Physics of small megavoltage photon beam dosimetry · Physics of small megavoltage photon beam dosimetry P Andreo, Professor of Medical Radiation Physics . Karolinska University Hospital,

Physics of small megavoltage photon beam dosimetry

P Andreo, Professor of Medical Radiation Physics Karolinska University Hospital, Stockholm, Sweden

ICARO2 – IAEA, Vienna, 2017

IAEA TRS-483

P Andreo - Physics of small field dosimetry 2 6/23/2017

2007-11-04

10 years

IAEA-AAPM working group

• Fundamental condition 1. Loss of Lateral Charged-Particle

Equilibrium (LCPE)

• Machine-related issues 2. Partial source occlusion

• Detector-related issues

3. Mismatch of detector vs field size and perturbation effects much larger than in broad beams

3

When a field is small?

P Andreo - Physics of small field dosimetry 6/23/2017

IPEM Report 103 (2010)

1. Loss of Lateral Charged-Particle Equilibrium

broad photon field

volume volume

narrow photon field

A small radiation field has dimension(s) smaller than the “lateral range” of charged particles

D/Kcol is a measure of the degree of CPE or TCPE

6/23/2017 P Andreo - Physics of small field dosimetry 4

Lateral Charged-Particle Equilibrium Range rLCPE: minimum beam radius for D=Kcol

5 P Andreo - Physics of small field dosimetry 6/23/2017

IAEA TRS-483 (2017)

rLCPE (cm) = a × Q – b where • Q is TPR20,10 or %dd(10)X • a and b are fit coeffs to MC data

Intrinsic condition

For a given beam quality, the distance from the detector outer boundary to the field edge

is less than rLCPE


d

=> to achieve CPE, FWHMfield must be ≥ 2 rLCPE + d

2. Partial source occlusion


IPEM Report 103 (2010)

Broad photon beam Narrow photon beam

penumbra overlap

Apparent widening of the field and decreased output

8 P Andreo - Physics of small field dosimetry

Ahnesjö and Saxner Radioth Oncol 81 (2006) S124 Das et al. Med Phys 35 (2008) 206

6/23/2017

Consequences of partial source occlusion

• Overlap of the penumbra Related to machine spot (source) size

• Reduction of relative central-axis dose Decreased machine output

• Apparent field widening Mismatch between FWHM (true field size)

and collimator setting (nominal field size) Severe impact on data required for the TPS!


Related issues: (i) hardening of energy spectrum

Decreasing field size: • Reduces head and phantom scatter • Filtering low energies => increase mean energy


0.0

5.0x10-18

1.0x10-17

1.5x10-17

2.0x10-17

0.01 0.1 1

Pho

ton

fluen

ce /

cm-2

MeV

-1

Photon energy / MeV

4 cm x 4 cm

2 cm x 2 cm 1 cm x 1 cm

0.5 cm x 0.5 cm

10 cm x 10 cm

<E> MeVcmxcm1.310x101.64x41.82x21.91x12.00.5x0.5

6 MV photon spectra for different field sizes at 10 cm depth (in a small water volume)

Benmakhlouf et al Med. Phys. 41 (2014)

• Water/air stopping-power ratios for ion-chamber reference dosimetry are practically independent of field size (and depth)

• Known since years, confirmed by other authors (e.g. Sánchez-Doblado et al 2003; Eklund & Ahnesjö, 2008)

Related issues: (ii) sw,air dependence on energy spectrum

P Andreo - Physics of small field dosimetry 6/23/2017

11

~0.3%

zref Andreo & Brahme Phys. Med. Biol. 31 (1986) 839

6 MV photons

3. Detector related issues

• Ion chambers have been the “backbone” of RT dosimetry 1) Not suitable in high-dose gradients or non-uniform beams 2) Constraints regarding size versus sensitivity 3) Require small fluence perturbation corrections

4) Require a region of uniform fluence around the chamber

Item (4) poses an additional chamber-size constraint, never of concern in broad beams,

but of great importance in small beams


Meltsner et al. Med Phys 36 (2009 ) 339 Wuerfel Med Phys Int 1 (2013 ) 81


inner outer

Exradin A16 diameters

Chamber-size related problems: Volume-averaging effect

Chamber reading provides a signal averaged over its volume

0.0

0.2

0.4

0.6

0.8

1.0

-20 -15 -10 -5 0 5 10 15 20

Measured beam profile

Gaussian beam profile

Dos

e re

lativ

e to

cen

tral a

xis

Distance to central axis / mm

FWHM = 10 mm

with a 5 mm long detector

detector

Field size < chamber Ø Fluence over detector not uniform

Ionization chamber perturbation factors in broad beams


0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85

Ove

rall

pertu

rbat

ion

corre

ctio

n fa

ctor

, pch

,Q

Photon beam quality, TPR20,10

C-552 r=4.8 mm

A-150 r=2.3 mm

A-150 r=2.0 mm

Most ionization chambers

Andreo et al FIORD (2017)

~6MV

w, ref air, ref w,air ch ,( ) ( )iQ Q Q

i

D z D z s p= ∏

Chamber-type related issues Perturbation factors in small fields

P Andreo - Physics of small field dosimetry 15

6/23/2017

0.90

0.95

1.00

1.05

1.10

0.0 0.2 0.4 0.6 0.8

Per

turb

atio

n co

rrect

ion

fact

or

Off-axis distance / cm

PTW PinPoint 31006 (steel electrode)

pwall

pcel

pdis

ptot

pvol

data from Crop et al Phys Med Biol 54(2009)2951

These are very large correction factors!

MC calcs for 6 MV, 0.8 cm x 0.8 cm field size, 10 cm depth

3. Detector related issues (cont.) • Volume averaging is critical for ion chamber dosimetry,

but Correction can be minimized if a small chamber is used and

chamber-to-field edge distance is larger than rLCPE, i.e. FWHM ≥ 2 rLCPE + d

MC-calculated overall perturbation factors include averaging

• Solid-state detectors Small size vs sensitivity overcomes some ion chamber

constraints, including most volume averaging issues Very appropriate for relative dosimetry Certain issues arise due to material, detector design, etc sometimes require quite large correction factors


Perturbation factors & Cavity Theory

• MC calcs do not require CPE, but current formulations for converting Ddet -> Dmed rely on CPE-based eqs (e.g. smed,det relies on assuming Φmed ≡ Φdet)

• Bragg-Gray and other theories assume SMALL and INDEPENDENT perturbation correction factors pdet,i


med, det, med,det det,( )Q Q iD P D s p= ∏[ ]

[ ]

max

max

el medBG 0med,det

el d

prim

med

pre

im

med t0

( ) / d

( ) / d

E

E

E

E

S E Es

S E E

ρ

ρ

Φ

Φ

=∫

∫

Perturbation factors & Cavity Theory

• In small MV fields, however, for many real detectors, often, there is no CPE correction factors can be LARGE (up to ~10%) some effects can be strongly CORRELATED

BASIC ASSUMPTIONS USED SO FAR BREAK DOWN!


med, det, med,det det,( )Q Q iD P D s p≠ ∏


Breakdown of Bragg-Gray theory

Andreo et al (2017)

Perturbation effects in small fields • Caused by changes in FLUENCE (Φmed ≠ Φdet)

but currently based on MC calcs of DOSE (Dmed/ Ddet) • Common assumption for Φmed ≠ Φdet: largely caused by

different mass density in med (water) and det (air, Si, C) Today: Φmed ≠ Φdet is caused by detector design and

different mass stopping powers in med and det, i.e. 1) Strong dependence on mean excitation energy (I-value) 2) Moderate dependence on electron density (~ ρ Z/A) 3) No direct dependence on mass density (ρ)

(1) and (2) enter into density-effect correction δ


2el 2

1 1 ( ) ln ( , , )Z ZS f I IA A

β δ ρ βρ β

∝ − −

0.80

0.82

0.84

0.86

0.88

0.90

Cem

a re

lativ

e to

wat

er

Dia

mon

d

Gra

phite

Silic

on

LiF

Pho

spho

rus

integrated ''dose spectra''

Detector (material): Fluence & Dose MC calcs for 6MV, field Ø=1cm, detector r=0.05cm h=0.003cm


0.6

0.7

0.8

0.9

1.0

0.001 0.01 0.1 1 10

[Sel(E

)/ρ] m

ed,w

Electron kinetic energy, E / MeV

graphite (1.7, 81)air (0.001,86)

silicon(2.33,173)

air

diamond (3.51,81)

phosphorus(2.20,173)

LiF (2.64,94)

water (ρ =0.998 g/cm3; I=78 eV)

approx onsetdensity-effect

watersilicon

0.000

0.005

0.010

0.015

0.020

0.025

0.001 0.01 0.1 1

Ele

ctro

n flu

ence

per

inci

dent

flue

nce


siliconphosphorus

LiFwaterdiamondgraphite

Andreo & Benmakhlouf Phys Med Biol 62(2017)1518

0

5x10-5

1x10-4

2x10-4

2x10-4

3x10-4

0.001 0.01 0.1 1

Pro

duct

ΦES

el(E

,∆)d

E at

ene

rgy

E


water

diamond-graphitesilicon

LiF-phosphorus

approx ''dose spectra''

Detectors (full simulation): photon fluence

22 P Andreo - Physics of small field dosimetry 6/23/2017 Benmakhlouf & Andreo Med Phys 44(2017)713

0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

0.01 0.1 1 10

WaterPTW T60003

Natural diamond detector

Pho

ton

fluen

ce /

cm-2

MeV

-1

Photon energy, k / MeV

10 cm x 10 cm

0.5 cm x 0.5 cm

0

1x10-5

2x10-5

4x10-5

0.01 0.1 1 10

WaterIBA PFD

Shielded silicon diode

Pho

ton

fluen

ce /

cm-2

MeV

-1


0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

0.01 0.1 1 10

WaterIBA EFD

Unshielded silicon diode

Pho

ton

fluen

ce /

cm-2

MeV

-1


0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

0.01 0.1 1 10

WaterPTW T60017

Unshielded silicon diode

Phot

on fl

uenc

e / c

m-2

MeV

-1


Practically no difference between spectra in water and in det, except…

Detectors (full simulation): electron fluence

23 P Andreo - Physics of small field dosimetry 6/23/2017 Benmakhlouf & Andreo Med Phys 44(2017)713

0.0

5.0x10-8

1.0x10-7

1.5x10-7

2.0x10-7

0.01 0.1 1 10

Electron fluence - Ionization chambers

10 cm x 10 cm - Water

0.5 cm x 0.5 cm - Water

10 cm x 10 cm - PTW T31016

0.5 cm x 0.5 cm - PTW T31016

10 cm x 10 cm - IBA CC01

0.5 cm x 0.5 cm - IBA CC01

10 cm x 10 cm - PTW T31018

0.5 cm x 0.5 cm - PTW T31018

Ele

ctro

n flu

ence

/ cm

-2 M

eV-1

Electron energy, E / MeV

0.0

5.0x10-8

1.0x10-7

1.5x10-7

2.0x10-7

0.01 0.1 1 10

Electron fluence - Diamond detectors



10 cm x 10 cm - PTW T60003

0.5 cm x 0.5 cm - PTW T60003

10 cm x 10 cm - PTW T60019

0.5 cm x 0.5 cm - PTW T60019Ele

ctro

n flu

ence

/ cm

-2 M

eV-1


0.0

5.0x10-8

1.0x10-7

1.5x10-7

2.0x10-7

2.5x10-7

0.01 0.1 1 10

Electron fluence - Shielded silicon diodes



10 cm x 10 cm - PTW T60016

0.5 cm x 0.5 cm - PTW T60016

10 cm x 10 cm - IBA PFD

0.5 cm x 0.5 cm - IBA PFD

Ele

ctro

n flu

ence

/ cm

-2 M

eV-1


0.0

5.0x10-8

1.0x10-7

1.5x10-7

2.0x10-7

2.5x10-7

0.01 0.1 1 10

Electron fluence - Unshielded silicon diodes10 cm x 10 cm - Water


10 cm x 10 cm - PTW T60017

0.5 cm x 0.5 cm - PTW T60017

10 cm x 10 cm - PTW T60018

0.5 cm x 0.5 cm - PTW T60018

10 cm x 10 cm - IBA EFD

0.5 cm x 0.5 cm - IBA EFD

10 cm x 10 cm - IBA SFD

0.5 cm x 0.5 cm - IBA SFD

Ele

ctro

n flu

ence

/ cm

-2 M

eV-1


small difference in spectra for air and diamond; large for Si

Detector design: electron fluence Radiation sensitive volume (RSV) & high-Z non-RSV components


Largest contribution to Φmed ≠ Φdet is due to high-Z components surrounding the RSV

(even for an unshielded-diode!)

Benmakhlouf & Andreo, Med Phys 44(2017)713

0.0

2.0x10-8

4.0x10-8

6.0x10-8

8.0x10-8

1.0x10-7

1.2x10-7

0.01 0.1 1

Fully modelled EFD diodeRSV = water+ density(non-RSV high-Z) = 1Water volumeE

lect

ron

fluen

ce /

cm-2

MeV

-1


0.5 cm x 0.5 cm field

1.0

1.1

1.2

1.3

1.4

0.01 0.1 1

Elec

tron

fluen

ce n

orm

aliz

ed to

wat

er


0.5 cm x 0.5 cm field

EFD diode

RSV = water

+ density(non-RSV high-Z) = 1

Presenter

Presentation Notes

3. Detector-related issues (cont.) Output factor

• Defined as a ratio of doses in two fields (fclin,fref) • In broad beams, common approach uses ratio of

detector readings

• Due to the approximate constancy of stopping power and perturbation ratios with field size


ref

ref ref

ref ref ref ref

clin clinclin

ref ref

( , ) ( , )( )( , ) ( , )z

D z M zO f fff f

FD z M z

= ≈

Output factors in small fields • Constancy arguments not valid for small fields

due to the detector-related effects discussed (mostly, perturbation factors incl volume averaging)

• Concept “re-defined” to field output factor as a “true" dose ratio

• is a correction factor to the ratio of detector readings, MC calculated or experimental (depends on reference detector)


clin clin

clin clinclin ref clin ref

clin ref clin refmsr ref

msr msr

,, ,, ,

,

f fw Q Qf f f f

Q Q Q Qf fw Q Q

D Mk

D MΩ = =

OF conventional clin msr

clin msr

,,

f fQ Qk

MC calculations constraints:

Manufacturer’s catalogue geometry description

Real geometry

Diagrams provided by manufacturers might be incorrect! See discussions on µDiamond geometry in:

• Andreo et al Phys. Med. Biol. 61, L1–L10 (2016) • http://medicalphysicsweb.org/cws/article/research/63793 • Marinelli et al Med. Phys. 43, 5205 (2016) and letters to editor


• detector-to-detector (same type) differences • geometry accuracy

http://medicalphysicsweb.org/cws/article/research/63793



Field output correction factors @ 6MV


Data from IAEA TRS-483 (2017) obtained from statistical average of MC and experimental published values

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

0.4 0.6 0.8 1 4 6 8

Exradin A14SL micro ShonkaExradin A16 microIBA/Wellhöfer CC01IBA/Wellhöfer CC04IBA/Wellhöfer CC13/IC10/IC15

PTW 31002 FlexiblePTW 31010 SemiflexPTW 31014 PinPointPTW 31016 PinPoint 3D

Out

put c

orre

ctio

n fa

ctor

,

Equivalent square field size / cm

cli

clin re

n

clinclin ref

clin ref ref

ref

f

clin ref

, ,, ,

fQf f

Q Q fQ

f fQ Q

MM

kΩ =

(a)

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

0.4 0.6 0.8 1 4 6 8

IBA PFD3G shielded diodeIBA EFD3G unshielded diodeIBA SFD unshielded diodePTW 60008 shielded diodePTW 60012 unshielded diodePTW 60016 shielded diodePTW 60017 unshielded diode

PTW 60018 unshielded diodePTW 60003 natural diamondPTW 60019 CVD diamondPTW 31018 liquid ion chamberSun Nuclear EDGE DetectorStandard Imaging W1 plastic sct

Out

put c

orre

ctio

n fa

ctor

,

Equivalent square field size / cm

cli

clin re

n

clinclin ref

clin ref ref

ref

f

clin ref

, ,, ,

fQf f

Q Q fQ

f fQ Q

MM

kΩ =

(b)

Ionization chambers Solid-state & other detectors

Note the log scale in the abscissa axis below about 2.5 cm field size

CyberKnife output factors


11%

33%

9% 3% 3%

6%

Pantelis et al Med Phys 37 (2010) 2369

Dose ratio Detector-reading ratio

- Smaller scatter of values - Change mean value

Conclusions

• Physics of small field dosimetry can be complex • Perturbation effects may have significant impact

on reference dosimetry, to the extent of breaking down Bragg-Gray theory

• Although relative dosimetry is conceptually simple, perturbation effects impact considerably field output factors

• Influence of detector design can be significant (e.g., silicon diodes)

• Comparing different detectors gives information on their adequacy for small field dosimetry


Acknowledgements Parts of the material for this presentation have been contributed by, or developed in collaboration with, different colleagues, particularly the members of the IAEA-AAPM Working Group* on ``Small and Non-standard Field Dosimetry".

Special thanks go to the co-authors of the IAEA-AAPM TRS-483 Code of Practice (underlined below). (*) R Alfonso, P Andreo, R Capote, K Christaki, S Huq, J Izewska, J Johansson,

W Kilby, T R Mackie, A Meghzifene, H Palmans (Chair), J Seuntjens and W Ullrich


http://eu.wiley.com/WileyCDA/WileyTitle/productCd-3527409211.html

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Physics of small megavoltage photon beam dosimetry · Physics of small megavoltage photon beam dosimetry P Andreo, Professor of Medical Radiation Physics . Karolinska University Hospital,