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International Atomic Energy Agency
ASSESSMENT OF OCCUPATIONAL EXPOSURE DUE TO INTAKES OF
RADIONUCLIDES
Uncertainties and Performance Criteria
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Interpretation of Measurement Results – Unit Objectives
The objective of this unit to identify and define the criteria that are used to characterize the quality of the measurement process for both direct and indirect methods. It will also identify sources of uncertainty in measurement and interpretation and give an estimate of expected magnitudes.
At the completion of this unit, the student should understand how to calculate Minimum Detectable Activity and establish adequate accuracy criteria for measurement bias and precision.
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Interpretation of Measurement Results - Unit Outline
Measurement Uncertainties
Intake and Dose Assessment Uncertainties
Performance Criteria: Accuracy
Performance Criteria: Sensitivity
MDAs - Examples
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Measurement Uncertainties
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Dose determination uncertainties
Measurement
?1
Direct or indirectmeasurements
Body/organ content, Mor
Excretion rate, R
Interpretation
e(g)j
m(t)
Estimatedintake
Committedeffective dose
?2
?3
Body/organ content, Mor
Excretion rate, R
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Measurement uncertainties
Usually most straightforward to estimate Counting statistics dominate at low activities For radionuclides that are,
Easily detected, and In sufficient quantity,
counting statistics are small compared to other uncertainties
Systematic uncertainties are important Correction for activity remaining previously
measured intakes may be necessary
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Common measurement uncertainties
Statistical counting errors Distribution in the body Absorption by overlying tissue (low energy
photons) External contamination of the subject or
measurement system Calibration errors
Source activity Simulation accuracy
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Estimated Direct Measurement uncertainties*
Source of uncertainty
Estimated magnitude
1 σChest wall thickness determination
15% to 300% worst case for 17 keV
Geometry errors – Subject size and shape departure from single-size calibration model
10% for good geometries (I m arc, linear w/front /back counts)
15-20% for common geometries (linear w/counts from 1 side, 50 cm arc)
40% for poor geometries (detector in contact w/body)
Positioning of subject 10-15% for whole body
* From ANSI 13.30 (1996)
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Typical uncertainties for assessing fission product isotopes*
Source of UncertaintyEstimated
Uncertainty
DepthLength WidthHeight-WeightAnalysis TechniqueCalibrationCounting StatisticsTotal Estimated Uncertainty
12%5%7%3%5%7%
40%
* From Toohey, et al,
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Typical uncertainties for U lung counting
Source of UncertaintyEstimated
UncertaintyChest DepthChest Wall ThicknessActivity LocationDetector PlacementSubject BackgroundCalibrationCounting StatisticsTotal Estimated Uncertainty
12%15%5%5%
10%5%
40%90%
* From Toohey, et al,
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Typical uncertainties for Pu lung counting
Source of error Uncertainty
Subject background 50%
Counting statistics 50%
Chest wall thickness 40%
Non-uniform distribution 70%
Calibration 20%
Overall uncertainty 110%
* From Toohey, et al,
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Estimated Indirect Measurement uncertainties
Several parameters contribute to indirect measurement uncertainties
The uncertainty associated with most are highly variable
Typical uncertainties associated with the radiochemistry are of the order of 3%
More details can be found in the USDOE Laboratory Accreditation Program report – ANSI N 13.30 and ISO 12790-1
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INTRODUCTION OF SF
• The recently developed IDEAS Guidelines for the assessment of internal doses from monitoring data suggest default measurement uncertainties (i.e. scattering factors, SF) to be used for different types of monitoring data.
• The SF values represent the geometric standard deviation of the distribution of all results, supposed to be approximated by log-normal distribution.
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INTRODUCTION OF SF
• The IDEAS guidelines consider two types of uncertainty : • Type A : connected to counting statistic
and decreasing with the increasing of activity and counting time (Poisson distribution)
• Type B : all other components of uncertainty also connected with inter and intra-subject variability (e.g. in excretion)
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INTRODUCTION OF SF
SF values are important. For these issues.
• They are needed to assess the uncertainty in the estimated intake and dose.
• They determine the relative weighting of data in fitting process and can effect the estimated intake when different types of monitoring data are used simultaneously.
• They enable rogue data to be identified objectively• They enable objective (statistical) criteria (goodness-of-fit)
to be calculated, which are used to determine whether the predictions of the biokinetic model (with a given set of parameter values) used to assess the intake and dose are inconsistent with the measurement data.
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INTRODUCTION OF SF
• The IDEAS Guidelines assume the overall uncertainty on an individual monitoring value can be described in terms of a lognormal distribution and the SF is defined as the geometric standard deviation (GSD).
• This approximation is valid if Type A errors are relatively small (<30%). Thus, it is assumed that if the measurements could be repeated, hypothetically at the same time, then the distribution of the measurement results could be described by a lognormal distribution.
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INTRODUCTION OF SF
• SF values depend on type of monitoring measurement. Default values are reported in the following slides.
• When the type A component of the uncertainty is small (< 30%) the type B component alone could be used for uncertainty.
BA SFSFSF 22 lnlnexp
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SF default values for in-vivo measurements
SF values depend on type of monitoring measurement. For in-vivo measurement types:
In vivo measurements
SF values
(Type B uncertainty)
Low photon energy
E < 20 keV2.1
Intermediate photon energy
20 keV < E < 100 keV1.3
High photon energy
E > 100 keV1.2
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SF default values for in-vivo measurements
SF values depend on type of monitoring measurement. For in-vitro measurement types:
In vitro
measurements
SF values
(Type B uncertainty)
URINE
For HTO after inhalation1.1
URINE
Normalized 24 h excretion1.7
URINE
Spot urine data2.0
FECES
Inhalation (Pu-Am)2.5
FECES
Wound (Pu)3.1
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Intake and Dose Assessment Uncertainties
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Some sources of assessment uncertainty
Mode of intake
Physical and chemical form of material
Particle size (AMAD) of the aerosol
Time pattern of intake (acute vs. chronic)
Errors in biokinetic and dosimetric models
Individual variability in biokinetic and dosimetric parameters
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Intake assessment uncertainties
Difficult to quantify in routine monitoring - measurements are made at pre-determined times are unrelated to time of intakes
Compromise between measurement interpretation quality and the practical limitations linked to measurement frequency
Monitoring intervals should be selected so that underestimates due to unknown time of intake are ≤ 3
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Intake assessment uncertainties
Practically, this is a maximum since the actual distribution of the exposure in time is unknown
Statistically, the error is not systematically the same for all the assessments
The random distribution of the exposure makes such an error clearly lower than a factor of 3
If intake occurs just before sampling or measurement, it could be overestimated ≥ 3
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Intake assessment uncertainties
Particularly important for excreta monitoring daily fractions excreted can change rapidly immediately after intake
If a high result is found in routine monitoring, it would be appropriate to repeat the sampling or measurement a few days later adjust the estimate of intake accordingly
Samples could also be collected after a period of non-exposure, e.g. after weekend or holiday
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Assessment uncertainties
Models used to describe radionuclide behavior are used to assess intake and dose
Reliability of dose estimates depends on the accuracy of the models, and limitations on their application
This will depend upon many factors, including: Knowledge of the time of intake, and Whether the intake was acute or chronic
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Assessment uncertainties
If the sampling period does not enable the estimation of the biological half-life, assumption of a long body retention may lead to an underestimate of the intake and the committed effective dose
The degree of over- or under-estimation of the dose depends on the body retention pattern
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Assessment uncertainties
Radionuclide behavior in the body depends upon their physicochemical characteristics
Particle size of inhaled radionuclides is a particularly important for influencing deposition in the respiratory system
Gut absorption factor f1 substantially influences effective dose following ingestion
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Assessment uncertainties
When exposures during routine monitoring are well within limits on intake, default parameters may be sufficient to assess intake
If exposures approach or exceed these limits, more specific information on;
Physical form and chemical form of the intake, and
Characteristics of the individual,
may be needed to improve the accuracy of the model predictions
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Intake fraction, m(t) depends on several factors
Time after intake, d0 10 100 1000 10000
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
m(t)Whole body
Lungs
Urine
Feces
Intake pattern (acut. vs. chr.) Deposition siteTime after intake Particle size Absorption rate (F, M or S) Mode of intake
60Co, inhalation type M
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Performance Criteria:Accuracy
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Performance criteria
Accuracy Bias (Systematic errors)
How well can a given measurement be reproduced.
Repeatability or Precision (Random errors)How close is the mean of a series of measurements to the true value
Sensitivity (MDA)
What is the lowest value of a quantity that can be measured?
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Performance criteria - Bias
ai
aiiri A
AAB
where: Bri = relative bias for the ith measurement
Ai = measured activityAai = actual activity for the ith
measurement
Definition:
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Performance criteria - Bias
For a test or measurement category,
Where: Br = Relative bias for the category
n = number of replicate measurements
n
BBB
n
iri
rir
1
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Performance criteria – Repeatability*
Definition:
where: SBr = measurement repeatability for the test or measurement category
* Also termed Precision
11
2
n
BBS
n
irri
Br
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Accuracy - How close is close enough?
When the activity Aai is at or above the specified Minimum Testing Level (MTL),
Relative bias, Br
- 0.25 Br +0.50
Relative repeatability, SBr
SBr 0.40
These values used by ISO and USDOE Laboratory Accreditation Program
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MTL Values for Direct Measurements
Measurement Category Type Radionuclide MTL
I. Transuranium elements via L x-rays
Lung 238Pu 9 kBq
II. Americium-241 Lung 241Am 0.1 kBq
III. Thorium 234Lung
234Th in equilibrium w/ parent 238U
0.5 kBq
IV. Uranium-235 Lung 235U 30 kBq
V. Fission and activation products
Lung
Any two: 54Mn, 58Co, 60Co, 144Ce + 134Cs & 137Cs/137Ba
3 kBq
30 kBq
3 kBq
VI. Fission and activation productsTotal body
All of: 134Cs, 137Cs/137mBa, 60Co & 54Mn
3 kBq
VII. Radionuclides in the thyroid Thyroid 131I or 125I 3 kBq
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MTL Values for Indirect Measurements
Measurement category Radionuclide MTL(per L or per sample)
I. BETA activity: average energy < 100keV
3H, 14C35S228Ra
2 kBq
20 kBq
0.9 kBq
II. BETA activity: average energy ≤ 100 keV
32P89, 90Sr or 90Sr
4 Bq
III. ALPHA activity: isotopic analysis
228,/230Th or 232Th234/235U or 238U237Np238Pu or 239/240Pu
241Am
0.02 Bq
0.02 Bq
0.01 Bq
0.01 Bq
0.01 Bq
IV. Elements (mass/volume) Uranium 20 μg
V. GAMMA (photon) activity
137Cs/137mBa60Co125I
2 Bq
2 Bq
0.4 kBq
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Accuracy - How close is close enough?
ICRP Publication 75, General Principles for the Radiation Protection of Workers:
For external dosimetry a factor of 1.5 at the limits (20 mSv/year)
The overall uncertainty in the dose from internal exposure, is likely to be greater than for external exposure
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Accuracy - How close is close enough?
ICRP Publication 75, General Principles for the Radiation Protection of Workers:
Sampling frequencies should be chosen to avoid errors due to intake uncertainties of more than about a factor 3
For less simple programs, e.g. for insoluble plutonium, total uncertainties may be about one order of magnitude.
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Performance Criteria: Sensitivity
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Two terms describe sensitivity
Minimum Detectable Activity (MDA) (a priori)
Minimum activity that can be detected
Probability, α, of false positive (Type I error)
Probability, β, of false negative (Type II error)
Decision level, LC, (a posteriori)
The total count value or final measurement of a statistical quantity, LC, at or above which the decision is made that the result is positive
Probability, α, of false positive (Type I error)
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Confidence levels and k values
α 1-β k0.001 0.999 3.090
0.005 0.995 2.576
0.010 0.990 2.326
0.025 0.975 1.960
0.050 0.950 1.645
0.100 0.900 1.282
0.200 0.800 0.842
0.250 0.750 0.675
0.300 0.700 0.525
0.400 0.600 0.254
0.500 0.500 0
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Standard Deviation
11
2
N
xxs
N
ii
where: s = standard deviation of a set of N measurementsxi = ith measurement in the set
x = mean of the set of measurements
Estimate of the relative standard deviation for a single measurement:
sB = standard deviation of the appropriate blank samples0 = standard deviation of the net subject or sample count
i
i
Xx
s
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Illustration of LC and MDA relationship
0 Lc MDA
(a) (b)α
Background
Not detected May be
Will be
Detected
kαsB
sB
(c)s0kβs0
0 – Value of background distribution
LC – The likelihood that the sample distribution characterized by LC was not really positive (false positive) is α
MDA – The likelihood that a sample distribution characterized by the MDA will be missed (false negative) is β and is not really positive (false positive) is α
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Minimum detectable activity - MDA
Values assigned to MDA depends on the risk of making an error, false positive or false negative.
Simplification: Assume β = α, and β = α = 0.05Then kα = k1-β = 1.645 = k
where: s0 = standard deviation of net subject countsK = efficiencyT = subject counting time
TK
s.
TK
skMDA
329332 00
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Minimum detectable activity - MDA
202
210
1BB s
mss
where: sB1 = standard deviation in subject counts with no actual activity
sB0 = standard deviation in unadjusted blank counts
It can be assumed that sB1 = sB0 = s0, and m = 1Then, s0 = sB2 = 1.415sB, where sB is the standard deviation of a total blank count
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Minimum detectable activity - MDA
TK
s.MDA B
3654
For direct measurements, MDA becomes:
For indirect measurements:
where: R = chemical recoveryλ = radiological decay constant Δt = elapsed time between reference time and time of count
tB
eTRK
s.MDA
3654
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Direct measurement MDAs*
Measurement category Organ MDAI. Transuranium elements via x-rays Lungs 185 Bq/A
II. 241Am Lungs 26 Bq
III. 234Th Lungs 110 Bq
IV. 235U Lungs 7.4 Bq
V. Fission and activation products Lungs 740 Bq/A
VI. Fission and activation products Whole body 740 Bq/A
VII. Radionuclides in the thyroid Thyroid 740 Bq/A
* From ANSI 13.30 A is the number of photons per nuclear transformation – L x-rays
for transuranium elements, and gamma rays for fission and activation products
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Indirect measurement MDCs (urine)*
Measurement Category
Nuclide MDC
I Beta - Average energy ≤ 100 keV
3H, 14C, 35S147Pm210Pb, 228Ra, 241Pu
370 Bq/L
0.37 Bq/L
0.19 Bq/L
II. Beta – Average energy > 100 KeV
32P, 89/90Sr or 90Sr131I
0.74 Bq/L
3.7 Bq/L
III. Alpha – Isotopic specific measurements
210Po, 226Ra, 228/230/232Th, 234/235/238U237Np, 238/239/240Pu, 241Am, 242/244Cm
3.7 mBq/L2.2 mBq/L
IV. Mass determination Uranium (natural) 5 μg/L
V. Gamma or x-rays Emitters with photons ≤ 100 keV 2 Bq L-1/A
VI. Gamma or x-rays Emitters with photons > 100 keV 2 Bq L-1/A
* From ANSI 13.30A is the number of photons per nuclear transformation – L x-rays for transuranium elements, and gamma rays for fission and activation products
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Indirect measurement MDAs (faeces)*
Measurement Category
Nuclide MDA
VII. Alpha – Isotope specific measurements
234/235/238U, 228/230/232Th, 238/239/240Pu, 241Am
37 mBq/sample
VIII. Beta – Average energy > 100 keV
89/90Sr or 90Sr 0.74 Bq/sample
IX. Gamma or x-rays Emitters with photons ≤ 100 keV 2/A Bq/sample
X. Gamma or x-rays Emitters with photons > 100 keV 2/A Bq/sample
* Minimum detectable concentration - From ANSI 13.30A is the number of photons per nuclear transformation – L x-rays for transuranium elements, and gamma rays for fission and activation products
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MDAs – Examples
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Determination of MDA - Example
90Sr by Beta Gas Flow Proportional Counting
20 reagent blanks were counted for 1 hour each – 3600 s
Total counts
83 69 53 72 59
77 70 62 88 53
66 73 59 55 74
72 70 65 68 61
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Determination of MDA - Example
90Sr by Beta Gas Flow Proportional Counting
B = 67.4 counts
SB = [(Xi – 67.4)2/19] = 9.4
Counting efficiency, K = 0.36
Chemical yield = 0.81
Bq.
..
..MDA 0440
8103603600
349654
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Determination of MDA - Example
Whole body counting for fission and activation products
Radionuclide 137Cs 60Co
Organ Body Lungs
Counts in peak region - B 9 8
SB =B 3 2.8
Count time, T – s 600 600
Calibration factor, K 1.3510-4 2.9710-4
MDA - Bq 209 90
TK
s.MDA B
3654
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References
HEALTH PHYSICS SOCIETY, Performance Criteria for Radiobioassy, An American National Standard, HPS N13.30-1996 (1996).
INTERNATIONAL ATOMIC ENERGY AGENCY, Occupational Radiation Protection, Safety Guide No. RS-G-1.1, ISBN 92-0-102299-9 (1999).
INTERNATIONAL ATOMIC ENERGY AGENCY, Assessment of Occupational Exposure Due to Intakes of Radionuclides, Safety Guide No. RS-G-1.2, ISBN 92-0-101999-8 (1999).
INTERNATIONAL ATOMIC ENERGY AGENCY, Indirect Methods for Assessing Intakes of Radionuclides Causing Occupational Exposure, Safety Guide, Safety Reports Series No. 18, ISBN 92-0-100600-4 (2002).
International Standards Organization, Radiation Protection – Performance Criteria for Radiobioassay – Part 1: General Principles, ISO TC 85/SC2 (1999).