1

Dosimetry and beam calibration

Hugo Palmans1,2 and Stanislav Vatnitksy1

1 EBG MedAustron GmbH, Wiener Neustadt, Austria 2 National Physical Laboratory, Teddington, UK

2

Overview - Learning objectives

• What are potential primary standard instruments for proton dosimetry, how do they work specifically for protons.

• The principles of reference dosimetry using calibrated ionization chambers

• Dosimetry protocols and data

• Reference dosimetry of small and scanned beams

• Instruments for micro- and nano-dosimetry

3

Calorimetry

Radiation energy turns into heat

heat is tiny, but measurable – our primary standards for

absorbed dose are calorimeters

4

𝐷𝑚𝑒𝑑 = 𝑐𝑚𝑒𝑑∆𝑇

Calorimetry: principle

C

(j.kg-1.k-1)

T/D

(mk.Gy-1)

(m2.s-1)

water 4182 0.24 1.44x10-7

graphite 704 1.42 0.80x10-4

𝐷𝑚𝑒𝑑 = 𝑐𝑚𝑒𝑑∆𝑇1

1 − ℎΠ𝑘𝑖

𝜕𝑇

𝜕𝑡= 𝛼𝛻2𝑇 +

𝜕𝐷

𝑐𝜕𝑡

5

Water calorimeter – phantom & enclosure

Cooling fluid

Air 4ºC

Beam

6

Water calorimetry - heat conduction

Total

Field

Cylinder

Probe

photons protons

7

Water calorimetry - scanned protons

Sassowsky and Pedroni (2005) Phys Med Biol. 50:5381-400

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

time / s

tem

pera

ture

in

cre

as

e /

mK

heat source / arbitrary units

temperature increase

8

Water calorimetry - scanned protons

Gagnebin et al. (2010) Nucl Instrum Meth B 268:524-528

9

Water calorimeter – chemical heat defect

080915

H2O+ e

- H2O*

H3O+ e

-aq H• OH•

+ (10-7s)

H2 H2O2 OH-

(10-12 s)

10

Water calorimetry / chemical heat defect protons Experiment Simulations

H20/Ar

H20/H2

H20+NaCOOH/O2

0,0

1,0

2,0

3,0

LET (keV.mm-1)

G (

100 e

V-1

)

10-1 100 101 102

H+ OH•

e¯aq

H•

OH¯

H2

HO2

H2O2

60Co (100 MeV) (1MeV) protons

0,00

1,00

2,00

3,00

4,00

0,0 0,2 0,4 0,6 0,8 1,0 t (s)

G (

100eV

-1) (-) H2O

H2 H• H2O2

H+ OH• e-

aq

OH-

11

Water calorimetry / chemical heat defect protons

0.98

1.00

1.02

1.04

1.06

1.08

0 200 400 600

D acc / Gy

D ca

l / D ca

l , ss

0 200 400

H 2 O/H 2

H 2 O/ Ar

NaCOOH /O 2

85 MeV protons

60 Co

H 2 O/H 2

H 2 O/ Ar

0.98

1.00

1.02

1.04

1.06

1.08

0 200 400 600

D acc / Gy

D ca

l / D ca

l , ss

0 200 400

H 2 O/H 2

H 2 O/ Ar

NaCOOH /O 2

85 MeV protons

60 Co

H 2 O/H 2

H 2 O/ Ar

Palmans et al (1996) Med. Phys. 23:643-50

12

Water calorimetry / chemical heat defect ions

Brede et al. 2006 Phys. Med. Biol. 51:3667-82

-1

0

1

2

3

4

5

6

7

0 20 40 60 80 100 120 140

LET / keV mm-1

ch

em

ical

he

at

de

fec

t /

%

p d

He C

13

Chemical heat defect – scanned beams Sassowsky and Pedroni (2005) Phys Med Biol. 50:5381-400

14

Water calorimetry - uncertainty

080915

Seuntjens and Duane 2009 Metrologia 46:S39

15

Graphite calorimetry

080915

15

Beam

DC Dw

16

Palmans et al (2004) Phys Med Biol 49:3737

Graphite calorimetry

NPL primary standard level proton calorimeter under development:

Core

Inner jacket

Outer jacket

Annular PCB

Graphite vacuum body

17

Graphite calorimetry

Seuntjens and Duane (2009) Metrologia 46:S39-58

18

𝐷𝑚 =𝐸𝑚

𝑚𝑚 𝑘

𝐷𝑚 = 𝑐𝑝,𝑚 ∆𝑇 𝑘

Quasi-adiabatic mode

Isothermal mode

Graphite calorimetry – operation modes

19

Graphite – heat defect?

Schulz et al (1990) Phys. Med. Biol. 35:1563-74

graphite:

kHD = 1.004 ± 0.003

A150:

kHD = 1.042 ± 0.004

Dose conversion graphite calorimetry

0.60

0.70

0.80

0.90

1.00

1.10

1.20

0 50 100 150 200 250

proton energy / MeV

(L/

)w,g

or

(<E

>

/A)w

,g

Stopping power ratio

Total non-elastic absorption

Emitted protons

Emitted deuterons Emitted alpha particles

?

w

g

ggww

SzDzD

)()( kfl

w

g

ggww

SzDzD

)()(

21

Dose conversion graphite calorimetry – stopping power ratio

1.110

1.115

1.120

1.125

1.130

0.0 0.5 1.0 1.5 2.0 2.5 3.0

z w-eq / g cm-2

sw

,g

0.0 5.0 10.0 15.0 20.0 25.0

ICRU49

Geant4

Burns & Paul

22

Dose conversion graphite calorimetry – fluence correction factor

0.96

0.98

1.00

1.02

0.0 0.5 1.0 1.5 2.0 2.5 3.0

z w-eq / g cm-2

kfl

0.96

0.98

1.00

1.02

1.04

1.06

0.0 5.0 10.0 15.0 20.0 25.0

60 MeV

200 MeV

23

Step aside – kfl other low-Z materials

Geant4 simulations

24

Graphite calorimetry – heat transfer within core

24

0.0

0.5

1.0

1.5

2.0

2.5

3.0

100 110 120 130 140

tem

peratu

re r

ise /

mK

time / s

thermistor

1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

100 110 120 130 140

tem

peratu

re r

ise /

mK

time / s

thermistor

1

1.0

1.2

1.4

1.6

1.8

2.0

104 105 106 107 108

tem

peratu

re r

ise /

mK

time / s

thermistor

1thermistor

2

1.0

1.2

1.4

1.6

1.8

2.0

104 105 106 107 108

tem

peratu

re r

ise /

mK

time / s

thermistor 1

thermistor 2

25

Graphite calorimetry – uncertainty Seuntjens and Duane 2009 Metrologia 46:S39

sw,air 1.0

kfl 0.5

Dw 1.2

(remember water calorimetry: 0.4%)

26

Absolute dosimetry – Fluence based methods

N protons A

med

med

S

A

N D

27

Absolute dosimetry – Faraday cup

guard

collecting electrode housing entrance window

winding

N protons

(e.g. Pedroni et al 2005, Phys Med Biol 50:541-61, Grusell et al 1995, Phys Med Biol 40:1831-40)

B

28

Absolute dosimetry – Activation measurement

12C(p,pn)11C reaction

4p bg-coincidence counting

(Nichoporov 2003, Med Phys 30:972-8)

29

Graphite calorimetry – dose-area-product

Large area ion chamber: pdd(z)

Faraday cup: N/MU

S/ρ: DAP(z0 or zref)

Integrate lateral dose profiles over all spots

Calorimeter: DAP(zref)

30

Dose determination with ion chamber

Q: charge produced in the air of the chamber W: mean energy required to produce an ion-pair in air Unfortunately, for commercially available chambers, the volume V is not known with the necessary accuracy (would otherwise be a primary standard!). We have to rely on methods other than “first principles”, which involve the use of ion chamber calibration factors (courtesy Pedro Andreo)

p s D D air w, air w

Wair m

Q D

air

air Wair

V

Q

air

31

Simple absorbed dose protocol

𝐷𝑤,𝑄 = 𝑀𝑄𝑁𝐷,𝑤,𝑄

But we have 𝑁𝐷,𝑤,𝑄0with 𝑄0 ≠ 𝑄 →

𝐷𝑤,𝑄 = 𝑀𝑄𝑁𝐷,𝑤,𝑄0𝑘𝑄,𝑄0

This is formalism of IAEA TRS-398 and ICRU Report 78

32

Derivation 𝑘𝑄,𝑄0

𝐷𝑤,𝑄0 = 𝐷𝑎𝑖𝑟,𝑄0 𝑠𝑤,𝑎𝑖𝑟 𝑄0𝑝𝑄0

𝐷𝑤,𝑄 = 𝐷𝑎𝑖𝑟,𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄

𝑝𝑄

33

Derivation 𝑘𝑄,𝑄0

𝐷𝑤,𝑄0 = 𝐷𝑎𝑖𝑟,𝑄0 𝑠𝑤,𝑎𝑖𝑟 𝑄0𝑝𝑄0

𝐷𝑤,𝑄 = 𝐷𝑎𝑖𝑟,𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄

𝑝𝑄

𝐷𝑤,𝑄0 = 𝑀𝑄0𝑁𝐷,𝑎𝑖𝑟,𝑄0 𝑠𝑤,𝑎𝑖𝑟 𝑄0𝑝𝑄0 with 𝑁𝐷,𝑎𝑖𝑟,𝑄0 =

𝑊𝑎𝑖𝑟 𝑄0

𝜌𝑎𝑖𝑟𝑉

𝐷𝑤,𝑄 = 𝑀𝑄𝑁𝐷,𝑎𝑖𝑟,𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄𝑝𝑄 with 𝑁𝐷,𝑎𝑖𝑟,𝑄 =

𝑊𝑎𝑖𝑟 𝑄

𝜌𝑎𝑖𝑟𝑉

𝑘𝑄,𝑄0 =𝑁𝐷,𝑤,𝑄

𝑁𝐷,𝑤,𝑄0=

𝐷𝑤,𝑄 𝑀𝑄

𝐷𝑤,𝑄0 𝑀𝑄0

=𝑁𝐷,𝑎𝑖𝑟,𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄

𝑝𝑄

𝑁𝐷,𝑎𝑖𝑟,𝑄0 𝑠𝑤,𝑎𝑖𝑟 𝑄0𝑝𝑄0

𝑘𝑄,𝑄0 =𝑊𝑎𝑖𝑟 𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄

𝑝𝑄

𝑊𝑎𝑖𝑟 𝑄0 𝑠𝑤,𝑎𝑖𝑟 𝑄0𝑝𝑄0

𝑁𝐷,𝑎𝑖𝑟,𝑄0 =𝑁𝐷,𝑤,𝑄0

𝑠𝑤,𝑎𝑖𝑟 𝑄0𝑝𝑄0

note that in AAPM notation 𝑠𝑤,𝑎𝑖𝑟 =𝐿

𝜌 𝑎𝑖𝑟

𝑤

34

Factorisation

𝐷𝑤,𝑄 = 𝑀𝑄

1

𝜌𝑎𝑖𝑟𝑉𝑐𝑎𝑣𝑊𝑎𝑖𝑟 𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄

𝑝𝑄

Helpful to compare codes of practice:

e.g. TRS-398: 1

𝜌air𝑉cav=

𝑁𝐷,𝑤,𝑄0𝑊air 𝑄0 𝑠𝑤,air 𝑄0

𝑝𝑄0

ICRU 59: 1

𝜌air𝑉cav=

𝑁𝐾(1−𝑔)𝐴wall𝐴ion

𝑊air 𝑐𝑠wall,𝑔 𝜇en 𝜌 air,wall𝐾hum

35

Wair / protons

TRS-398

36

Wair / protons

TRS-398

37

Ion chambers : water to air stopping power ratio

1.125

1.130

1.135

1.140

1.145

1.150

1.155

1.160

0 50 100 150 200 250

Eeff (MeV)

(S/

) air

Janni (1982)

ICRU report 49 (1993)

Medin and Andreo (1997)

w

38

Ion chambers – perturbation correction factors for proton beams

Overall perturbation correction factor

pQ = 1 assumed in IAEA TRS-398 and ICRU 78

Gradient correction factors

pdis = 1 assumed in SOBP or plateau

Secondary electron correction factors

ignored in IAEA TRS-398 and ICRU 78

39

Gradient corrections for cylindrical ionization chambers

Palmans 2001, Phys Med Biol. 46:1187-1204

40

Ion chambers – cavity theory for pcav protons

SA d-electrons

med

air

air med

S D D

med

air

air

S D

cav,e p

med

air

med

air

e cav

S S p

SA

,

41

Compared with Medin and Andreo (1997)

0.998

1.000

1.002

1.004

1.006

1.008

0.5 1.0 1.5 2.0 2.5

log(E eff )

p ca

v o

r s

w,a

ir

cavity model monoE

Medin and Andreo (1997)

plateau

0.97.z 0

42

Ion chambers – cavity theory for pwall d-electrons SA

protons

(cfr. Nahum, in Dosimetry in Radiotherapy. Vienna: IAEA, 1988: for electron beams.)

med

air

air med

S D D

med

wall

S wall

med

air

air

S D

wall,e p

SA

med

air

wall

air

wall,e p S

SA

med

wall

S S

SA

43

Secondary electron -> pwall and pcel

Palmans 2011, IDOS

44

Ionization chamber perturbations

0.995

1.000

1.005

1.010

1.015

1.020

0 5 10 15

Chamber #

D

w,N

E2

57

1

/D

w

,Ch

C-C &PTW30002

A150-Al &NE2581

PMMA-Al &PTW30001

Nylon66-Al

IC18

ExrT2

45

In summary: 𝑘𝑄,𝑄0 – 𝑄0 is 60Co

Palmans 2012, Dosimetry, In: Proton Therapy Physics / Paganetti

46

In summary: 𝑘𝑄,𝑄0 – 𝑄0 is a proton beam

for ALL chambers !!!

47

Influence quantities

Pressure, temperature, humidity

Polarity effects

Ion recombination

48

Initial recombination

E

49

Volume recombination

50

Volume recombination – continuous radiation – plane-parallel chamber

-> 2-voltage: quadratic

𝑘𝑠 =

𝑉1𝑉2

2−1

𝑉1𝑉2

2−𝑀1𝑀2

+ -

0 x d

dx

+ -

0 x d

dx

𝑘𝑠 = 1 +𝑚2𝑔

𝑉2𝑖𝑠𝑎𝑡

51

Volume recombination – pulsed radiation – plane-parallel chamber

-> 2-voltage: linear

k+V/d

k–V/d

t=T1

k+V/d

k–V/d

t=T2

k+V/d

k–V/d

t=T3

k+V/d

k–V/d

t=T

0 d

t=0

- +

𝑘𝑠 =𝑢

𝑙𝑛 1 + 𝑢

≈ 1 +𝑢

2

𝑢 =𝛼

𝑒 𝑘− + 𝑘+𝑟𝑑2

𝑉

52

Ion recombination in ionization chambers

0.0

0.1

0.2

0.3

0.4

0.0 0.2 0.4 0.6 0.8 1.0

Time (in 1/8 revolutions)

Do

se

ra

te (

Gy s

-1)

surface

z = 23 mmz = 20 mm

z = 10 mm

1.000

1.010

1.020

1.030

1.040

1.050

1.060

1.070

1.080

0.0 1.0 2.0 3.0

IV or IV,eff (nA)

I V/I

V/n

(d)

0.998

1.000

1.002

1.004

1.006

1.008

1.010

1.012

1.014

1.016

1.018

Equ

ation

(1)

Pulse

d (B

oag)

Mar

kus 1

Mar

kus 2

pio

n

53

Ion recombination for time-dependent spatial ionisation distribution in cavity

Similar as for IMRT deliveries [4], in the near saturation regime:

𝑝𝑖𝑜𝑛 =𝑖𝑠𝑎𝑡𝑖𝑉

≈ 1 +𝐴

𝑉+𝐵

𝑉2 𝜆 𝑠𝑎𝑡

2𝑧, 𝑡 𝑑𝑧𝑑𝑡

𝜆 𝑠𝑎𝑡 𝑧, 𝑡 𝑑𝑧𝑑𝑡

where V is the polarizing voltage, 𝜆 𝑠𝑎𝑡 𝑧 is the linear ionization rate density, A is an initial recombination parameter and B a volume recombination parameter.

54

Cumulative recombination patterns and voltage-dependence continuous

pulsed

250 μs pulse

55

Volume recombination vs pulse length

56

Volume recombination vs pulse length

57

Volume recombination vs pulse length

𝑘𝑖𝑜𝑛 = 1 + 𝑎𝑉𝑒𝑥𝑝 −0.0023𝑇𝑝𝑢𝑙𝑠𝑒

𝑉2

58

Beam monitor calibration of scanned beams

59

Reference dosimetry scanned beams

Gillin et al 2010

Med Phys 37:154

𝐷𝐴𝑃𝑤,𝑄𝐵𝑃 =𝑀𝑄

𝐵𝑃𝑁𝐷𝐴𝑃,𝑤,𝑄0𝐵𝑃 κ𝑄,𝑄0

𝐵𝑃

𝑁=𝐷𝐴𝑃𝑤,𝑄

∞ (𝑆 ρ )𝑤

=𝐷𝐴𝑃𝑤,𝑄

𝐵𝑃 (𝑆 ρ )𝑤

× 𝐶𝐹

60

Reference dosimetry scanned beams

Gillin et al 2010

Med Phys 37:154

𝐷𝐴𝑃𝑤,𝑄𝐵𝑃 =𝑀𝑄

𝐵𝑃𝑁𝐷𝐴𝑃,𝑤,𝑄0𝐵𝑃 κ𝑄,𝑄0

𝐵𝑃

𝑁=𝐷𝐴𝑃𝑤,𝑄

∞ (𝑆 ρ )𝑤

=𝐷𝐴𝑃𝑤,𝑄

𝐵𝑃 (𝑆 ρ )𝑤

× 𝐶𝐹

61

Large-area chamber – cross calibration

𝑁DAP,𝑤,𝑄cross =𝑀𝑄cross𝑁𝐷,𝑤,𝑄0𝑘𝑄cross,𝑄0 REF

𝑀𝑄cross BP

× OAR 𝑥, 𝑦 𝑑𝑥𝑑𝑦

𝐴

62

Calculation κ𝑄,𝑄0

κ𝑄,𝑄0 =𝑊𝑎𝑖𝑟 𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄

𝑝𝑄

𝑊𝑎𝑖𝑟 𝑄0 𝑠𝑤,𝑎𝑖𝑟 𝑄0𝑝𝑄0

Main problem is 𝑝𝑄0

Same assumptions for photon and electrons as pp chambers

63

Reference dosimetry scanned beams

Jaekel et al Phys Med

Biol2004

ΔX

ΔY

𝐷𝑤,𝑄𝑐𝑦𝑙

=𝑀𝑄𝑐𝑦𝑙𝑁𝐷,𝑤,𝑄0𝑐𝑦𝑙

𝑘𝑄,𝑄0𝑐𝑦𝑙

𝑁=𝐷𝑤,𝑄𝑐𝑦𝑙ΔXΔY

(𝑆 ρ )𝑤

64

Uncertainty of DAPw determination Contribution BP xcal in 60Co BP xcal in 200

MeVp

FA cal in

60Co

𝑁𝐷,𝑤,𝑄0𝐹𝐴 0.55 0.55 0.55

𝑘𝑄,𝑄0𝐹𝐴 1.70

uniformity ∆𝑥∆𝑦 0.50

𝑘𝑄𝑐𝑟𝑜𝑠𝑠,𝑄0𝐹𝐴 1.70

𝜅𝑄,𝑄𝑐𝑟𝑜𝑠𝑠𝐵𝑃 1.60 0.10

𝑘𝑖𝑜𝑛 𝑄𝐹𝐴 0.50

𝐷𝐴𝑃𝑤,𝑄∞ 1.7-1.8 1.8-1.9 2.0

𝑆 𝜌 𝑤 2.0 2.0 2.0

𝑁 =𝐷𝐴𝑃𝑤,𝑄

∞

𝑆 𝜌 𝑤

2.6-2.7 2.7 2.8

Microdosimetry

66

Mini-TEPC

about 3mm

Davide Moro, INFN-LNL

Cathode (A-150 plastic)

Rexolite®

Sensitive Volume: 0.9x0.9 mm2

Gas Out

Gas In

Aluminium

Rollet et al 2010, Rad Prot Dosim 143:445

62 MeVp

67

Si-microtelescope

500 µm 14 µm

9 µm

E stage

Guard~2 μm

∆E element

500 µm 14 µm

9 µm

E stage

Guard~2 μm

∆E element

Andrea Pola, Politecnico di Milano

1 10 100 10000.0

0.2

0.4

0.6

0.8

1.0

silicon telescope 21.8 mm

cylindrical TEPC 22 mm

(threshold)

cylindrical TEPC 22 mm

(no threshold)

y d

(y)

y (keV mm-1)

62 MeVp distal edge

Agosteo et al 2010 Radiat Meas 45:1284

68

Microcalorimetry

Sebastian Galer PhD: Hao et al 2003 IEEE TAS

13:622-5:

103

102

101

100

10-

1

10-

2

10-

3

10-

4

Nanodosimetry

70

Ion counter Shchemelinin et al 1997 In: Proc MicroDos 12 PTB: Hilgers et al Rad Prot Dosim 126:467 LLU: Schulte et al 2008 Z Med Phys 18:286

71

Schulte et al 2011 AIP Conf Proc 1345:249

72

Jet Counter Bantsar et al 2004 Rad Prot Dosim 110:845 Schulte et al 2011 AIP Conf Proc 1345:249

73

StarTrack - INFN

Conte et al 2010, Radiat Meas 45:1213

74

Conclusions – take home messages • Calorimeters and calibrated ionization chambers

established for proton beam reference dosimetry; main uncertainties:

-water calorimetry: heat defect

- graphite calorimetry: conversion 𝐷𝑔 → 𝐷𝑤

- ionometry: product 𝑊𝑎𝑖𝑟 𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄 + 60Co data

• Factorisation 𝐷𝑤,𝑄 = 𝑀𝑄1

𝜌𝑎𝑖𝑟𝑉𝑐𝑎𝑣𝑊𝑎𝑖𝑟 𝑄 𝑠𝑤,𝑎𝑖𝑟 𝑄

𝑝𝑄

allows easy comparison between codes of practice

• Advantage of calibrations in proton beams

• Issues scanned beams (DAP vs N, ion recombination)

• Some examples microdosimetry&nanodosimety instruments

75

Reading

C. P. Karger, O. Jäkel, H. Palmans and T. Kanai, “Dosimetry for Ion Beam Radiotherapy,” Phys. Med. Biol. 55(21) R193-R234, 2010

H. Palmans, A. Kacperek and O. Jäkel, “Hadron dosimetry” In: Clinical Dosimetry Measurements in Radiotherapy (AAPM 2009 Summer School), Ed. D. W. O. Rogers and J. Cygler, (Madison WI, USA: Medical Physics Publishing), 2009, pp. 669-722

H. Palmans, “Dosimetry,” In: Proton Therapy Physics, Ed. H. Paganetti (London: Taylor & Francis), 2011, pp. 191-219

H. Palmans, “Monte Carlo for proton and ion beam dosimetry,” In: Monte Carlo Applications in Radiation Therapy, Ed. F. Verhaegen and J Seco, (London: Taylor & Francis), 2013, pp. 185-199