1

Chapter 8 Measurement of Absorbed Dose

The most direct measurement of radiation dose in a medium is to measure the heat generated in the medium due to the radiation. But the temperature increase in the medium is generally very small, making this type of measurement very difficult.

2

Commonly used dosimeters

• Ionization chambers.

• cylindrical: photons, high-energy electrons (>10 MeV)

• parallel plate (plane parallel): low energy electrons (<10 MeV)

• Diodes.

• Thermo luminescent dosimeters (chips, powders).

• Film, radiochromic film.

3

Ionization Chamber

An ion chamber is a volume of air (cavity), usually surrounded by a layer of material (chamber wall) just thick enough to provide electron equilibrium. The electrons generated in the wall enter the cavity, causing ionization. The ions produced in the air cavity are collected and read out through an electrometer.An ion chamber may be sealed (used in machines as monitor chamber) or unsealed (used for routine calibrations).There are 2 major designs of unsealed ion chambers, cylindrical and parallel-plate.

wall

air cavity

electrodeelectrode

air cavity wall

4

8.1 Radiation Absorbed Dose

Exposure: applicable only to photon beams, in air, E < 3 MeVAbsorbed dose is defined for all types of radiation (charged,

uncharged particles); all materials; and all energies.Dose is defined as the mean energy imparted by ionizing radiation to a given material per unit mass.

dm

ddose

Old unit: 1 rad = 100 ergs/g = 10-2 J/kg New unit: 1 Gy = 1 J/kg = 100 rad, or 1 cGy = 1 rad

5

8.2-A Relationship Between KERMA, Exposure, and Absorbed Dose (KERMA)

KERMA (K) (kinetic energy released in the medium) is defined as dEtr/dm, where dEtr is the sum of the kinetic energies of all the charged particles liberated by the neutral particles (photons) in a material of mass dm.

trK

K = Kcol + Krad

Kcol is the part of the energy loss due to collision with the atoms, resulting in ionization and excitation.

Krad is the part of energy loss in producing bremsstrahlung photons.

)1()1(

g

gggK enentrtr

6

Energy Transfer and Energy Absorption

The transfer of energies from a photon beam to the medium is a two-step process: (1) The photon interacts with the atom, causing one or more electrons ejected from the atom. All or part of the photon energy is transferred to the electron(s). (2) the kinetic energy the ejected electron(s) is absorbed by the medium through ionization and excitation (excluding the bremsstrahlung photons produced by these electrons).

hv’

hv

e-

hv’’

ray

7

Energy Transfer Coefficients

Energy transfer coefficient: (cm-1)

is the average energy transferred into the kinetic energy of the charged particles per interaction, hv is the original photon energy.

tr is the fraction of energy transferred per unit pathlength traversed by the photon.

Mass Energy transfer coefficient: tr/ (cm2/g)

h

Etrtr

trE

8

KERMAKERMA (Kinetic Energy Released in the Medium). It occurs at a point. K = <dEtr>/dm, where <dEtr> is the average kinetic energy transferred from photons to electrons in a volume element whose mass is dm.

hv’

hv

e-

photo-electron

hv

K L

dEtr= hv- hv’hv- Bk dEtr hv

Compton scattering Photo-electric effect

9

trEK

is the photon fluence (# photons /cm2),

is the linear attenuation coefficient: number of collisions per unit pathlength (cm), per incident photon (# collisions/photon/cm).

is the number of collisions per unit volume (# collisions /cm3).

Etr is the average kinetic energy transferred to the electron(s) per collision, (MeV/collision).

Etr is the amount of kinetic energy transferred per unit volume (MeV/cm3).

Etr is the amount of kinetic energy transferred per unit mass (MeV/g or J/kg or Gy).

10

trtr

tr hEK

trtr/hthe fractional energy transferred per unit pathlength (/cm).

= h, energy fluence (MeV/cm2).

tris the energy transferred per unit volume (MeV/cm3).

tris the energy transferred per unit mass (MeV/g or J/kg or Gy)

11

For a spectrum of photon energies, the KERMA is defined as:

dEEEE

EK tr

E)(

)()(

max

0

Example: A beam of 10 MeV photons with fluence of 1014/m2 is incident on a small block of carbon. Calculate the Kerma:

Given () = 0.00196 m2/kg and Etr = 7.30 MeV

K = 1014 (/m2) x 0.00196 (m2/kg) x 7.30 MeV

= 1.43x1012 (MeV/kg)

= 1.43x1012 (MeV/kg) x 1.602x10-13 (J/MeV)

= 0.229 J/kg = 0.229 Gy

12

DOSE

Energy is transferred to electron(s) at the point of collision, but not all of it is retained in the medium; some of it radiated away as bremsstrahlung. The absorbed dose is the energy actually deposited in the medium along the electron track.

KERMA (at a point) and energy deposition (over a distance) do not take place at the same location.

hv’

hv0

e-

hv’’

Kc (collision kerma)

r (radiative kerma)

cr

13

Energy Absorption Coefficient

Energy absorption coefficient: en = tr (1-g) (cm-1)

‘g’ is the fraction of the energy of secondary charged particles that is lost to bremsstrahlung in the material.

Thus, en represents the fractional energy absorbed locally in the material.

Mass Energy absorption coefficient: en/ (cm2/g)

In soft tissues (low Z materials), g 0. Thus, en tr .

Sometimes ab is used instead of en.

14

The absorbed dose is defined as D = <dEab>/dm.

<dEab> is the mean energy imparted by the electrons to a mass dm of the medium.

The absorbed dose is also defined at a point, including all electron tracks coming in and going out of a small volume dV (containing mass dm) at that point.

The unit for the dose is Gray: 1 Gray = 1 J/kg1 Gy = 100 cGy = 100 rad (old unit, has been phased out).

dV

dm

15

hv1

hv0

e-hv2

’’

Vm

K = T / m = (hv0 -hv1) / m

D = (T-T’-hv2) / m

Example: Kerma and Dose as a result of a Compton scattering

T = initial kinetic energy of the electron

T’ = kinetic energy of the electron when crossing the boundary of volume V

17

hv0

e- hv=0.511 MeV

Vm

K = (T1+T2) / m = (hv0-1.022 MeV) / m

D = (T1+T2) / m

Example: Kerma and Dose involving pair production and annihilation

e+

hv=0.511 MeV

18

8.2-B Relationship Between KERMA and Exposure

eW

KX aircol

eW

Xair

enair

e

W is the amount of energy required to produce 1 ion pair in air, 33.97 eV/ion-pair, or 33.97 J/C.

Exposure defined as ionization produced in air, applicable to photons up to 3 MeV only.

19

Exposure is defined (only for photons in air) as: X = dQ/dm, where

dQ is the total charge of the ions of either sign produced in air when all of the electrons liberated by photons in a volume element of air having a mass dm are completely stopped in air.

The unit of exposure is the roentgen (R), defined as the exposure to produce 1 esu of charge in 1 cm3 of air under STP.

1 R = 1 esu / 1 cm3 of air under STP = 3.3310-10 C / 0.001293 g of air = 2.5810-4 C / kg of air

hv’

hv0

e-

hv’’

X

dQ = charges produced along the track

air

dm

20

eWair is the mean energy expended in air to produce one ion

pair, ~34 eV/ion-pair, or 34 J/C.

34/,

airceW

airc KKX air

eairW

airEen

RmRm

J

RmJ

RmJ

kgJR

kgJ

kgm

airmJ

photonsJh

X

X en

2

2

22

2

2

1313

/00876.01

1096.110602.1

14.3

14.300279.0

00876.0

00279.0)(

Example: calculate the energy fluence and photon fluence per R for h = 1 MeV. Given enair = 0.0279 m2/kg.

1 R = 2.5810-4 C/kg of air = 2.5810-4 C/kg of air (34 J/C)

= 0.00876 J/kg of air

21

depth

Ker

ma

or d

ose

Relationship between Kerma and Dose(no attenuation of the photon beam)

trEK

Electron track

dose

kerma

Buildup region

equilibrium region

dose

22

depth

Ker

ma

or d

ose

Relationship between Kerma and Dose(with attenuation of the photon beam)

trEK

dose

Buildup region

transient equilibrium region

kerma

dose

Electron track

700800

9001000

23

8.2-C Relationship Between KERMA and Absorbed Dose

<1>1

KERMADose

depth

Abs

orbe

d do

se a

nd K

erm

a

= D/Kcol = 1

Under (transient) electron equilibrium conditions, depends on the beam energy, not material. For Co-60, =1.005

Buildup region

(Transient) equilibrium

region

enD

cep

24

8.3 Calculation of Absorbed Dose from Exposure (A- absorbed dose to air)

Under conditions of electron equilibrium:

e

WXKD air

colair

Dair(J/kg) = X(R) • 2.5810-4 (C/kg/R) • 33.97 (J/C)

Dair(cGy) = 0.876 (cGy/R) • X(R)

1 roentgen (R) of exposure produces 2.58×10-4 coulombs of charges per Kg of air.

roentgen-to-rad conversion factor for air

25

8.3 Calculation of Absorbed Dose from Exposure (B- absorbed dose to any medium)

medenmedmedD Under conditions of charged particle equilibrium:

airmed

airen

meden

airenair

medenmed

air

med AwhereAD

D

,

AXf

AX

Ae

WXD

med

airen

meden

airen

medenairmed

876.0

fmed (f-factor) is the roentgen-to-rad conversion factor (dose-to-air to dose-to-medium conversion). It is a function of the material composition and photon energy.

26

8.3 Calculation of Absorbed Dose from Exposure (C- dose calibration with ion chamber in air)

air air

P P

For megavoltage beams, build-up cap is needed to provide electron equilibrium

M X=M•Nx

M is the corrected reading

Nx is the exposure calibration factor for the given chamber for the same beam

quality

air

P

Dfs= ftissue• X•Aeq

Equilibrium mass of tissue

ftissue is the f-factor (exposure-to-dose

conversion factor) for tissue Aeq =Ψtissue/Ψair

27

8.3 Calculation of Absorbed Dose from Exposure (D- dose measurement from exposure with ion chamber in a medium)

P PP

chamber with build-up cap

M X=M•Nx Dmed= fmed• X•Am

medium

Air cavity

ΨbΨc Ψm

Am =Ψm/Ψc

m

med

air

enxmed A

e

WNMD

28

8.4 The Bragg-Gray Cavity Theory (how to convert dose-to-cavity-air to dose-to-medium)

0

0

00

0

0

00 )(

)()(

)()()( E

E

EE

dEE

dEESE

dEEdEESED

(# e-/cm2)

S(energy loss/cm)

S (energy loss/cm3)

is the electron fluence at the point of measurement,

is the mass collision stopping power averaged

over the electron energy spectrum

S

E0 is the maximum electron energy

S

D

29

8.4 The Bragg-Gray Cavity Theory (how to convert dose-to-cavity-air to dose-to-medium)

med

g

gmed

g

med

g

med S

e

WJDor

S

S

D

D

med

med

SD

medium

×

cavity removed, assuming not affected

e

WJ

SD g

g

g

medium

gas

×

Jg is charge produced per unit mass of air

30

Bragg-Gray Conditions

1. The cavity is so small that it does not perturb the electron fluence, i.e. Φ is not changed

2. Absorbed dose (energy) deposited in the cavity is entirely due to electrons crossing it, i.e., no electrons produced nor lost in the cavity.

Φ

A B

Electron fluence Φ is continuous and unchanged across the boundary between A and B, since nothing is produced nor lost at the interface

Φ

A B

The condition remains true if a slab of ‘vacuum’ is sandwiched between A and B, since no interaction takes place inside the vacuum.

vacu

um Φ

A B

air

The situation is no longer true for a slab of ‘air’- low energy electrons are stopped in and high energy -rays produced in and escaped from the slab

31

8.4 The Bragg-Gray Cavity Theory (A- Stopping power, the Spencer-Attix formulation)

med

g

gmed

L

e

WJD

0

0

)(

)()(

E

E

dEE

dEEL

EL

To exclude low-energy electrons (E<) that enter and then stop in the cavity

is the electron energy required to cross the cavity, typically ~10 kev)

L is the restricted mass collision stopping power with as the cutoff energy

To exclude high-energy -rays (E>) that are produced and then escape from the cavity

32

8.4 The Bragg-Gray Cavity Theory (B-chamber volume)

If chamber volume V is known, then Jg can be obtained from:

V

QJ g

where Q is the charge produced, is the density of (cavity) air

But V cannot be accurately measured directly.

However, it can be indirectly determined from the chamber exposure calibration factor Nx.

33

air

P

mass of wall material

wall

aircav

wall

airairchamwall

LDD

8.4 The Bragg-Gray Cavity Theory (B-chamber volume)

Electron fluence ratio

Bragg-Gray theory

wall

aircav

wall

airairchamwall

LDD

transient electron equilibrium exists

air

P

chamber with wall & buildup cap

e

WJD air

aircham

Jair= charge produced per unit mass in air in chamber volume

air

P

air

wallcham

air

wall

enwallair DD

34

8.4 The Bragg-Gray Cavity Theory (B-chamber volume)

Combining the equations for Dcham-air, Dwall, and Dair, we have:

air

wallchamwall

aircav

air

wall

en

wall

air

airair

L

e

WJD

Dair can also be measured with a chamber with an exposure calibration factor NX:

airionxionair e

WkANPMD

chamber reading corrected for recombination

chamber exposure calibration factor corrected for recombination

exposure (R)2.58x10-4 C/kg/R

33.97 J/C

Converts from kerma to dose

35

wall

wall

air

en

air

wall

wallionxionair AL

kANPMJ

8.4 The Bragg-Gray Cavity Theory (B-chamber volume)

Combining the two previous equations for Dair, we have:

wall

airchamair

wallcav

wall

air

en

air

wall

wallionxionair

LkANPMJ

Awall = change of photon energy fluence due to the wall and buildup cap

A

wall

cap

air

en

air

cap

wall

air

en

air

wall

wallionxionair

ALL

kANPMJ

1

wall and buildup cap made of different materials, is the fraction of electrons generated in wall

36

8.4 The Bragg-Gray Cavity Theory (B-chamber volume)

Jair is the charge produced per unit mass of air in the chamber:

cair

ionair V

PMJ

where air = density of air,

Vc = chamber volume

wallwallionxairc AAANk

V

1

Combining the two equations above, we have the relationship between Vc and Nx:

wallwallionxionair AAkANPMJ From the previous slide:

37

8.4 The Bragg-Gray Cavity Theory (C- effective point of measurement)

Effective point of measurement

For parallel plate chambers, the effective point of measurement is at the inner face of the front plate

Effective point of measurement

For cylindrical chambers, the effective point of measurement is displaced 0.85r from the center

0.85r

38

8.4 The Bragg-Gray Cavity Theory (C- effective point of measurement)

d

ds

2/

0

2/

0

cos2

cos2

dsx

dsxxxeff

xr

2x

cosrx Xeff = 8r/3= 0.85r

Area perpendicular to electron fluence

Number of electrons entering the circle through ds

Tracklength of each electron entering through ds amount of ionization produced

Total amount of ionization produced due to electrons entering through ds

41

Ngas = Dair / Q

where Dair is the dose to the chamber cavity air, Q is the charge produced in the cavity, or

Ngas = Dair / (M P‧ ion)

where M is the collected charge (or meter reading), corrected for recombination loss Pion.

8.5 Calibration of Megavoltage Beams: TG-21 Protocol (A. Cavity-Gas Calibration Factor)

The cavity-gas calibration factor Ngas, is defined as the absorbed dose to the cavity gas per unit charge produced in the cavity. It has a unit of Gy/C.

Co-60

M

chamber with wall & buildup cap

CGy

mVVm

Q

QQ

DN

ccair

eW

eW

airgas /

)(

379.2813

Ngas is unique to each ionization chamber, determined entirely by its cavity volume.

3197.1

97.33

mkg

CJeW

air

42

8.5 Calibration of Megavoltage Beams: TG-21 Protocol (A. Cavity-Gas Calibration Factor)

Conversion from Nx to Ngas:

andPM

eWJ

PM

DN

ion

air

ion

airgas ,

wall

cap

air

en

air

cap

wall

air

en

air

wall

wallionxionair

ALL

kANPMJ

1

wall

cap

air

en

air

cap

wall

air

en

air

wall

wallionxgas

ALL

eWkANN

1

43

8.5 Calibration of Megavoltage Beams: TG-21 Protocol (B. Chamber as a Bragg-Gray Cavity) Conversion from Dose-to-air to Dose-to-medium

Dair

gasionair NPMD

Dwall

repl

wall

air

airwall PL

DD

Dmed

x

wall

med

wall

wallmed PL

DD

replwall

med

air

airmed PPL

DD

medium wall

44

Dair Dmed

x

Thin-wall approximation

Dair

med

ium

wall

air

LairairD

med

LmedmedD

airL

air

medL

med

air

med

DD

Thick-wall approximation

Dair Dwall

x wall

air

wall

airL

DD

cavair

wall

medmedmed

CPE

medenD

wallwallwall

CPE

wallenD

med

wall

med

wallchambwall

med en

D

D

med

air

L

med

aircavmedair

45

Dair(med)Dmed

medium

wall

Dair(wall)

x

From the previous slide: Thin-wall

approximation:

Thick-wall approximation: med

wall

med

wallchambwall

aircav

wall

airL

airmedenDD

med

aircav

med

airL

airmed DD

(1-)

1

1

)()1()(

wall

med

wall

medchambmed

wallcav

med

wallL

med

aircav

med

airL

gasion

med

air

medcav

air

medL

wall

med

wall

medchambair

wallcav

air

wallL

medair

airairair

en

en

NPMD

DD

medDwallDD

replPairD

wallP/1

= fraction of electrons generated in ‘wall’.

1- = fraction of electrons generated in ‘medium’.

46

Alternative approach to Prepl

Dair

replwall

med

air

airmed PPL

DPD

)(

medium cavity air

xd

Dmed(P)

Dair Dmed(P’)wall

med

air

airmed PL

DPD

)'(

mediumeffective point of measurement x

dηr

)(

)(

)'(

)()(

rdD

dD

PD

PDdPrepl

47

For electron beams:

Dair z

z

E

medaircav

med

airairmed

E

repl

med

airairmed

LDD

orPL

DD

medium cavity air

xz

Dmed

Pwall is assumed to be 1.

zat energy electron mean theis where zE

dose-depth ionization-depth therefore

dependentdepth not are thusandenergy electron beams,photon For

ratios'power stopping' apply the

dose,-depth toionization-depth from converting when therefore,

dependentdepth are thusandenergy electron beams,electron For

:Note

medair

medair

medair

L

L

L

48

For electron beams:

• Calibration made at dmax. (gradient correction = 1)

• For depth-dose measurement:

– Apply stopping power ratios correction

– For parallel-plate chambers, Prepl = 1

– For cylindrical chambers, the gradient correction part of Prepl is handled by shifting the effective point of measurement towards the surface by 0.5r.

Prepl has two parts: Prepl = Pfl ‧ Pgr

1. Fluence correction (Pfl): accounts for in-scattering effect and obliquity effect.

2. Gradient correction (Pgr): accounts for displacement in the effective point of measurement.

49

Conversion from dose-to-water to dose-to-muscle

For photon beams:

muscle

water

enwatermuscle DD

For electron beams:

muscle

water

watermuscleS

DD

99.0

muscle

water

muscle

water

en S

50

The TG-51 protocol (Med Phys 26, 1847-70, 1999)

The TG-51 protocol is based on ‘absorbed dose to water’ calibration (also in a Co-60 beam).

The chamber calibration factor is denoted .

The calibrated chamber can be used in any beam modality (photon or electron beams) and any energy, in water.

The formalism is simpler than the TG-21, but it is applicable in water only.

CowDN

60

,

51

• Ion chamber and electrometer

– calibration traceable to standard laboratory

• waterproofing for ion chamber ( if needed) <1mm PMMA

• water phantom (at least 30x30x30 cm3)

• lead foil for photons 10MV and above

– 1 mm 20%

• system to measure air pressure and water temperature

Equipment Needed

52

Obtain an Absorbed-dose to Water Calibration Factor CowDN

60

,

M (corrected)

rdgorC

Gy

M

DN Co

wD

60

,

60Co sourced m

ax

D

Dose to water per unit charge (reading)

53

Quality Conversion Factor

Ideally, for a given chamber individual calibration factor should be obtained for each beam quality used in the clinic. So that:

This is impractical, as the standard laboratory may not have the particular beam quality Q available, thus a quality conversion factor kQ is introduced to convert the calibration factor for Co-60 to that for the beam quality Q.

QwDN ,

QwD

Qw NMD ,

CowDQ

QwD NkN

60

,,

54

General Formalism

In a Co-60 beam:

CowDQ

Qw NkMD

60

,

In any other photon beam:(only cylindrical chamber allowed at present)

)(6060

, correctedisMNMD CowD

Cow

In any electron beam:(both cylindrical and parallel-plate chambers allowed)

CowDecalR

Qgr

Qw NkkPMD

60

50 ,'

55

Charge measurement

rawpolelecion MPPPPM TP

raw

-rawraw

pol 2

-

M

MMP

P

TPTP

33.101

222.273

2.273

Polarity correction

Press/temperature

Electrometer correction Pelec

L

HLraw

Hraw

L

H

Hion

VV

M

M

VV

VP

-

-1)( Ion recombination correction

56

kQ values for cylindrical chambers in photon beams

NRC-CNRCNRC-CNRC

57

Point of Measurement and Effective Point of Measurement

point of measurement

Effective point of measurement

cylindrical parallel plate

rcav

r

Photon: r = 0.6 rcav

electron: r = 0.5 rcav

58

Percent Depth-Dose (ionization) for photon beams

Depth in water (cm)5 10 15 20

20

40

60

80

100

% d

epth

-dos

e (i

oniz

atio

n)

III

Parallel-plate chamber: measured curve II.

Cylindrical chamber: measured curve I, needs to be shifted by 0.6 rcav to get curve II.

Curve II is the percent dose (percent ionization) curve, including contaminated electrons.

Percent depth dose to be measured at SSD = 100 cm for a 1010 cm2 field size.

%dd(10)

59

Beam Quality Specification (photons)

For this protocol, the photon beam quality is specified by %dd(10)x, the percent depth-dose at 10 cm depth in water due to the photon component only, that is, excluding contaminated electrons.

For low energy photons (<10 MV with %dd(10) < 75%) %dd(10)x = %dd(10) (contaminated electron is negligible)

For high energy photons (>10 MV with 75%<%dd(10)<89%) %dd(10)x 1.267%dd(10) – 20.0

A more accurate method requires the use of a 1-mm thick lead foil placed about 50 cm from the surface.

%dd(10)x = [0.8905+0.00150%dd(10)pb] %dd(10)pb

[foil at 50 cm, %dd(10)pb>73%]

60

Percent depth dose measured at SSD = 100 cm for a 1010 cm2 field size with a 1mm Pb filter placed at ~50 cm from the surface.

Depth in water (cm)5 10 15 20

20

40

60

80

100

(% d

d)P

b

III

%dd(10)Pb

1mm Pb filter

~50 cm

Curve II is the (%dd)Pb curve, with the contaminated electrons in the original beam removed, but generates its own contaminated electrons.%dd(10)x = [0.8905+0.00150%dd(10)pb] %dd(10)pb

61

Reference conditions for Photon Beams

photon source

SSD setup SAD setup

1010 cm2

100

cm

10 c

m

10 c

m

1010 cm2

water water

62

Photon Beam Dosimetry

CowDQ

Qw NkMD

60

,

where

M is the fully corrected (temperature, pressure, polarity, recombination) chamber reading,

kQ is the quality conversion factor,

is the absorbed dose to water chamber calibration factorCowDN

60

,

63

Reference conditions for Electron Beams

Depth: dref = 0.6 R50 - 0.1 cm

where R50 is the depth in water at which the dose is 50% of the maximum dose. dref is approx. at dmax

field size: (why different field sizes for different energies?)

> 10x10 cm2 on surface R50<8.5 cm

> 20x20 cm2 on surface R50>8.5 cm

SSD: as used in clinic between 90 cm and 110 cm (typically 100 cm)

SSD setupd re

f

water

Electron source

SS

D

CowDecalR

Qgr

Qw NkkPMD

60

50 ,'

64

Percent Depth-ionization for electron beams

Depth in water (cm)2 4 6 8

20

40

60

80

100

% d

epth

-ion

izat

ion I

II

Parallel-plate chamber: measured curve II.

Cylindrical chamber: measured curve I, needs to be shifted by 0.5 rcav to get curve II.

Curve II is the percent ionization curve.

Percent depth ionization to be measured at SSD = 100 cm for field size 1010 cm2 (or 2020 cm2 for E>20 MeV).

I50

R50 = 1.029I50 – 0.06 (cm) for 2I50 10

cmR50 = 1.059I50 – 0.37 (cm)

for I50 > 10 cm

66

Electron Beam Dosimetry ( )

depends on user’s beam must be measured in clinic.

Cylindrical chamber:

parallel plate chamber:

0.1QgrP

QgrP

)(

)5.0(

refraw

cavrefrawQgr dM

rdMP

Same as shifting the point of

measurement upstream by 0.5rcav.

QgrP

67

Electron Beam Dosimetry (Kecal )

Kecal is the photon-to-electron conversion factor, for an arbitrary electron beam quality Qecal, taken as R50 = 7.5 cm.

The values of Kecal are available in the TG-51 protocol.

chamber Attix Capintec PTB Exradin Holt Markus NACP

kecal 0.883 0.921 0.901 0.888 0.900 0.905 0.888

Parallel-plate chambers:

chamberExradin

A12NE2571 NE2581 PR-06 N23331 N30004 …

kecal 0.906 0.903 0.885 0.900 0.896 0.905 …

cylindrical chambers:

ecalQCo

wDwD NN ,,

60

68

Electron Beam Dosimetry ( )'

50Rk

'

50Rk is the electron quality conversion factor converting from Qecal to Q.

'

50Rk for a number of cylindrical and parallel-plate chambers are available in Figs. 5-8 in the TG-51 protocol. It can also be calculated from the following expressions:

Cylindrical:67.3' 50

500710.09905.0)( R

R ecylk

Parallel-plate:214.0

50' )(145.02239.1)(

50RppkR

69

k’R50 for Cylindrical Chambers

NRC-CNRCNRC-CNRC

70

k’R50 for Parallel Plate Chambers

NRC-CNRCNRC-CNRC

71

Electron Beam Dosimetry

CowDecalR

Qgr

Qw NkkPMD

60

50 ,'

where

M is the fully corrected chamber reading,

is the correction factor that accounts for the ionization gradient at the point of measurement (for cylindrical chamber only)

is the electron quality conversion factor.

kecal is the photon to electron conversion factor, fixed for a given chamber model

is the absorbed dose to water chamber calibration factorCowDN

60

,

QgrP

'

50Rk

72

Summary - photons

• get a traceable

• measure %dd(10)Pb with lead foil (shift depth if necessary)

• deduce %dd(10)x for open beam from %dd(10)Pb

• measure Mraw at 10 cm depth in water (no depth shift !!!)

• M = PionPTPPelecPpol Mraw

• lookup kQ for your chamber

Co

wDN60

,

Co

wDQQw NkMD

60

,

73

Summary - electrons

• get a traceable

• measure I50 to give R50 (shift depth if necessary)

• deduce dref = 0.6 R50 -0.1 cm (approx. at dmax)

• measure Mraw at dref (no depth shift !!!)

• M = PionPTPPelecPpol Mraw

• lookup kecal for your chamber

• determine (fig, formula)

• establish (Mraw 2 depths)

Co

wDN60

,

'

50RkQ

grPCo

wDRQ

grQw NkkPMD

60

50 ,ecal'

74

8.8 Exposure from Radioactive Sources

Exposure rate from a radioactive source can be determined from the photon energy fluence and the relevant mass energy absorption coefficients for air, assuming charged particle equilibrium:

airair

en

air

en

airair

W

eX

therefore

e

WXD

,

75

N

iii Ef

12

10

)1(4

3600107.3 source Ci-1 from 1mat fluence/h energy

where fi is the number of photons of energy Ei emitted per decay.

airiair

enN

iii W

eEf

,1

2

10

)1(4

3600107.3

X source Ci-1 from 1mat exposure/h

photon fluence

JRkgJeW air-13101.602MeV 1 ),/(00876.0 ngsubstituti

iair

enN

iii EfhR

,1

93.81 )/(X

76

)/()(93.81 )(

:constant rate exposure thedefine

2

,1

112

2

kgmMeVEfCihRm

XA

l

iair

enN

iii

The exposure rate constant is a property of the radioactive isotope.

Example: calculate the exposure rate constant for 60Co:

fi

Ei(MeV)

1 1.17 0.00270

1 1.33 0.00261

)/( 2, kgmiairen

11229.1

)00261.033.100270.017.1(8.193

CihRm

Exposure rate (R/min) from 5,000-Ci 60Co source at 80cm:

min/168

60/80

100500029.1/

22

R

lAX

77

8.9 Other Methods of Measuring Absorbed Dose

A. Calorimetry

B. Chemical Dosimetry

C. Solid State Methods

D. Silicon Diodes

E. Radiographic Film

78

8.9 (A-calorimetry & B-chemical dosimetry)

Calorimetry is based on the principle that the energy absorbed in a medium from radiation eventually appears as heat energy, resulting in a small rise in temperature, which can be measured with a thermistor. The temperature increase in water produced by 1 Gy is 2.3910-4°C

Chemical dosimetry is based on the principle that energy absorbed from radiation may cause chemical change. Most developed system is the ferrous sulfate (Fricke dosimetry). The absorbed dose D, can be determined by the measured chemical change M, and the G-value (# of molecules produced per 100 eV of absorbed dose) of the chemical.

These methods are used in national standards laboratories.

79

8.9-C Solid State Methods (TLD)

When certain crystal is irradiated, a small fraction of the absorbed energy is stored in the crystal. Some of this energy can be recovered later as visible light when the crystal is heated. This phenomenon is called thermoluminescence (TL).

The emitted light is amplified by the photomultiplier tube.

valence band

conduction band

ener

gy

irradiation

electron trap

heatingionizing

radiat

ion

TL photon

80

8.9-C Solid State Methods (TLD)

When a previously exposed sample of TLD is heated, the light output as a function of time is called a ‘glow curve’. The area under the glow curve can be used to measure dose.

81

The most commonly used TLD material is lithium fluoride (LiF). Prior to use, the LiF is annealed for 1 hour at 400° C, followed by 24 hours at 80° C (pre-irradiation annealing).

In radiation therapy, TLD is primarily used for in vivo measurement (if placed on skin, proper build-up is needed, e.g. bolus). TLD is available in different forms (powder, chips, rods) and sizes.

For megavoltage dosimetry, TLD can provide accuracy of ±3%.

8.9-C Solid State Methods (TLD)

83

Diode is a solid state semi-conductor device which generates a current when exposed to radiation.

Small size, instantaneous response, ruggedness, and high sensitivity, but is energy, directional, and temperature dependent, also suffers from radiation damage.

Primarily used for relative dose measurement (dose distribution)

It can also be used for in-vivo dosimetry (does not require 300 V high voltage).

Absolute dose measurement (machine output calibration) is done with a chamber.

8.9-D Silicon Diodes

84

8.9-D Silicon Diodes (theory)

Silicon diode p-type (receptor)

+

++

+

++

-

-

-

--

-

--

n-type (donor)

A silicon (14Si) doped with impurities to make p-type (electron receptor, e.g. 5B) and n-type (electron donor, e.g. 15P).

--

-

--

--

--

+

++

+

++

++

At equilibrium, a built-in potential is established in the depletion zone.

+

++

+

++

-

-

-

--

-

--

depletion zone

(built-in potential)+ V –

Silicon diode p-type (receptor)

n-type (donor)

Carriers near the interface diffuse across the boundary and recombine with the opposite carrier, forming a depletion zone

-

-+

+

+

- +-

The ion pairs produced along the electron track are attracted towards to +/- sides of the depletion zone, generating a current that can be measured.

85

8.9-D Silicon Diodes

• no bias voltage applied.

• diodes are more sensitive than ion chambers –

• (W/e)Si ~ 3.5 eV [In contrast, (W/e)air ~ 34 eV ]

• Si ~ 1800 air

• energy dependency for photons (due to Z=14 for Si), but not for electrons (therefore can be used for electron relative depth-dose measurement).

• angular dependency.

• temperature dependency, but independent of pressure.

• radiation damage – needs periodic calibration.

• used for patient dose monitoring and when small detector size is needed.

86

8.9-E Radiographic Film

Film base, cellulose acetate or polyester resin, ~0.1 mm.

Emulsion containing silver bromide crystals

Radiation or visible light

When the film is exposed to ionizing radiation, chemical change takes place in the crystals to form the latent image. When the film is developed, the affected crystals reduced to small grains of metallic silver, and the film is fixed. The unaffected granules are removed by the fixing solution. The metallic silver remains on the film, causing darkness. The degree of blackening depends on the dose.

87

net o

ptic

al d

ensi

ty

3.0

2.0

1.0

The degree of blackening is measured by optical density, defined as: OD = log10 (I0/It), where I0, It are incident and transmitted light intensities, respectively.

In dosimetry, the background fog (OD of unexposed processed film) should be subtracted to obtain the net optical density, whose relationship with dose is called H-D curve, or sensitometric curve.

Dose (cGy)

5 10 15Each box of films may have different characteristics, prior to use, H-D curve should be obtained for samples from the box.

8.9-E Radiographic Film

xv-2

(for illustration only)

RPM-2

50 100 150

RPM-2

xv-2

88

• Advantages:

High spatial resolution ( < 1 mm)

Ideal for 1D or 2D relative dose distribution measurement. (beam profiles, isodose distributions), accurate to within ~ 3%.

Inexpensive for personnel dosimetry (film badge, accurate to within 10%)

• Disadvantages:

Requires careful calibration prior to use.

Over responds to low energy photons (due to increased photo-electric events in silver bromide), not suitable for absolute dose measurement.

8.9-E Radiographic Film

89

Comparison of Calculation and Measurement

Film Calc.

90

• large dynamic range (10-2-106 Gy): suitable for brachy source dose distribution measurement.• no dark room processing required: the radiochromic film is insensitive to visible light, the emulsion changes color when exposed to radiation without any processing.

• tissue equivalent (zeff 6.0 to 6.5)• less energy dependency compared to conventional film• film response dependent on room temperature. Acceptable range of room temperatures 20-30° C.• sensitive to ultraviolet light (do not expose to fluorescent light)• more expensive, requires special densitometer (laser scanner at specific wavelength 610-670 nm)

Radiochromic film