorsbelow3%.Correlationswere foundbetweenabsorbedfractionandtumorcomposition,tumorsize,andelectronenergy. ThecomparisonofsofttissuesfromORNL'sTM-8381andICRU44yieldedverysimilar results.

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Introduction Thespecicabsorbedfractionisdenedasthefractionofenergyreleasedfromthesource thatisabsorbedinthetarget,dividedbythetargetmassShultisandFaw.2000.Itis importantinnuclearmedicineandiscommonlycomputedusingMonteCarlotechniques. Spheresofdierentradiiwereusedtoestimatethefractionofelectronenergythatwouldbe absorbedintoatumorfoundinthebody. AccordingtoICRP30,itisrecommendedthatwhencalculatingabsorbedfractionsAF foralphaandbetaparticles,theAFiszeroforcaseswherethesourceandtargetorgans aredierent.Forselfdosecalculationswherethetargetandsourceorgansarethesame, theAFistakentobeunityformostcases.Thisapproximationmayhavebeenadequate forcasesinthepastbutnewadvancesinnuclearmedicinerequiremoreaccuratevaluesfor absorbedfractions.Thisismostevidentinnewtherapiesthatinvolvetaggingmonoclonal antibodiesMabswithradionuclides.TheseMabstransporthighelectronenergyemitters tosmalltumors,wheremostofthedoseisdepositedlocally.Furthermore,therearecases whereatumormaymetastasizeandrequirethetreatmentforcancerousskeletaltissuewith theuseofnuclearmedicine.Thecurrenttabulatedabsorbedfractionsforbetaparticlesare strictlyformadeforhomogeneoustumors.Sincenuclearmedicineisnotabletotreatsmall tumorswithdierentcompositions,especiallywheretheelectronrangeislargeenoughthat considerationofelectronenergylossisimportant,dosecalculationstakingintoaccountofa heterogeneousmediuminvolvingbothboneandtissuecompositionsareneeded. MaterialsandMethod MonteCarloN-ParticleMCNPisaparticletransportcodethatwasusedtodetermine thespecicabsorbedfractionsforsphericaltumorsin100%softtissue,75%softtissue-25% bone,50%softtissue-50%boneelementalcompositionslistedintheOakRidgeNational Laboratory'stechnicalreportORNLTM-8381.Inaddition,thespecicabsorbedfractions 1

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forsofttissuefromORNLTM-8381werecomparedwiththesofttissuefromICRUReport No.44.Thesphericaltumorhadradiiof0.5cm,1.0cm,1.5cm,2.0cm,and2.5cmand eachtumorwassurroundedby3mofsofttissuetoaccountforelectronbackscatterand additionaldoseduetoBremstrahlungphotonemissions.Amonoenergeticelectronsourceat 21dierentenergies,rangingbetween10keVand4MeV,hadaradiusof10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(13 cmlessthan theradiusofthetumorandwasplacedinthecenterofthetumor;the10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(13 cmdierence wastopreventerrorsassociatedwithMCNPwhileachievingtheaccuracyneededforthe dataanalysis.ForeachMCNPinputle,anenergydepositiontallyF6wasplacedinthe tumortocountthetotalnumberofelectronsandsecondaryphotonsdepositedinthetumor. Lastly,10millionparticlesweresimulatedtoachieveerrorsunder3%.Figure1showsthe imagegeneratedbyMCNP. Figure1:Thesphericaltumorredsurroundedbysofttissueblue Thespecicabsorbedfractionwascomputedwiththefollowingequation SAF = E e + E p E o whereE e istheenergycontributionfromtheelectrons,E p istheenergycontributionfrom thesecondaryphotons,andE o istheenergyofthesource. 2

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Results ThespecicabsorbedfractionsforthevesphericaltumorsareshowninFigures2to6. Table1showsthepercentdierenceforthesofttissuesfromORNL'sTM-8381andICRU 44. Figure2:ElectronAFforsofttissuesphericaltumors 3

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Figure3:ElectronAFfor75%softtissue-25%bonesphericaltumors Figure4:ElectronAFfor50%softtissue-50%bonesphericaltumors 4

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Figure5:ElectronAFfor25%softtissue-75%bonesphericaltumors Figure6:ElectronAFforbonetissuesphericaltumors 5

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Table1:PercentdierencebetweenORNL'sTM-8381andICRU44softtissue Energy[MeV]PercentDierence[%] 0.0100.003 0.0150.002 0.0200.000 0.030-0.002 0.040-0.003 0.050-0.003 0.060-0.004 0.080-0.005 0.100-0.006 0.150-0.010 0.200-0.015 0.300-0.025 0.400-0.034 0.500-0.047 0.600-0.060 0.800-0.088 1.000-0.116 1.500-0.196 2.000-0.273 3.000-0.445 4.000-0.626 Discussion CorrelationsintheData Therstcorrelationoccursbetweentheabsorbedfractionandtheradiusofthespherical tumor.Astheradiusofthesphericaltumorincreases,theabsorbedfractionincreases.The increaseintumorsizemeansthattheelectronhastotravelagreaterpathlengthinorder toescape.Sincetheelectronwillhavelowerprobabilitytoescape,itwillmostlikelybe absorbedinthesphericaltumor. Acorrelationbetweenthetissuescanbeobservedbyanalyzingtheabsorbedfraction ofeachtissueforallradii.Asthebonecompositioninthetissueincreases,theabsorbed fractionincreases.Thisisbestexplainedwiththecontinuousslowing-downapproximation CSDATheCSDAestimatestheaveragepathlengthachargedparticlewilltravelthrougha 6

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medium.Thefollowingapproximationisforparticleswiththesameinitialspeedindierent media, m=z 2 Z=A where isthedensityofmedium,istheCSDArange,mistheparticlemass,zisthe particlechargenumber,Zistheatomicnumberofthestoppingmedium,andAisitsatomic weightShultisandFaw.2000.Thevalueof m=z 2 Z=A willnotsignicantlychange, leaving tobetheonlyvariable.Whenthefractionofboneincreasesinthesphericaltumor, thedensityofthesphericaltumoralsoincreases.Sincethedensityofthesphericaltumor andtheabsorbedfractionareinverselyproportional,anincreaseindensitywillresultina decreaseintheparticle'spathlength.Thedecreasedpathlengthrepresentsthattheparticle willhavealowerprobabilitytoescapethesphericaltumor. Thenalcorrelationthatcanbeobservedisbetweentheelectronenergyandabsorbed fraction.Astheenergyoftheelectronincreases,theabsorbedfractiondecreases.Sincea higherenergyelectronhasagreaterpathlengththanalowerenergyelectron,itwillhavea higherprobabilityofescapingthesphericaltumor. ItisshownfromTable1thatthespecicabsorbedfractiondoesnotchangemuchbetween thesofttissuesfromORNL'sTM-8381andICRU44.Thisisexpectedsincethecomposition ofsofttissuewillnotdrasticallychangeovertime.Itshouldalsobenotedthattheerror associatedateachenergytendtoincreasewithenergy.Thisisduetotheelectronswith higherenergyhavingagreaterprobabilitytoescapethesphericaltumor,leadingtoless particlesbeingtalliedinMCNP. AccuracyversusTime Greateraccuracycouldhavebeenobtainedifthetotalnumberofelectronsemittedfrom thesourcewereincreased.Themainreasonforwhygreateraccuracywasnotpursuedwas 7

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becausethecomputerruntimewouldhavebeensignicantlylonger.Ittookroughly37,800 secondstoruneachMCNPsimulationusing10 7 electrons;byincreasingthenumberofelectronsemittedfromthesourceto10 9 ,theamountoftimethatMCNPwillrunwouldincrease toabout3,780,000secondsor1,050hours.Time-eciencyanalysismustbeconsidered.In thetimerequiredtorunonesimulationusing10 9 electrons,onecanrunmultiplesimulationsoftheothermaterialcompositionsatthespeciedenergiesusing10 7 electrons.By obtainingmanyreasonablyaccurateresultsinsametimethatitwouldtakereceiveonevery accurateresult,onewouldbeabletoanalyzemoredataandmakebetterconjecturesthan anindividualwhocanonlyanalyzeonedatum.Analternativethoughtcouldcomefrom consideringerrors.Errorswithinthecodecaneasilybedetectedbyobtainingtheoutput letoseeifthevaluesarereasonableornot.Theindividualusing10 9 electronswouldhave towaitalittleunder44daysbeforelookingattheiroutput.Usingthepointslistedinthis minoranalysis,itwasconcludedthatachievingmorerunsismoreimportantthanobtaining agreateraccuracy. Conclusion Using10millionparticles,theerrorsassociatedwiththedatawerelessthan3%.The correlationsfromthisdatasetshouldalsobetrueforallothersofttissue-bonecompositions. Anempiricalformulacouldpossiblybemadewiththecurrentdatatorelatethespecic absorbedfractionwiththesizeofthetumor,softtissue-bonecomposition,andelectron energy. 8

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References ShultisKJ,FawRE.RadiationShielding.In:AnonymousRadiationShielding.Illinois: AmericanNuclearSociety;2000:213-223. 9



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SpecificAbsorbedFractionofSphericalTumorsVarying TissueComposition,Radius,andElectronEnergy TimothyMitchell Gainesville,Florida32608 (727)271-1898 hizskedo@ur.edu

PAGE 2

Abstract MonteCarloN-Particlewasusedtodeterminethespecifcabsorbedfractionfor sphericaltumorsin100%softtissue,75%softtissue-25%bone,50%softtissue-50%bone, 25%softtissue-75%bone,and100%boneelementalcompositionslistedintheOakRidge NationalLaboratory'stechnicalreportORNLTM-8381.Inaddition,thespecifcabsorbed fractionsforsofttissuefromORNLTM-8381werecomparedwiththesofttissuefromICRU ReportNo.44.Thesphericaltumorhadradiiof0.5cm,1.0cm,1.5cm,2.0cm,and2.5cm andeachtumorwassurroundedby3mofsofttissuetoaccountforelectronbackscatterand additionaldoseduetoBremstrahlungphotonemissions.Amonoenergeticelectronsource at21dierentenergies,rangingbetween10keVand4MeV,hadaninsignifcantlysmaller radiusthantheradiusofthetumorandwasplacedinthecenterofthetumor.Foreach MonteCarloN-Particleinputfle,energydepositiontallieswereplacedinthetumorto countthetotalnumberofelectronsandsecondaryphotonsdepositedinthetumor.Lastly, 10millionparticlesweresimulatedtoachieverelativeerrorsbelow3%.Correlationswere foundbetweenabsorbedfractionandtumorcomposition,tumorsize,andelectronenergy. ThecomparisonofsofttissuesfromORNL'sTM-8381andICRU44yieldedverysimilar results.

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Introduction Thespecifcabsorbedfractionisdefnedasthefractionofenergyreleasedfromthesource thatisabsorbedinthetarget,dividedbythetargetmass(ShultisandFaw.2000).Itis importantinnuclearmedicineandiscommonlycomputedusingMonteCarlotechniques. Spheresofdierentradiiwereusedtoestimatethefractionofelectronenergythatwouldbe absorbedintoatumorfoundinthebody. AccordingtoICRP30,itisrecommendedthatwhencalculatingabsorbedfractions(AF) foralphaandbetaparticles,theAFiszeroforcaseswherethesourceandtargetorgans aredierent.Forselfdosecalculations(wherethetargetandsourceorgansarethesame), theAFistakentobeunityformostcases.Thisapproximationmayhavebeenadequate forcasesinthepastbutnewadvancesinnuclearmedicinerequiremoreaccuratevaluesfor absorbedfractions.Thisismostevidentinnewtherapiesthatinvolvetaggingmonoclonal antibodies(Mabs)withradionuclides.TheseMabstransporthighelectronenergyemitters tosmalltumors,wheremostofthedoseisdepositedlocally.Furthermore,therearecases whereatumormaymetastasizeandrequirethetreatmentforcancerousskeletaltissuewith theuseofnuclearmedicine.Thecurrenttabulatedabsorbedfractionsforbetaparticlesare strictlyformadeforhomogeneoustumors.Sincenuclearmedicineisnotabletotreatsmall tumorswithdierentcompositions,especiallywheretheelectronrangeislargeenoughthat considerationofelectronenergylossisimportant,dosecalculationstakingintoaccountofa heterogeneousmediuminvolvingbothboneandtissuecompositionsareneeded. MaterialsandMethod MonteCarloN-Particle(MCNP)isaparticletransportcodethatwasusedtodetermine thespecifcabsorbedfractionsforsphericaltumorsin100%softtissue,75%softtissue-25% bone,50%softtissue-50%boneelementalcompositionslistedintheOakRidgeNational Laboratory'stechnicalreportORNLTM-8381.Inaddition,thespecifcabsorbedfractions 1

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forsofttissuefromORNLTM-8381werecomparedwiththesofttissuefromICRUReport No.44.Thesphericaltumorhadradiiof0.5cm,1.0cm,1.5cm,2.0cm,and2.5cmand eachtumorwassurroundedby3mofsofttissuetoaccountforelectronbackscatterand additionaldoseduetoBremstrahlungphotonemissions.Amonoenergeticelectronsourceat 21dierentenergies,rangingbetween10keVand4MeV,hadaradiusof10 )Tj/T1_2 7.97 Tf(13 cmlessthan theradiusofthetumorandwasplacedinthecenterofthetumor;the10 )Tj/T1_2 7.97 Tf(13 cmdierence wastopreventerrorsassociatedwithMCNPwhileachievingtheaccuracyneededforthe dataanalysis.ForeachMCNPinputfle,anenergydepositiontally(F6)wasplacedinthe tumortocountthetotalnumberofelectronsandsecondaryphotonsdepositedinthetumor. Lastly,10millionparticlesweresimulatedtoachieveerrorsunder3%.Figure1showsthe imagegeneratedbyMCNP. Figure1:Thesphericaltumor(red)surroundedbysofttissue(blue) Thespecifcabsorbedfractionwascomputedwiththefollowingequation SAF = E e + E p E o (1) whereE e istheenergycontributionfromtheelectrons,E p istheenergycontributionfrom thesecondaryphotons,andE o istheenergyofthesource. 2

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Results ThespecifcabsorbedfractionsforthefvesphericaltumorsareshowninFigures2to6. Table1showsthepercentdierenceforthesofttissuesfromORNL'sTM-8381andICRU 44. Figure2:ElectronAFforsofttissuesphericaltumors 3

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Figure3:ElectronAFfor75%softtissue-25%bonesphericaltumors Figure4:ElectronAFfor50%softtissue-50%bonesphericaltumors 4

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Figure5:ElectronAFfor25%softtissue-75%bonesphericaltumors Figure6:ElectronAFforbonetissuesphericaltumors 5

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Table1:PercentdierencebetweenORNL'sTM-8381andICRU44softtissue Energy[MeV]PercentDierence[%] 0.0100.003 0.0150.002 0.0200.000 0.030-0.002 0.040-0.003 0.050-0.003 0.060-0.004 0.080-0.005 0.100-0.006 0.150-0.010 0.200-0.015 0.300-0.025 0.400-0.034 0.500-0.047 0.600-0.060 0.800-0.088 1.000-0.116 1.500-0.196 2.000-0.273 3.000-0.445 4.000-0.626 Discussion CorrelationsintheData Thefrstcorrelationoccursbetweentheabsorbedfractionandtheradiusofthespherical tumor.Astheradiusofthesphericaltumorincreases,theabsorbedfractionincreases.The increaseintumorsizemeansthattheelectronhastotravelagreaterpathlengthinorder toescape.Sincetheelectronwillhavelowerprobabilitytoescape,itwillmostlikelybe absorbedinthesphericaltumor. Acorrelationbetweenthetissuescanbeobservedbyanalyzingtheabsorbedfraction ofeachtissueforallradii.Asthebonecompositioninthetissueincreases,theabsorbed fractionincreases.Thisisbestexplainedwiththecontinuousslowing-downapproximation (CSDA)TheCSDAestimatestheaveragepathlengthachargedparticlewilltravelthrougha 6

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medium.Thefollowingapproximationisforparticleswiththesameinitialspeedindierent media, (m=z 2 )(Z=A) (2) where isthedensityofmedium,istheCSDArange,mistheparticlemass,zisthe particlechargenumber,Zistheatomicnumberofthestoppingmedium,andAisitsatomic weight(ShultisandFaw.2000).Thevalueof( m=z 2 )(Z=A)willnotsignifcantlychange, leaving tobetheonlyvariable.Whenthefractionofboneincreasesinthesphericaltumor, thedensityofthesphericaltumoralsoincreases.Sincethedensityofthesphericaltumor andtheabsorbedfractionareinverselyproportional,anincreaseindensitywillresultina decreaseintheparticle'spathlength.Thedecreasedpathlengthrepresentsthattheparticle willhavealowerprobabilitytoescapethesphericaltumor. Thefnalcorrelationthatcanbeobservedisbetweentheelectronenergyandabsorbed fraction.Astheenergyoftheelectronincreases,theabsorbedfractiondecreases.Sincea higherenergyelectronhasagreaterpathlengththanalowerenergyelectron,itwillhavea higherprobabilityofescapingthesphericaltumor. ItisshownfromTable1thatthespecifcabsorbedfractiondoesnotchangemuchbetween thesofttissuesfromORNL'sTM-8381andICRU44.Thisisexpectedsincethecomposition ofsofttissuewillnotdrasticallychangeovertime.Itshouldalsobenotedthattheerror associatedateachenergytendtoincreasewithenergy.Thisisduetotheelectronswith higherenergyhavingagreaterprobabilitytoescapethesphericaltumor,leadingtoless particlesbeingtalliedinMCNP. AccuracyversusTime Greateraccuracycouldhavebeenobtainedifthetotalnumberofelectronsemittedfrom thesourcewereincreased.Themainreasonforwhygreateraccuracywasnotpursuedwas 7

PAGE 10

becausethecomputerruntimewouldhavebeensignifcantlylonger.Ittookroughly37,800 secondstoruneachMCNPsimulationusing10 7 electrons;byincreasingthenumberofelectronsemittedfromthesourceto10 9 ,theamountoftimethatMCNPwillrunwouldincrease toabout3,780,000secondsor1,050hours.Time-eciencyanalysismustbeconsidered.In thetimerequiredtorunonesimulationusing10 9 electrons,onecanrunmultiplesimulationsoftheothermaterialcompositionsatthespecifedenergiesusing10 7 electrons.By obtainingmanyreasonablyaccurateresultsinsametimethatitwouldtakereceiveonevery accurateresult,onewouldbeabletoanalyzemoredataandmakebetterconjecturesthan anindividualwhocanonlyanalyzeonedatum.Analternativethoughtcouldcomefrom consideringerrors.Errorswithinthecodecaneasilybedetectedbyobtainingtheoutput fletoseeifthevaluesarereasonableornot.Theindividualusing10 9 electronswouldhave towaitalittleunder44daysbeforelookingattheiroutput.Usingthepointslistedinthis minoranalysis,itwasconcludedthatachievingmorerunsismoreimportantthanobtaining agreateraccuracy. Conclusion Using10millionparticles,theerrorsassociatedwiththedatawerelessthan3%.The correlationsfromthisdatasetshouldalsobetrueforallothersofttissue-bonecompositions. Anempiricalformulacouldpossiblybemadewiththecurrentdatatorelatethespecifc absorbedfractionwiththesizeofthetumor,softtissue-bonecomposition,andelectron energy. 8

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References ShultisKJ,FawRE.RadiationShielding.In:AnonymousRadiationShielding.Illinois: AmericanNuclearSociety;2000:213-223. 9