Uncertainty in internal doses: using Bayes to transfer information
from one worker to another
Anthony Jamesa*, Alan Birchallb and Matthew Puncherb
a
United States Transuranium and Uranium Registries, Washington State University,
1845 Terminal Drive, Suite 201, Richland, WA 99354-4949, USA.
b
Radiation Protection Division of the Health Protection Agency (HPA-RPD), Chilton,
Didcot, Oxon OX11 0RQ, United Kingdom.
Abstract. Uncertainty in estimates of internal doses to can arise for a variety of reasons, which include a lack
of knowledge about assumed model parameters, uncertainty in exposure conditions, paucity of measurement
data, and variability between individuals. In some cases, for example, causation or epidemiological studies, it is
essential to be able to quantify this uncertainty for each individual in the study. It is often the case that some
individuals within a cohort will have been subject to extensive measurements, enabling precise estimates of
organ doses to be derived, while for others, the measurement data are sparse. The question is how can one make
use of the measurement data on the former individuals to improve dose estimates for the latter? It will be seen
that Bayesian inference provides the mechanism for doing this, since the essence of the Bayesian approach is to
start with knowledge before the measurement data are known (prior knowledge), and then use the measurement
data to revise it (posterior knowledge). This paper illustrates the Bayesian method by taking two such cases,
who were both exposed by accidental inhalation of the same form of americium compound. Essentially, the
comprehensive bioassay data available for the first worker is used to derive posterior probability distributions of
absorption parameters for the americium material, which are used as prior information to improve the dose
assessment for the second worker. Direct assessment of the uncertainty in the second worker’s dose, both with
and without the additional information from the first worker, quantifies the improvement in dose assessment
obtained.
KEYWORDS: Internal; Dose; Americium; Bayes; Uncertainty; Epidemiology; USTUR; WeLMoS
1. Introduction
This paper demonstrates how knowledge of the absorption behavior of inhaled americium dioxide
(241AmO2), based on comprehensive bioassay follow-up of one individual, can be used to improve the
reliability of dose estimates for other workers exposed to this material. It describes the application of
the Weighted Likelihood Monte Carlo Sampling (WeLMoS) method [1-2] to derive the posterior
probability distributions of doses for a worker whose time of intake is not known precisely, and for
whom relatively sparse bioassay data are available.
In this example, which is not hypothetical, major sources of uncertainty are in the relative imprecision
of some routine urine-monitoring results, and, as in all cases, in the individual’s particle transport
rates. The WeLMoS method is used here to derive the quantities of interest (posterior distributions of
doses) directly from the bioassay data:
•
•
*
first assuming no prior knowledge of the absorption characteristics of 241AmO2;
then, utilizing as informative priors the posterior probability distributions of
absorption parameters obtained from the more comprehensively studied case.
Presenting author, E-mail: [email protected]
241
AmO2
2. Prior Information on 241AmO2 Physical Characteristics
2.1 Material Characterization
Both workers were exposed accidentally by inhalation, where the source of the inhaled material was
‘leakage’ from nominally ‘sealed’ americium dry powder sources. The physical nature and particle
size characteristics of the 241AmO2 material used in the manufacture of similar commercial sources are
known [3]. Fig. 1 is an electron micrograph of particles of ball-milled 241AmO2 powder. The powder
was sampled (in 1976) from a glove box line at Amersham Ltd (UK) used in the manufacture of
sealed α-foil (for use in fire detectors). The particles shown in this micrograph were collected by
filtering an aqueous suspension of the sampled powder using a 220-nm pore diameter membrane. The
larger particles clearly exhibit the crystalline structure (and facet angles) expected for americium (IV)
oxide. Also, highly respirable micron- and sub-micron particles are present in this source material.
Fig. 2 (also from ref. [3]) is an electron micrograph of particles from the same sample as Fig. 1, but
aged 5 months in aqueous suspension. These ‘aged’ particles are amorphous (and probably composed
of an hydroxide). Clearly, 241AmO2 is substantially less stable in an aqueous environment than, for
example, the ceramic oxides of 239PuO2 and UO2; but the transformed americium compound is not
readily dissolved by water.
Figure 1: Electron micrograph of particles filtered Figure 2: Electron micrograph of americium
from aqueous suspension of americium oxide dioxide particles after 5 months aging in
powder (inset shows crystal structure of americium aqueous suspension
(IV) dioxide)
3. Exposure Scenarios
3.1 Case with Comprehensive Follow-up (USTUR Case 0855)
In 1996, while examining an old 370 MBq supposedly ‘sealed’ 241Am source, this worker discovered
α-contamination in the vicinity of his work area. Survey revealed loose 241Am contamination, with
‘hot spots’ higher than 1 kBq/100 cm2. Approximately 6 weeks after his acute accidental intake of
americium (in the form of inhaled 241AmO2 particles) the worker, a healthy 38-y-old non-smoker,
voluntarily enrolled in the U.S. Transuranium and Uranium Registries (USTUR), as Case 0855. He
agreed to participate in a long-term bioassay and external counting study.
3.2 Case with Less Comprehensive Bioassay Data
This individual was involved in the ‘clean-up’ of a worksite that had been heavily contaminated with
241
AmO2 and other radionuclides. He did not participate directly in the cleanup work (which was
carried out with full respiratory protection), but was involved in checking other workers out of
radiation controlled areas. No specific details of the individual’s exposure circumstances can be
published at this time.
4. Available Measurements
4.1 USTUR Case 0855
The initial results of the bioassay and external counting study of Case 0855 (through 2002) were
published previously [4]. In addition to lung retention, the amount of 241Am activity taken up by the
skeleton was also measured reliably, as was the rate of urinary excretion of 241Am over the 6-y period
following the intake (Table 1).
Table 1: 241Am bioassay data available for USTUR Case 0855 Daily Urinary Excretion, mBq,
Lung Activity,
Date
Estimated from 241Am Activity in
Bq
Sampled Volume (L)*
02/10/1996
555 ± 37 (0.95)
03/20/1996
179 ± 5 (0.79)
315 ± 5
04/25/1996
169 ± 4 (0.46)
241 ± 5
05/23/1996
47 ± 2 (0.25)
246 ± 5
06/20/1996
42 ± 2 (0.80)
226 ± 5
07/25/1996
214 ± 5
08/22/1996
27 ± 3 (0.35)
195 ± 4
09/26/1996
156 ± 4
12/12/1996
146 ± 4
04/30/1997
131 ± 4
05/01/1997
29 ± 1 (0.44)
10/16/1998
109 ± 3
10/23/1998
11 ± 2 (0.70)
12/06/2001
82 ± 6
01/23/2002
7 ± 1 (0.80)
-
Skeletal Activity,
Bq
60 ± 7
68 ± 7
85 ± 7
91 ± 6
103 ± 10
103 ± 10
88 ± 10
108 ± 10
133 ± 113
168 ± 13
165 ± 14
-
*Daily excretion was estimated from the 241Am concentration measured in the collected volumes of urine
(shown in parentheses) by scaling each sample to the standard 1.6-L daily urinary volume [3].
4.2 Clean-up Worker
Table 2 gives the bioassay data available for the worker involved in worksite clean-up [5]. Several
different radiochemistry service laboratories were used to analyze his urine samples and report the
results. The sensitivity (241Am detection limit) varied substantially for these analyses. For the urine
samples between 2.1 and 384.1 d after the start of employment (Table 2), i.e., all but one of the
samples, the measured aliquots comprised a relatively small fraction of the daily excretion. The bulk
of this urine was taken for external measurement of other radionuclides of potential concern (by γspectrometry). Thus, over this period, the minimum detectable concentration of 241Am-in-urine was
relatively high, and the estimated uncertainty in each measurement is dominated by the Poisson
counting statistics, i.e., the reported standard deviation.
For the urine sample (2.345 L) collected at 1,481 d after the start of employment, the concentration of
Am was measured precisely (1.37 ± 0.24 Bq/L). However, as noted in Table 2, the true urine
collection period for this sample was longer than the reported value (of 0.88 d), giving rise to a
biased-high estimate of the daily excretion at 1,481 d. In the evaluation of dose below, no attempt is
made to correct for this sample bias.
241
Table 2: 241Am bioassay data available for this individual
Daily Urinary Excretion, mBq,
Reported Minimum
Time since
Lung Activity,
241
Estimated from Am Activity
Detectable Activity
starting work, d
Bq
in Sample Aliquot Volume (L)*
(MDA), mBq
2.1
1.52 ± 1.08 ( - )
1.12
24
0.51 ± 1.55 (0.20)
4.96
106.5
33.0 ± 10.9 (0.10)
12.4
324
17.2 ± 4.3
363
12.7 ± 2.8
380.1
-2.89 ± 4.47 (0.20)
17.5
382.1
-1.49 ± 4.80 (0.20)
22.3
384.1
5.13 ± 3.73 (0.20)
10.0
#
0.36
1,481
2.91 ×/÷ 1.20 (1.88)
241
*Except for the value at 1,481 d, daily excretion was estimated from the reported Am concentration
(measured in the aliquot volumes shown in parentheses) by scaling each sample to the standard 1.6-L daily
urinary volume [6]. The actual volume of urine excreted per day was not reported.
#
For the sample collected at 1,481 d, the actual volume of urine was recorded (2.345 L from a recorded 0.88-d
sampling period). However, the actual sampling period was not recorded. The recorded value (0.88 d) is the
time difference between the first collected urine void and the start of last urine bottle. The proper recording
time for the first urine sample should have been end of the previous (uncollected) urine void. Also, the proper
recording time for the third urine sample should have been the end of this urine void (which was also not
recorded). Therefore, the recorded sampling period (0.88 d) is biased low, and the daily urinary excretion rate
calculated for the 1,481-d sample is biased high (in the same proportion).
The physiological variability in urinary excretion over a true 24-h period is represented by a
geometric standard deviation, σg, of about 1.1 [7-8]. Here, it is assumed that a larger overall
uncertainty (σg = 1.20) is appropriate for the measured value at 1,481 d. This accounts for the
additional Poisson uncertainty in the sample count, but not for the sample bias noted in the recorded
collection period (footnote to Table 2).
5. Evaluation of specific 241AmO2 absorption characteristics using Case 0855 data
5.1 Maximum Likelihood Point Estimates
Manual, iterative application of the maximum likelihood fitting method in the IMBA Professional
Plus (IPP) software [9] yielded a simultaneous ‘best fit’ to the urine, lung and skeletal 241Am data with
overall χ2 = 37.2, for the number of degrees of freedom, NDF = 30 (P = 0.17) [10-11]. This fit, which
applies the ICRP Publication 66 Human Respiratory Tract Model (HRTM) [12] together with the
ICRP Publication 67 biokinetic model for americium [13], cannot be rejected with the χ2 test (at the
5% level of significance). The corresponding ‘most likely’ value of the 241Am intake is 11,256 Bq;
with rapidly absorbed fraction, fr = 0.45, associated ‘rapid’ rate of absorption, sr = 0.032 d-1, and slow
rate of absorption, ss = 1 × 10-4 d-1. It is notable that these ‘point estimates’ of the applicable
absorption parameters for 241AmO2 are very different from the ‘default’ values (Type M –
representing ‘moderately fast’ absorption) recommended for all americium compounds (fr = 0.1, sr =
100 d-1, and ss = 5 × 10-3 d-1) [14]. Assumption of these Type M parameter values yielded a very poor
‘best fit’ to the bioassay data (χ2 = 2,470, NDF = 30, P ∼ 0).
5.2 Bayesian Evaluation of Probability Distributions
Using the WeLMoS method [1-2], the Case 0855 bioassay data yielded directly the probability
distributions of the quantities of primary regulatory interest, i.e., the effective dose and equivalent
dose to bone surface [10-11]. We note for protection purposes, ICRP [15] defines equivalent dose and
effective dose to a reference worker using reference models and parameter values, and that doses to
individuals and associated uncertainties are primarily of concern in other applications, including
epidemiology. However, we present uncertainties in equivalent and effective dose here to illustrate
methodology, recognizing that such analyses may not be required for regulatory purposes and that all
sources of uncertainty are not addressed.
Bayesian ‘priors’ for the absorption parameters (fr, sr and ss) were chosen to represent a complete lack
of knowledge about their true values. However, this uncertainty analysis was also able to take account
of the additional uncertainty in the parameter values characterizing the rates of particle transport
within and from the respiratory tract (in this individual). The uncertainty in particle transport rates
was represented by a variable factor, KPT. This is assumed to multiply all ICRP-recommended particle
transport rates. In Publication 66 [12], ICRP expressed the uncertainty in their recommended particle
transport rates by such a multiplying factor, where 95% of the possible values lie within an order of
magnitude (approximately the recommended value × 3 and ÷ 3). Table 3 shows the priors used to
analyze the Case 0855 bioassay data. Dependences between the parameters are defined by the
resulting posterior distribution. The parameters themselves were sampled independently from their
respective priors.
Table 3: Prior distributions used to analyze bioassay data
Parameter
Range
Rapidly absorbed fraction, fr
Distribution
0–1
Uniform
Rapid absorption rate, sr (d )
0.01 – 100
Log-uniform
Slow absorption rate, ss (d-1)
1 × 10-7 – 0.01
Log-uniform
Particle transport rate factor, KPT
Median = 1, σg = 1.7
Lognormal
-1
As described elsewhere [10-11], the WeLMoS method produces the quantities of interest (e.g.,
effective dose and equivalent dose to bone surfaces) without any prior knowledge of the absorption
rates from the lung. In other words, the resulting posterior distributions of dose represent all that can
be obtained from the measurement data together with the prior information on the absorption rates, in
this case none (i.e., priors based on ignorance). However, during the Monte Carlo simulation, which
covers the whole range of possible values of clearance model parameters, the results are stored for
each iteration. By integrating over the joint posterior distribution, it is possible to obtain the
distribution of individual parameters given the data. These distributions, although not used to estimate
doses for the individual, nevertheless provide valuable new information (on absorption parameter
values for inhaled 241AmO2) which, as demonstrated below, can be applied to improve dose estimates
in other cases. The posterior probability distributions of the four clearance parameters varied in the
analysis of Case 0855’s bioassay data are shown in Fig. 3.
The summary statistics of these probability distributions are compared in Table 4. It can be seen that
the posterior probability distributions of KPT, fr, and sr are all well defined (by the Case 0855 bioassay
data). These distributions are approximately lognormal, with geometric standard deviation, σg, of
1.40, 1.07 and 1.22, respectively. Note that the value of σg for ss is very high (4.85), which implies
that the measurement data do not contain any useful information about ss. In essence, the information
in the measurement data cannot define accurately the value of a rate constant on the order of 10-5 d-1
(half-time on the order of 100 y). The relatively short (6-y) follow-up in this case is insufficient to
achieve this.
Nevertheless, despite the large uncertainty in the value of ss, the effective and bone surface doses for
this individual, i.e., the quantities of direct interest, are evaluated precisely. The uncertainty, σg, is
only 1.08 for effective dose and 1.06 for bone surface dose [10-11].
For this individual, it is notable that ICRP’s recommended (default) parameter values [12]
(represented by KPT = 1.0) lie at the upper bound of the 95% credible interval (C.I.) for the particle
clearance factor. The modal value of KPT = 0.3, with a mean value of 0.59. Therefore, the data
indicate that particle clearance in this individual is substantially slower than assumed for the
‘reference worker,’ at least for this inhaled material (241AmO2). Without further specific evidence,
however, this ‘individual’ finding cannot be expected to apply to other individuals. In this case,
consideration of the uncertainty in particle transport rates increased both the mean assessed effective
and bone surface doses by about 30% over the values calculated by assuming the ICRP-recommended
(default) transport rates [11].
Figure 3: Posterior probability distributions of the absorption and lung clearance parameters for
USTUR Case 0855
Table 4: Statistics of posterior probability distributions for particle clearance rates in Case 0855 and
241
AmO2 absorption behavior
Parameter, unit
Statistic
KPT
fr
sr, d-1
ss, d-1
Mean
0.59
0.519
0.019
4.72 × 10-5
SD
0.19
0.035
0.004
6.66 × 10-5
Geometric Mean
0.56
0.517
0.019
1.65 × 10-5
GSD
1.40
1.07
1.22
4.85
Mode
0.30
0.504
0.023
1.95 × 10-4
Median
0.57
0.517
0.019
1.73 × 10-5
95% C.I.
0.26 – 1.01
0.452 – 0.589
0.013 – 0.028
1.09 × 10-6 – 2.47 × 10-4
99% C.I.
0.18 – 1.19
0.425 – 0.612
0.012 – 0.032
1.04 × 10-6 – 3.19 × 10-4
6. Dose Assessment for Clean-up Worker
For the clean-up worker, the actual time course of intake was not known. This must be inferred from
the excretion of 241Am measured in periodic ‘routine’ urine samples (Table 2). The earliest ‘positive’
urine result is for the sample collected at 106.5 d after the start of employment. The previous
‘negative’ sample was collected at 24 d after the start of employment. Therefore, it must be assumed
that a measurable intake of 241Am occurred at some unknown time (or times) between 24 and 105.5 d.
It has been shown [16-17] that in these situations, an unbiased estimate of intake can be obtained by
fitting a constant chronic intake throughout this interval.
For this example, the effective dose (50-y committed weighted dose equivalent) was calculated by
assuming the tissue weighting factors, wT, and treatment of remainder tissue doses prescribed in the
U.S. for occupational dose calculations by Regulation 10CFR835 [18]. Also, the degree of
overestimation of the daily 241Am-in-urine excretion for the 1,481-d urine sample (Table 2) was not
considered. Therefore, the dose assessment below must be treated as ‘hypothetical,’ and likely to be
biased high. This assessment is presented here only for the purpose of illustrating the application of
Bayesian inference.
6.1 Evaluation of Uncertainties in Doses with Non-informative Priors
The WeLMoS method was applied with 2,000 iterations, and for each iteration, random values of the
clearance rates were chosen from the uninformative priors shown in Table 3. The resulting posterior
probability distributions for effective and bone surface dose are shown in Fig. 4.
Figure 4: Posterior probability distributions of effective dose and committed equivalent dose to bone
surfaces calculated for non-informative prior probability distributions of lung absorption and particle
clearance parameters
It is notable that, even with less than comprehensive bioassay data in this case, the posterior
probability distributions of dose are reasonably well defined. From the 2,000 parameter iterations
tried, the mean value of effective dose is about 47 mSv (95% credible interval 34 – 62 mSv). The
mean value of bone surface dose is about 929 mSv (95% credible interval 661 – 1,249 mSv).
6.2 Evaluation of Uncertainties in Doses Using Informative Priors
Again, it should be noted that the WeLMoS method produces the quantities of interest (effective dose
and equivalent dose to bone surfaces illustrated here) without any explicit knowledge of the
absorption rates from the lung. However, the information (posterior distributions of absorption rates)
obtained from the above analysis of Case 0855 data provides usable ‘prior’ knowledge, in the form of
the prior probability distributions shown in Table 5. (Note that the prior for KPT is ‘non-specific’ for
this individual, and is derived from the range of uncertainty recommended in ICRP Publication 66
[12]).
Table 5: Prior distributions used to improve analysis of bioassay data for clean-up worker
Parameter
Range
Distribution
Rapidly absorbed fraction, fr
-1
Rapid absorption rate, sr (d )
-1
Slow absorption rate, ss (d )
Particle transport rate factor, KPT
Median = 0.517, σg = 1.07
Lognormal
Median = 0.0188, σg = 1.22
Lognormal
-5
Median = 1.73 × 10 , σg = 4.85
Median = 1, σg = 1.7
Lognormal
Lognormal
Fig. 5 shows the posterior probability distributions of effective and bone surface dose that result when
the prior information on the absorption parameters for inhaled 241AmO2 (Table 5) is incorporated into
the analysis of the available bioassay data for this individual (the clean-up worker).
Figure 5: Posterior probability distributions of effective dose and committed equivalent dose to bone
surfaces calculated for informative prior probability distributions of 241AmO2 lung absorption
parameters
The statistics of these probability distributions of dose are summarized in Table 6, where they are
compared with those derived with no prior knowledge of the absorption behavior of inhaled 241AmO2.
Table 6: Statistics of posterior probability distributions for effective and bone surface dose given by
(a) non-informative, and (b) informative prior knowledge of 241AmO2 lung absorption parameters
Statistic
Mean
SD
Geometric Mean
GSD
Mode
Median
95% C.I.
99% C.I.
Dose Distribution by Type of Absorption Prior
(a) Non-informative
(b) Informative
Effective
Bone Surface
Effective
Bone Surface
(mSv)
(mSv)
(mSv)
(mSv)
46.6
928.9
40.5
766.5
7.0
151.2
4.9
101.6
46.1
916.7
40.2
759.9
1.16
1.18
1.10
1.14
46.4
986.9
44.9
831.5
46.2
919.4
40.2
760.0
34.1 – 61.5
660.7 – 1,249
31.8 – 51.1
586.8 – 984.8
30.9 – 66.9
594.0 – 1,365
29.5 – 55.1
541.1 – 1,068
7. Conclusion
The effect of incorporating specific knowledge of the absorption rates for inhaled 241AmO2 from one
worker in the assessment of doses to another worker is primarily to reduce the uncertainty in
evaluated doses. The standard deviation of the probability distribution of effective dose is reduced
from 7.0 mSv to 4.9 mSv (σg from 1.16 to 1.10), while that for bone surface dose is reduced from
about 151 mSv to about 102 mSv (σg from 1.18 to 1.14). The corresponding mean estimate of
effective dose is reduced from about 47 mSv to about 41 mSv (median from about 46 mSv to about 40
mSv), while that for bone surface dose is reduced from about 929 mSv to about 767 mSv. The
corresponding upper 97.5% credible value for effective dose is reduced from about 62 mSv to about
51 mSv, while that for bone surface dose is reduced from 1,249 mSv to about 985 mSv.
In this particular example (of an exposed clean-up worker), the quality of the bioassay data is
sufficient to define reasonably accurately the posterior distributions of dose, even without any
information on the absorption behavior of inhaled 241AmO2, and so the reduction in uncertainty using
specific information of absorption is not as great as it could be. In cases with less reliable bioassay
data, the Bayesian method automatically places greater reliance on the prior knowledge. In cases with
no bioassay data, i.e., prospective dose assessments, absolute reliance must be placed on prior
knowledge (or assumptions) about the applicable HRTM model parameter values.
It should also be noted that, in this example, the unknown time of intake was not treated explicitly.
This would have the effect of increasing the uncertainty in doses (both with and without knowledge of
absorption rates). It was also assumed (for simplicity) that the posterior distributions of absorption
parameters from USTUR Case 0855 (Fig. 3) could be approximated by exact lognormal distributions
(Table 5), and that the absorption parameters were independent. In principle, these distributions could
be stored and sampled directly to avoid imprecision caused by the lognormal approximations. Another
advantage of using the joint distribution of parameters, rather than the independent lognormal
approximations, is that the relationship between parameters is preserved.
It is proposed to use the Bayesian methodology described here to estimate uncertainties in lung and
bone marrow doses for nuclear power workers in the UK, France and Belgium, as part of a European
epidemiological study (Alpha Risk) aimed at quantifying the risk from alpha irradiation. It is also
hoped to extend this methodology to improve the quality of dosimetric data for members of the
Mayak Worker and Techa River Cohorts in the Southern Urals, as part of another European Project
and the U.S. DOE’s Russian Health Studies Program [19].
Acknowledgements
Support from the U.S. Department of Energy, Office of Illness and Injury Prevention Programs (HS13), under Grant Award Number DE-FG06-92EH89181 to WSU, is gratefully acknowledged. The
authors also wish to thank USTUR Registrant 0855 for his collaboration and cooperation in the 6-y
follow-up bioassay study, and for his willingness to continue this study. The work of Drs. Birchall and
Puncher was supported by HPA-RPD, and Dr. John Harrison provided helpful comments on the
manuscript.
Disclaimer
This paper was prepared as an account of work sponsored by an agency of the United States
Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes
any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy,
completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its
use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or
service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its
endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views
and opinions of authors expressed herein do not necessarily state or reflect those of the United States
Government or any agency thereof.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
PUNCHER, M., and BIRCHALL, A., Estimating uncertainty on internal dose assessments,
Radiat. Prot. Dosim. 127 (2007) 544.
PUNCHER, M., and BIRCHALL, A., A Monte Carlo method for calculating Bayesian
uncertainties in internal dosimetry, Radiat. Prot. Dosim. (in press).
JAMES, A.C., et al., “Measurement of physical properties and retention in hamster lung of
actinide oxides used in the manufacture of commercially available products,” Annual Research
and Development Report 1976. National Radiological Protection Board, Harwell (1977) 31-44.
KATHREN, R.L., LYNCH, T.P., and TRAUB, R.J. Six-year follow-up of an acute 241Am
inhalation intake, Health Phys. 84 (2003) 576.
JAMES, A.C., ACJ & Associates, Inc., Richland, WA, personal communication, 2008.
INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, Basic anatomical
and physiological data for use in radiological protection: Reference values, Publication 89,
Ann. ICRP 32(3-4), Elsevier Science, Oxford and New York (2002).
MARSH, J.W., et al., Evaluation of the scattering factor values for internal dose assessment
following the IDEAS guidelines: Preliminary results, Radiat. Prot. Dosim. 127 (2007) 339.
MOSS, W.D., et al., A study of the variations found in plutonium urinary data, Health Phys. 17
(1969) 571.
BIRCHALL, A., et al., IMBA Professional Plus: A flexible approach to internal dosimetry,
Radiat. Prot. Dosim. 125 (2007) 194.
JAMES, A.C., et al., Using in vivo measurements and urine bioassay to characterize the
absorption of inhaled 241AmO2 and evaluate the probability distribution of doses (Abstract in
Proc. 42nd Ann. Mtg. Japan Health Phys. Soc., Okinawa, 2008) JHPS 43 (2008) 103. (Full
presentation at http://www.ustur.wsu.edu/Conferences/2008/2008_JHPS42.html).
JAMES, A.C., et al., Direct characterization of the absorption of inhaled 241AmO2 and the
probability distribution of doses from in vivo measurements and urine bioassay (in preparation).
INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, Human
respiratory tract model for radiological protection, Publication 66, Ann. ICRP 24(1-3), Elsevier
Science, Oxford and New York (1994).
INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, Age-dependent
doses to members of the public from intake of radionuclides: Part 2, ingestion dose coefficients,
Publication 67, Ann. ICRP 23(3-4), Elsevier Science, Oxford and New York (1993).
INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, Dose coefficients
for intakes of radionuclides by workers, Publication 68, Ann. ICRP 24(4), Elsevier Science,
Oxford and New York (1994).
INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, 2007
Recommendations of the International Commission on Radiological Protection, Publication
103, Ann. ICRP 37(2-4), Elsevier Science, Oxford and New York (2007).
PUNCHER, M., BIRCHALL, A., and MARSH, J.W., Obtaining an unbiased estimate of intake
in routine monitoring when the time of intake is unknown, Radiat. Prot. Dosim. 118 (2006)
280.
BIRCHALL, A., PUNCHER, M., and MARSH, J.W., Avoiding biased estimates of dose when
the time of intake is unknown, Radiat. Prot. Dosim. 127 (2007) 343.
U.S. DEPARTMENT OF ENERGY, Code of Federal Regulations. Part 835: Occupational
Radiation Protection, 10 CFR 835.
FOUNTOS, B.N., and ROBOVSKY, J.L., The Department of Energy’s Russian Health Studies
Program, Health Phys. 93 (2007) 187.