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Applications of Monte Carlo simulations to radiation dosimetry
D.W.O. Rogers
Carleton Laboratory for Radiotherapy Physics.
Physics Dept, Carleton University,
Ottawa
http://www.physics.carleton.ca/~drogers
ICTP, Trieste, Nov 14, 2007
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Papers in PMB and Med Phys with Monte Carlo in title or abstract
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Radiation dosimetry in radiotherapy
• primary standards– air kerma, – absorbed dose
• electron & photon beams• beta-ray fields
• clinical dosimetry protocols– dose in a water tank
• TG51, TG61, TG43, TRS-398• radiotherapy treatment planning
– dose in a (CT) patient
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radiation dosimeters
• many types of radiation dosimeters for radiotherapy– ion chambers - the work horse for clinical reference
dosimetry and air kerma primary standards– calorimeters for absorbed dose primary standards– free air chambers for x-ray air kerma standards– TLDs LiF– diodes, MOSFETS– radiographic and radiochromic films– chemical (Fricke) dosimeters
Monte Carlo calculations have been used to elucidate all of these.
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Ion chambers
Farmer ion chamber
from John McCaffrey, NRC
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Cavity theory: stopping-power ratios
Relates dose in cavity to dose in medium.
gas
med
sprs are fundamental to
-dosimetry protocols
-primary standards
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What is (L/ρ)?
A Spencer-Attix spr - stopping-power ratio
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Dosimetry in a phantom
Pwall, Pgr, Pfl, Pcel all 1% or less effects
-major variation comes from spr
for complete definitions of Pwall etc see http://www.physics.carleton.ca/~drogers/pubs/papers/ss96.pdf
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Electron beam depth-dose curve
12 MeV
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sprs in electron beams
Ding et al, Med Phys 22(1995) 489-501
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Realistic electron beam sprs
Ding et al Med Phys 22 (1995)489BEAM code used to simulate realistic accelerator beams
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Effects of realistic sprs
Ding et al MP 22(1995)489
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How to use realistic sprs
David Burns noted:
changing dref simplifies everything.
dref = 0.6 R50 - 0.1 (cm)
Burns et al MP 23(1996)383
The basis of electron beam dosimetry in IAEA TRS-398 and AAPM TG-51 clinical protocols
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Realistic sprs: dref=0.6R50 - 0.1
Burns et al MP 23(1996)383
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Photon beams: specifying beam quality
• NAP -nominal accelerating potential• %dd(10) -percentage depth dose at 10 cm depth
in a 10x10 cm2 field on surface at SSD 100 cm
• %dd(10)X -the photon component of %dd(10)(i.e., ignoring electron contamination)
• TPR2010 -ratio of absorbed doses at depths 20
and 10 cm in a water phantom, measured with a constant source-chamber distance of 100 cm and a field size of 10x10 cm2 at the plane of the chamber
TG-51
TRS-398
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sprs for photon beams
Kalach and Rogers 30 (2003) 1546-1555
filled: heavily filtered open: lightly filtered
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sprs for photon beams
filled: heavily filtered open: lightly filtered
Kalach and Rogers 30 (2003) 1546-1555
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What happens without a flattening filter?
Xiong and Rogers, in prep, 2007 Based on full BEAM simulations.
For IMRT, flattening filter is not needed(Titt et al, Med Phys 33(2006) 3270).
A single fit handles both sets of beams using %dd(10)x.
Major effect is on %dd(10)x due to non-flat beams
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Flattening filter free: TPR
Two sets of kQ values will be needed, one for with flattening filters, one for machines without them.
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Summary: protocol dosimetry
• the major quantity which varies in protocol dosimetry is the stopping power ratio– hence the discussion of it
• but other aspects of protocols such as TG-51 and TRS-398 which are based on MC calculated values– Pwall for plane parallel chambers in Co-60 beams– Pcel for aluminium electrodes– relationship between I50 and R50 in e- beams
• plus on-going research on other aspects– Pwall for all beams, Prepl, effective point of
measurement
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Primary standards of air-kerma in Co-60
Primary standards in Co-60 beams are based on cavity ion chambers and S-A cavity theory
Dgas Dwall/Dgas Dair/Dwall
for complete definitions see http://www.physics.carleton.ca/~drogers/pubs/papers/fundamentals_ss90.pdf
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How accurately can we calculate ion chamber response?
Fano cavity chamber, - walls and gas the same material (assume graphite) with a density ratio of about 1000.
- establish kerma to graphite in a parallel 60Co beam.
Fano’s theorem => no fluence correction (traditionally ignored, but in principle needed). All other K = 1.00
ie we can check our Dgas calculation
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How accurately can we calculate ion chamber response? (cont)
This is the toughest test I know for any electron-photon Monte Carlo code
-cover of EGSnrc manual
-against own cross sections
-ESTEPE is max
fractional step size
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How accurately can we calculate ion chamber response? (cont)
Kawrakow & Rogers, MC2000, p135 based on data of Nilsson et al, IAEA Proceedings, 1988
against measured
data
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Kwall: attenuation and scatterKair eqn ignores attenuation and scatter in chamber walls
Monte Carlo Kwall scores Dgas without / Dgas with scatter and attenuationor
Or regenerate interacting photons & ignore scattered photons
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Kwall: non-linear extrapolation
Rogers & Bielajew, PMB 35 (1990) 1065
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Some measured confirmations of MC Kwall
graphite walled chamber at NRC
rotate the chamber in Co-60
response*Kwall=response/Awall
should be constant
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McCaffrey et al PMB 49(2004) 2491
Response vs angle of Mark IV
If Awall is correct, R/Awall should be constant.
It is, within 0.3% despite 8% variation.
(residual 0.3% is a Kaneffect)
29/64Büermann et al PMB 48 (2003) 3581
PTB/OMH: cylindrical chamber
axis of rotation
measured response vs wall thickness.
Should all extrapolate to same value.
Only the calculated Kwall correction gave a constant response
radialaxial
45
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Kan: axial non-uniformityBielajew developed an analytic theory to account for point
sources not parallel beams (PMB 35(1990)501 & 517)
A brute force MC calculation with a parallel beam or a point source, confirms the analytic theory.
The corrections are all very small for Co-60 sources at 1 m from typical chambers
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Revision of air-kerma standards
Using EGSnrc calculated Kwall and Kan values, revise the reported values
Rogers and Treurniet, 1999 (NRC Report PIRS-663)extending work of
Bielajew and Rogers, PMB 37(1992)1283
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Revision of air-kerma standards (cont)
Note: the BIPM baseline moved up
by 0.3%. ------
Monte Carlo => world’s air kerma
standards increased 0.8% (double stated uncertainty)
Rogers & Treurniet1999 NRC Report
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How accurate are calculations?
If we are going to use Monte Carlo calculated factors, we need to know their uncertainty
How sensitive are they to:-algorithm/computer code used
-cross sections-spectrum used-size of source
Rogers & Kawrakow Med Phys 30 (2003)521
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Calculated response of NRC 3C chamber
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Kwall for NRC 3C
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(L/ρ) for different algorithms
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Kwall vs incident spectrum
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Kan vs incident spectrum
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spr vs incident spectrum
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Kan for 3C vs source radius
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Uncertainty estimates (%)
spr Kwall Kan Kcomp
Stats <0.01 <0.01 0.04 0.03Algorithm 0.02 0.02 0.02 0.02Spectrum 0.01 <0.01 0.04 0.04e- X-sec 0.65 0.01 - 0.08γ X-sec - 0.01 - 0.14
Rogers & Kawrakow Med Phys 30 (2003)521
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Verification of cavity theory?
Can Monte Carlo verify the accuracy of cavity theory? EGSnrc can calculate Dgas to 0.1%
(proof: Fano cavity calculations)
Cavity theory assumes that photon interactions in the cavity do not occur
But Ma and Nahum showed they did.PMB 36(1991)413
So does cavity theory hold for Ir-192 or lower energy photon beams?
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Accuracy of Spencer-Attix cavity theory
Another thought/computational experimentFor a parallel beam incident on a
stemless chamber filled with dry air
spectrum
CAVRZnrc
SPRRZnrcDOSRZnrc
EGSnrc
CAVRZnrc
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Accuracy of Spencer-Attix cavity theory
Borg et al, Med Phys 27(2000)1804
Only this good because graphite and air so similar.
Calculations used ∆ = 10 keV for spr. Using larger values brings value within 0.1% of unity
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The use of silicon diode detectors
• a common assumption is that diode detectors measure dose directly – ie no spr correction etc
• but sprs actually change quite a bit as the beam quality changes
• Why don’t we need to correct for this?
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water/silicon stopping powers are not constant
Wang Med Phys 34 (2007) 1734
calculate ratioof dose in small active region of diode detector isolated from rest of detector to dose to waterat same location.
Use CSnrc which uses correlated sampling
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model of diode detector (Scanditronix EFD)
McKerracher and ThwaitesRadioth Oncol 79(06) 348
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dose water/dose silicon active region
Wang Med Phys 34 (2007) 1734
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effect of backscatter from rest of chip
Wang Med Phys 34 (2007) 1734
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diode response at dmax vs field size
mostly a change in spr
effect as dmax changes
Wang Med Phys 34 (2007) 1734
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Summary re diode detectors
• diodes measure dose directly within +-1% as a function of depth and beam quality in electron beams– one exception - small radius electron beams
• the silicon backing of the active region and the epoxy play an important role in the flat response
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PTP: the pressure-temperature correction for ion chambers
te-
ion chamber
PTP is constructed so
independent of ρSo Edep(ρ) is proportional to the density ρ.
Edep(ρο) is independent of the density ρ.
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PTP (cont)
e-
ion chamber
independent of ρ
Edep(ρ) is no longer proportional to the density ρ.
Hence the standard PTP correction factor may no longer work.
What happens if the electron does not cross the cavity?
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Pressure vs. altitude
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NE2571 A12
“A4”
NRC x-ray monitor
• EGSnrc Monte Carlo code
• cross-sections for DRY air of different densities
• calculate Dcav (dose to air)
• standard PTP correction inherent in results
• PTB catalogued spectra
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Thimble chamber calculations
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Conclusions of PTP paper I
• there is a significant breakdown of the standard PTP
correction for low energy photon beams
• basic cause: e- stopping in the cavity, not crossing
• magnitude of the effect depends on:
– mismatch of wall to air cross sections
– fraction of dose due to photon interactions in the cavity air
• a similar effect was reported in 2005 by the UW ADCL for well ion chambers for I-125
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Experiments at NRC to demonstrate the effect
complete BEAMnrc model to give x-ray spectrum
with Malcolm McEwen
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A variety of chambers studied
Kawrakow’s egs_view
A12A2 NE2571
NE2505 A19
C552 aluminium
C552 graphite dural, C552
Calculations with cavity.cpp, using Kawrakow’sC++ geometry package & interface to EGSnrc
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Farmer-like chambers: 60 kV
Closed symbols:PTP corrected measured responses
open symbols:
calculated responses
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Effects of geometry details
CAVRZnrcuses a cylindrical model
cavity.cppincludes the conical end.
These geometry differences have no effect in a Co-60 beam
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Summary re PPT corrections
• measurements confirm the calculated breakdownof the PTP correction factor for low-energy x-rays
• EGSnrc is capable of reproducing air-kerma calibration coefficients well within 1% – NK vs beam quality curves allow quantification
of the size of impurity effects• geometry details have some effects at these low
energies although not at Co-60 • impurities are important at low photon energies
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MC techniques play a fundamental role in radiation dosimetry
Summary
• sprs and other corrections for ion chambers used in clinical dosimetry
• correction factors for primary standards• verification of cavity theory accuracy• elucidation of detector response (eg was diode)• investigation of pressure-temperature effects• and much, much more
– TLDs, OSL, alanine,Fricke, well chambers, brachytherapy dosimetry etc
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Acknowledgements
• The work described here has been done in conjunction with many colleagues, grad students and research associates, without whom it wouldn’t get done.
• the various works described involved: Iwan Kawrakow, David Burns, George Ding, Guoming Xiong, Nina Kalach, Jette Borg, Alex Bielajew, John McCaffrey, Joanne Truerniet, Lilie Wang and Dan La Russa, but many more were involved in the overall project of Monte Carlo in radiation dosimetry
• Support from the Canada Research Chairs program and