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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