Dosimetric Uncertainties in Reference and Relative Dosimetry of

Small Fields

Jan Seuntjens, Ph.D., FAAPM, FCCPMMcGill University Health Centre

Canada

Outline of Presentation• Uncertainty concepts and requirements• Dosimetry standards, calibration chain and

calibration uncertainties• Recap of physics of small fields & dosimetric

uncertainties• Small field reference dosimetry and sources of

uncertainty• Output factors and sources of uncertainty

Learning Objectives

• Learn about the sources of uncertainties in reference dosimetry of conventional and small fields

• Learn about new upcoming dosimetryrecommendations for small field dosimetry and components of uncertainty

Uncertainties - GUM

• GUM: ISO Guide to the Expression of Uncertainty in Measurement – procedure to estimate the total uncertainty in your measurement – more than you ever wanted to know about probability distributions, uncertainty

budgets, degrees of freedom, coverage factors and how to turn a guess into an estimate

• More useful: the best way to ensure that you take all uncertainty components into account properly – how to build an uncertainty budget!

• NIST produced an explanatory document to the GUM (- NIST Technical Note 1297)

Uncertainty categories • An Error is the difference between the true value of a quantity or

variable and its estimate. If we know the Error, we can apply a correction to arrive at the true value of the quantity

• Uncertainties are not Errors!• Categories or types of uncertainties: A and B

– Type A. those which are evaluated by statistical methods; sometimes wrongly called random uncertainties, more correctly: "component of uncertainty arising from a random effect"

– Type B. those which are evaluated by other means; sometimes wrongly called systematic uncertainties, more correctly: “component of uncertainty arising from a systematic effect”

• A type A uncertainty from one uncertainty budget can become a Type B uncertainty in another uncertainty budget

Uncertainty requirements in SRT• Gradients are on the order of 20% per mm• With this gradient, a 10% dose uncertainty will lead to an uncertainty

in a profile width of 10%/20% * 1 mm = 0.5 mm on both sides of the profile, i.e., 1 mm width uncertainty

• GammaKnife: 10% higher dose in centre of the field means a 1 mm widening of the 50% isodose line

• For a 18 mm target this means the treated volume may increase by 25%!

the effect of dosimetric uncertainty translates in significant changes in treated volume

Traceability

Radiation Dosimetry

Calibration Chain Verification, QAand audits

8

Clinical beam

DwclinicQ

Calibration chain

IROC

ADCLbeam

Q ND,wclinic

PSDL(NIST or NRCC)

ND,wADCL,SSDL

AAPM-CLA

Primary Dosimetry Standard• Instrument that allows the determination of absorbed

dose according to its definition• Preferably with a direct path to SI quantities not involved

with ionizing radiation• SI base unit: meter, kilogram, second, ampere, kelvin,

mole, and candela• SI derived units: J, Gy, etc.• the path to base SI units is not always as “direct” as we

would like• PSDLs are primary standards dosimetry laboratories

Absorbed dose to water• Dose to water is determined directly, at a point, by

measuring the temperature increase:

cw: specific heat capacity of water (4180 J kg-1K-1): temperature increase (0.25 mK/Gy)

kc:heat loss correction factorkp: perturbation of radiation field correction factorkdd: non-uniformity of lateral dose profile corr. Factor

: water density difference correction factor h: heat defect

Practical realization

The NRC water calorimeter, Ottawa, Canada(Seuntjens et al 1999 A status report on the NRC sealed water calorimeter. PIRS 0584)

Uncertainty: primary standard

Seuntjens and Duane (2009)Metrologia 46 S39

~0.5%

Uncertainty: reference dosimetry

McEwen et al Medical Physics 41, 041501 (2014)

TG-51 Update:Uncertainty budget broken downinto:• Measurement• Calibration data• Influence quantities

Typical values discussed butemphasis on individual usersconstructing site-specific uncertaintybudgets for their calibrationsituations

Physics of small fields and impact on uncertainties

18

Recap:What constitutes small-field conditions?

• Beam-related small-field conditions– the existence of lateral charged particle disequilibrium– partial geometrical shielding of the primary photon

source as seen from the point of measurement • Detector-related small-field condition

– detector size compared to field size

Lateral charged particle loss broad photon field

volume volume

narrow photon field

A small field can be defined as a field with size smaller than the “lateral range” of charged particles

is a measure of the degree of charged particle equilibrium or transient equilibrium

Concept of rLCPE

Lateral charged particle loss

MC calculations, Seuntjens (2013)

Detector size relative to field size• Small field conditions exist when one of the

edges of the sensitive volume of a detector is less then a lateral charged particle equilibrium range (rLCPE) away from the edge of the field

(Li et al. 1995 Med Phys 22, 1167-1170)

rLCPE (in cm) = 5.973•TPR20,10 – 2.688

Slide courtesy: H. Palmans

Source occlusion

Large field conditionsSmall field conditions

(Figure courtesy M.M. Aspradakis et al, IPEM Report 103)

Overlapping of beam penumbras

Das et al. 2008 Med Phys 35: 206-15

definition of field

size is not unique

Detector-related small field condition

Based on criterion 1, one could claim that the GammaKnife18 or 14 mm diameter fields are not small (quasi point source + electron equilibrium length about 6 mm).

Meltsner et al., Med Phys 36:339 (2009)

Exradin A16 inner diameter

Exradin A16 outer diameter

Detector dependence of output factor

From Sanchez-Doblado et al. 2007 Phys Med 23:58-66

Measurements with small-field detectors

Sauer & WilbertMed Phys 34, 1983-88 (2007)IC = PTW 31010 (0.125 cm3)PiP = PTW 31006 (Pinpoint)

SES = size of equivalent square

Detector issues in small field dosimetry

• Energy dependence of the response• Perturbation effects

– Central electrode– Wall effects– Fact that cavity is different from water, fluence perturbation– Volume averaging

• These effects depend somewhat on the beam spot size

Dosimetry protocol values (e.g., TG-51) of these factors are applicable usually only in TCPE and only for the conditions:10 x 10 cm2; zref = 10 cm; SSD or SAD 100 cm

Detector issues in small field dosimetry

29

Stopping power ratio water to air

Eklund and Ahnesjö, Phys Med Biol 53:4231 (2008)Eklund and Ahnesjö, Phys Med Biol 53:4231 (2008)

Very small

effects!

0.5% effect

Role of different perturbation factors

080915

Crop et al., Phys Med Biol 54:2951 (2009)

PP31006 and PP31016 chambers

Magnitude of correction factors

080915

Crop et al., Phys Med Biol 54:2951 (2009)

8 mm x 8 mm field, 10 cm depth (0.6 mm, 2 mm spot sizes)

Very large effects!

Narrow 1.5 mm fieldRatio of dose-to-water to dose-

to-air averaged over cavity volume

Off-axis distance (mm)

Collecting electrode diameter: 1.5 mmSeparation: 1 mm

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

0 2 4 6 8

Dw/D

air

Stopping power ratio w/air

Paskalev, Seuntjens, Podgorsak (2002) AAPM Proc. Series 13, Med. Phys. Publishing, Madison, Wi, 298 – 318.

60%

A14P chamber

Summary of issues leading to dosimetricuncertainties in small fields

• Beam dependent issues– Beam focal spot size – Lateral disequilibrium– How do we measure beam quality in practice?

• Detector effects– There is no ideal detector– Volume averaging and fluence perturbation effects– Corrections depend on beam spot size

Small fields: upcoming guidelines, data and uncertainties

35

1. Clinical reference beam

2. Clinical small field

Med. Phys. 35 , 5179 (2008)

2 components:

36

0 0

,, , , , ,

msr refmsr msr

msr msr msr

f ff fwQ Q D wQ Q Q Q QD M N k k msrclin

msrclin

msr

msr

clin

clin

ffQQ

fQw

fQw DD ,

,,, Machine specific

reference field fmsrClinical field

fclin

Tomotherapy5 cm x 20 cm

REFERENCE DOSIMETRY RELATIVE DOSIMETRY

GammaKnifed = 1.6/1.8 cm

CyberKnife6 cm

Ionizationchamber

Broad beamreference field

fref

00 ,,, QQQwD kNHypothetical

reference field fref

micro MLC10 cm x 10 cm

refmsr

msr

ffQQk ,,

Radiosurgical collimatorsd = 1.8 cm

refmsr

msr

ffQQk ,,

msrclin

msrclinmsr

msr

clin

clinmsrclin

msrclin

ffQQf

Q

fQff

QQ kMM ,

,,,

37

Components of small field reference dosimetry

How to specify beam quality in small fields?

Sauer (2009) Med. Phys. 36: 4168

Data from BJR Suppl 25

Beam quality in small fieldse.g. for PDD10X(10) = %dd(10)X

11

110

10

2

10

110

10

ts

ts

ec

ecsPDDPDD

)()(

075100201026710751010

101010

101010 .)(,.)(.

.)(),()(

PDDPDDPDDPDD

PDD x

Palmans 2012 Med Phys 39 (9), 5514

55

60

65

70

75

80

85

2 4 6 8

s / cm

PDD

10(s

)

4 MV

10 MV

8 MV

6 MV

5 MV

25 MV

21 MV18 MV

15 MV

12 MV

(TG-51)

AAPM TG-148 (Langen et al. 2010 Med Phys 37:4817-53): “dd(10)x[HT-ref]”

Beam quality specifier for Tomotherapy

Correction factor data

• correction factors are small for the larger-field msr

Francescon et al: Phys. Med. Biol. 57 (2012) 3741–3758

Correction factor data (cont’d)

Correction factor data (cont’d)

• correction factors are small for the larger field msr

Volume averaging in FFF beams

Slide courtesy: H Palmans

A chamber of cavity length of 24 mm underestimates dose by 1.5 % in the6 cm field on Cyberknife!

Volume averaging in FFF beams

Pantelis et al. 2009 Med Phys 37:2369

Volume averaging in FFF beams

Slide courtesy: H Palmans

Components of small field output factors

Output factors

)1()2(

)2()2(

)1()1(

)2()1(

,

,,,

,,

clin

clin

clin

clin

msr

msr

clin

clin

clin

clin

msr

msr

msrclin

msrclin

msrclin

msrclin

fQrel

fQrel

fQ

fQ

fQ

fQ

ffQQ

ffQQ

MM

MM

MM

kk

msrclin

msrclinmsr

msr

clin

clin

msr

msr

msr

msr

clin

clin

clin

clin

msr

msr

clin

clin

msr

msr

clin

clinmsrclin

msrclin

ffQQf

Q

fQ

fQ

fQw

fQ

fQw

fQ

fQ

fQw

fQwff

QQ kMM

MDMD

MM

DD ,

,,

,

,

,,,

clin

clin

msr

msr

msr

msr

clin

clinmsrclin

msrclin fQ

fQ

fQw

fQwff

QQ MM

DD

k ,

,,,Where:

Output factors – example CyberKnife

0.600

0.650

0.700

0.750

0.800

0.850

0.900

0.950

1.000

1.050

0 5 10 15 20

diameter / mm

M /

M60

A16PinPointDiode 60008Diode 60012EDGEAlanineTLDEBT filmPolymer gel

0.950

1.000

1.050

1.100

1.150

1.200

1.250

1.300

0 5 10 15 20

diameter / mm

(M/M

60) 2/(

M/M

60) 1

PinPointDiode 60008Diode 60012EDGEAlanineTLDEBT f ilmPolymer gel

0.950

1.000

1.050

1.100

1.150

1.200

1.250

1.300

0 5 10 15 20

diameter / mm

ratio

of c

orre

ctio

n fa

ctor

s (M

C o

r vol

) PinPoint

Diode 60008

Diode 60012

EDGE

Alanine

)2()1(

, ,, ,

msr

clin

msr

clin

msr

clin

msr

clin

ff

QQ

ff

QQ

kk

0.85

0.90

0.95

1.00

1.05

1.10

1.15

Diode 60008

Diode 60012

EDGE

TLD

EBT film

Polymer gel

A16

Pin

Poi

nt

Dio

de 6

0008

Dio

de 6

0012

ED

GE

Ala

nine

TLD

EB

T fil

m

Pol

ymer

gel

0.50

0.55

0.60

0.65

0.70

0.75

detector

Mcl

in /

Mre

f

(Mclin / M

ref )* kclin,m

sr

ExrA16 PinPoint SHD USD EDGE alanine TLD EBT GEL

Pantelis et al. 2010 Med Phys37: 2369

Slide courtesy:H. Palmans

Experimental and MC studiesE.g. PTW-60012 unshielded diode in MLC collimated square fields

Experiment: Monte Carlo:

0.910

0.920

0.930

0.940

0.950

0.960

0.970

0.980

0.990

1.000

1.010

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

square field size / cm

corr

ectio

n fa

ctor

with

ref f

int

Griesbach et al 2005 Med Phys 32:3750 (rel. diamond)

Krauss 2008 - w w w (rel. LIC)

Ralston et al 2012 PMB 57:2587 (rel. PS / z = 5 cm, diode 1)

Ralston et al 2012 PMB 57:2587 (rel. PS / z = 5 cm, diode 2)

f it

Experimental Data for Table

0.930

0.940

0.950

0.960

0.970

0.980

0.990

1.000

1.010

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

square field size / cm

corr

ectio

n fa

ctor

with

ref f

int

f it

Monte Carlo Data for Table

Monte Carlo < Francescon et al. 2011 MedPhys 38:6513

Effect of different parameters on the correction factors

Parameters varied:1. Linac model2. Spot size FWHM3. Energy of the electron source4. Distance between exit window and target

P. Francescon, et al, Med. Phys. 38, 6513–6527 (2011).

Uncertainty in correction factor introduced due to field size definition

Cranmer Sargison et al Med. Phys. 38, 6592–6602 (2011) Benmakhlouf et al Med. Phys. 41, 041711 (2014)

Summary• Small field dosimetry is complex

– There are hefty perturbation effects that can have significant impact on reference dosimetry procedures and output factors

• Current good practice for reference and relative dosimetry in static small MV photon fields can be expressed as – Choice of suitably small detector which is known to minimally perturb

fluence– Careful experimental setup – Correct for volume averaging and energy dependence of detectors– Corroboration of data with peers and use of detectors of different design

• New protocol is upcoming– Machine-specific reference fields defined, corrections are small– Data on correction factors is being collected– Uncertainty analyses ongoing

The 1-sigma uncertainty on the realization of absorbed dose to water under reference conditions in broad photon beams, in the primary standards laboratory, is typically:

1%68%12%17%2% 1. 4%

2. 2%3. 1%4. 0.5%5. 0.1%

Correct answer: (4) 0.5%

Discussion: Uncertainties in absorbed dose to water standards vary slightly from primary laboratory to primary laboratory but all PSDLS arrive at typical values of around 0.5%. The uncertainty on calibrations in a clinical context vary anywhere from 0.9% to 2.1% in ideal versus more routine occasions, respectively.

Ref: for example, Seuntjens and Duane 2009 Photon Absorbed Dose Standards. Metrologia 46 S39. McEwen et al 2014 Med. Phys. 41 (4), 041501-1

A condition for radiation fields to be small for the purpose of reference dosimetry can generally be formulated as

6%

3%9%

76%

6% 1. Radiation fields with diameter of less than 3 cm

2. Radiation fields for which lateral charged particle equilibrium is lost whether the detector is absent or not;

3. Radiation fields for which the stopping power ratio, water-to-air, is drastically (> 3%) different from the value in TG-51 reference (10 x 10 cm2) fields;

4. Radiation fields for which the PSDL-traceable ionization chamber calibration coefficient is valid;

5. Radiation fields in which the absorbed dose to water cannot be measured accurately.

Correct answer: (2) Radiation fields for which lateral charged particle equilibrium is lost in absence or presence of the detector.

Discussion: Stopping power ratios do not vary significantly in small fields. PSDL traceable calibration coefficients in small fields do not (yet) exist. Absorbed dose can be measured accurately in small fields.

Ref: for example, Aspradakis et al, IPEM Report 103, Small field MV photon dosimetry

Indicate the single set of two largest contributors to correction factors and their uncertainties for commercial air-filled ionization chambers in small photon fields

3%

15%

77%

3%

2% 1. The stopping power ratio water to air and the central electrode effect

2. The stopping power ration water to air, and the chamber wall effect

3. The fluence perturbation effect and the volume averaging effect

4. The stopping power ratio, water to air, and the volume averaging effect

5. The ionization chamber wall effect and the stem effect

Correct answer: (3) The fluence perturbation effect and the volume averaging effect

Discussion: stopping power ratios are not very sensitive to changes in radiation beam size, nor are wall correction, central electrode corrections or stem effects. The large effects observed in small fields lie in volume averaging and fluence perturbation effects.

Ref: example: Crop et al 2009 Phys Med Biol 54(9). p.2951-2969

Reviews on small field dosimetry• R. Alfonso, P. Andreo, R. Capote, M. S. Huq, W. Kilby, P. Kjäll, T. R. Mackie, H.

Palmans, K. Rosser, J. Seuntjens, W. Ullrich, and S. Vatnitsky, “A new formalism for reference dosimetry of small and nonstandard fields,” Med. Phys. 35, 5179–5187 (2008).

• I. J. Das, G. X. Ding, and A. Ahnesjö, “Small fields: Nonequilibrium radiation dosimetry,” Med. Phys. 35, 206–215 (2008)

• M. Aspradakis, J. Byrne, H. Palmans, J. Conway, K. Rosser, J. Warrington, and S. Duane, “Small field MV photon dosimetry,” IPEM Report No. 103 (Institute of Physics and Engineering in Medicine, York, 2010).

• H Palmans (2011) CN-182-INV006, Small and composite field dosimetry: the problems and recent progress. IDOS Conference, Vienna.

Note: There is a literature explosion (since 2008) on the subject of small field dosimetryand correction factors. The reviews / reports above are not that recent! `

Acknowledgments• IAEA committee

– Palmans (Chair)– Andreo– Huq– Mackie – Ulrich– Kilby– Izewska– Capote– Alfonso– Seuntjens

• AAPM Committees– TG-178 (Goetsch et al)– TG-155 (Das et al)– WGDPCB (Seuntjens et al)

• ICRU Report Committee: Prescription, Recording and Reporting of Stereotactic Radiosurgery using small fields

– Seuntjens (Chair)– Lartigau (Co-chair)– Ding– Goetsch– Cora– Roberge– Nuyttens– Grégoire, Jones– Main commission

Dosimetric Uncertainties in Reference and Relative Dosimetry of

Small Fields

Jan Seuntjens, Ph.D., FAAPM, FCCPMMcGill University Health Centre

Canada