radiation dosimetry (measurement of absorbed dose) faiz khan (chapter 8) podgorsak (chapter 2)

Radiation DosimetryRadiation Dosimetry(Measurement of Absorbed (Measurement of Absorbed

Dose)Dose)Faiz Khan (Chapter 8)Faiz Khan (Chapter 8)

Podgorsak (Chapter 2)Podgorsak (Chapter 2)

IntroductionIntroduction

Dosimetry attempts to quantitatively Dosimetry attempts to quantitatively relate specific radiation measurements to relate specific radiation measurements to chemical/biological changes that could be chemical/biological changes that could be producedproduced

Essential for quantifying biological Essential for quantifying biological changes as a function of radiation receivedchanges as a function of radiation received

For comparing experimentsFor comparing experiments

IntroductionIntroduction continuedcontinued

Radiation interactionRadiation interaction• Produces ionized and excited atoms and Produces ionized and excited atoms and

moleculesmolecules• Secondary electronsSecondary electrons

Produce additional ionizations and excitationsProduce additional ionizations and excitations Finally all energies are expended.Finally all energies are expended.

• Initial electronic transitions rapid (<10Initial electronic transitions rapid (<10-15-15ss))

• Represent the initial physical perturbations from Represent the initial physical perturbations from which all effects evolve.which all effects evolve.

So, ionization and energy absorption are the So, ionization and energy absorption are the starting point for radiation dosimetrystarting point for radiation dosimetry

Quantities and UnitsQuantities and Units

• Absorbed dose is a measure of the Absorbed dose is a measure of the biologically significant effects biologically significant effects produced by ionizing radiationproduced by ionizing radiation•Definition of absorbed dose, Definition of absorbed dose, dEdEavgavg//dmdm

• dEdEavgavg : the mean energy imparted by : the mean energy imparted by ionizing radiation to material of mass ionizing radiation to material of mass dmdm

•UnitUnit• The old unit of dose is The old unit of dose is rad, rad,

1 1 radrad = 100 ergs/g = 10 = 100 ergs/g = 10-2-2J/kgJ/kg

•The SI The SI unit unit of dose is the of dose is the gray (Gy), gray (Gy), 1 Gy = 1J/Kg1 Gy = 1J/Kg

Quantities and UnitsQuantities and Units

ExposureExposure• Defined for X and gamma radiationDefined for X and gamma radiation

In terms of ionization of airIn terms of ionization of air Old unit called “roentgen” (R) Old unit called “roentgen” (R) Initially defined in 1928, current definition Initially defined in 1928, current definition

is:is: 1 R 1 R 2.58 x 10 2.58 x 10-4-4C kgC kg-1-1 of air, of air, exactlyexactly

• Applies only to electromagnetic Applies only to electromagnetic radiation; the charge and mass refer radiation; the charge and mass refer only to aironly to air..

Roentgen - original definitionRoentgen - original definition Amount of radiation that produced 1 esu of Amount of radiation that produced 1 esu of

charge in 1 cmcharge in 1 cm33 of air at STP of air at STP• 1 esu = 3.335 x 101 esu = 3.335 x 10-10-10CC

• At STP air has a density of 0.001293 g cmAt STP air has a density of 0.001293 g cm-3-3

• 1 kg of air has a volume of 7.734 x 101 kg of air has a volume of 7.734 x 1055 cm cm33

1 R = 3.335 x 101 R = 3.335 x 10-10 -10 C cmC cm-3 -3 of airof air How much energy is absorbed in air from 1R? How much energy is absorbed in air from 1R?

Absorbed Dose and ExposureAbsorbed Dose and Exposure

What is the absorbed dose in air when the What is the absorbed dose in air when the exposure is 1 R?exposure is 1 R?• Need to know W for air (energy to produce ion Need to know W for air (energy to produce ion

pair in air) pair in air) 33.7 eV/ip = 33.7 J/C.33.7 eV/ip = 33.7 J/C.

• 1 R 1 R 2.58 x 10 2.58 x 10-4-4C/kg x 33.7 J/C = 8.8 x 10C/kg x 33.7 J/C = 8.8 x 10-3-3 J kg J kg-1-1

This equals 8.8 x 10This equals 8.8 x 10-3-3 Gy (0.88 rad) Gy (0.88 rad) Similar calculations show that 1R would produce a dose Similar calculations show that 1R would produce a dose

of 9.5 x10of 9.5 x10-3-3 Gy (=0.95 rad) in soft tissue. Gy (=0.95 rad) in soft tissue. Why is there a difference between air and tissue???Why is there a difference between air and tissue??? This is why one can say that 1 R ~ 1 rad in tissue.This is why one can say that 1 R ~ 1 rad in tissue.

Exposure Measurement - Exposure Measurement - Free Air ChamberFree Air Chamber

Feasible to measure exposure at radiation Feasible to measure exposure at radiation energies between few keV and several energies between few keV and several MeVMeV

Definitive measure is by laboratory device Definitive measure is by laboratory device known as free air chamberknown as free air chamber

X-ray beam enters through a portal and X-ray beam enters through a portal and interacts with cylindrical column of air interacts with cylindrical column of air defined by entry diaphragmdefined by entry diaphragm

Ions created in defined space are Ions created in defined space are measuredmeasured

Parallel Plate Free-air Parallel Plate Free-air Ionization ChambersIonization Chambers

Electrometer

Xray beam

Diaphragm

HV

Monitor

Wires

e1e2

e3

e4

scattered photon

All the energy of the primary electrons expended in chamber

Free Air ChamberFree Air Chamber

Photons enter chamber and interact with Photons enter chamber and interact with fixed quantity of airfixed quantity of air• PE, CSPE, CS

Ions from air collected by platesIons from air collected by plates Lead lined (shielded)Lead lined (shielded) Electric fields are kept perpendicular to Electric fields are kept perpendicular to

plates by guard rings and guard wiresplates by guard rings and guard wires• Guard wires assure uniform potential drop Guard wires assure uniform potential drop

across platesacross plates

Free Air ChamberFree Air Chamber

Field intensity is ~ 100 V/cmField intensity is ~ 100 V/cm Collect ions prior to recombinationCollect ions prior to recombination Voltage low enough so no secondary Voltage low enough so no secondary

ionizationsionizations Current flow is measuredCurrent flow is measured All energy of primary electrons must All energy of primary electrons must

be deposited in sensitive volume of be deposited in sensitive volume of air for meter to work properlyair for meter to work properly

Free Air ChamberFree Air Chamber

What if all primary electrons are not What if all primary electrons are not collected in sensitive volume?collected in sensitive volume?

If equal number coming in from If equal number coming in from outside of sensitive volume as is outside of sensitive volume as is going out: Electronic Equilibriumgoing out: Electronic Equilibrium

Electronic EquilibriumElectronic Equilibrium

+ + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - -

e-

e-

e-

Electronic EquilibriumElectronic Equilibrium

For every electron which escapes the For every electron which escapes the sensitive volume, another electron of sensitive volume, another electron of equal energy enters the sensitive volume equal energy enters the sensitive volume and deposits energy in the detectorand deposits energy in the detector

A layer of air between entrance port of A layer of air between entrance port of free air chamber and the sensitive volume free air chamber and the sensitive volume can provide enough air so that electronic can provide enough air so that electronic equilibrium is attainedequilibrium is attained

Free-Air Ionization ChamberFree-Air Ionization Chamber

http://physics.nist.gov/Divisions/Div846/Gp2/wafac.html

Measuring ExposureMeasuring Exposure

Free air chamber practical only as Free air chamber practical only as laboratory devicelaboratory device

Portable instrument neededPortable instrument needed

Exposure Measurement: Exposure Measurement: Air Wall ChamberAir Wall Chamber

Practical alternative to free-air chamberPractical alternative to free-air chamber Built as a capacitorBuilt as a capacitor

• Central anode, insulated from rest of chamberCentral anode, insulated from rest of chamber• Given an initial chargeGiven an initial charge• When exposed to photons, 2When exposed to photons, 200 electrons electrons

neutralize charge & lower potential between neutralize charge & lower potential between anode and wallanode and wall

• Change in potential difference is proportional Change in potential difference is proportional to total ionization (and therefore exposure)to total ionization (and therefore exposure)

Plastic

Anode

Charging diaphragm

Air Wall ChamberAir Wall Chamber Better for field use than the Free Air Better for field use than the Free Air

ChamberChamber Simulates compressing air into a small Simulates compressing air into a small

volume by using ‘air equivalent’ materialvolume by using ‘air equivalent’ material X-ray absorption properties similar to that of airX-ray absorption properties similar to that of air

Walls must be thick enough to generate Walls must be thick enough to generate

enough primary electrons enough primary electrons Walls must be thin enough so that primary Walls must be thin enough so that primary

radiation is not shieldedradiation is not shielded

Air Wall ChamberAir Wall Chamber Ideal air wall chambers have only Ideal air wall chambers have only

primary electrons ionizing the air primary electrons ionizing the air in the sensitive volumein the sensitive volume

Ideal wall thickness is almost Ideal wall thickness is almost energy independent over a range energy independent over a range from 200 keV to almost 2 MeV from 200 keV to almost 2 MeV

Air Wall ChamberAir Wall Chamber

Greater than 3 MeV primary electrons Greater than 3 MeV primary electrons have long rangehave long range

Impractical to build air wall chamber of Impractical to build air wall chamber of sufficient sizesufficient size• When walls are made thick enough to When walls are made thick enough to

generate primary electrons, radiation is generate primary electrons, radiation is attenuated significantlyattenuated significantly

• Radiation intensity will no longer be Radiation intensity will no longer be constantconstant

• Primary electrons not produced uniformlyPrimary electrons not produced uniformly• No electronic equilibriumNo electronic equilibrium

Exposure-Dose RelationshipExposure-Dose Relationship

ExposureExposure • measures charge produced in a mass of measures charge produced in a mass of

airair• C/kgC/kg

Absorbed doseAbsorbed dose• Measures energy absorbed per mass Measures energy absorbed per mass • J/kgJ/kg

How to relate measurement in air to How to relate measurement in air to absorbed dose in something absorbed dose in something besides besides airair??

Exposure-Dose RelationshipExposure-Dose Relationship

Energy absorption in air Energy absorption in air energy energy absorption in tissueabsorption in tissue

Dose in air Dose in air dose in tissue dose in tissue 1 R = 87.7 ergs/g1 R = 87.7 ergs/gairair = 95 ergs/g = 95 ergs/gtissuetissue

1 rad = 100 ergs/g1 rad = 100 ergs/gtissuetissue

For regulatory purposes, frequently 1 For regulatory purposes, frequently 1 R is assumed to be equal to 1 radR is assumed to be equal to 1 rad

Conversion can be done if requiredConversion can be done if required

Exposure to Dose ConversionExposure to Dose Conversion

mm = Energy absorption coefficient for = Energy absorption coefficient for tissuetissue

aa = Energy absorption coefficient = Energy absorption coefficient for airfor air

m m = Tissue density= Tissue density aa = Air density = Air density

roentgens100

7.87rads

a

a

m

m

Bragg-Grey TheoryBragg-Grey Theory How to measure absorbed dose?How to measure absorbed dose? The best way would be The best way would be

calorimetry...but not very practical. calorimetry...but not very practical. Instead, absorbed dose is Instead, absorbed dose is measured by:measured by:• measuring ionizationmeasuring ionization• use of correction factorsuse of correction factors• calculating (approximating) dosecalculating (approximating) dose

This is done with BRAGG-GREY This is done with BRAGG-GREY CAVITY THEORYCAVITY THEORY

Measurement of Absorbed Measurement of Absorbed DoseDose

Bragg-Gray principle relates Bragg-Gray principle relates ionization measurements in a gas to ionization measurements in a gas to absorbed dose in some material.absorbed dose in some material.

Consider a gas in a walled enclosure Consider a gas in a walled enclosure irradiated by photons:irradiated by photons:

e1

e2

GasWall

Bragg-Gray, Bragg-Gray, cont’dcont’d

Photons interact in cavity and wallPhotons interact in cavity and wall Chose wall material that has similar radiation Chose wall material that has similar radiation

absorption properties as tissue (e.g., Z)absorption properties as tissue (e.g., Z)

• Cavity is very small Cavity is very small (doesn’t change angular and velocity (doesn’t change angular and velocity

distributions of secondarydistributions of secondary electrons)electrons)

• ““Electronic equilibriumElectronic equilibrium” exists in cavity ” exists in cavity (# e(# e-- stopping = # e stopping = # e-- starting in cavity) starting in cavity) requires wall thickness > range of secondary requires wall thickness > range of secondary

ee

e1

e2

GasWall

Bragg-Gray cont’dBragg-Gray cont’d

Ionizations in the gas Ionizations in the gas Can measure the charge liberated. Can measure the charge liberated. If you know the energy required to If you know the energy required to

ionize the gas,ionize the gas,

Then the dose to the gas is:Then the dose to the gas is:

) air for ( C

J= 33.85

pair ion

eV= 33.85 W

Wm

QD

gas

gas

Bragg-Gray, cont’dBragg-Gray, cont’d where,where,

• Q = coulombs of charge liberatedQ = coulombs of charge liberated• W = average ionization energy for the gasW = average ionization energy for the gas• m = kg of gas in the cavitym = kg of gas in the cavity

Example: A cavity filled with (1 cmExample: A cavity filled with (1 cm33) air ) air at STP is exposed to a radiation field at STP is exposed to a radiation field that liberates 3.336X10that liberates 3.336X10-10-10 C. What is C. What is the dose to the air? the dose to the air?

At STP:At STP:

kg 101.293X= cm

m10

m

kg 1.293 )cm(1= m

6-

3

36-

3

3gas

Example, cont’dExample, cont’d

Know the dose to the gas. Know the dose to the gas. • What about the dose to the medium What about the dose to the medium

surrounding it?surrounding it? Assume our cavity is really Assume our cavity is really

small...small...small enough that it does small enough that it does not disrupt the electron not disrupt the electron spectrumspectrum..

kg

J 108.73X=

C

J33.85

kg 101.293X

C 103.336X= D

3-

6-

10-

gas

Bragg-Gray, Bragg-Gray, contdcontd

Wall thickness must be as great as range as Wall thickness must be as great as range as secondary charged particles (not too great to secondary charged particles (not too great to attenuate beam)attenuate beam)

Then energy absorbed per unit mass of wall is Then energy absorbed per unit mass of wall is related to that absorbed per unit mass of gas by:related to that absorbed per unit mass of gas by:

Note - this special case is where the wall and Note - this special case is where the wall and gas are the same type of materialgas are the same type of material

e1

e2

GasWall

m

WNDD g

gw

Bragg-GrayBragg-Gray, contd, contde1

e2

GasWall

DDww is the dose to the wall is the dose to the wall DDgg is the dose to the gas is the dose to the gas NNqq is the number of ions produced in is the number of ions produced in

the gasthe gas W is eV required to produce ion pairW is eV required to produce ion pair m is the mass of gas in the cavitym is the mass of gas in the cavity

Bragg-GrayBragg-Gray, contd, contde1

e2

GasWall

If gas and wall don’t have same atomic If gas and wall don’t have same atomic composition, a slight modification is composition, a slight modification is required:required:

where Swhere Sg,wg,w are the mass stopping powers of are the mass stopping powers of the wall and the gasthe wall and the gas

the cavity and gas pressure must be small the cavity and gas pressure must be small

g

wg

g

wgw mS

WSN

S

SDD

ExampleExample 1 cm1 cm33 of air in a block of carbon is exposed to of air in a block of carbon is exposed to 6060Co γ Co γ

• Q=3X10Q=3X10-8-8 C is produced. C is produced. What is the absorbed dose to the carbon?What is the absorbed dose to the carbon?

Mean mass stopping power ratio for Mean mass stopping power ratio for 6060Co γ in carbon Co γ in carbon relative to air = 1.009relative to air = 1.009 kg 101.293X=

m

kg1.293 )m10(= m STP at 3-

3

36-gas

Example, continuedExample, continued

This equation allows us to measure This equation allows us to measure the ionizations in a gas and relate it the ionizations in a gas and relate it to dose to the medium. to dose to the medium.

rad 79.2= Gy 0.792= kg

J0.792=

(1.009) C

J33.85

kg) 10(1.293X

C) 10(3X= D 3-

8-

carbon

Bragg-GrayBragg-Gray contd contde1

e2

GasWall

If neutrons are present, the wall If neutrons are present, the wall must be at least as thick as the must be at least as thick as the maximum energy range of any maximum energy range of any secondary charged recoil nuclei secondary charged recoil nuclei produced by the nuclear interactions.produced by the nuclear interactions.

Chambers that meet these Chambers that meet these conditions can be used to measure conditions can be used to measure absorbed dose to the mediumabsorbed dose to the medium

KermaKerma

““Sum of the initial kinetic energies per Sum of the initial kinetic energies per unit mass of all charged particles unit mass of all charged particles produced by the radiation”produced by the radiation”

• This is regardless of where the energy is This is regardless of where the energy is depositeddeposited

• Bremsstrahlung photons are not counted, Bremsstrahlung photons are not counted, whether they escape or notwhether they escape or not

• Annihilation radiation is not counted, Annihilation radiation is not counted, regardless of fate of annihilation photonsregardless of fate of annihilation photons Initial positron, if primary ionizing particle, is Initial positron, if primary ionizing particle, is

countedcounted

Energy Transfer - A Two Stage Energy Transfer - A Two Stage Process - Kerma and Absorbed DoseProcess - Kerma and Absorbed Dose

h

h’

h”

Scattered photon

Primary ionizing particle (pe, cs electron, e+e- pairs, scattered nuclei (neutrons)

Quantity of transferred energy is called Kerma (j/kg)

KermaKerma

EEtrtr is just the kinetic energy received by is just the kinetic energy received by charged particles in a specified volume V, charged particles in a specified volume V, regardless of where or how they spend the regardless of where or how they spend the energyenergy

Kerma is the expectation value of the Kerma is the expectation value of the energy transferred to charged particles per energy transferred to charged particles per unit mass at a point of interestunit mass at a point of interest, , including including radiative-loss energyradiative-loss energy, , but excluding but excluding energy passed from one charged particle energy passed from one charged particle to anotherto another

)( 1980,ICRUdm

d

dm

EdK trtr

Quantities to Describe a Radiation Quantities to Describe a Radiation BeamBeam

FluenceFluence• # photons/area# photons/area = dN/da= dN/da

Energy fluenceEnergy fluence• Energy / areaEnergy / area• = dN h= dN h/da/da

Fluence rateFluence rate• # photons/(time # photons/(time

area)area) = d= d/dt/dt

Energy fluence rateEnergy fluence rate• Energy / (time area)Energy / (time area)• = d= d /dt /dt

Relationship of Kerma to Relationship of Kerma to Photon FluencePhoton Fluence

• gives the number of photon interactions that gives the number of photon interactions that take place per unit mass of material.take place per unit mass of material.

is attenuation coefficientis attenuation coefficient is densityis density

E = K tr

Relationship of Kerma to Photon Relationship of Kerma to Photon FluenceFluence

For a spectrum of energies that can For a spectrum of energies that can be described by dΦ(hv) /d hv, then:be described by dΦ(hv) /d hv, then:

dhhE h

dh

hd= K tr

h

)(

)()(max

0

E = K tr

MeV 7.3= E kgm 0.00196= tr

2

Given incident on a block of carbonGiven incident on a block of carbon• 10 MeV photons10 MeV photons = 10= 1014 14 mm-2-2

What is kerma?What is kerma?

Calculating KermaCalculating Kerma

Calculating Kerma, cont’dCalculating Kerma, cont’d

Kerma is easy to calculate - but Kerma is easy to calculate - but very difficult to measure!very difficult to measure!

kg

J

MeV

J1.602x10MeV

kg

m

mK 13-

229.0

30.700196.010 2

2

14

KermaKerma• a measure of kinetic energy transferred at a a measure of kinetic energy transferred at a

point in space. point in space. Absorbed dose is more Absorbed dose is more ““interestinginteresting””. .

• Energy is transferred in the mediumEnergy is transferred in the medium• not all is retained there. not all is retained there. • absorbed dose is the energy retained in the absorbed dose is the energy retained in the

medium brought about by the ionizations medium brought about by the ionizations along along the trackthe track of the charged particle. of the charged particle.

Kerma and Absorbed Dose do not take Kerma and Absorbed Dose do not take place at the same locationplace at the same location

Relating Kerma & Absorbed Relating Kerma & Absorbed DoseDose

Calculating Absorbed DoseCalculating Absorbed Dose

ddabab is the mean energy “imparted” by the is the mean energy “imparted” by the ionizing radiation into a mass, dm. ionizing radiation into a mass, dm. • Mass should be sufficiently small so that the Mass should be sufficiently small so that the

absorbed dose is defined at a point, but not so absorbed dose is defined at a point, but not so small that statistical fluctuations become importantsmall that statistical fluctuations become important

From the previous example, dFrom the previous example, dtrtr = 7.3 MeV = 7.3 MeV • fraction of 10 MeV photon energy transferred to the fraction of 10 MeV photon energy transferred to the

medium.medium. A smaller amount is absorbed along the A smaller amount is absorbed along the

electron track: delectron track: dabab = 7.06MeV = 7.06MeV

dm

EdD

ab

Kerma and Absorbed Dose, Kerma and Absorbed Dose, cont’dcont’d

ddtrtr- d- dabab • The difference, 7.30-7.06 = 0.24 MeV, is The difference, 7.30-7.06 = 0.24 MeV, is

bremsstrahlung. bremsstrahlung. What is the path length of the 7.3 MeV What is the path length of the 7.3 MeV

electron in C?electron in C?• Estimate from graphs or tables of Estimate from graphs or tables of

electron ranges from literature,electron ranges from literature,• ~ 4.2 g cm~ 4.2 g cm-2-2. . • Divide by the density of carbon Divide by the density of carbon • Path length: 1.9 cm. Path length: 1.9 cm.

Dose and KermaDose and Kerma

E = K tr

abED

Important Relationship Important Relationship

Relate absorbed dose in air to Relate absorbed dose in air to exposure:exposure:• assuming CPE (electronic equilibrium)assuming CPE (electronic equilibrium)

airaircair WXKD )(

J/kg J/kg C/kg J/C

Electronic (Charged-Particle) Electronic (Charged-Particle) EquilibriumEquilibrium

The transfer of energy (kerma) The transfer of energy (kerma) occurs upstream from the absorbed occurs upstream from the absorbed dose. dose. • Kerma can be easily calculated from Kerma can be easily calculated from

fluencefluence• Absorbed dose cannot. Why?Absorbed dose cannot. Why?• Kerma remains constant Kerma remains constant • Absorbed dose takes time to build up as Absorbed dose takes time to build up as

upstream electrons increase:upstream electrons increase:

No Attenuation of Photon Beam, No Attenuation of Photon Beam, Φ Φ ConstantConstant

Number of electron tracks set in motion by photon Number of electron tracks set in motion by photon interaction interaction • Φ constant with depth (small # interactions)Φ constant with depth (small # interactions)• Same # electrons Same # electrons set in motion set in motion in each squarein each square• i.e., interactions per volume constant through targeti.e., interactions per volume constant through target

A B C D E F G

Range R

100100100100

Absorbed Dose and KermaAbsorbed Dose and Kerma

100100100100

Build up region Electronic equilibrium

depth

kerma

Absorbed dose

A B C D E F G

Beam UnattenuatedBeam Unattenuated

Same number of photon tracks set in Same number of photon tracks set in motion in each squaremotion in each square• e.g., square D is traversed by 400 trackse.g., square D is traversed by 400 tracks• ionization in D is the same as total ionization in D is the same as total

ionization started in Aionization started in A• absorbed dose is proportional to ionization absorbed dose is proportional to ionization

produced in each squareproduced in each square• dose reaches a maximum at R (range of dose reaches a maximum at R (range of

2ndary electron)2ndary electron)• kerma constant with depth, equals kerma constant with depth, equals

absorbed dose beyond Rabsorbed dose beyond R

Absorbed Dose and KermaAbsorbed Dose and Kerma

869095100

Build up regionEquilibrium thickness

depth

kermaAbsorbed dose

8278

In this region there is notstrict electronic equilibrium

Attenuation of Photon BeamAttenuation of Photon Beam

Beam attenuation,Beam attenuation, Φ decreases with depth. Φ decreases with depth. Dose increases to a maximum (at Dose increases to a maximum (at

maximum range of particle) maximum range of particle) overshoots, then tracks kerma.overshoots, then tracks kerma.

Attenuation of Photons in Attenuation of Photons in TissueTissue

CPE will generally exist in a uniform medium at a CPE will generally exist in a uniform medium at a point more than the maximum range for the point more than the maximum range for the secondary charged particles from the secondary charged particles from the boundary of the mediumboundary of the medium

Isotope MaximumDose Depth

( mm inTissue)

BeamAttenuation

(% oforiginalbeam)

137Cs 2 160Co 5 2

6 MV 15 6

Relating Energy Fluence and Relating Energy Fluence and ExposureExposure

Radioactive beam incident on an areaRadioactive beam incident on an area• What is relationship between energy fluence What is relationship between energy fluence

and exposure at point p?and exposure at point p? Assume small mass of air at pAssume small mass of air at p The dose at p is: D= The dose at p is: D= ((//))ĒĒabab= = ( (abab//))

• Can relate to R as:Can relate to R as: 1 R = 0.00873 J/kg, then 1 R = 0.00873 J/kg, then /X = 0.00873 J/ ((/X = 0.00873 J/ ((abab//)kg R))kg R) Complicated variation of energy absorption Complicated variation of energy absorption

coefficient for air and energy of beamcoefficient for air and energy of beam

p

Relating photon fluence to Relating photon fluence to exposureexposure

Relationship between energy fluence Relationship between energy fluence and photon fluence:and photon fluence: = dN/da= dN/da= dN h= dN h/da/da• So, So, = = h h, and, and

Rkgh

J

X

air

ab

00873.0