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Transcript of RDII - Chapter 11 Handout
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Dosimetry Fundamentals
Chapter 11
F.A. Attix, Introduction to Radiological
Physics and Radiation Dosimetry
Outline
Introduction
Dosimeter model
Interpretation of dosimeter measurements
Photons and neutrons
Charged particles
General characteristics of dosimeters
Summary
Introduction
Radiation dosimetry deals with the determination(i.e., by measurement or calculation) of theabsorbed dose or dose rate resulting from theinteraction of ionizing radiation with matter
Other radiologically relevant quantities areexposure, kerma, fluence, dose equivalent, energyimparted, etc. can be determined
Measuring one quantity (usually the absorbed
dose) another one can be derived throughcalculations based on the defined relationships
Dosimeter
A dosimetercan be generally defined as
any device that is capable of providing a
readingR that is a measure of the absorbed
doseDgdeposited in itssensitive volume V
by ionizing radiation
If the dose is not homogeneous
throughout the sensitive
volume, thenR is a measure of
mean value
Dosimeter
Ordinarily one is not interested in measuringthe absorbed dose in a dosimeters sensitivevolume itself, but rather as a means ofdetermining the dose (or a related quantity) foranother medium in which direct measurementsare not feasible
Interpretation of a dosimeter reading is thecentral problem in dosimetry, usuallyexceeding in difficulty the actual measurement
Simple dosimeter model
A dosimeter can generally be considered asconsisting of a sensitive volume Vfilled with a
mediumg, surrounded by a wall (or envelope,
container, etc.) of another medium w having a
thickness t 0
A simple dosimeter can be treated in
terms of cavity theory, the sensitive
volume being identified as the
cavity, which may contain a
gaseous, liquid, or solid medium g
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Simple dosimeter model The dosimeter wallcan serve a number of functions
simultaneously:
being a source of secondary charged particles that contributeto the dose in V, and provide CPE or TCPE in some cases
shielding Vfrom charged particles that originate outside thewall
protecting Vfrom hostile influences such as mechanicaldamage, dirt, humidity, light, electrostatic or RF fields, etc.,that may alter the reading
serving as a container forgthat is a gas, liquid, or powder
containing radiation filters to modify the energy dependencyof the dosimeter
Interpretation of dosimeter
measurements: photons and neutrons
Under CPE condition
Consider a dosimeter with a wall of medium w, thick enough
to exclude all charged particles generated elsewhere, and at
least as thick as the maximum range of secondary charged
particles generated in it by the photon or neutron field
If the wall is uniformly irradiated, CPE exists in the wall
near the cavity, therefore knowing Dw can calculate energy
fluence Y of the primary field
CPE en /cD K Y
Interpretation of dosimeter
measurements: photons and neutrons
The dosimeter reading provides us with a measureof the doseDgin the dosimeters sensitive volume
If the latter is small enough to satisfy the B-Gconditions, we can find Dw fromDg
The doseDx in any other medium x replacing thedosimeter and given an identical irradiation underCPE conditions can be obtained from
photonsfor//
wen
xen
w
CPE
x DD
Interpretation of dosimeter
measurements: photons and neutrons
For neutrons the CPE condition results in
Fn is kerma-factor, F is neutron fluence
Therefore the doseDx in the medium of interest x
CPE
nD K F F
CPE
for neutronsn x
x wn w
FD D
F
Interpretation of dosimeter
measurements: photons and neutrons
For higher-energy radiation (h 1 MeV orTn 10 MeV), CPE fails but TCPE takes its place indosimeters with walls of sufficient thickness
For photons TCPE condition provides relationship
For neutrons
RelatingDw to Y orF then requires evaluation of =D/Kc for each case
TCPE
en1 /
c cD K x K Y
TCPE
1nD K x K F F
Interpretation of dosimeter
measurements: photons and neutrons
The exposureX(C/kg) for photons can in turn bederived from the absorbed doseDair(forx = air)through this relation:
This relationship can be extended for higherenergies where TCPE exists, dividing Dairby
CPEair
air
air 33.97
DeX D
W
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Interpretation of dosimeter
measurements: photons and neutrons
The value of is generally not much greater than
unity for radiation energies up to a few tens of MeV,and it is not strongly dependent on atomic number
Thus for media w andx not differing very greatly in
Z, the equations forDx are still approximately valid
If the dosimeter has too large a sensitive volume for
the application of B-G theory, Burlin theory can be
used to calculate the equilibrium dose Dw from
requires sensitive-volume size dparameter
gD
Advantages of media matching
Matching parameters:
Atomic compositions
The density state (gaseous vs. condensed), which
influences the collision-stopping-power ratios for
electrons by the polarization effect
Advantages:
Influence of cavity theory is minimized
No need to know the radiation energy spectrum
Advantages of media matching
w=g: if the wall and sensitive-volume media of the
dosimeter are identical with respect to composition
and density, thenDw =Dgfor all homogeneous
irradiations
w=g=x: the dosimeter would be truly representative
of that medium with respect to radiation interactions,
andDx =Dw =Dg
Unfortunately, dosimeters are only available in afinite variety, therefore have to rely on cavity theory
Media matching in photon
dosimeters (w=g) The Burlin cavity relation
Ifw andgare matched, the dosesDw= Dgand
This relationship is hard to satisfy, especially forwandgof different atomic compositions
en(1 )
g
g g
m w
w w
Dd S d
D
en 1
g
g
m w
w
S
Media matching in photon
dosimeters (w=g)
A more flexible and practical relationship
The Burling relation then becomes independent of d
since
It is relevant, for example, if photons interact onlyby the Compton effect ingand w: en/ ~the masscollision scattering power of the secondary electrons~ to the number of electrons per gram, NAZ/A;
n (Z/A)g/(Z/A)w
en
g
g
m w
w
S n
nDD wg /
Matching the dosimeter to the
medium of interest when wg
If the wall medium wg, matching to medium xdepends on the dosimeter volume size
If the sensitive volume is small (d= 1 in Burlins
cavity theory), then the wall should be matched to
mediumx, to minimize the need for spectral
information
Dose inx can be obtained from
en
w
g g gwm w
x w x x
D D DS
D D D
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Matching the dosimeter to the
medium of interest when wg If the sensitive volume is large (d= 0 in Burlins
cavity theory), the wall influence on the dose in themediumgis entirely lost
Mediumx should be matched togand dose inx can be
obtained from
For a general case of intermediate size cavity (0
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Interpretation of dosimeter
measurements: charged particles
One of the functions of the dosimeter wall is to provide -rayCPE for the sensitive volume
This will occur if: 1) the wall matches the sensitive volumewith respect to atomic number and density state, 2) is at leastas thick as the -ray range, and 3) is uniformly irradiatedthroughout by the primary charged particles
The importance of the wall as a -ray generator is greatest formeasurements of the dose in free space
For measurements where dosimeter is immersed in a medium:
Wall thickness is not important if the medium, the wall, and thesensitive volume are all similar in composition
If they differ significantly electron scattering affects the result the most
Interpretation of dosimeter
measurements: charged particles
There is no general and physically realistic cavity
theory for relating the dose in a dosimeter to that inthe medium at the point of measurement in an
electron beam
The problem appears to be with electron scattering,
resulting in the measured dose dependence on the
shape and orientation of the cavity
A successful theory must account for it as a first-
order effect
General characteristics of
dosimeters
Absoluteness
Precision and accuracy
Dose range
Dose rate range
Stability
Energy dependence
Miscellany (configuration, relevantcalibration, reusability, etc.)
Absoluteness
An absolute dosimetercan be assembled and used tomeasure the absorbed dose deposited in its ownsensitive volume without requiring calibration in aknown field of radiation
It may need some calibration not involving radiation(e.g, electrical-heating for a calorimetric dosimeter)
Calibration, however, offers certain advantages:
It can be stated in terms of some quantity of interest such astissue dose (as opposed to dose in g) or exposure
It can also provide traceability to a standardizationlaboratory thus minimizing errors that may go undetected
Absoluteness Three types of dosimeters are generally regarded as
being capable of absoluteness: Calorimetric dosimeters
Ionization chambers
Fricke ferrous sulfate dosimeters
The calorimetric dosimeter has the fundamentaladvantage of directly measuring the heat to whichthe absorbed dose degrades, without dependence onany coefficient of conversion such as to ionizationor to chemical yield
The absoluteness of a dosimeter is independent ofits precision or its accuracy
Precision and accuracy
The concept of theprecision or reproducibility ofdosimeter measurements has to do with random errorsdue to fluctuations in instrumental characteristics,ambient conditions, and so on, and the stochasticnature of radiation fields
Precision can be estimated from the data obtained inrepeated measurements, and is usually stated in termsof the standard deviation
High precision is associated with a small standarddeviation; a high-precision instrument is capable ofexcellent measurement reproducibility if properly used
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Precision and accuracy
The accuracy of dosimeter measurements expressesthe proximity of their expectation value to the true
value of the quantity being measured
It is impossible to evaluate the accuracy of data fromthe data itself, as is done to assess their precision
Accuracy is a measure of the collective effect of theerrors that influence the measurements (propercalibration, exactly known volume, etc.), relevant tooperation of the dosimeter as an absolute instrument
In experiments that are limited to relativemeasurements, only the precision is important
Dose range: sensitivity
To be useful, a dosimeter must have adequate dosesensitivity throughout the dose range to bemeasured
A constant dose sensitivity throughout the rangeprovides a linear response (dr/dDg=const), that isdesirable for ease of calibration and interpretation
However, knowing the function r(Dg), evennonlinear but single-valued, may be acceptable,though it requires that the calibration be carried outat multiple doses to provide a calibration curve
Dose range: lower limit
The lower limit of the useful dose range may beimposed by the instrumental backgroundor zero-dose reading r0, observed whenDg= 0 (sometimesreferred to as spurious response)
Examples ofr0 include charge readings due to ion-chamber insulator leakage, and thermo-luminescence dosimeter readings resulting fromresponse of the reader to infrared light emission bythe dosimeter heater
The instrumental background should be subtractedfrom any dosimeter reading
Dose range: lower limit
The lower limit of the practical dose range of adosimeter is usually estimated to be the dose necessaryto double the instrumental background reading
If is the S.D. of the average of a group of radiationreadings r, and 0 is the S.D. of the average of thebackground readings r0, then the S.D. of the netradiation reading rr0 is given by
2 2
net 0
Dose range: lower limit
If the background reading is negligibly small, thenthe lower dose limit is imposed by the capability
of the dosimeter readout instrument to provide a
readable value ofrfor the dose to be measured Dg
Readable value ris typically considered to be
10% of full scale on analogue instruments, or
contain more than three significant figures on
digital readouts
A more sensitive scale may be required
Dose range: upper limit
The upper limit of the useful dose range of a dosimetermay be imposed simply by external instrumentallimitations (reading off scale of an electrometer)
Alternatively, an inherent limit may be imposed by thedosimeter itself due to:
a) Exhaustion of the supply of atoms, molecules, or solid-stateentities (traps) being acted upon by the radiation to
produce the reading
b) Competing reactions by radiation products, for example inchemical dosimeters
c) Radiation damage to the dosimeter (e.g., discoloration oflight-emitting dosimeters, damage to electrical insulators)
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Dose range: upper limit
Usually the upper limit of the dose range is manifested by adecrease in the dose sensitivity (dr/dDg) to an unacceptablevalue
It may be reduced to zero, or to a negative value, whichcauses the dose-response function to become double-valued
Dose-rate range: integrating
dosimeters If a dosimeter is used for measuring the time-integrated
dose (not the dose rate), then its reading should notdepend on the dose rate
Usually the low-dose-rate limitation is imposed by thelower dose limits of the dosimeter
One case of a genuine low-dose-rate limitation isreciprocity-law failure in photographic film dosimeters
It occurs only with low-LET radiation (x rays or electrons)
It is due to the necessity for several ionizing events to occurin a single grain of silver bromide to make it developable
Dose-rate range: integrating
dosimeters The upper limit of dose-rate independence usually
occurs when charged-particle tracks are createdclose enough together in space and time to allow theions, electron-hole pairs, or active chemical productssuch as free radicals to interact between tracks
In an ion chamber this is called general or volumeionic recombination
Similar back reactions also occur in solid or liquid
dosimeters, resulting in a loss of contribution to thereading r
Dose-rate range: dose-rate meters
The dose-rate-measuring dosimeters should providereadings proportional to the dose rate dDg/dt, or at leastto be a single-valued function of it
The upper limit on the usable dose-rate range is usuallyimposed by saturation such as ionic recombination, etc.
The counting of two or more events as one when theyoccur temporally too close together in pulse-countingdosimeters also may cause saturation
The response time constantcharacterizes the capabilityof the dosimeter to resolve separate pulses and possiblymeasure the pulse shape in a pulsed radiation field
Stability
The characteristics of a dosimeter should be stablewith time until it is used
That includes shelf life and time spent in situ untilirradiated (e.g., worn by personnel if a health-physicsmonitoring dosimeter)
Effects of temperature, atmospheric oxygen orhumidity, light, and so on can cause a gradual changein the dose sensitivity or the instrumental background
Photographic, chemical, or solid-state dosimeters aregenerally more susceptible to these influences than ionchambers or counters
Stability
After irradiation the latent reading in some types ofintegrating dosimeters (e.g., photographic,chemical, solid-state) may be unstable, sufferingfading losses during the time interval betweenirradiation and readout
Harsh ambient conditions may aggravate this effect
If time-dependent fading losses are unavoidable, itis advantageous to make them as reproducible aspossible through standardization of laboratorytechnique so that a fading correction can be appliedto the readings
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Energy dependence
The energy dependence of a dosimeter is the dependence of its
reading r, per unit of the quantity it is supposed to measure,
upon the quantum or kinetic energy of the radiation
The reading robtained from adosimeter vs. some dosimetricquantity J(such as exposure,absorbed dose in water, etc.)
A: The calibration curves obtainedat the three different energies
C: Plot r/J vs. energy to obtain theenergy-dependence curves; forJ1andJ2 they are different forE>E1
D: Energy-independent dosimeter:r vs. J is the same for all energies
linear linear
non-linear non-linear
energy-
dependent
energy-
independent
Energy dependence in health physics
Dependence of the dosimeter reading, per unit of x- or-rayexposure, on the quality of the beam, r/Xvs.E
60Co -rays are frequently used as the reference energy fornormalization, producing energy-dependence curves for dosimetersmade of materials >, =, and < than airin atomic number
Energy dependence in health physics The shape of the curves can be estimated by:
where grefers to the material in the dosimeters sensitive volume
This equation is based on the assumptions that:
1. The dosimeters sensitive volume is in charged-particle equilibrium, andthe wall medium w =g
2. Attenuation is negligible in the dosimeter, both for incident photons andfluorescence photons generated in the dosimeter
3. A given absorbed dose to the sensitive volume produces the same reading,irrespective of photon energy (i.e., the dosimeter is LET-independent)
en
en air
en
1.25en air
1.25
/
/
/
/
g
E E
g
r
X
r
X
Energy dependence in radiation
therapy: absorbed dose
Dependence of the dosimeter reading per unit of
absorbed dose in water on the photon or electron-
beam energy
Absorbed dose always refers to water (or muscle
tissue) unless otherwise specified
In the megavolt region the differences between
water and tissue are small (~1%)
Energy dependence in radiation
therapy: absorbed dose
For x rays the equation by which a homogeneousdosimeters energy dependence can be estimated is
which depends on water as a reference material and60Co rays for normalization
This equation can be used over the energy rangefrom 1.25 to 50 MeV for LiF and bone-equivalentdosimeters
en en waterwater
water 1.25 en en water 1.25
/ / //
/ / / /
gE E
g
r D
r D
Energy dependence in radiation
therapy : absorbed dose
X-ray energy dependence estimated for a LiF and a bone-equivalent dosimeter, in terms of response per unit absorbed dosein water, normalized to 60Co rays
The rise at higher energies results from increase in pair production
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Energy dependence in radiation
therapy : absorbed dose Because of the large secondary-electron ranges at
MeV energies, this equation is only satisfied to theextent that TCPE is present, g= w, and parameteris the same in water as in the dosimeter
This requires wall thickness that would produceconsiderable x-ray attenuation, and just beimpractical for the size of the resulting dosimeter
In radiotherapy dosimetry these problems areusually avoided by doing the measurements in aphantom, letting it comprise most of the dosimeterswall thickness
Energy dependence in radiation
therapy: absorbed dose
For electron beams of kinetic energy T(MeV), the
corresponding equation for estimating energydependence in terms of the dose to water,
normalized to T= 1 MeV, is
,
,waterwater
,
water 1 MeV ,water 1 MeV
/
/
/
/
c g
cT T
c g
c
dT dxr
dT dxD
dT dxr
D dT dx
Energy dependence in radiation
therapy: absorbed dose This approximation assumes that:
1. CPE exists for-rays entering and leaving the sensitive
volume
2. The incident electrons lose only a very small fraction of
their energy in traversing the dosimeter
3. Electron scattering is the same ingas in water
4. The reading per unit dose to the dosimeters sensitive
volume remains energy-independent (LET-independent)
Items 1 and 3 are suspect, while 2 and 4 are easily satisfied in
the energy region above 1 MeV
Energy dependence in radiation
therapy: absorbed dose
Electron-energy dependence estimated for LiF, a bone-equivalentdosimeter, and an air-filled ion chamber, in terms of response per
unit absorbed dose in water, normalized to T= 1 MeV Neither LiF nor a bone-equivalent dosimeter shows much
dependence since collision stopping-power ratios are insensitive toelectron energy unless the polarization effect is involved
Energy dependence
Dependence of the dosimeter reading per unit of absorbeddose to the material in the sensitive volume itself, on theradiation energy or beam quality
The most fundamental as it reflects the dosimeters energyefficiency, i.e., the ability of the dosimeter to give the samereading for the same amount of absorbed energy in its ownsensitive volume, regardless of radiation type or quality
It is often called LET dependence because it usuallymanifests itself as a change in the reading per unit dose asa function of charged-particle track density, due to ionicrecombination or other second-order effects that depend onthe proximity of radiation products to the dosimeter
Miscellany
The configuration of a dosimeter sometimes iscrucial to its use; for example, small size of adosimeter is of primary importance in itsapplication in vivo in patients or test animals
A dosimeter needs a relevant calibration that isappropriate to the radiation type and quality, aswell as to the quantity to be measured
The reusability of a dosimeter has severalimportant implications: reusable TLDs can beindividually calibrated; single-use dosimeters suchas film badges cannot
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Summary
General dosimeter model
Interpretation of dosimeter measurements
Photons and neutrons
Charged particles
General characteristics of dosimeters: absoluteness,precision and accuracy, dose range, dose rate range,stability, energy dependence, and others
F
max
0,
T
xc
xdT
dx
dTTD
CPEen
en
/for photons
/
xx w
w
D D