Chapter 7: Radiation Dosimetry

Chapter 7: Radiation Dosimetry

NPRE 441, Principles of Radiation Protection, Spring 2020



Table of ContentsF Units of exposure and dose

F Experimental methods for measuring absorbed dose.

1. Exposure measurement with free-air chamber and air-wall chamber.

2. Exposure-dose relationship

3. Direct measurement of absorbed dose: Bragg-Gray Principle

F Source strength: specific gamma-ray emission

F Beta radiation

1. Dose from contaminated surface

2. Skin contamination

3. Submersion dose

F Internally deposited radioisotopes

1. Corpuscular radiation and the specific effective energy (SEE)

2. Effective half-life

3. Total dose commitment

4. Evaluate the internal dose from gamma ray emitters

5. MIRD method – partial energy absorption of gamma ray energy in tissues

F Neutron dose



Units for Absorbed Dose

F Radiation damage depends on the energy absorption from the radiation and isapproximately proportional to the concentration of absorbed energy in tissue.

F The basic unit of radiation dose is expressed in terms of absorbed energy perunit mass of tissue, which is called Gary (Gy)

unit. SI-non a is which Dose, AbsorbedRadiation for stands Rad where100/11 radKgJGy ==

F The Gary is universally applicable to all types of ionizing radiation dosimetry –irradiation due to external field of gamma rays, neutrons or charged particles aswell as that due to internally deposited radioisotopes.



The SI Unit for Exposure

air /1 1 KgCunitX =

F For external radiation of any given energy flux, the absorbed dose to any pointwithin an organism depends on the type and energy of radiation, the depthwithin the organism of the point at which the absorbed dose is required andthe elemental composition of the absorbing medium at that point.

F The x-ray fields to which an organism may be exposed is normally specified inexposure unit.


F Alternatively, exposure is also measured with the unit Roentgen (R),

1 R=2.58´10-4 C×kg-1



F Methods for measuring absorbed dose.





F Beta radiation



3. Submersion dose







F Neutron dose



Exposure Measurement: The Free Air Chamber

Turner, pp. 365.


Electronic Equilibrium, or Charged-Particle Equilibrium (CPE)


Charged-Particle Equilibrium (CPE)Chapter 7: Radiation Dosimetry

From <<Introduction to Radiological Physics and Radiation Dosimetry>>


Exposure Measurement: The Free Air ChamberChapter 7: Radiation Dosimetry

Exposure Measurement: The Air Wall ChamberChapter 7: Radiation Dosimetry



Solution








F Beta radiation



3. Submersion dose







F Neutron dose



Does-Exposure RelationshipChapter 7: Radiation Dosimetry

F Air wall chamber measures exposure in air, which should in some instances, beconverted to the energy absorption in tissue.

F Since energy absorption is approximately proportional to the electron densityof the absorber in the energy region where exposure units are valid, the tissuedoes is NOT necessarily equal to the air dose for any given exposure.


Exposure Measurement: The Free Air Chamber

How do we convert the exposure measured with a free-air chamber to dose totissue exposure to the same x-ray radiation field?




air /1 1 KgCunitX =





1 R=2.58´10-4 C×kg-1



F Another example (Cember, p178)

Energy Transfer by a Gamma Ray BeamChapter 4: Interaction of Radiation with Matter – Interaction of Photons with Matter

All characteristicX-rays escaped

Multiple Compton scattering ignored

All Compton scattered gamma rays escaped

Compton scatterin

g

Photoelectric effect

All photoelectrons, auger electrons and Compton recoil electrons are absorbed

All annihilation gamma rays escaped

Pair production

What is Energy Absorption Coefficients?

Chapter 4: Interaction of Radiation with Matter – Interaction of Photons with Matter


The total mass energy transfer coefficient is given by

÷÷ø

öççè

æ-+÷÷

ø

öççè

æ+÷øö

çèæ -=

urk

urs

ud

rt

rµ

hmc

hE

havgtr

2211

Consider the fraction of energy that may be carried away by the subsequentbremsstrahlung photons, one can define the mass energy-absorption coefficient as

( )gtren -= 1rµ

rµ

where g is the average fraction of energy of the initial kinetic energy transferred toelectrons that is subsequently emitted as bremsstrahlung photons.

Calculation of Energy Transfer and Energy Absorption



For simplicity, we consider an idealized case, in which

F Photons are assumed to be monoenergetic and in broad parallel beam.

F Multiple Compton scattering of photons is negligible.

F Virtually all fluorescence and bremsstrahlung photons escape from the absorber.

F All secondary electrons (Auger electrons, photoelectrons and Compton electrons) generated are stopped in the slab.

Under these conditions, the transmitted energy intensity (the amount of energy transmitted through a unit area within each second) can be given by

xene µ-Y=Y 0!!

Calculation of Energy Transfer and Energy Absorption


Assuming µenx<<1, which is consistent with the thin slab approximation and the energy fluence rate carried by the incident gamma ray beam is Ψ̇! J ⋅ cm"# ⋅ s"$ . Then the energy absorbed in the thin slab per second over a unit cross section area is given by

�̇�!𝜇%&𝑥 (𝐽 ⋅ 𝑐𝑚"# ⋅ 𝑠"$)

𝐴�̇�!𝜇%&𝑥 (𝐽 ⋅ 𝑠"$)

The rate of energy absorbed in the slab of area A (cm#) and thickness x is

Given the density of the material is r, the rate of energy absorption per unit mass (Dose Rate) in the slab is

�̇� = 0 12! ⋅3̇" 4⋅12#!⋅5#$ ⋅6%&(12#$)⋅9 (12): ;⋅12#' ⋅0 12! ⋅9 12

,

𝐷𝑜𝑠𝑒 𝑟𝑎𝑡𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑟: �̇� 𝐽 ⋅ 𝑔!" ⋅ 𝑠!" = �̇�𝟎(𝐽 ⋅ 𝑐𝑚!$ ⋅ 𝑠!")𝝁𝒆𝒏 𝑐𝑚!"

𝝆 ⁄𝑔 𝑐𝑚'



F Another example (Cember, p178)



D =φ ⋅E ⋅µm

ρm


F The relationship between exposure and dose is obtained from the ratio of theabsorbed dose rate and the exposure rate,

F For an X-ray flux that could induce 1 X-unit of exposure in air, it could lead tothe following amount of dose in a given tissue


F The relationship between exposure and dose is obtained from the ratio of theabsorbed dose rate and the exposure rate,

and similarly

F For an X-ray flux that could induce 1 X unit of exposure in air, it could lead to


An example:



air /1 1 KgCunitX =





1 R=2.58´10-4 C×kg-1


A few remarks:

F In the case of tissue, the ratio of dose to exposure remains approximatelyconstant over the quantum energy range of about 0.1 to 10MeV. (Why?)

F At lower energy, material with greater atomic number absorbs much moreenergy.

Photoelectric Effect

F Photoelectric interaction is with the atom in a whole and can not take place with free electrons.

photon theof frenquency theisconstant sPlanck' theis

vh

EhvE be -=-

F Photoelectric effect creates a vacancy in one of the electron shells, which leaves the atom at an excited state.


In photoelectric process, an incident photon transfer its energy to an orbital electron, causing it to be ejected from the atom.


Photoelectric Effect Cross Section

Probability of photoelectric absorption per atom is

ïïî

ïïí

ì

µenergyhigh

hvZ

energylowhvZ

5.3

5

5.3

4

)(

)(s

F The interaction cross section for photoelectric effect depends strongly on Z.

Page 49, Radiation Detection and Measurements, Third Edition, G. F. Knoll, John Wiley & Sons, 1999.

F Photoelectric effect is favored at lower photon energies. It is the major interaction process for photons at low hundred keV energy range.










F Beta radiation



3. Submersion dose







F Neutron dose



How is the human dose typically measured?

Bragg-Gray Principle




Solution

Bragg-Gray Principle: Problem StatementChapter 7: Radiation Dosimetry

F.A. Attix, Introduction to Radiological Physics and Radiation Dosimetry

• Homogeneous medium, wall (w)

• Probe - cavity - thin layer of gas (g)

• Charged particles crossing w-g interface

• Objective: find a relation between the dose

in a probe to that in the medium

• Basis for dosimetry

wall Dw

+-

gasDg

Q

Bragg-Gray PrincipleChapter 7: Radiation Dosimetry

wall Dw

+-

gasDg

Q

If we look at the very thin layers of wall media immediately adjacent to the interface, then the flux of the charged particles is almost unchanged across the boundary. The dose rate to the wall is given by

where 𝛍w is the linear energy absorption coefficient.

Then the ratio of dose (rate) in the wall and in the gas is

For charged particles, the linear energy absorption coefficient 𝜇 is roughly the same as the linear stopping power, 𝑠 = !"

!#,

therefore



•Two conditions:

• Thickness of gas layer is much smaller than the range of secondary

charged particles (medium g is close to w in atomic number).

• The absorbed dose in the cavity is deposited entirely by the charged

particles crossing it.

•Additional assumptions:

• Existence of CPE.

• Absence of bremsstrahlung generation.

• No backscattering of charged particles.

Absorbed Dose Measurement: Bragg-Gray Principle


Conditions for Reaching the Electronic EquilibriumF Dimension of the gas volume is small compared to the range of the secondary

charged particles.F Wall thickness > maximum range of secondary charged particles.F Wall thickness is not great enough to significantly attenuate the incident radiation.F Wall and gas have similar atomic compositions.

Absorbed Dose Measurement: Bragg-Gray Principle


tracks of secondary electrons


Absorbed Dose Measurement: Bragg-Gray PrincipleChapter 7: Radiation Dosimetry

F The Bragg-Gray principle provides a means of relating ionizationmeasurements in a gas volume to the absorbed dose in some convenientmaterials (such tissue equivalent materials) from which a dosimeter can befabricated.

F If the gas cavity is surrounded by a wall medium of proper thickness toestablish electronic equilibrium, then the energy absorbed per unit mass of thewall, dEm/dMm, is related to the energy absorbed per unit mass of gas,dEg/dMg, by

where Sm is the main mass stopping power of the wall medium and Sg is themass stopping power of the gas to the secondary electrons.


where Sm is the mean mass stopping power of the wall medium to theequilibrium secondary electrons generated by the specific radiation-of-interest.

𝑆 = #!

"

𝑆 𝐸 ⋅ 𝑃 𝐸 ⋅ 𝑑𝐸 = (

!

"

)𝑑𝑇𝑑𝑥 #

⋅ 𝑃 𝐸 ⋅ 𝑑𝐸 ,

where ;()(* +

is the linear stopping power of

the given media to electrons of energy E.


Chapter 5: Interaction of Radiation with Matter – Interaction of Beta Particles

Specific energy loss: the linear rate of energy loss by an electron though excitationand ionization, which is given by

Specific Energy Loss and Specific Ionization

medium. absorbing theofdensity theis where

)gcm( dxdE

)cmgdensity()cm(lossenergy specific 2

3

rr

×== MeVMeVS


Measurement of X- and Gamma Ray DoseChapter 7: Radiation Dosimetry

F For gamma rays with greater energies

Chapter 7: Radiation Dosimetry

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Transcript of Chapter 7: Radiation Dosimetry