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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
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Lateral Charged-Particle Equilibrium Range rLCPE: minimum beam radius for D=Kcol
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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
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d
=> to achieve CPE, FWHMfield must be ≥ 2 rLCPE + d
2. Partial source occlusion
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IPEM Report 103 (2010)
Broad photon beam Narrow photon beam
penumbra overlap
Apparent widening of the field and decreased output
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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!
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Related issues: (i) hardening of energy spectrum
Decreasing field size: • Reduces head and phantom scatter • Filtering low energies => increase mean energy
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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
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Meltsner et al. Med Phys 36 (2009 ) 339 Wuerfel Med Phys Int 1 (2013 ) 81
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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
P Andreo - Physics of small field dosimetry 14 6/23/2017
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
16 P Andreo - Physics of small field dosimetry 6/23/2017
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
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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!
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med, det, med,det det,( )Q Q iD P D s p≠ ∏
19 P Andreo - Physics of small field dosimetry 6/23/2017
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
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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
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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
Electron kinetic energy, E / MeV
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
Electron kinetic energy, E / MeV
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
Photon energy, k / MeV
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
Photon energy, k / MeV
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
Photon energy, k / MeV
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 - Water
0.5 cm x 0.5 cm - Water
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
Electron energy, E / MeV
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 - Water
0.5 cm x 0.5 cm - Water
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
Electron energy, E / MeV
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
0.5 cm x 0.5 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
Electron energy, E / MeV
small difference in spectra for air and diamond; large for Si
Detector design: electron fluence Radiation sensitive volume (RSV) & high-Z non-RSV components
24 P Andreo - Physics of small field dosimetry 6/23/2017
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
Electron energy, E / MeV
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
Electron energy, E / MeV
0.5 cm x 0.5 cm field
EFD diode
RSV = water
+ density(non-RSV high-Z) = 1
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
25 P Andreo - Physics of small field dosimetry 6/23/2017
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)
26 P Andreo - Physics of small field dosimetry 6/23/2017
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
6/23/2017 P Andreo - Physics of small field dosimetry 27
• detector-to-detector (same type) differences • geometry accuracy
Field output correction factors @ 6MV
6/23/2017 P Andreo - Physics of small field dosimetry 28
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
P Andreo - Physics of small field dosimetry 29 6/23/2017
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
6/23/2017 P Andreo - Physics of small field dosimetry 30
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
6/23/2017 P Andreo - Physics of small field dosimetry 31
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