Radiation Dosimetry

AGEN-698Advances in Food Engineering

IntroductionRadiation dosimetry is the branch of science that attempts to quantitatively relate specific measurement in a radiation field to chemical and/or biological changes that the radiation would produce in a target

RadiationWhen radiation interact with matter it produces:

Excited and ionized atoms and moleculesA large number of secondary electrons

ExposureIt is defined for gamma and X-rays in terms of the amount of ionization they produce in airUnits: roentgen [R] – 1 R = 2.58x10-4 C/kg∆Q is the sum of all charges of one sign produced in air when all the electrons liberated by photons in a mass ∆m of air are completely stopped in airApplies only to electromagnetic radiation and the mass and roentgen refer only to air

mQExposure

∆∆

=

Absorbed doseThe energy absorbed per unit mass from any kind of ionizing radiation in any kind of matterTraditional unit: rad = 100 erg/gNew SI unit: gray (Gy)Absorbed dose is often referred to simply as the dose

radg

ergg

ergkgJGy

10010

101011

4

3

7

==

==≡

Dose equivalentThe absorbed dose to achieve a given level of biological damage (e.g., 50% cell killing) is often different for different kinds of radiationEquivalent dose, H, is defined as the product of the absorbed dose D and the dimensionless quantity Q, which depends on LET

QDH =

Dependence of Q on LET

1γ-rays, X-rays, electrons, positrons of any LET

10-2053-175

5-1023-53

2-57.0-23

1-23.5-7.0

13.5 or less

QLET [MeV/cm]

Measurement of ExposureExposure can be measured operationally with ‘free-air’ or ‘standard’ ionization chamber

Free-air ionization chamberX-rays emerge from the target T of an X-ray tubeEnter the free-air chamber thru a circular aperture of are A defining a circular cone TBC of raysParallel plates Q and Q’ in the chamber collect the ions produced in the volume of air between them and the center P’

Larea A

P

d'

Q'

P'

d

G

DE

F

area A'

B

C

e2 e1

T

Q

Free-air ionization chamberThe plates collect all of the ions between them Not only those originated from X-ray interactions in the volume DEFGSome ions produced by X-ray escape this volumeSome ions produced outside this volume are also collected

Larea A

P

d'

Q'

P'

d

G

DE

F

area A'

B

C

e2 e1

T

Q

Free-air ionization chamberIf the distance P to DG is large enough (10 cm for 300 keV X-rays) electronic equilibrium will be realizedThere will be almost exact compensation between ionization lost from the volume DEFG by electrons (e2 that escape and e1 that enter)

Larea A

P

d'

Q'

P'

d

G

DE

F

area A'

B

C

e2 e1

T

Q

Free-air ionization chamberThe distance P to DG should not be so large As to attenuate the beam significantly between P and P’So, when the charge q is collected, the exposure P’ is:

Larea A

P

d'

Q'

P'

d

G

DE

F

area A'

B

C

e2 e1

T

Q

LAq

MqEP '' ρ==

Free-air ionization chamberIn practice, one prefers to know the exposure Ep at P rather than Ep’:

Larea A

P

d'

Q'

P'

d

G

DE

F

area A'

B

C

e2 e1

T

Q

ALq

LAq

ddE

AddA

EddE

P

PP

ρρ=

=

=

=

''

''

'

2

'

2

'

2

Air-wall ionization chamberFree-air ionization chamber is not practical instrument for measuring routine exposureChambers can be built with walls of a solid material having photon response properties similar to those of air

Air-wall ionization chamber

plastic

anode

Built as a capacitorA central anode, insulated, is given an initial charge from a charge-reader device (attached before wearing)When exposed to photons, the secondary electrons liberated in the walls and enclosed air tend to neutralize the charge on the anode and lower the potential difference between it and the wallThe change in potential difference is directly proportional to the total ionization produced (so exposure)

Air-wall ionization chamber

plastic

anode

After exposure to photons, measurement of the change in potential difference from its initial value (fully charged chamber) can be used to find exposureDirect-reading pocket ion chamber are available

Measurement of absorbed dose

gaswall

incidentphotons

scatteredphotons

Bragg-Gray principleMeans of relating ionization measurements in a gas to the absorbed dose in some material from which a dosimeter can be fabricated

Measurement of absorbed dose

gaswall

incidentphotons

scatteredphotons

e1

e2

Photons lose energy in the gas by producing secondary electrons thereThe ration of the energy deposited and the mass of the gas is the absorbed dose in gasThis energy is proportional to the amount of ionization in the gas when equilibrium exists between the wall and the gas

Measurement of absorbed dose

gaswall

incidentphotons

scatteredphotons

e1

e2

The electron produced by a photon in gas, e1, enters the wall before losing all of its energyThe electron produced in wall and stopped in the gas, e2, compensates for e1.When wall and gas have the same atomic composition, the energy spectra of these electrons will be the same

Measurement of absorbed dose

gaswall

incidentphotons

scatteredphotons

e1

e2

For electronic equilibrium, the wall thickness must be at least as great as the maximum range of secondary charged particlesGas in cavity enclosed by wall

Bragg-Gary principleIf a gas is enclosed by a wall of the same atomic composition and if the wall meets the thickness conditions, then the energy absorbed per unit mass in the gas is equal to the number of ion pairs produced times the W value divided by the mass m of the gasSo, the absorbed dose in the gas is equal to the absorbed dose in the wall

Bragg-Gary principle

mWN

DD ggw ==

Where Ng = number of ions in gasW = average energy needed to produce an ion pair

Bragg-Gary principleFor wall and gas are of different atomic composition

The cavity size and gas pressure must be small (so the secondary particles lose on a small fraction of their energy in gas)

g

wg

g

wgw mS

WSNS

SDD ==

Sw/Sg = ratio of the mass stopping powers of the wall and gas

Measurement of X and Gamma-ray dose

This chamber satisfies the Bragg-Gray conditionsThe dose Dc in the carbon wall can be obtained from the measured ionization in the CO2

CO2

C

insulator

CO2

Graphite-walled CO2 chamber

Dose measurement for charged-particle beams

recorder

ionchamber

waterbeam

Dose or dose rate is determined by measuring the current from a thin-walled ionization chamber placed at different depths in a water target exposed to the beamDose rate is proportional to the current

Dose calculationsCharged-particle beamsPoint source of gamma rays

Charged-particle BeamsUniform, parallel beam of charged particles normally incident on thick tissue slabConsider a thin, disc-shaped volume element with thickness ∆x in the x-direction and area A normal to the beam

∆xx

φ.

Fluence rate [cm-2 s-1]

Charged-particle Beams

−=

∆∆−

=dxdE

xAxdxdEAD ϕ

ρϕ

&&& )/(

Fluence rate [cm-2 s-1]

Rate of energy deposition

Point-Source of γ-raysThe dose rate in air from a point γ-ray source of strength C curies that emits an average total photon energy of E[MeV] per disintegration can be calculatedThe rate of energy released in the form of photons escaping from the source is:

sec]/[1092.5/106.1sec107.3][

4

61110

ergCEMeVergCiCiMeVCE

×=

×××× −−−

Point-Source of γ-raysNeglecting attenuation in air, we can write the rate of energy flow per unit area (=intensity) through the surface of a sphere of radius r (cm) surrounding the source:

×

=sec

1071.422

3

cmerg

rCEI

Point-Source of γ-rays

r

I

1 cm2

source

dr

The rate of energy absorption in a volume element of air, having a unit area and thickness dr at r is given by IµAdr where µA is the average energy absorption coefficient in cm-1 for photonsIf the density of air is ρ [g/cm3], the mass of air in the volume element in grams is ρdr:

×==

sec1071.4

2

3

gerg

rCE

drdrID AA

ρµ

ρµ&

KERMAKinetic energy released per unit massIt includes energy that may subsequently appears as bremsstralung and Auger-electron energiesThe absorbed dose builds up behind a surface irradiated by a beam of particles to a depth comparable with the range of secondary charged particles generatedThe kerma, on the other hand, decreases steadily because of the attenuation of the primary radiation with increasing depth