Radiation Protection Dosimetry (2012), Vol. 149, No. 3, pp. 347– 352
Advance Access publication 29 June 2011
doi:10.1093/rpd/ncr252
NOTE
PERSONAL DOSE EQUIVALENT CONVERSION COEFFICIENTS
FOR ELECTRONS TO 1 GE V
K. G. Veinot1,* and N. E. Hertel2
1
Y-12 National Security Complex, PO Box 2009, M.S. 8105, Oak Ridge, TN 37831-8105, USA
2
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta,
GA 30332-0405, USA
*Corresponding author: [email protected]
Received March 17 2011, revised May 3 2011, accepted May 19 2011
In a previous paper, conversion coefficients for the personal dose equivalent, Hp(d ), for photons were reported. This note
reports values for electrons calculated using similar techniques. The personal dose equivalent is the quantity used to approximate the protection quantity effective dose when performing personal dosemeter calibrations and in practice the personal dose
equivalent is determined using a 30330315 cm slab-type phantom. Conversion coefficients to 1 GeV have been calculated
for Hp(10), Hp(3) and Hp(0.07) in the recommended slab phantom. Although the conversion coefficients were determined for
discrete incident energies, analytical fits of the conversion coefficients over the energy range are provided using a similar formulation as in the photon results previously reported. The conversion coefficients for the personal dose equivalent are compared with the appropriate protection quantity, calculated according to the recommendations of the latest International
Commission on Radiological Protection guidance. Effects of eyewear on Hp(3) are also discussed.
INTRODUCTION
The personal dose equivalent, Hp(d), is the quantity
recommended by the International Commission on
Radiation Units and Measurements (ICRU) to be
used as an approximation of the protection quantity
effective dose(1, 2). The personal dose equivalent can
be defined for any location and depth within the
body although three specific depths are typically
used for radiation protection settings, namely 0.07, 3
and 10 mm. The most common wear position for
personal dosemeters is the trunk, so calibrations are
typically performed using a 303015 cm slab-type
phantom. The depths, d, are taken to be 0.07 mm
for non-penetrating and 10 mm for penetrating radiation. In operational radiation protection a third
depth, 3 mm, is included to approximate the lens of
the eye.
Conversion coefficients for electrons incident on
slab and sphere phantoms are available; however,
data to higher energies are limited, especially for the
personal dose equivalent (3, 4). Additionally, the
assumptions and modelling conditions chosen by
the various authors differ as do the computational
codes used. In the present work, conversion coefficients have been calculated in a 303015 cm slabtype phantom constructed of ICRU tissue substitute.
Absorbed dose calculations were performed at
depths of 0.07, 3 and 10 mm since these depths are
used as approximations of skin equivalent dose, eye
lens equivalent dose, and effective dose, respectively.
The range of energies considered spanned from 0.06
MeV to 1 GeV for d¼0.07 mm, from 0.7 MeV to 1
Published by Oxford University Press on behalf of the US Government 2011.
GeV for a depth of 3 mm and from 2 MeV to 1
GeV for a depth of 10 mm. The lower energy limits
represent the lowest particle energies capable of
penetrating to the corresponding depth in the
phantom and depositing energy. Discrete particle
energies were used, however, analytical fits are provided for each data set to allow interpolation of
values at other energies. The computed conversion
coefficients are compared with the corresponding
protection quantities determined according to the
latest recommendations of the ICRP(2).
A more detailed model of the eye has been developed by other authors(5) and conversion coefficients
at targeted sensitive cells reported. The conversion
coefficients for the newer eye model reported in
Reference(5) are included for comparison to values of
Hp(3) computed in this work. The values determined
using the newer eye model may form the basis for
the protection quantity equivalent dose to the lens
of the eye.
In operational settings there are additional considerations. Recently, the equivalent dose to the lens
of the eye has gained interest. At many facilities
workers are required to wear protective eyewear,
while others may or may not wear corrective eyeglasses. Since the attenuation of electrons from these
devices may be significant a cursory investigation
into the effects was included in this work.
METHODOLOGY
The dose conversion coefficients for Hp(0.07),
Hp(3) and Hp(10) were calculated using the
K. G. VEINOT AND N. E. HERTEL
Monte-Carlo transport code MCNPX version
2.6.0(6). The model consisted of a parallel broad
beam of electrons impinging perpendicular to the
front face of a 303015 cm slab-type phantom
consisting of ICRU tissue substitute (10.1 %
hydrogen, 11.1 % carbon, 2.6 % nitrogen and
76.2 % oxygen). The source beam was sufficiently
large (radius of 22 cm) to fully illuminate the
phantom face. Deposition calculations were performed within a 0.001 cm thick volume centred at
a depth of 0.07 mm for Hp(0.07) and within a
0.01 cm thick volume for Hp(3) and Hp(10). The
scoring volume was defined as a cylinder having
radius equal to 5 cm and thickness quoted above.
Sufficient particle histories were generated so that
the tally errors were ,3 %. All appropriate
physics models were included (e.g. Bremsstrahlung)
and all particles included in MCNPX were transported. Since this included photoneutrons, the
S(a,b) thermal neutron treatment was included to
account for up-scatter at low energies. The
Cascade-Exciton Model (CEM) version CEM03(6)
was used for all energies.
To allow for determination of conversion coefficients at energies other than those calculated here
analytical fits are provided. These fits were performed
using
a
non-linear
least-squares
Marquardt-Levenberg algorithm. Fits are of the
form
f ðxÞ ¼
a
2
þ
d
2
þ
h
1 þ ðb þ cxÞ 1 þ ð f þ gxÞ 1 þ ð j þ kxÞ2
l
o
þ
: ð1Þ
þ
1 þ expðm þ nxÞ 1 þ expð p þ qxÞ
where f (x) is the logarithmic (base 10) value of
the conversion coefficient and x equals log10(E)
with E numerically coincident with the energy
expressed in MeV.
In order to compare the operational quantities
with the protection quantities, the conversion coefficients for the equivalent dose to the skin, equivalent
dose to the lens of the eye and the effective dose are
compared with the present calculations. The protection quantity calculations were performed using the
phantoms described in ICRP-110(7) according to the
guidelines given in ICRP-103(2). Details of these calculations will be reported in a separate paper. The
MCNPX code was used and phantoms were irradiated in a vacuum in the anterior–posterior geometry. The organ conversion coefficients shown in
Figures 1 and 2 are the averages of the male and
female phantom organ equivalent doses. Conversion
coefficients for the equivalent dose to the lens of the
eye using the newer eye model were taken from
Reference(5).
The calculations of Hp(3) were repeated for
certain energies with a 2 mm thick layer of polycarbonate (5.5491 % hydrogen, 75.5751 % carbon,
18.8758 % oxygen, r¼1.2 g cm23) placed on the
front face of the phantom to simulate the effects
of a person wearing eyeglasses. This thickness and
composition may be representative of typical
eyewear, though other compositions and thicknesses are certainly possible and would vary based
on the prescription of the wearer. In general,
safety glasses are more robust and would have
different shielding characteristics. Effects of shielding (except possibly air) are not routinely included
in the calculation of dose conversion coefficients,
but they are included here as a demonstration of
the additional considerations necessary in operational environments.
RESULTS AND DISCUSSION
The calculated conversion coefficients are listed in
Table 1 and shown in Figures 1–3. Table 2 lists the
fitting constants for each of the quantities according
to Equation (1) along with the sum of the squares of
the residuals (SSR) of the fits.
The values of Hp(0.07) provide a reasonable
approximation to the equivalent dose to the skin
for most energies with some underestimation
above 100 MeV. The dimensions of the phantom
voxels (2.082.088 mm for the male phantom
and 1.8751.8755 mm for the female) do not
allow tallies specifically at the 0.07 mm depth, so
the size of the voxels themselves likely impacted
the calculations as well. The lens of the eye
equivalent dose calculated using the voxel phantoms described in ICRP-110 is reasonably approximated by Hp(3) except below about 0.8 MeV
where it underestimates the protection value.
Closer agreement is seen between Hp(3) and the
values reported in Reference(5) for equivalent dose
to the lens of the eye using the newer eye model.
The effective dose is approximated conservatively
by Hp(10) above 2.25 MeV. The effective dose is
of course influenced by the equivalent dose to the
skin, but other organs (breast, red bone marrow,
bone surface, and male gonads as well as some
remainder organs) also contributed to the effective
dose at energies below 1 MeV. The inclusion of
the 2 mm layer of simulated eyeglass material
attenuated electrons below 2 MeV and lowered the
conversion coefficients. At higher energies the conversion coefficients with the additional material
were higher since at these energies maximum
energy deposition occurs at deeper depths. The
size and shape of the tally volume at 3 mm were
not changed between the two computational
models. These values are compared with those of
Hp(3) without the additional material in Table 3.
348
ELECTRON DOSE CONVERSION COEFFICIENTS
Figure 1. Conversion coefficients for Hp(0.07) in units of pSv cm2 along with the fits determined using the values in
Table 2 according to Equation (1). Also shown are the values of H’(0.07) given in Reference(3) and for Hp(0.07) given in
Reference(4) and for the equivalent dose to the skin using the phantoms of ICRP-110.
Figure 2. Conversion coefficients for Hp(3) in units of pSv cm2 along with the fits determined using the values in Table 2
according to Equation (1). Also shown are the values of H’(3) given in Reference(3) and for Hp(3) given in Reference(4),
values of equivalent dose to the eye from Reference(5), and for the equivalent dose to the eyes using the phantoms of
ICRP-110.
Above about 10 MeV the differences in Hp(3)
with and without the simulated eyeglass material
are relatively minor, although the magnitude of
the difference may increase for other eyewear
thicknesses and compositions. Contributions to
Hp(10) from particles other than electrons were
not directly tallied, but based on the number of
particles present in the tally volume their impact
on the absorbed dose were negligible. The total
number of particles other than electrons or
349
K. G. VEINOT AND N. E. HERTEL
Table 1. Personal dose equivalent, Hp(d), in the ICRU slab phantom.
Energy (MeV)
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.1
0.1125
0.125
0.15
0.175
0.2
0.25
0.3
0.4
0.5
0.6
0.7
0.8
0.85
0.9
0.95
1
1.125
1.25
1.5
1.75
2
2.5
2.75
3
3.25
3.5
4
4.5
5
5.5
6
7
8
10
15
20
25
30
40
50
70
100
200
500
1000
Hp(0.07)
(pSv cm2)
Uncert.
(pSv cm2)
Hp(3)
(pSv cm2)
Uncert.
(pSv cm2)
Hp(10)
(pSv cm2)
Uncert.
(pSv cm2)
3.4
80.3
418.8
885.5
1284.0
1480.9
1602.0
1618.5
1506.7
1357.4
1105.5
909.8
774.0
609.9
519.8
438.3
385.9
362.3
338.1
333.6
323.3
319.8
316.4
315.1
305.8
307.5
295.1
288.0
284.1
274.3
274.2
269.9
270.0
269.8
269.0
272.6
276.4
274.8
269.2
277.2
279.1
278.3
285.7
284.5
284.4
279.5
279.3
282.9
281.5
281.8
278.6
278.5
274.8
0.1
0.6
1.3
5.0
5.8
9.2
9.1
3.9
7.1
4.2
8.7
6.0
5.8
1.8
4.8
4.3
4.0
4.8
0.8
3.8
2.7
4.5
3.4
4.6
2.1
5.3
5.4
4.6
3.2
7.5
4.5
9.5
5.7
6.3
5.9
5.3
3.3
3.8
3.3
4.2
4.4
5.1
5.1
5.2
5.7
3.9
5.7
4.7
5.8
5.6
6.5
7.7
10.1
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
0.5
62.3
150.0
244.9
312.1
377.9
465.9
517.8
532.0
499.2
463.6
404.0
379.4
363.9
351.9
342.5
327.9
316.4
314.3
313.6
311.8
309.0
306.2
304.7
305.2
306.4
306.7
306.8
308.0
306.0
305.3
306.1
304.0
307.9
302.8
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
0.0
1.2
1.2
2.8
2.3
3.2
1.6
4.3
4.0
3.0
1.9
3.4
1.9
4.0
2.4
2.7
2.4
2.0
1.3
1.4
1.1
1.6
1.7
1.9
2.3
2.2
2.5
1.4
1.9
1.8
2.0
2.1
2.2
2.3
3.2
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
3.6
206.4
318.1
391.4
430.5
455.7
464.7
451.1
421.1
400.6
380.9
356.9
341.8
329.3
321.0
319.6
319.9
321.5
323.5
323.5
322.3
319.1
323.2
322.2
317.7
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
0.2
2.6
1.8
4.1
2.8
3.1
2.8
2.1
1.3
1.5
1.1
1.5
1.7
1.8
2.2
2.2
2.5
1.4
1.8
1.7
2.0
2.1
2.0
2.3
3.2
photons (e.g. neutrons, muons, protons, tritons,
etc.) in the tally volume was ,0.05 % of the
number of electrons in the volume.
CONCLUSION
The calculated conversion coefficients provide
additional information for higher energy electrons.
350
ELECTRON DOSE CONVERSION COEFFICIENTS
Figure 3. Conversion coefficients for Hp(10) in units of pSv cm2 along with the fits determined using the values in Table 2
according to Equation (1). Also shown are the values of H*(10) given by Ferrari and Pelliccioni (3) and for Hp(10) given by
Chartier et al. (4) and for the effective dose using the phantoms of ICRP-110.
Table
a
b
c
d
f
g
h
j
k
l
m
n
o
p
q
SSR
2. Analytical
fit values for
coefficients.
Hp(d)
conversion
Hp(0.07)
Hp(3)
Hp(10)
0.00000Eþ00
0.00000Eþ00
0.00000Eþ00
2.28538Eþ00
5.47047Eþ00
5.26064Eþ00
2.99892Eþ00
1.77067Eþ01
1.50617Eþ01
2.41815Eþ00
25.45675Eþ01
24.78299Eþ01
22.85755Eþ00
1.13726Eþ01
1.18478Eþ01
0.0097
29.17202Eþ00
1.07748Eþ00
2.98075E203
3.56813E201
8.70562E201
25.66019Eþ00
1.21225Eþ00
21.74448Eþ00
21.40033Eþ01
1.56034E201
7.05332Eþ00
22.79743Eþ01
6.54168Eþ00
23.33105Eþ00
22.33622Eþ01
0.0008
1.06130Eþ00
4.26778Eþ00
21.26050Eþ01
21.44847Eþ00
1.38694Eþ00
22.72475Eþ00
5.40744Eþ00
1.92784Eþ00
24.97399Eþ00
24.79346Eþ00
3.62313Eþ00
22.52886Eþ01
7.29895Eþ00
5.57345Eþ00
21.21404Eþ01
0.0001
Table 3. Conversion coefficients for Hp(3) with and without
simulated eyeglasses having thickness of 2 mm.
Without glasses
Variables coincide with those given in Equation (1). Also
listed is the sum of SSR of the fit to the calculated data
points. The fits for each quantity should only be used for
the energy ranges listed in Table 1.
Although it is unlikely that dosemeter calibrations
would be performed at these high energies, they may
be of use for accidental exposures. The values computed here agree well with those published for the
ICRU sphere indicating that differences in the
With glasses
Energy
(MeV)
Hp(3)
(pSv
cm2)
Uncert.
(pSv
cm2)
Hp(3)
(pSv
cm2)
Uncert.
(pSv
cm2)
(%)
difference
1.25
1.5
1.75
2
2.5
3
4
5
7
10
20
50
100
517.8
532.0
499.2
463.6
404.0
363.9
327.9
314.3
309.0
304.7
306.4
306.0
306.1
4.3
4.0
3.0
1.9
3.4
4.0
2.4
1.3
1.6
1.9
2.2
1.8
2.1
50.1
288.7
424.5
484.7
488.4
447.8
380.0
344.9
325.8
314.3
315.7
317.0
316.8
0.5
1.3
3.8
3.4
2.9
2.1
3.5
2.9
3.7
0.7
2.5
5.5
5.9
290.3
245.7
215.0
4.6
20.9
23.0
15.9
9.7
5.4
3.2
3.0
3.6
3.5
phantoms do not significantly impact the conversion
coefficients, at least when the irradiations are performed along the principal axis of the phantom. The
minor differences in the reported values could be a
result of variations in tally volumes, shape and transport codes/cross sections used as well as uncertainties
in the scoring results. As was previously noted in the
case of photons(8), the minimal impact of phantom
351
K. G. VEINOT AND N. E. HERTEL
size and shape indicates that evaluations of operational quantities could include reported values for
Hp(10) and H*(10). The personal dose equivalent
provides a conservative estimate of the protection
quantities for most energies. In operational settings,
it is important to consider additional shields such as
eyeglasses or other protective eyewear when evaluating the dose to the lens of the eye. More study is
needed to quantify effects of eyewear in operational
settings, particularly given the variability in compositions and dimensions of glasses and protective
eyewear. The analytical fits provide convenient
methods for determining conversion coefficients for
specific energies or spectra of electrons. Overall, conversion coefficients calculated with the ICRU slab
phantom reasonably approximate the protection
quantities for most energies.
REFERENCES
1. International Commission on Radiation Units and
Measurements (ICRU). Conversion coefficients for use in
radiological protection against external radiation. ICRU
Publication 57. ICRU (1998).
2. International Commission on Radiological Protection
(ICRP). The 2007 Recommendations of the International
Commission on Radiological Protection. ICRP
Publication 103. Ann. ICRP 37. Elsevier (2007).
3. Ferrari, A. and Pelliccioni, M. Dose equivalents for
monoenergetic electrons incident on the ICRU sphere.
Radiat. Prot. Dosim. 55(3), 207–210 (1994).
4. Chartier, J. L., Grosswendt, B., Gualdrini, G. F.,
Hirayama, H., Ma, C.-M., Padoani, F., Petoussi, N.,
Seltzer, S. M. and Terrissol, M. Reference fluence-todose-equivalent conversion coefficients and angular
dependence factors for 4-element ICRU tissue, water
and PMMA slab phantoms irradiated by broad electron beams. Radiat. Prot. Dosim.
63(1), 7 –14 (1996).
5. Behrens, R., Dietze, G. and Zankl, M. Dose conversion
coefficients for electron exposure of the human eye lens.
Phys. Med. Biol. 54(13), 4069 (2009).
6. Pelowicz,, D. B (ed). MCNPX Ver. 2.6.0. Los Alamos
National Laboratory (2008).
7. International Commission on Radiological Protection
(ICRP). Adult reference computational phantoms. ICRP
Publication 110. Ann. ICRP 39. Elsevier (2009).
8. Veinot, K. G. and Hertel, N. E. Personal dose equivalent
conversion coefficients for photons to 1 GeV. Radiat.
Prot. Dosim. 145(1), 28– 35 (2011).
352