Geant4-SPENVIS1 2006/11/08 Pasadena Geant4 validation on proton stopping power Tsukasa Aso Toyama National College of Maritime Technology, JST CREST

Geant4-SPENVISGeant4-SPENVIS 112006/11/08 Pasadena2006/11/08 Pasadena

Geant4 validation on proton stopping Geant4 validation on proton stopping powerpower

Tsukasa AsoTsukasa AsoToyama National College of Maritime Technology,Toyama National College of Maritime Technology,

JST CRESTJST CREST

2006/11/08 Pasadena2006/11/08 Pasadena Geant4-SPENVISGeant4-SPENVIS, , Tsukasa AsoTsukasa Aso TNCMTTNCMT 22

IntroductionIntroduction

• The validation of proton physics models with respect to The validation of proton physics models with respect to reference data is a critical issuereference data is a critical issue

• Proton physics is fundamental for space and medical Proton physics is fundamental for space and medical applicationapplication– i.e. Proton radiation therapy demands rigorous i.e. Proton radiation therapy demands rigorous

comparisons for patient’s safetycomparisons for patient’s safety– Position determination < 1 mmPosition determination < 1 mm– Dose determination < 5 %Dose determination < 5 %

• Bragg peak distribution must agree between the simulation Bragg peak distribution must agree between the simulation and the measurementand the measurement– Bragg peak consists of many physics processes such as Bragg peak consists of many physics processes such as

ionization, multiple scattering, hadronic process etc.ionization, multiple scattering, hadronic process etc.


Bragg peak and processesBragg peak and processes

• (1) Ionisation energy loss(1) Ionisation energy loss

• (2) (2) (1)(1)+Energy fluctuation+Energy fluctuation

• (3) (3) (2)(2)+Multiple Coulomb Scattering+Multiple Coulomb Scattering

• (4) (4) (3)(3)+Hadron elastic scattering+Hadron elastic scattering

• (5) (5) (4)(4)+Hadron inelastic scattering+Hadron inelastic scattering

• Stopping power ~ RangeStopping power ~ Range

• Excitation energy of material Excitation energy of material

• Best interaction modelsBest interaction models

• Peak position (Range)Peak position (Range)

• Width of peakWidth of peak

• Peak to Plateau ratio Peak to Plateau ratio

Proton Bragg peak in Water

Observables Basis of observable quantities


Previous worksPrevious works

Using Low energy EM with SRIM2000, transition energy 10 MeV.

Range cut 3 micron.100 micron sliced geometry

Lines : PSTAR NISTRed symbols: Simulation

• ValidationValidation– ““Comparison of Geant4 Electromagnetic Physics Models Against the NIST ReferenComparison of Geant4 Electromagnetic Physics Models Against the NIST Referen

ce Data” had already been published in IEEE TNS 52-4(2005)910-918, K.Amako ce Data” had already been published in IEEE TNS 52-4(2005)910-918, K.Amako et al., under the condition without multiple scattering and energy fluctuationset al., under the condition without multiple scattering and energy fluctuations

• Our previous workOur previous work– “Verification of the Dose Distributions

with Geant4 Simulation for Proton Therapy” ,IEEE TNS, 52-4(2005) 896-901

• The agreement is better than 0.1%, 0.3%, and 0.2% for water, lead, and aluminum, respectively

• There was a long story to reachthese results

• It must be understood systematically

G4v7


This workThis work

• Study of more detail comparison concentrating on proton stopping Study of more detail comparison concentrating on proton stopping power for power for sub-millimetersub-millimeter scale consistency scale consistency

– Proton range validation to NIST/ICRU reference valueProton range validation to NIST/ICRU reference value

Using SUsing Stopping power modelstopping power models

Range cut / step limit dependencies Range cut / step limit dependencies

Std EM and Low EM differencesStd EM and Low EM differences

The validation is done in terms of “Proton range”The validation is done in terms of “Proton range”


Electromagnetic physics models in Electromagnetic physics models in Geant4Geant4

Multiple scatteringBremsstrahlungIonisationAnnihilationPhotoelectric effectCompton scatteringRayleigh effectgamma conversione+e- pair productionSynchrotron radiationtransition radiationCherenkovRefractionReflectionAbsorptionScintillationFluorescenceAuger

Standard EM

LowEnergy EM

• Many choice of stopping power Many choice of stopping power parameterisations for protonsparameterisations for protons

Specialized according to - the particle type - energy range of process

ICRU composite material ~ 11 Al_2O_3, CO_2, CH_4, (C_2H_4)_N-Polyethylene, (C_2H_4)_N-Polypropylene, (C_8H_8)_N, C_3H_8, SiO_2, H_2OH_2O, H_2O-Gas, Graphite

Bethe-Bloch formula

Below 2 MeV by default

Proton Ionisation:: Stopping power

e+e-/gamma down to Ek~100 eV

e+e-/gamma down to Ek~1 keV

NIST for NIST material(G4_Water) [v8.x]ICRU49 (ChemicalFormula)Bragg rule (ICRU49 element)

Below 2 MeV by default

Below 2 MeV by defaultZiegler1977 (Bragg rule)ICRU49 (ChemicalFormula)Ziegler1985 (Bragg rule)SRIM2000 (Bragg rule)Bragg rule (ICRU49 element)

• Geant4 electromagnetic Geant4 electromagnetic processesprocesses

Energy fluctuation model

dE/dX tableIonisation energy loss =+


Range study(1) : Validation of stopping Range study(1) : Validation of stopping powerpower• 100 microns sliced water phantom100 microns sliced water phantom• 200 MeV proton200 MeV proton• CSDA rangeCSDA range

– Only Ionisation processOnly Ionisation process• Multiple scattering, Hadronic interaction (Elastic/Inelastic)Multiple scattering, Hadronic interaction (Elastic/Inelastic)

are turned offare turned off• Range cut is set to 3 micronRange cut is set to 3 micron

– Count number of protons in each layerCount number of protons in each layerdz = 100 micron

200 MeV proton


Comparison of STD EM with Low EMComparison of STD EM with Low EM

e-,e+,gamma = 3um RED G4hIonisation BLK G4hLowEnergyIonisation

w/o ChemicalFormula(“H_2O”)NuclearStoppingOffi.e. Bragg rule is applied

200 MeV proton

ICRU 259.6mm

w/ MeanExcitationEnergy = 75eV (ICRU)

Depth in water (mm)

Pro

ton

sur

viva

l pro

babi

lity

G4v7

Low energy EM process gives consistent range with NIST PSTAR prediction

Standard EM process gives shorter range than NIST PSTAR prediction

Under specified circumstances :

Discussion will be back later,but let’s adopt Low EM for study


Comparison of stopping power Comparison of stopping power functionsfunctions

200 MeV protonin Water

ICRU49 259.6mm

G4v7 G4hLowEnergyIonisation BLK: Bragg rule　 NuclearStoppingOff BLU: ICRU H_2O parameterization NuclearStoppingOff GRN: ICRU H_2O parameterization NuclearStoppingOn

diff. ~ 500 micronLow EM : Bragg rule or ICRU param.?

Low energy EM process + ICRU parameterization function for water

Depth in water(mm)

Pro

ton s

urv

ival pro

babili

ty

But why?

Low energy EM process + ICRU Bragg rule


Proton Range in water - Ionization Loss Table -Proton Range in water - Ionization Loss Table -

En

erg

y L

oss

(M

eV

/mm

)

KinE (MeV)

E_tr=2MeV

Bethe-BlochAt low energy region,RED: Bragg ruleGRN: ICRU49 param. function

G4hLowEnergyIonisation

Energy loss with ICRU49 parameterisationtends to be overestimated than Bragg rule’s calculationat the kinetic energy range from 100s MeV to 1 MeV.

Rat

io o

f Ene

rgy

Loss

(%

)

KinE (MeV)

G4v7

Energy loss in Bethe-Bloch formulais factored to ensure a smooth transitionto the low energy model.


Correction Factor: ParamBCorrection Factor: ParamB

G4v8.1.p01

The collection factor to the Bethe-Bloch formula is called as “ParamB” in low energy EM.

i.e. eloss *= (1+paramB*kinetic_energy/Transition_energy)

Stopping power function connectivity

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 2 4 6 8 10 12Transition Energy (MeV)

Cor

rect

ion

fact

or

LowE SRIM2000LowE ICRU param.LowE ICRU Bragg ruleStd. ICRU param.Std. ICRU Bragg ruleStd. G4WATER NIST

SRIM2000with 10 MeV cutoff was used in

our previous study

Smooth connectivity of stopping power

parameterization is desirable for precise

range calculation


Range cut and step size dependenceRange cut and step size dependence• Range cutRange cut may be set by users according to expected simulation accuracy. may be set by users according to expected simulation accuracy.

– ( Step limit can be set by users, but normally it is limited by geometry. )( Step limit can be set by users, but normally it is limited by geometry. )– The assurance of simulated result should be kept consistent within the accuracyThe assurance of simulated result should be kept consistent within the accuracy

• We observed a systematic variation of simulated range compared to the expected value fWe observed a systematic variation of simulated range compared to the expected value from the production cut.rom the production cut.– The range of The range of 200 MeV200 MeV proton becomes about 3 mm longer than NIST prediction by a proton becomes about 3 mm longer than NIST prediction by a

pplying a looser production cut. pplying a looser production cut.

200MeV Proton, ICRU predicts259.6mm

G4hLowEnergyIonisation No ChemicalFormula　 NuclearStoppingOff

Geometry: Sliced in 100um thickness

500um100um 50um 10um 5um 3um 1um

Su

rviv

ed p

roto

n p

rob

abili

ty

Depth in Water ( mm )

Production Cut

G4v7

We have to applyvery tiny productioncut in order to getreasonable result?

diff. ~ 3 mm


Range study(2): Range cut and Step limit Range study(2): Range cut and Step limit optimizationoptimization

• Bulk Water ( no geometrical slices )Bulk Water ( no geometrical slices )• 190 MeV proton190 MeV proton• Range cut dependence: 0.015, 0.050, 0.1, 0.5, 1 mmRange cut dependence: 0.015, 0.050, 0.1, 0.5, 1 mm• Step limit dependence: 0.01, 0.015, 0.020, 0.040, 0.050,Step limit dependence: 0.01, 0.015, 0.020, 0.040, 0.050,

0.100, 0.500, 1.0 mm 0.100, 0.500, 1.0 mm

190 MeV proton


Production Cuts

234

235

236

237

238

239

240

241

242

0.01 0.1 1

Production Cut (mm)

Pro

ton

Ran

ge (m

m)

Step. 0.01mm

Step. 0.05mm

Step.0.10mm

Step.0.50mm

Step.1mm

Step.0.04mm

Step.0.03mm

Step.0.02

Step. Default

NIST 237.7mm

Step Limits

diff = 6 mm

diff = 3 mm

Only 10um Step Limit reproduces NIST range.The range is independent to the production cutin this case.

Proton Range in bulk waterProton Range in bulk water

G4v7

G4hLowEnergyIonisation SRIM2000p blow 10 MeV190MeV proton


Proton Range in bulk waterProton Range in bulk water

Step limits

237

237.5

238

238.5

239

239.5

240

240.5

241

241.5

0.01 0.1 1Step limit length (mm)

Pro

ton

Ran

ge (

mm

)

Prod.1mmProd.0.5mmProd.0.1mmProd.0.05mmProd.0.015mm

NIST 237.7mm

Simulated Range changes with the step limit size.Range becomes longest when step limit is around 100um.

G4v7

G4hLowEnergyIonisation SRIM2000p 10 MeV


Energy fluctuation: ElectronicLossFluctuation()Energy fluctuation: ElectronicLossFluctuation()

(Fluctuated Eloss) - ( Eloss by dE/dX ) [keV]

if( EnlossFlucFlag && 0.0 < eloss && finalT > MinKineticEnergy) { // now the electron loss with fluctuation eloss = ElectronicLossFluctuation(particle, couple, eloss, step) ; if(eloss < 0.0) eloss = 0.0; finalT = kineticEnergy - eloss - nloss; } Eloss by dE/dX Table

Eloss dE/dX = 0.21 MeV / 500um

Eloss dE/dX = 0.0417 MeV / 100um

Eloss dE/dX = 0.00417 MeV / 10umThese values aretypical for 225MeVproton

Mean value of these distributions are:

-7.163 (keV)/500um-1.244(keV)/100um

-0.01013(keV)/10um

Fluctuated Eloss

RangeCut=10mm


Range with or without Energy fluctuationRange with or without Energy fluctuation

• G4hLowEnergyhIonisationG4hLowEnergyhIonisation• 225 MeV proton in Water225 MeV proton in Water• Range cut = 10 mmRange cut = 10 mm

313.0

314.0

315.0

316.0

317.0

318.0

319.0

320.0

321.0

322.0

323.0

0.001 0.01 0.1 1 10 100 1000

Step limits(mm)

Ran

ge (m

m)

LowEM SRIM2000 w/ o Efluc

LowEM SRIM2000 w/ EFluc

Without energy fluctuation, LowEM hIoni. reproduces NIST range at the step size below 5 mm.Energy fluctuation obviously distorts energy deposition with the underestimation.

1.00

10.00

100.00

1000.00

10000.00

100000.00

1000000.00

0.001 0.01 0.1 1 10 100 1000

Step Limits(mm)N

umbe

r of

cal

ls

NUserStepNLowEhIoni

NIST 317.4mm


Low EM or Std EMLow EM or Std EM

e-,e+,gamma = 3um RED G4hIonisation BLK G4hLowEnergyIonisation

w/o ChemicalFormula(“H_2O”)NuclearStoppingOffi.e. Bragg rule is applied

200 MeV proton

ICRU49 259.6mm

w/ MeanExcitationEnergy = 75eV (ICRU)

Depth in water (mm)

Pro

ton

sur

viva

l pro

babi

lity

G4v7

Low energy EM process gives consistent range with NIST PSTAR prediction

Standard EM process gives shorter range than NIST PSTAR prediction

What is the source of problem?


Range with or without energy fluctuationRange with or without energy fluctuationRange Study

313.0

314.0

315.0

316.0

317.0

318.0

319.0

320.0

321.0

322.0

323.0

0.001 0.01 0.1 1 10 100 1000StepLimit (mm)

Ran

ge (m

m)

LowE SRIM w/ o EflucStd ICRU w/ o EflucStd NIST w/ o EflucStd ICRU w/ o Fluc (BINS)

With Energy Fluctuation

313.0

314.0

315.0

316.0

317.0

318.0

319.0

320.0

321.0

322.0

323.0

0.001 0.01 0.1 1 10 100 1000Step Limits (mm)

Ran

ge (m

m)

LowE SRIM w/ EFlucStd ICRU param. w/ EFlucStd G4NIST w/ EFluc

Std EM uses G4UniversalFluctuationLowE EM uses G4hLowEnergyIonisation::ElectronicFluctuation() Both calculation based on “Energy loss in thin layers in GEANT4”,NIM A362(1995)416-422. But the implementation is slightly different.

0.1keV-100TeV 120bin=>0.1keV-1GeV 36000bins


SummarySummary• Source of problem and desired improvementsSource of problem and desired improvements

– Importing stopping power functionImporting stopping power function• Interconnectivity to the Bethe-Bloch formulaInterconnectivity to the Bethe-Bloch formula

– ~10% difference causes ~500um shift of range in water~10% difference causes ~500um shift of range in water

Should Geant4 be capable to import user’s stopping power functioShould Geant4 be capable to import user’s stopping power function? or Need to ensure non-stress way for interpolationn? or Need to ensure non-stress way for interpolation

– Energy fluctuation modelEnergy fluctuation model• Calculation model does not stable at around 100 micron step sizeCalculation model does not stable at around 100 micron step size

– Underestimation of energy loss makes the range longerUnderestimation of energy loss makes the range longer

Need to fix the unstable behaviorNeed to fix the unstable behavior– dE/dX table resolution might be neededdE/dX table resolution might be needed

• The fine binning The fine binning – It changes expected range about 1 mmIt changes expected range about 1 mm

Table binning should be adjustable for the applicationTable binning should be adjustable for the application


Accuracy versus Execution time?Accuracy versus Execution time?

• Geometry: Sliced in 100um thicknessGeometry: Sliced in 100um thickness• 225MeV proton225MeV proton• ProductionCut=1mm,StepLimit=DefaultProductionCut=1mm,StepLimit=Default

– Range 322.2mmRange 322.2mm– CPU 915.89s/10000evCPU 915.89s/10000ev

• ProductionCut=1mm,StepLimit=10umProductionCut=1mm,StepLimit=10um– RangeRange 　　 317.487mm317.487mm– CPU CPU 56095609s/10000evs/10000ev

• ProductionCut=3um, StepLimit=DefaultProductionCut=3um, StepLimit=Default– Range 317.787mmRange 317.787mm– CPU CPU 99219921s/10000eVs/10000eV



0.01

0.1

10.01 0.1 1

Step Limits (mm)

Ave

rage

ste

p le

ngth

(m

m)

Prod.1mmProd.0.5mmProd.0.1mmProd.0.05mmProd.0.015mm

Step Limits を 10um にすると、ProductionCut 15um と同じ意味になる


Proton range in waterProton range in waterRange in Si

165.0

166.0

167.0

168.0

169.0

170.0

171.0

0.001 0.01 0.1 1 10 100 1000

Step Limit (mm)

Ran

ge (m

m)

Std NIST w/ o FlucStd NIST w/ Fluc

Documents

Geant4-SPENVIS1 2006/11/08 Pasadena Geant4 validation on proton stopping power Tsukasa Aso Toyama National College of Maritime Technology, JST CREST