Full text of DOI:10.1093/oxfordjournals.rpd.a006436

Radiation Protection Dosimetry
Vol. 93, No. 3, pp. 245–260 (2001)
Nuclear Technology Publishing
MONTE CARLO CALCULATIONS OF THE DOSE
DISTRIBUTION IN TEETH DUE TO INTERNAL EXPOSURE
90
FROM Sr: APPLICATION TO EPR TOOTH DOSIMETRY
S. M. Seltzer, A. A. Romanyukha* and V. Nagy
National Institute of Standards and Technology
Gaithersburg, MD 20899–8460, USA
Received June 7 2000, amended August 15 2000, accepted August 31 2000
Abstract — This paper addresses issues in the application of the electron paramagnetic resonance (EPR) retrospective dosimetry
with dental tissues exposed by radionuclides accumulated in the dentin. A simple dosimetric model of a tooth incorporating 90Sr
is presented. The tooth is modelled as two concentric cylinders: the inner cylinder composed of dentin, and the outer cylindrical
shell of enamel. Extensive Monte Carlo calculations were done to obtain the distributions of absorbed dose in dentin and enamel
for teeth of different sizes. The results were used to calculate the mean absorbed doses in enamel that are directly measurable
by EPR. A relationship between such measured doses and the specific activity of 90Sr in dentin was derived based on a simple
model of 90Sr accumulation. The roles of different tooth tissues as dose detectors are analysed, and the importance of dentin as
a dosimetric material for internal exposure is pointed out.
INTRODUCTION
tooth enamel measured with EPR can be used by radi-
ation biologists and epidemiologists in a fairly straight-
forward way.
Electron paramagnetic resonance (EPR) dosimetry
with teeth has proved to be a reliable technique of
retrospective dose reconstruction. The method is based
on measurements of concentrations of stable free rad-
icals produced by radiation in the mineral component
of the dental calcified tissues, namely, hydroxyapatite
Ca10(PO4)6(OH)2. The principles of this method and
results of its application have been described in many
publications (see, e.g., References 1–8). EPR dosimetry
with tooth enamel has been applied to reconstruction of
doses from the atomic bomb explosions in Hiroshima
and Nagasaki(1,9), from the Chernobyl accident(10), and
from workplace exposures of South Urals nuclear
workers(3). A number of blind intercomparisons(11–14)
have demonstrated that absorbed doses in tooth enamel
can, in most cases, be accurately measured by EPR.
Until recently, EPR tooth dosimetry has been applied
primarily to the relatively simple case of external high
energy irradiation. The rather uniform radiation fields
typically associated with such irradiations, combined
with the negligible attenuation of the radiation by body
tissues, results in a fairly uniform dose and the radical
concentration throughout the tooth enamel. Similar con-
ditions are reproduced in additional, controlled labora-
tory irradiations that can provide an accurate assessment
of the initial dose using the back-extrapolation tech-
nique. External high energy irradiation provides roughly
the same doses in teeth as in other, more important,
organs, including bone marrow. Therefore, doses in
The problem of dose reconstruction becomes far more
difficult when the irradiation is to a significant extent or
exclusively from emitters internal to the body and the
radiation energy is not very high. A typical example of
this is internal irradiation from 90Sr, which is accumu-
lated in bones and dentin and emits beta particles with
a penetration range in tooth enamel of just 1–2 mm (see
Table 4), comparable to the enamel thickness. In such
cases, the distribution of absorbed dose in the tooth
enamel (as well as in the dentin) is not uniform, and its
specific pattern depends on the sizes and shapes of the
dentin and enamel constituents, as well as on the radi-
ation energy. Accordingly, the concentration of radicals
producing the EPR signal is also non-uniform, and
application of the usual techniques of sample prep-
aration results in a difficult-to-estimate degree of
dilution of the highly irradiated enamel parts with the
enamel that received much lower doses. As a result of
these complications, doses estimated directly from the
average EPR signal in the standard way are not very
meaningful. Thus doses reconstructed from tooth
enamel of two different-size teeth of the same person
may be considerably different, and, even when these
values are close to each other, they cannot be converted
to the dose to more important organs, such as bone
marrow, as easily as in the case of an external high
energy irradiation. For this reason, dose reconstructions
with EPR in cases of internal radiation have been rather
limited so far(4,15)
.
Strontium-90 is one of the most hazardous radio-
nuclides for humans among those released from anthro-
pogenic sources because of the combination of the fol-
*On leave from Institute of Metal Physics, Ekaterinburg,
620219, Russia
245

S. M. SELTZER, A. A. ROMANYUKHA and V. NAGY
lowing three factors: (i) a significant decay energy, (ii) a
From the EPR dosimetric viewpoint, the important
long lifetime in the human body (its biological half-life components of a tooth are its calcified tissues, namely,
in the body is about 20 y), and (iii) rapid accumulation tooth enamel, dentin, and cementum. Because of the
in the body’s calcified tissues from the contaminated differences in their chemical compositions and the asso-
environment. The accumulation is very effective ciated metabolic processes, these three dental tissues
because 90Sr is chemically similar to calcium, and sub- accumulate different dosimetric information, and they
stitution occurs within tissues in the human body (bone have different scales and fields of application in EPR
and teeth). This radionuclide in the environment is retrospective dosimetry. From the chemical point of
especially dangerous in adolescence, when the skeleton view, all the calcified tissues are basically compositions
rapidly consumes a lot of calcium to increase the bone of the same three components, mineral hydroxyapatite,
mass. Strontium-90 can be presented to the body from water, and organic matter, although their relative
a number of sources, including intentional releases by concentrations vary significantly. Hydroxyapatite, the
nuclear plants, radiation accidents and weapon test component in which the stable free radicals accumulate
fallout.
and that stores the information on the absorbed dose,
One of the most interesting cohorts in the world from constitutes 95–97% of tooth enamel, 70–75% of dentin,
the viewpoint of radiation epidemiology is the popu- and 50–60% of cementum.
lation of the Techa riverside in Russia, who received
Tooth enamel is composed of hydroxyapatite needle
large radiation doses (over 1 Gy in some cases) due to crystallites about 0.5–0.6 ␮m long dispersed in an aque-
continual consumption of the river water that contained ous-organic gel. This is the only human tissue without
highly radioactive releases from the first Soviet nuclear a cellular structure. Due to this, metabolism in mature
plant Mayak(16). For many of these people, the doses tooth enamel is extremely weak, and the chemical com-
received are mostly due to long-lived 90Sr. A compre- position of the enamel is very stable.
hensive review of the available information on 90Sr con-
In contrast to tooth enamel, dentin has a cellular
tent in teeth and skeletons for the Techa riverside popu- structure and, therefore, participates in metabolism to a
lation has been made recently by Tolstykh and co- much larger degree. The organic component of dentin
workers(17). At present, doses from the internal 90Sr consists of collagenous fibrils and a ground substance
irradiation are estimated mostly from the results of of mucopolysaccharides. Hydroxyapatite crystals (about
whole-body counting; however, this method has certain 0.04 ␮m) cover the individual collagen fibres. The cellu-
weaknesses discussed below. Therefore, development of lar structure of dentin is quite specific: the dentin cells
an alternative technique for retrospective dosimetry for (odonoblasts) are located outside of dentin, on its pulpal
this case would be very helpful. The study reported in surface (Figure 1). Every odonoblast has one branch
this paper was motivated by the need to interpret the (cytoplasmic extension), the so-called tubule, which tra-
results of an EPR dose reconstruction for the population verses the entire dentin layer to terminate at the junction
of the lower and middle Techa riverside performed with the enamel or cementum. In the mature tooth, all
earlier(4,15) and of an EPR study of calcified tissues from living processes occur in the dentinal tubules. Depo-
a dog injected with 90Sr(18). Recently results of the sition of dentin continues throughout the human life,
model calculations described in the present paper were although this process is much slower after the tooth
applied to the correction of the radiation doses measured eruption. The parts of dentin formed after eruption are
by EPR in tooth-enamel samples prepared from the teeth
of near 100 Techa riverside residents(19), where they
reduced or eliminated some serious inconsistencies in
the experimental results.
TOOTH AS AN EPR DOSIMETRIC SYSTEM
Reconstruction of doses from internal or mixed
irradiation requires a deeper insight into the anatomy
and physiology of a tooth than was sufficient for recon-
structing external doses. This section provides a sum-
mary of such information compiled from the books by
Bhaskar(20), Driessens and Verbeeck,(21) and Graber(22)
.
Anatomically the tooth consists of two parts: the
crown (the upper part of the tooth covered with enamel)
and the root (the lower part providing attachment of the
tooth to the gum and jawbone) (Figure 1). The root is
covered with cementum. There is a cavity called the
pulp channel inside the tooth where the soft tissue pulp
is located.
Figure 1. Schematic of
a human tooth. Reproduced with
permission from Reference 20.
246

MONTE CARLO CALCULATIONS OF 90Sr DOSE IN TEETH
often called secondary dentin, and, in cross sections, consider in selecting an appropriate tissue for dose
they are separated from that previously formed primary reconstruction in each particular case.
An important issue regarding biokinetics in teeth and
bone was studied in the extensive experimental work of
Goldman et al(23,24), based on more than 500 beagles
reared for 1.5 years on diets containing 90Sr and sub-
sequently followed over a period of 12 years. Their
results showed that while the skeleton exhibited a con-
siderable reduction in retained 90Sr after discontinuing
90Sr ingestion, due to bone remodelling, the teeth had a
very small change in 90Sr content. This suggests the
nearly exclusive suitability of teeth for the reconstruc-
tion of previous 90Sr intake.
dentin by a dark stained line. Secondary dentin is
deposited on the entire pulpal surface, and it is best
observable in premolars and molars. In the pulpal cham-
bers of these teeth, deposits of the secondary dentin on
the ceiling are much larger than on the walls. The
growth of dentin can be thought of roughly as a process
similar to development of tree rings. However, unlike
tree rings, the largest ‘core’ portion of dentin is the
initial primary dentin with a low mineral turnover. This
part of dentin loses virtually none of the accumulated
calcium. Bone-seeking radionuclides supplied to the
body after the tooth is erupted are accumulated prim-
arily in the secondary dentin with only minute absorp-
tion in the primary dentin near the tubules.
The third calcified tissue of tooth is cementum. This
connective tissue serves as a membrane between the
gum and the tooth root. The portion of organic matter
in this tissue, the highest as compared with tooth enamel
and dentin, reaches 50%. The mineral turnover in
cementum is relatively high.
The differences among the calcified tissues of teeth
in the degree of the involvement in metabolism are of
great importance for EPR dosimetry. Tooth enamel is
hardly involved, and, thus, is not able to absorb bone-
seeking radionuclides to any noticeable degree, unless
their supply into the body coincides with the relatively
short period of the enamel formation. Hence, it can be
irradiated only from outside, in particular, by radio-
nuclides residing in the other parts of the tooth. From
internal irradiation from osteotropic radionuclides with
limited depth of penetration, absorbed doses in tooth
enamel are usually lower than the absorbed doses in the
other calcified tissues. Dentin participates in metabolism
to a much greater extent, and, therefore, can absorb 90Sr
coming into the body not only in the period of its pre-
eruptive formation, but also when the tooth is in the
mature state. However, new supplies are presumably
accommodated mostly in the secondary dentin. There-
fore, 90Sr-containing dentin irradiates both itself and the
neighbouring tissues, including enamel. The dentin dose
from bone-seeking radionuclides is typically higher than
to the enamel. Root dentin has the highest absorbed
dose, because the growth of the secondary dentin in the
root is more extensive than in the crown and, addition-
ally, the root gets significant external irradiation from
the adjacent bone. The high chemical turnover in
cementum makes this tissue unsuitable for recon-
structing doses received long ago, but, in terms of radio-
nuclide accommodation and geometry of irradiation, it
behaves rather like compact bone. Thus, the differences
between enamel, crown dentin, root dentin, and cemen-
tum in terms of their accessibility for radionuclides, the
degree of radionuclide turnover, spatial distribution of
the radionuclides, and the resulting differences in the
The other important aspect is the difference in the
EPR signals of the tooth components. Qualitatively, the
EPR spectra of irradiated tooth enamel, dentin, and
cementum are similar. In all these cases, the useful,
dose-dependent signal is due mainly to the extremely
stable ion radicals COϪ2(25) that are produced by radi-
ation from the diamagnetic carbonate ions occurring in
hydroxyapatite as impurities. The interfering, radiation-
irrelevant, background signal comes mainly from the
organic components of the calcified tissues(26). How-
ever, there are significant quantitative differences.
As expected, the relative usefulness of the three calc-
ified tissues for EPR dosimetry depends on the relative
amounts of hydroxyapatite and the organic matter in
these tissues, as well as on the concentration of the car-
bonate precursors in hydroxyapatite. The average car-
bonate contents of hydroxyapatite in tooth enamel,
dentin, and cementum are 3.2% (dry weight), 4.6% (dry
weight), and 6–10%, respectively(21). However, because
the concentration of the organic matter in tooth enamel
is the lowest (about 1%), and the concentration of hyd-
roxyapatite is the highest, this material would seem to
offer the best opportunity for dose reconstruction: the
background signal is the weakest in this case, and the
resolution of the two signals in question is, therefore,
the best. As a result, the detection limit achievable with
tooth enamel is the lowest among the calcified tissues:
a recent direct experimental estimate produced the value
of 29 mGy at 95% confidence level(27). Dentin and
cementum, with their much higher organic matter con-
centrations, exhibit roughly 10-fold stronger native sig-
nals, which hampers their use in reconstructing doses
lower than a few gray without special chemical treat-
ment to dissolve the organic component(28,29). One has
to take these important differences into account when
the anatomical and physiological properties discussed
above suggest that a non-enamel material would, in
principle, provide better information on the internally
received dose than would tooth enamel.
In summary, for the case of internal irradiation, the
tooth represents a somewhat complex system for retro-
spective EPR dosimetry. The complexity stems from
both the spatial and the chronological non-uniformity.
In addition to the possibly (and most probably) varying
intensity of EPR signals are very important factors to supply of a radionuclide into the teeth during its life-
247

S. M. SELTZER, A. A. ROMANYUKHA and V. NAGY
time, there is the simultaneous partial removal from the ignored in this model. The dimensions of the dentin cyl-
teeth due to turnover. The removal rate in each parti- inder were associated with representative dimensions of
cular microscopic area of a material may change in time, crown dentin in various tooth positions (Table 1). Such
for example, as a result of dentin growth. At any a very simplified model of the tooth does not fully take
moment, the distribution of a radionuclide within the into account the rather more complicated morphology
tooth as a whole and even within a selected constituent of dental tissues discussed above. However, it allows
is not uniform. If the energy of radiation (and, hence, one to take advantage of the cylindrical symmetry,
its penetration depth) is not very high, the dose distri- which makes the calculations much more efficient.
bution is non-uniform even if the radionuclide is distrib- Therefore, the results obtained are applicable mainly to
uted uniformly over one of the calcified tissues, e.g. teeth whose shapes are similar to cylinders, such as
dentin.
molars and premolars. This does not seem a serious
Obviously, the problem of such a degree of com- limitation as front teeth are rarely used in EPR tooth
plexity cannot be solved completely, and simplified dosimetry both because of sun exposure(33) and because
approaches based on idealised models are inevitable. In of the relatively small amount of available tooth enamel.
this particular work, we largely ignore the temporal fac- Some estimates of the uncertainties in our results due
tors and focus mostly on the spatial non-uniformity. The to the deviation of teeth from cylinders are given later.
goal is to develop procedures for relating the absorbed
A uniform, isotropic source of electron emission from
doses in enamel and in dentin to more meaningful ‘nor- 90Sr/90Y decay was assumed in the dentin cylinder.
malised’ characteristics that would then be comparable Thus, it was assumed that the radionuclide uniformly
for different teeth of the same or different persons. If occupies only the dentin volume so that the emitted
successful, such procedures would be useful in future radiation must cross into the enamel shell to deposit
models relating doses in dental tissues to doses in energy there. No other sources of radiation were taken
other organs.
into account. These assumptions appear founded for the
To achieve this goal, we need quantitative infor- case of the residents of the middle and lower Techa riv-
mation on dose profiles in tooth enamel. We have erside, who were irradiated mostly internally from
obtained such profiles for a simplified model of a tooth radionuclides consumed from the river water(4,15). From
using Monte Carlo calculations. Similar problems for the composition of the radioactive waste released into
different geometries that are typical for EPR dating the river (Table 2) it follows that most of the irradiation
were addressed by Gru¨n et al(30), Brennan et al(31), and over the years was provided by 90Sr/90Y, and that the
Yang et al(32)
.
primary location of the parent bone-seeking 90Sr, from
which enamel was irradiated, was dentin.
The assumed composition of the dental tissues used
in the calculations is given in Table 3. Estimates are
MONTE CARLO MODEL
The tooth was modelled as two concentric cylinders: given in Table 4 of the radial distances from a point
the inner cylinder composed of dentin, and the outer source of 90Sr/90Y (assumed in secular equilibrium)
cylindrical shell composed of enamel (Figure 2). within which various fractions of the decay energy are
Accordingly, only crown dentin and enamel are taken absorbed in such materials. Results are based on beta
into consideration; root dentin and cementum are spectra calculated from the LOGFT program(34) in con-
junction with the Evaluated Nuclear Structure Data File
from the National Nuclear Data Center, Brookhaven
National Laboratory. The spectra are consistent with
those given by Cross et al(35) and in ICRU Report 56(36)
.
Some characteristic parameters used for 90Sr/90Y decay
are given in Table 5.
The Monte Carlo calculations of the transport of elec-
trons and secondary photons were done with the CYL-
TRAN code from the Integrated Tiger Series (ITS), ver-
sion 3.0(37). The ITS transport physics and cross sections
are based on the ETRAN code for coupled electron–
photon transport(38–40), and take into account in a rather
accurate way the diffusion and slowing down of all
radiations in the electron–photon cascade established in
the media. A straightforward code change was made in
CYLTRAN to enable sampling from the source
assumed in the chosen model. A cylindrical shell of
enamel assumed to extend 2 mm beyond the dentin cyl-
inder was found to capture nearly all of the resultant
absorbed dose (Table 4). The absorbed dose was scored
Figure 2. Simplified model of the tooth, composed of an inner
cylinder of dentin and an outer concentric cylindrical shell of
enamel.
248

MONTE CARLO CALCULATIONS OF 90Sr DOSE IN TEETH
10
1
10
(a)
(b)
z : 0–0.1mm
z : 4.4–4.5mm
z : 4.5–4.6mm
z : 0–0.1mm
z : 3.9–4.0mm
z : 4.0–4.1mm
1
z : 4.9–5.0mm
z : 5.4–5.5mm
z : 5.9–6.0mm
z : 4.4–4.5mm
z : 4.9–5.0mm
10-1
10-2
10-3
10-4
10-1
z : 5.4–5.5mm
z : 6.4–6.5mm
z : 5.9–6.0mm
10-2
10-3
Dentin: 9 mm x 2 mm diam.
Dentin: 8 mm x 10 mm diam.
10-4
0
0.6
1.2
1.8
2.4
3.0
0
0
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Radial distance from centre (mm)
Radial distance from centre (mm)
10
1
10
1
z : 0–0.1mm
z : 3.4–3.5mm
z : 3.5–3.6mm
(c)
(d)
r : 0–0.1mm
r : 0.9–1.0mm
r : 1.0–1.1mm
z : 3.9–4.0mm
z : 4.4–4.5mm
r : 1.4–1.5mm
r : 1.9–2.0mm
z : 4.9–5.0mm
z : 5.4–5.5mm
10-1
10-2
10-3
10-4
10-1
10-2
10-3
10-4
r : 2.4–2.5mm
r : 2.9–3.0mm
Dentin: 7 mm x 5 mm diam.
Dentin: 9 mm x 2 mm diam.
0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Radial distance from centre (mm)
1.0
2.0
3.0
4.0
5.0
6.0
Axial distance from centre (mm)
10
1
10
1
r : 0–0.1mm
r : 4.9–5.0mm
r : 0–0.1mm
r : 2.4–2.5mm
r : 2.5–2.6mm
(e)
(f)
r : 5.0–5.1mm
r : 5.4–5.5mm
r : 2.9–3.0mm
r : 3.4–3.50mm
r : 5.9–6.0mm
r : 6.4–6.5mm
10-1
10-2
10-3
10-4
10-1
10-2
10-3
10-4
r : 3.9–4.0mm
r : 4.4–4.5mm
r : 6.9–7.0mm
Dentin: 8 mm x 10 mm diam.
Dentin: 7 mm x 5 mm diam.
0
1.0
2.0
3.0
4.0
5.0
6.0
1.0
2.0
3.0
4.0
5.0
6.0
Axial distance from centre (mm)
Axial distance from centre (mm)
Figure 3. Spatial distributions of absorbed dose rate in tooth tissue, for an assumed uniform distribution of 90Sr/90Y in the dentin.
(a) Radial distribution for a 9 mm ϫ 2 mm diameter dentin cylinder. (b) Radial distribution for a 8 mm ϫ 10 mm diameter dentin
cylinder. (c) Radial distribution for a 7 mm ϫ 5 mm diameter dentin cylinder. (d) Axial distribution for a 9 mm ϫ 2 mm diameter
dentin cylinder. (e) Axial distribution for a 8 mm ϫ 10 mm diameter dentin cylinder. (f) Axial distribution for a 7 mm ϫ 5 mm
diameter dentin cylinder.
249

S. M. SELTZER, A. A. ROMANYUKHA and V. NAGY
Table 3. Assumed composition of dental tissues.
throughout the double cylinder in annular rings of
0.1 mm in height and 0.1 mm in radial thickness.
Although each calculation had to be made for specific Element
dimensions of the dentin, it is assumed that the distri-
bution of absorbed dose in an enamel layer less than
2 mm thick would not be greatly affected by the pres-
Atomic
number
Fraction by weight
Dentin
Enamel
ence of a real boundary. This assumption is perhaps jus-
tified to the extent of the only modest effect (see Figures
5(a) and (b)) apparent in the absorbed-dose distribution
near the enamel/vacuum interface at 2 mm. An actual
tooth would likely have tissue or the enamel of other
teeth in close proximity in many directions, at least par-
tially mitigating enamel/vacuum interface effects (note,
however, that the presence of high-Z restorations and
structures could introduce other, more severe, inter-
face effects).
Calculations were performed for 16 different dentin
cylinder dimensions whose heights and diameters Fe
ranged from 2 to 10 mm. All results are based on a sam-
ple of 15M histories of emitted beta particles. Because
of the geometry assumed for the calculation, the
H
C
N
O
1
6
7
8
0.030773
0.113246
0.025240
0.361391
0.000170
0.002000
0.011000
0
0.150000
0.000300
0.000700
0.305000
0
0.009788
0.014743
0.001298
0.419226
0.000130
0.006000
0.004000
0.000030
0.175000
0.002500
0.003000
0.364000
0.000025
0.000100
0.000160
2.95
F
9
Na
Mg
Si
P
Cl
K
11
12
14
15
17
19
20
26
29
30
Ca
Cu
Zn
0
0.000180
2.14
Density, ␳ (g.cmϪ3
)
Table 1. Representative dimensions of human teeth.
Tooth
position
Crown
dentin
dimensions
hϫd
Enamel thickness
(mm)
Table 4. Estimated percentile radial distances, in mm, in
dental tissues within which various percentages of the decay
energy of a point source of 90Sr/90Y are absorbed.
Lateral
surface
Masticatory
surface
(mm)
Percentage
(%)
Percentile distance (mm)
Dentin Enamel
0.1 0.1
Upper jaw
4 (1st premolar)
5 (2nd premolar)
6 (1st molar)
7 (2nd molar)
8 (3rd molar)
Lower Jaw
4 (1st premolar)
5 (2nd premolar)
6 (1st molar)
7 (2nd molar)
8 (3rd molar)
7ϫ6
7ϫ5
5ϫ4
6ϫ10
5ϫ9
0.5
0.6
0.6
0.5
10
30
50
70
90
95
98
1.3
2.0
0.4
0.8
1.4
2.3
2.7
3.2
0.3
0.6
1.0
1.6
1.9
2.3
0.65
0.60
0.70
0.75
8ϫ4
7ϫ6
5ϫ5
8ϫ10
8ϫ10
0.5
0.7
1.2
0.6
0.6
0.5
0.7
1.5
0.75
0.75
Table 5. Parameters of 90Sr and 90Y beta decay. Emax is the
end-point energy of the emitted beta spectrum; Eav is the
average beta energy emitted; and the probabilities per dis-
integration are calculated for 90Sr and 90Y assumed to be
in secular equilibrium.
Table 2. Composition of radioactive wastes released into the
Techa river.
Radioisotope
Radioisotope
abundance
(%)
Nuclide
Physical
Emax
Eav
Probability
(disϪ1
half-life, T1/2 (MeV)
(MeV)
)
90Sr
11.6
8.8
12.2
13.6
25.9
26.9
89Sr
90Sr
29.12 y
64.1 d
29.12 y
0.546
2.279
2.279
0.1958
0.9326
0.5642
0.49994
0.49998*
0.99992*
137Cs
90Y
95Zr, 95Nb
103Ru, 106Ru
Rare-earth elements
90Sr/90Y
*This result reflects the neglect of a low energy beta transition
that occurs in 0.016% of 90Y decays.
250

MONTE CARLO CALCULATIONS OF 90Sr DOSE IN TEETH
absorbed dose distribution is a function only of the of a particular scale length for the cylinders. We have
radius r and the height z in the cylinders, and is sym- chosen the scale length xs as the mean chord length for
metric about a plane bisecting the axis of the cylinders an external uniform field of straight lines*, which from
(see Figure 2). Thus, the results could be averaged over Cauchy’s theorem is simply xs ϭ 4V/A (see, e.g.
corresponding positive and negative axial distances z, Kellerer(41)), where V is the volume and A the surface
measured from the centre of the cylinders. Complete area of the cylinder. The results are shown in Figure 4,
information on the distribution of absorbed dose in the where we have plotted the reciprocal of the mean dose
dentin and in the enamel is rather voluminous, so only rate as a function of the reciprocal of the scale length.
illustrative and summary information will be given here. The use of reciprocals allows inclusion of the result for
an infinite volume plotted at 1/xs ϭ 0. The mean dose
rate for the infinite volume is simply Eav/␳dentin, which
CALCULATED RESULTS
for 90Sr/90Y decay is 4.22 cGy.sϪ1.GBqϪ1.cm3. The
Beta particles emitted in the dentin of course will dashed line in Figure 4 fits the data to within less than
deposit energy in the dentin itself and in the neighbour- 1% and is a simple 2nd order polynomial:
·
ing regions of enamel. The resultant absorbed dose dis-
tribution is expected to be non-uniform in both
DdϪe1ntin ϭ a0 ϩ a1xsϪ1 ϩ a2xsϪ2
(1)
materials: in the dentin near the dentin/enamel interface whose coefficients are a0 ϭ 0.2366, a1 ϭ 0.2618, and
because of the net leakage of energy into the enamel, a2 ϭ 0.2124. This scaling thus appears to cover any
and in the enamel because of the increasing attenuation dentin size with scale lengths from 1.8 mm to infinity,
with increasing distance from the interface. In Figures with the mean dose rate a function only of the ratio of
3(a–f) are shown the calculated distributions of volume to surface area. For example, the same mean
absorbed dose rate in the tooth model for three of the dose rate can be expected for dentin cylinders of such
assumed dentin sizes. There are marked differences in different dimensions as h ϭ d ϭ 5 mm and h ϭ 10 mm,
the distributions of absorbed dose at the dentin/enamel d ϭ 4 mm. Indeed, the direct Monte Carlo calculations
interfaces, while the distributions away from the inter- for these sizes give mean dose rates in the dentin within
faces tend to have similar shapes. All results are given ෂ1% of each other. The combination of the limited vari-
in terms of the absorbed dose rate per unit specific ation (a) of scale lengths among typical tooth dimen-
activity, and so represent the absorbed dose distributions sions, and (b) of the mean dose rate on the scale length,
for a fixed concentration of 90Sr/90Y in dentin. Thus we is fortunate for tooth dosimetry because it renders the
will use absorbed dose rate and absorbed dose inter- mean dose rate in dentin only weakly dependent on the
changeably when there is little possibility of confusion. tooth type, particularly among molars and premolars.
Uncertainties in the basic Monte Carlo calculations,
In our model, the tooth enamel does not contain any
aside from those associated with the assumed compo- emitters and thus can only absorb radiation from the
sitions and the applicability of the results to real teeth, dentin that it surrounds. The absorption gives rise to
include an estimated 3–4% associated with the accuracy distributions of absorbed dose in the enamel that exhibit
of cross sections and of algorithms, along with statistical large gradients, with the absorbed dose falling to negli-
uncertainties associated with the scored results. For gible values at distances greater than the ෂ2 mm range
example, the results shown in Figures 3(a–f) of the of 90Sr/90Y beta particles. For EPR dosimetry, the quan-
spatial distribution of absorbed dose throughout the tity of practical interest is the mean absorbed dose in
tooth have standard deviations from about 1% to about an enamel sample. Information on the mean absorbed
20%, depending on the magnitude of the dose in the dose in enamel was generated by averaging over the
small annular scoring volumes (the uncertainty increases calculated distributions of absorbed-dose rate in the fol-
as the dose decreases). However, averages over these lowing way. For the mean absorbed dose as a function
distributions have far smaller statistical uncertainties. of radial (lateral) thickness, the absorbed dose rate in
Thus the doses averaged over the entire dentin region the enamel was averaged over axial distances z up to
have statistical uncertainties of a small fraction of one the height of the dentin cylinder and radial distances out
per cent, and doses averaged over large annular or disc to the thickness of interest. For the mean absorbed dose
regions (as given in Table 6) have statistical uncer-
tainties also of less than 1%.
* For the more appropriate interior radiator randomness, the
actual mean chord length is related to the adopted exterior radi-
ator mean chord length, but by a more complicated quantity
not in general obtainable in analytic form. For the right circular
cylinders of dimensions considered here, the interior radiator
results are ෂ5–10% larger than the simpler adopted scale
lengths(42). However, the finite range of the beta particles would
reduce the mean chord length. Regardless of any consideration
of theoretical justification, the adopted scale length can be
When a dose is reconstructed from the complete
dentin, the original signal (i.e. the signal measured
before any additional irradiations) represents the aver-
age concentration of free radicals, which corresponds to
the mean absorbed dose in dentin. Although the mean
dose rate seemingly depends in a complex way on the
cylinder diameter and height, it turns out that the mean
absorbed dose rates in the various dentin cylinders tend
to form a rather smooth curve if plotted as a function considered simply as an empirical parameter.
251

S. M. SELTZER, A. A. ROMANYUKHA and V. NAGY
252

MONTE CARLO CALCULATIONS OF 90Sr DOSE IN TEETH
253

S. M. SELTZER, A. A. ROMANYUKHA and V. NAGY
as a function of axial or masticatory thickness, the this difficulty and allows one to estimate the total
absorbed dose rate in the enamel was averaged over enamel dose using the summary results in Tables 6(a)
radial distances r up to the radius of the dentin cylinder and (b), without recourse to the basic Monte Carlo data.
and axial distances out to the masticatory thickness of The approximation is illustrated in the following recipe
interest. In both cases, the results were normalised to and applies to the assumption that the masticatory and
the mean absorbed dose rate in the dentin cylinder and lateral enamel layers form a cylindrical ‘cap’ whose
so expressed as fractions of the mean absorbed dose in sides extend down to the bottom of the crown dentin
the dentin. The results are given in Tables 6(a) and 6(b), cylinder. For the assumed lateral enamel thickness, tr,
for all of the 16 dentin cylinders used in our calcu- calculate the volume Vr of the annulus surrounding the
lations; the columns are arranged in order of increasing full height of the dentin cylinder. For the assumed mas-
scale length of the cylinders. The fractional mean ticatory enamel thickness, ta, calculate the volume Va of
absorbed dose is plotted as a function of enamel thick- a disc whose radius equals that of the dentin. Then cal-
ness also in Figures 5a and b. The data for all the tooth culate the volume Vc of the corner annulus that extends
models tend to form a single distribution, perhaps less
so for the axial case, particularly for the more asym-
metrical 9 mm ϫ 2 mm diameter dentin cylinder. The
curve in both Figures 5(a) and 5(b) is from a least-
squares fit:
Radial or lateral enamel
1
(a)
·
4
D(t)
·
ln
ϭ
b ti
(2)
͸
ͩ
ͪ
i
10-1
10-2
10-3
Ddentin
iϭ0
where t is the enamel thickness and b0 ϭ Ϫ0.7496,
b1 ϭ Ϫ2.9292, b2 ϭ 1.1868, b3 ϭ Ϫ0.5335, and b4 ϭ
0.02906. The results of the fit are within ෂ10–15% of
the data, except for the 9 mm ϫ 2 mm diameter dentin
cylinder for which the data are ෂ30–40% below the
results of the fit.
Current EPR measurements make use of the total
available amount of enamel from the whole tooth (or
from half of it), both the lateral and masticatory enamel.
Our summary results are, in principle, inadequate for
this because they do not include the absorbed dose in
the ‘corner’ region, i.e. the annulus for which both r and
z are outside those of the dentin cylinder. An approxi-
mation has been found that seems largely to overcome
0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Enamel thickness (mm)
Axial or masticatory enamel
1
10-1
10-2
10-3
(b)
0.48
0.44
0.40
0.36
0.32
0.28
0.24
0.20
0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Enamel thickness (mm)
Figure 5. Mean absorbed dose rate in the contiguous enamel
expressed as a fraction of the mean absorbed dose rate in the
dentin. (a) Radial, or lateral, enamel. The results, averaged over
the thickness of the enamel annulus extending from the bottom
to the top of the dentin cylinder, are given as a function of the
enamel thickness. (b) Axial, or masticatory, enamel. The
0
0.1
0.2
0.3
0.4
0.5
0.6
Inverse of dentin scale length (mm-1)
Figure 4. Mean absorbed dose rate in dentin. Results are given
in terms of the absorbed dose rate in dentin per unit specific results, averaged over the thickness of the enamel disc whose
activity in the dentin, as a function of the scale length for the
dentin volume.
radius is that of the dentin cylinder, are given as a function of
the enamel thickness.
254

MONTE CARLO CALCULATIONS OF 90Sr DOSE IN TEETH
from the top of the dentin to the top of the masticatory provided that the time course of the radionuclide
surface and from the dentin radius to that of the lateral accumulation in dentin is known and assuming that the
enamel. The relative weights, ␻r, ␻a, and ␻c, are simply accumulation results in a uniform increase of the 90Sr
the respective volumes divided by the total enamel concentration over the whole dentin volume. Results in
volume. The fractional dose rate in the enamel is then
this paper have been given in terms proportional to
·
·
·
·
·
(D/␭N), where D where is the absorbed dose rate and
N is the total activity of 90Sr ϩ 90Y in the dentin,
assumed in secular equilibrium. In this case, then, NSr
ϭ 0.4985 N. If we assume a continuous incorporation
of activity at a constant rate c into the dentin over a
time 0 to Tc, then the integrated dose at some time T
later than Tc is
D
D(tr)
D(ta)
Ϸ ␻
ϩ ␻
r
ͩ ͪ
r
a
ͩ
ͪ
a
·
·
·
Ddentin
Ddentin
Ddentin
·
␻
D(tr)
c
ϩ
(3)
ͩ ͪ
r
·
5
Ddentin
where
·
·
·
D
N
c
␭
1
␭
D(tr)
D(ta)
c
c
D(T) ϭ
Tc Ϫ eϪ␭(T Ϫ T ) 1 Ϫ eϪ␭T
(4)
and
ͩ
ͪ ͫ
ͩ
ͪͬ
ͩ
ͪ
r
ͩ ͪ
a
·
·
Ddentin
Ddentin
where ␭ (ϭ ln2/T1/2) is the decay constant* of 90Sr. If
TϾϾTc and ␭TcϽϽ1,
are from Table 6(a) and 6(b), respectively. The last term
of Equation 3 represents the approximation. Justification
for the use of one-fifth of the mean radial dose rate is
strictly empirical. For lateral enamel thicknesses from
0.3 to 1.7 mm and for masticatory enamel thicknesses
from 0.3 to 2.0 mm, Equation 3 gives results within ෂ1–
2% of that from the appropriate sum of the basic Monte
Carlo data for the 16 dentin sizes considered. Extension
to other sizes could be done using Equation 3 in con-
junction with Equations 1 and 2, but with the much
larger errors associated with the global fits. For a sample
taken from enamel layers not contiguous with the dentin
surface (e.g. in cases where chemical etching was
applied after dentin removal), the mean absorbed dose
can be obtained from the differences between appropri-
ate values in Tables 6(a) and (b).
·
D
N
cTc
␭
D(T) ϭ
1 Ϫ eϪ␭T
(5)
ͩ
ͪ ͩ
ͪ
Note that cTc is the total activity introduced in the
dentin. In terms of current activity N(T),
·
D
N
N(T)
␭
␭Tc
␭(T Ϫ T ) Ϫ 1
(6)
(7)
c
D(T) ϭ
e
ͩ
ͩ
ͪ ͫ
ͬ
1 Ϫ eϪ␭T
c
or
·
D
N(T)
␭
␭T
D(T) Ϸ
e
Ϫ 1
ͪ ͩ ͪ
N
for TϾϾTc and ␭TcϽϽ1.
As an example, consider Tc ϭ 1.5 y and T Ϫ Tc ϭ
47 y. For ␭ ϭ ln2/29.12 yϪ1, evaluation of Equation 6
using the mean absorbed dose rate in dentin, per unit
specific activity, from Table 6 gives the estimates found
in Table 8 of the ratio of mean absorbed dose in dentin
to 90Sr activity measured at T. (If one assumed a shorter
biological half-life of, say 25 y, the results in Table 8
would be larger by about 12%.)
Thus, using Tables 6(a) and 6(b), one can determine
the mean dose to dentin from the experimentally recon-
structed dose in tooth enamel, and then, using Equation
6 or 7, calculate the activity of 90Sr in dentin at the time
of the dose reconstruction.
RELATIONSHIPS BETWEEN RECONSTRUCTED
DOSES AND INCORPORATED 90Sr ACTIVITIES
The ultimate goal of dose reconstruction from the
viewpoint of radiation biology and epidemiology is to
determine doses to certain critical organs, such as bone
marrow. This is not easy in the case of low energy emit-
ters whose distribution over the body is not uniform.
The dose to tooth enamel, which can be reconstructed
with EPR, generally is not equal to the dose to bone
marrow, although these values are related in some com-
plicated way. Finding this relationship is a task outside
the scope of this paper, but a solution can perhaps be
facilitated with our results.
The dose from 90Sr to bone marrow will probably be
easier to relate to the 90Sr activity (or concentration) in
dentin than to the absorbed dose in tooth enamel. The
activity in dentin is obviously related to mean absorbed
dose in the dentin (and to the corresponding mean
absorbed dose in the enamel) and can be determined
from these experimentally measurable characteristics,
DISCUSSION
Some experience in using these Monte Carlo results
to analyse EPR measurements in our laboratory indi-
cates their usefulness and suggests some conclusions.
First, they provide a link between the mean absorbed
doses in enamel to the mean absorbed dose in dentin.
This appears to be a more significant quantity because,
for the same specific activity of the radionuclides in
dentin, the absorbed dose in dentin depends on the tooth
type (size) to a much smaller extent than does the
absorbed dose in the enamel. This theoretical conclusion
* It would seem more appropriate to use the biological half life
of the 90Sr in the dentin, rather than the physical half life.
255

S. M. SELTZER, A. A. ROMANYUKHA and V. NAGY
Table 7. Variation of the mean absorbed dose in enamel.
(a) Results typical for a 3rd molar. Dentin dimensions: h ؍ 5 mm, d ؍ 9 mm; enamel layer thicknesses: masticatory
0.8 mm, and lateral 0.6 mm.
Fractional absorbed dose
Deviation from nominal value
Masticatory thickness Lateral thickness
Masticatory thickness Lateral thickness
(mm)
(mm)
(mm)
(mm)
0.5
0.6
0.7
0.5
0.6
0.7
0.7
0.8
0.9
0.233
0.224
0.216
0.218
0.211
0.204
0.205
0.199
0.192
0.7
0.8
0.9
10.4%
6.2%
2.4%
3.3%
0.0%
Ϫ3.3%
Ϫ2.8%
Ϫ5.7%
Ϫ9.0%
(b) Results typical for a 1st molar. Dentin dimensions: h ؍ 5 mm, d ؍ 5 mm; enamel thicknesses: masticatory 1.5 mm,
and lateral 1.2 mm.
Fractional absorbed dose
Deviation from nominal value
Masticatory thickness Lateral thickness
Masticatory thickness Lateral thickness
(mm)
(mm)
(mm)
(mm)
1.0
1.2
1.4
1.0
1.2
1.4
1.3
1.5
1.7
0.141
0.134
0.128
0.123
0.118
0.113
0.108
0.104
0.100
1.3
1.5
1.7
19.5%
13.6%
8.5%
4.2%
0.0%
Ϫ4.2%
Ϫ8.5%
Ϫ11.9%
Ϫ15.3%
Table 8. Estimates of the ratio of the mean absorbed dose in dentin to the 90Sr activity as measured 47 y after incorporation
of activity at a constant rate for 1.5 y. A half-life for 90Sr of 29.12 y was assumed. Results are given for dentin dimensions,
given as height ؋ diameter, assuming a density for dentin of ␳ ؍ 2.14 g.cm؊3
.
Dentin
dimensions
(mm)
Dentin
volume, Vd
(cm3)
Scale length,
xs ϭ 4Vd/Ad
(mm)
D(T)/[␭NSr(T)]
(cGy/Bq)
␳VdD(T)/[␭NSr(T)]
(cGy/(Bq/g)
9 ϫ 2
4 ϫ 3
5 ϫ 4
8 ϫ 4
9 ϫ 4
10 ϫ 4
5 ϫ 5
7 ϫ 5
8 ϫ 5
9 ϫ 5
7 ϫ 6
5 ϫ 9
6 ϫ 8
6 ϫ 10
7 ϫ 9
8 ϫ 10
0.02827
0.02827
0.06283
0.10053
0.11310
0.12566
0.09817
0.13744
0.15708
0.17671
0.19792
0.31809
0.30159
0.47124
0.44532
0.62832
1.800
2.181
2.857
3.200
3.273
3.333
3.333
3.684
3.810
3.913
4.200
4.737
4.800
5.455
5.478
6.154
442
498
253
164
147
133
172
126
112
99.8
91.3
58.7
62.1
40.9
43.3
31.4
26.7
30.1
34.0
35.3
35.5
35.7
36.1
37.1
37.5
37.8
38.7
39.9
40.1
41.2
41.2
42.2
256

MONTE CARLO CALCULATIONS OF 90Sr DOSE IN TEETH
is consistent with the recent experimental findings for riverside population(19)). Although dentin is a consider-
different calcified tissues of a dog that was injected with ably more difficult material to use in EPR dosimetry
90Sr(18). Thus, the enamel measurements are mapped and the lower limit for detection is several times higher
onto more of a universal scale, which makes it far easier than for the enamel, the uncertainty in the dose recon-
to compare absorbed dose in teeth of different types. structed directly from dentin is about one order of mag-
This can help resolve previously inexplicable discrep- nitude lower than that achieved by way of determining
ancies between doses reconstructed from the same per- the mean dose in dentin through the measured dose in
son, and to make more meaningful comparisons of enamel. For internal irradiation by 90Sr, the doses in
doses reconstructed from teeth of different people. Note dentin is typically higher than the dose in enamel of the
that applying the Monte Carlo results at this level are, same tooth. Thus, for Techa riverside residents with a
so far, free of assumptions on the regimen of radio- high 90Sr body burden, ratios of these doses range from
nuclide intake into the body.
3 to 6(4,15,19). Hence, the inferior detection limit for
However, the geometric assumptions are still made: dentin is largely compensated by the higher doses
our shapes are assumed to be strictly cylindrical with presented for measurement. Dentin as a dosimetric
known dimensions, with the radionuclide distributed material will be even more important in reconstructing
uniformly in the dentin cylinder. Obviously, this is not internal doses from alpha emitters. Because of the very
true. Although it is not easy to estimate the uncertainty small penetration depth of alpha particles, their contri-
due to the non-uniformity of the radionuclide distri- bution to the dose to enamel will be negligible. These
bution in dentin (mainly due to lack of information on factors advocate using crown and root dentin as the pri-
its actual distribution), it is possible to get an idea of mary dosimetric materials in reconstruction of internal
possible uncertainties due to irregularities in shape. doses.
Because it is more difficult to calculate dose profiles for
Calculating the radionuclide activity in dentin from
irregular shapes, the easiest way to estimate the uncer- the EPR-reconstructed dose is based on additional
tainty is to compare mean absorbed doses for cylinders assumptions that contribute significant additional uncer-
slightly differing in dimensions.
tainties. However, such a calculation appears to be a
As follows from Figure 4, the average absorbed dose necessary link in any effort to relate the relatively easily
in dentin is rather insensitive to the cylinder dimensions measurable enamel or dentin doses to the absorbed dose
and, consequently, to irregularities in its shape. Simple in organs such as bone marrow. The assumptions fall
calculations show that, even if the errors in both the into two categories: the regimen of the radionuclide
diameter and the height of the cylinder reach 1 mm accumulation and retention in dentin and the radiation
each, the relative error in the mean absorbed dose will source. Moderate errors in the geometrical model of the
always be within 5.5%. The situation for tooth enamel tooth lead to relatively small errors in the dentin dose.
is not as favourable. Tables 7 show that errors of But failure to assign an accurate time course for the
0.1 mm in the lateral and masticatory thicknesses may accumulation and retention of the radionuclide could
result in errors of up to 10%. Errors of 0.2 mm may lead lead to large errors in the conversion of this dose to
in some cases (for specific types of teeth and particular estimated activities.
combinations of errors in the lateral and masticatory
The results given here are relevant to 90Sr, one of the
thicknesses) to an error of 30–40%. Therefore, errors of most important sources of internal irradiation. Similar
this magnitude in the enamel mean dose might be calculations can be performed for different emitters. The
expected to arise due to irregularities in the shapes of use only of our 90Sr results assumes there are neither
dentin and tooth enamel. If such errors are largely other radionuclides incorporated in the dentin (or in the
unavoidable, the global fit given by Equation 2 could enamel) nor significant contributions from external
be used in conjunction with Equation 1 to approximate sources to the measured enamel or dentin doses. The
by superposition the results for some irregular shapes experimental reconstruction of the doses in both dentin
and non-uniform distributions of activity in dentin.
and the enamel of the same tooth thus should reveal
The reason why the errors are larger in the enamel failures in the model assumptions. In simple cases (such
is easy to understand. For a given specific activity, a as internal irradiation from 90Sr in dentin plus uniform
change in the dimensions of a dentin cylinder results high energy external irradiation), it might even be poss-
in only a marginal change in the net energy leakage ible to separate the contributions. However, this depends
into the enamel. However, the very strong attenuation on the validity of all the other assumptions in the model.
of the beta particles in the enamel makes the mean
The methodology and data described here open the
absorbed dose quite sensitive to the uncertainties possibility of using EPR tooth dosimetry in the recon-
associated with the volume over which it is averaged. struction of doses received internally from 90Sr. Such
In view of this difference in the uncertainties, it is information is presently obtained mostly with two
reasonable to reconsider the relative suitability of dentin methods: model calculations of doses based on the
and enamel for dose reconstruction. At present, dentin is level of the 90Sr environmental contamination, and
practically unused in EPR dosimetry (the only exception whole-body counter (WBC) measurements of the 90Sr
being the recent EPR study of middle and lower Techa body burden. Unfortunately, the former method needs
257

S. M. SELTZER, A. A. ROMANYUKHA and V. NAGY
enamel clearly indicates internal exposure and sig-
to be verified against independent dose assessments
based, for example, on individual WBC measure-
ments. There are significant difficulties in interpreting
WBC measurements(43). In addition, whole-body coun-
ting is based on the measurements of current radioac-
tivity, which of course decays over time, making the
determination of doses received long ago rather diffi-
cult. A typical lower limit for detection of 90Sr is 1–2
kBq in the whole body, so, application of WBC is
limited to cases with relatively high environmental con-
tamination. In contrast, the EPR tooth dosimetry signal
increases with time, and would appear to offer an alter-
native method for evaluating internal doses from 90Sr.
Although EPR tooth dosimetry rests on its own
important assumptions, these assumptions are different
from those of WBC measurements, and the two methods
can perhaps compliment and verify each other.
nals the need for the type of analysis described
above. Such an analysis of the EPR dosimetry
results for internal exposure is more precise when
based on the dentin dose rather than the enamel
dose. The radiation-induced signal from dentin is
often more pronounced than that from enamel of the
same tooth because of the significantly higher dose
in dentin from internal irradiation. The dentin dose
is more directly related to the strontium burden of
dentin than is the enamel dose. Potentially, the
strontium burden of dentin can be related to the
strontium burden of other organs and of the whole
body. That would give a direct link between results
of EPR dosimetry, results of whole-body counter
measurements, and doses in organs other than teeth.
(3) Importance of distinguishing between crown and
root dentin. Because the geometry and metabolism
of dentin in these two locations are very different,
it is expedient to separate crown dentin from root
dentin and perform dose reconstruction for each
separately. From the dosimetric point of view, the
90Sr deposited in crown dentin should serve as the
main source for the irradiation of the tooth enamel.
Therefore, if the doses measured in the tooth enamel
and the crown dentin are consistent with the results
given in Tables 6(a) and 6(b), it would clearly indi-
cate a considerable (or predominant) internal 90Sr
contribution to the dose received by the tooth donor
(for practical examples, see also Romanyukha
et al(19)). In contrast, the absorbed dose in the root
dentin was found to be close to the absorbed dose
In summary, some practical conclusions are apparent:
(1) Importance of tooth geometry (shape and size). In
the case of low energy internal exposure, the results
of EPR tooth enamel dose reconstruction will sub-
stantially depend on the shape and dimensions of
the tooth. This makes it imperative to convert the
measured mean absorbed dose in enamel to a more
meaningful value, such as the mean absorbed dose
in dentin. Such a conversion can be made using the
results given in this paper. It is also important to
document the tooth shape in detail before destruc-
tion for possible reevaluation of the reconstructed
dose using future models that take into account
more complexities.
in the cortical jaw bone and in sinciput bones(18)
.
(2) Importance of dentin as a dosimetric material.
Dentin should be used more extensively in tooth
dosimetry for a number of reasons. A tooth with a
high dose in dentin compared with the dose in
Thus the absorbed dose in root dentin can help in
conversion of EPR-reconstructed doses to the
absorbed dose in more important organs, such as
bone marrow.
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