PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 52 (2007) 2107–2122
In vivo study of an x-ray fluorescence system to detect
bone strontium non-invasively
M Zamburlini1, A Pejovi´ c-Mili´ c2,1, D R Chettle1, C E Webber3and
1Medical Physics and Applied Radiation Science, McMaster University, Hamilton, L8S 4K1,
2Department of Physics, Ryerson University, Toronto, M5B 2K3, Canada
3Department of Nuclear Medicine, Hamilton Health Sciences
4Mohawk College, Hamilton, L8S 4K1, Canada
Received 9 October 2006, in final form 22 January 2007
Published 27 March 2007
Online at stacks.iop.org/PMB/52/2107
An x-ray fluorescence (XRF) system using125I as the source was developed to
measure strontium in bone in vivo. As part of an in vivo pilot study, 22 people
were measured at two bone sites, namely the index finger and the tibial ankle
joint. Ultrasound measurements were used to obtain the soft tissue thickness
at each site, which was necessary to correct the signal for tissue attenuation.
For all 22 people, the strontium peak was clearly distinguishable from the
background, proving that the system is able to measure Sr in vivo in people
having normal bone Sr levels. Monte Carlo simulations were carried out to
test the feasibility and the limitations of using the coherently scattered peak at
35.5 keV as a means to normalize the signal to correct for the bone size and
shape. These showed that the accuracy of the normalized Sr signal when
comparing different people is about 12%. An interesting result arising from
the possibility of a dietary or race dependence of the bone Sr concentration or
a different bone biology between races.
Strontium (Sr) is naturally present in water and soil and enters the human body through the
food chain. Being a bone seeker like calcium (Ca), it accumulates in the skeleton, where more
than 99% of the total Sr body burden is stored (Cabrera et al 1999). Sr ingested from a normal
diet is distributed uniformly in the skeleton (Hodges et al 1950, Thurber et al 1958); therefore
a measurement of Sr at any skeletal site should be representative of the Sr concentration in the
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2108 M Zamburlini et al
skeleton. However, it has been reported that after Sr injection or oral administration, Sr does
not distribute uniformly and it is retained by trabecular rather than by cortical bone and by
new bone rather than old bone (Boivin et al 1996). Therefore, after Sr administration different
skeletal sites contain different Sr concentrations (Pecher 1941, Dahl et al 2001).
Sr health effects are dose dependent. High levels of dietary Sr have been correlated with
skeletal abnormalities in animals (Nielsen 2004) and to rickets occurrence in children (¨Ozg¨ ur
et al 1996). High Sr bone concentration has been associated with osteomalacia (Cohen-Solal
2002). In contrast to these high-dose effects, treatment with low-Sr doses has been found to
have beneficial effects on bone in vitro as well as in vivo. In particular, in animals there is
evidence that the drug strontium ranelate (ProtelosR ?) reduces bone resorption and increases
bone formation without adversely affecting the bone mineralization (Marie et al 2001). Two
large randomized human studies have been conducted to test the ability of strontium ranelate
to reduce fracture occurrence in women affected by postmenopausal osteoporosis: SOTI
(Meunier et al 2004) and TROPOS (Register et al 2005). They demonstrated respectively
the ability of strontium ranelate to decrease the risk of vertebral and non-vertebral fractures.
(Marie 2006). More insight could perhaps be gained if a non-invasive method was available
that could measure the amount of Sr in bone in vivo repeatedly over time and thus follow the
amount of Sr stored in the bone during the treatment.
1.2. Methods to detect strontium in vivo
Two Sr measurement systems have been proposed in the past: one based on dual-photon
and Secord 1982, Wielopolski et al 1983, Pejovi´ c-Mili´ c et al 2004).
The DPA method is based on the determination of a Sr/Ca ratio in hydroxyapatite crystals
by exploiting the different attenuation properties of Sr and Ca at two different energies
(59.5 keV from241Am and 356 keV from133Ba). The in vivo pilot study (Nielsen et al
2004) showed that the system did not have sufficient sensitivity to detect Sr levels in the
normal population, but would detect a Sr/Ca ratio of the order of 5000–10000 µg Sr/g Ca.
The XRF method is based on the photoelectric effect, and requires irradiation of the organ
of interest with a suitable source of photons. The result of photoelectric absorption is the
creation of a vacancy in an atomic electron shell, which may be followed by the potential
emission of characteristic x-rays, which, once collected, can be associated with the amount of
element present in the part of the body irradiated.
The major limitation of Sr XRF bone measurements is the attenuation of the Sr signal by
soft tissue. The mean free path for the Sr Kαand Kβphotons (at 14.16 keV and 15.8 keV,
respectively)inskin(ICRP2002)is4.6mmand6.3mm, respectively(Bergeretal2005). The
technique is therefore limited to measuring Sr concentrations at bone sites that have minimal
overlying tissue. Pejovi´ c-Mili´ c et al (2002) investigated the average soft tissue thickness
at four skeletal sites, suitable for in vivo Sr XRF, in ten people using ultrasound. The four
overlying soft tissue thickness, and therefore represents a suitable measurement site.
Up to now, three bone Sr XRF in vivo measurement systems have been described. The
first was reported by Snyder and Secord (1982), who measured a time-dependent curve of Sr
in bone in rabbits and dogs after Sr administration. The second is a human study reported
by Wielopolski et al (1983). The measurement was done in the tibial shaft using a109Cd
or an125I source in a 90◦geometry. With this set-up, the authors were able to detect Sr in
normal volunteers with a minimum detection limit (MDL) (defined as three times the standard
In vivo study of an x-ray fluorescence system to detect bone strontium non-invasively2109
deviation above the background) of 15 µg Sr/g wet bone delivering a dose of 10 mGy. In
their in vivo study, the authors did not account for the attenuation of the Sr signal through the
soft tissue and therefore were not able to report a quantitative Sr concentration.
The third study was reported by our group (Pejovi´ c-Mili´ c et al 2004). In this case, a109Cd
source and a 90 degree geometry were used. An in vivo MDL (defined as the twice the median
value of the range of uncertainties) of 250 µg Sr/g Ca for the index finger (corresponding
to about 56 µg Sr/g hydrated cortical bone) was achieved in the pilot in vivo study with
a delivered dose of 0.46 mGy. Pejovi´ c-Mili´ c et al used the information of the soft tissue
thickness provided by an ultrasound measurement to correct for the soft tissue attenuation.
To improve the MDL, we compared different excitation sources (unpublished results) for
bone Sr XRF and identified125I, in the form of brachytherapy seeds, as the most promising.
together with a closer source to phantom distance resulted in an improvement in the MDL by
a factor of 5.5.
In the present study, we present a refinement of the system developed by Pejovi´ c-Mili´ c
et al (2004) and Zamburlini et al (2006). After having carried out dosimetry measurements
and simulations, the system was used to measure Sr in vivo in 22 healthy subjects with no
history of Sr intake. Two body sites were investigated: the index finger and the tibial ankle
joint. Corrections forsofttissueattenuation weremade based onsofttissuethickness obtained
from ultrasound measurements. Monte Carlo simulations were also carried out to determine
if coherently scattered photons at 35.5 keV were suitable as a means of internal calibration to
provide absolute measurements of bone Sr concentration.
2.1. XRF system
ProstaseedR ? 125I brachytherapy seeds with an initial activity of about 13 MBq/seed were used
as the source. Each seed consists of a titanium capsule of 4.5 mm of length and 0.8 mm
of diameter, which contains125I absorbed onto five silver (Ag) spheres. Table 1 shows the
energy of the photons emitted by the source as well as the probability for a photon at each of
these energies to undergo a photoelectric interaction with Sr. The tellurium (Te) x-rays are
emitted as a consequence of the electron capture decay of125I, while the Ag x-rays arise from
the interaction of the source gamma and x-rays with the Ag spheres. As it can be seen in
table 1, the Ag lines make this source particularly well adapted to excite Sr in bone because
they greatly enhance the probability of interaction. Table 1 also lists the relative probability
for a photon of each energy to be emitted by the source. These probabilities were obtained
measuring directly the source output and therefore they are free of confounding effects, such
as source self-absorption.
An EG&G Ortec Si(Li) detector with a 16 mm active diameter and 5.65 mm sensitive
thickness was used. The data were acquired and processed using an ORTEC DSPEC PlusTM
multichannel analyser operating MaestroTMsoftware.
because, even though it results in a slightly worse MDL with respect to the 90◦geometry (data
not shown), it allows for a more precise and reliable positioning of the bone site during an
in vivo measurement. Figure 1 shows a top view of the experimental set-up in the case of
the finger measurement. The ankle measurements were performed in the same geometry.
The125I seeds were inserted in a tungsten collimator, with a 5 mm internal diameter, 5.4 mm
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Figure 1. Top view of the experimental set-up in the case of the finger measurement. The ankle
measurement was performed in the same geometry. The function of the plastic holder was to
facilitate the positioning of the finger/ankle.
Table 1. Emission energies and interaction cross section for125I brachytherapy seeds.
27.202 and 27.472
30.944 and 30.995
21.990 and 22.163
24.912 and 24.943
47.8 Ag x-rays
bBerger et al (2005).
external diameter and 3 mm length. A plastic holder was used to facilitate the positioning of
2.2. Phantom measurements
Two sets of five Sr-doped plaster of Paris phantoms were prepared resembling the shape of a
finger bone (cylinder of about 7.5 mm of diameter and about 60 mm long) or an ankle (disc of
confirmed by the observation of a Sr Kα/Kβratio close to the theoretical predicted value (see
3.4). Each phantom was measured three times in random sequence for 1800 s clock time. The
finger and ankle phantoms were positioned in front of the source at a distance of about 5 and
3 mm, respectively. The source activity during the finger and ankle phantoms measurement
was 15.7 and 10.3 MBq, respectively.
In vivo study of an x-ray fluorescence system to detect bone strontium non-invasively2111
Figure 2. Schematic representation of the phantom used in the dosimetry measurements. The
position of the LiF chips with respect to the source is shown. The LiF chip at 40 cm away from
the source is not shown, as well as the chip used to measure the background dose.
The spectra were analysed using an in-house nonlinear least squares, Marquardt based,
fitting routine (Bevington). The region of the spectrum from 13.2 keV to 16.5 keV was fitted
as the sum of three Gaussians (one for Kα1,2, one for Kβ1,3and one for Kβ2) and an exponential
background. The position of the Kβ1,3and the Kβ2were fixed with respect to the Kα1,2. In the
following part of the text, Kαrefers to the Kα1,2peak and Kβrefers to the Kβ1,3peak.
From the calibration line, the MDL, defined as twice the uncertainty in the zero
concentration Sr phantom divided by the slope of the calibration line, was extracted. Since
an MDL for Sr Kαand Kβcan be obtained, these two values were pooled together using the
2.3.1. Dosimetry measurements.
phantom was constructed of an internal cylinder of plaster of Paris to simulate bone (diameter
11 mm), surrounded by 3 mm of wax to simulate soft tissue. A cavity was made between
the wax and plaster of Paris to allow insertion of a dosimeter to measure bone surface dose.
Measurements were made using chips of natural lithium fluoride (LiF) with dimensions of
(3.2 × 3.2 × 0.89) mm3(Global Dosimetry, www.globaldosimetry.com). The minimum
reportable dose was 0.2 mGy.
The dose was measured at five sites: two sites at the skin surface (in front of source and
1 cm above source), two sites at bone surface (in front of source and 1 cm above source)
and one site 40 cm away from the source to mimic the position of the bulk of the body
(figure 2). For each site, the measurement was repeated three times and accompanied with a
background measurement as a reference value. Each measurement lasted around 18 h. The
source–phantom distance during the dosimetry measurement was set to be 7 mm.
The absorbed dose of each dosimeter was converted to skin absorbed dose using the
In order to mimic the real measurement setting, a finger
2112 M Zamburlini et al
where piis the probability that the source emits a photon of energy Ei, (µen/ρ)iis the mass
energy absorption coefficient at the photon energy Ei and the sum is carried over all the
possible energies of the photons emitted from the source.
2.3.2. Dosimetry simulations.
the software MCNP5 (X-5 Monte Carlo Team 2003). The source was simulated as 15 point
sources positioned corresponding to the silver spheres on which the125I is absorbed (three
seeds, five spheres for each seed). The simulated source collimator had the same shape and
elemental composition as the one used to perform the dosimetry measurements. In MCNP5,
the absorbed energy was scored.
First, we wanted to benchmark the simulation.
be 7 mm in front of the source, or 1 cm above the source. We did not simulate the experiments
in which the dosimeter was positioned at the bone surface because it would have been difficult
to mimic the exact experimental geometry of the hole inside the phantom.
Once confident with the simulation, we calculated the absorbed dose to the finger and
the ankle in the same conditions as the in vivo measurements (see section 2.4.2).
finger was simulated to be two concentric cylinders: the inner one made of hydrated cortical
bone (ICRP 1995) with 10 mm diameter, and the external one made of skin (ICRP 2002)
2.5 mm thick. The ankle was simulated as a disc of skin (16 mm of diameter and 2.5 mm
thick) attached to a disc of hydrated cortical bone (10 mm thick).
The whole body effective dose was calculated using the formula:
E =Dskinwrwt skinvolumeirradiated skin/d
where d represents the skin thickness, Dskinrepresents the skin-absorbed dose and Dbone
represents the bone-absorbed dose, wrrepresents the radiation weighting factor (in this case
equal to 1) and wtrepresents the tissue weighting factor (being equal to 0.01 for both skin
and bone). The total skin surface and the total bone volume were taken as equal to those of
reference man (ICRP 1975, 1995).
The simulation of the absorbed dose was carried out using
For this reason, we performed the
+ Dbonewrwt bonevolumeirradiated bone
2.4. Normalization of Sr measurement
The size of the Sr x-ray peak will depend not only on the Sr concentration, but will also be
affected by other measuring conditions, such as the volume of the bone being measured, the
source to subject distance and the bone depth. Correction for these factors could be simplified
by the use of coherently scattered γ-rays. The coherent normalization has been successfully
used in bone lead and uranium XRF (Somervaille et al 1985, O’Meara et al 1997). The use
of the coherent peak as a means of normalization relies on the following four conditions: (1)
the coherent and x-ray photons exhibit similar absorption through soft tissue, (2) they are
produced by the same incident fluence, (3) the coherent signal arises from the same region
where the x-ray signal originates, (4) the coherent cross section is uniform about the scattering
angle. However, none of these assumptions is strictly met in a Sr XRF measurement. In
particular, the attenuation coefficient in skin (ICRP 2002) at 35.5 keV is 0.33 cm−1, while for
the Sr Kαand Kβ1,3is equal to 2.16 cm−1and 1.58 cm−1, respectively (Berger et al 2005).
Therefore the 35.5 keV peak is not expected to correct effectively for soft tissue attenuation.
Consequently, this correction was made before the normalization using the information on
the skin thickness obtained from the ultrasound measurement. Moreover the differential cross
section for coherent scattering in the backward direction at 35.5 keV is only about five times
In vivo study of an x-ray fluorescence system to detect bone strontium non-invasively2113
bigger in bone than in skin, and therefore the fraction of photons coherently scattered by the
skin might not be always negligible.
Since the aforementioned conditions for the coherent normalization are not met, we are
not expecting that the normalization of the Sr x-ray peak to the 35.5 keV coherent peak will
of bone sizes and soft tissue thicknesses expected, the normalization would help improve the
accuracy with which the Sr concentration can be determined.
A Monte Carlo simulation was performed using the program EGS4 (Electron Gamma
Shower, Nelson et al (1985), Sakamoto (1993)), as it was previously found that this program
reproduces an XRF Sr in vivo measurement more satisfactorily than MCNP5 (Zamburlini
et al 2007). Simulations were performed using a geometry reproducing the human ankle
from 1.5 mm to 4 mm. The range of variation of skin thickness was chosen according to the
values obtained from the ultrasound measurement of the people who participated in this study.
2.5. In vivo measurements
After obtaining ethical approval from the McMaster and Ryerson University Research Ethics
Boards, 22 volunteers (11 males and 11 females), aged from 26 to 68 years, were recruited.
The median age of the recruited people was 31 years. None of the volunteers suffered from
any bone disease nor were taking any Sr based drugs. One volunteer was taking calcium pills.
First, the volunteers underwent an ultrasound measurement. An indelible marker (which
was tested for Sr content and found negative) was used to mark the skin at the exact location
at which the ultrasound measurement was to be performed. The mark was then used as the
reference point to perform the XRF measurement.
2.5.1. Ultrasound measurements.
measure the overlying soft tissue thickness at the bone sites under examination. The skeletal
Ultrasound measurements were carried out in order to
(1) the finger at a point on the dorsal surface of the index finger (right hand) in the centre of
the middle phalanx and
(2) the ankle joint at the most prominent part of the medial malleolus of the tibia of the right
The ankle joint was chosen because it has a rather thin overlying soft tissue and has the
advantage over the finger of having a bigger bone area that can be irradiated.
One subject (subject 22) had a superficial vein on the surface of the medial tibia location
that obviated the measurement. This person was therefore measured at the lateral tibia-fibula
(HDI5000 Reference Manual 2000). The uncertainty on each measured thickness is 1%
(Philips R&D group, personal communication).
measuring site and the transducer. The gel pad was used to avoid an entrance reverberation
artefact and to minimize the pressure exerted by the transducer on the skin, which would have
resulted in an underestimation of the measured skin thickness.
A gel pad was interposed between the
2.5.2. XRF measurements.
was fixed in front of the source at about 3 mm from the collimator face (source–finger distance
Each XRF measurement lasted 1800 s clock time. The finger
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was about 5 mm). For each finger measurement the activity ranged from 24 to 39 MBq. The
ankle was fixed at about 1 mm from the collimator face (source–ankle distance was about
3 mm). For each ankle measurement, the source activity ranged from 12 to 26 MBq. A smaller
source activity was used when measuring the ankle than the finger to keep the dead time in the
former case under 50%. Since digital electronics were used to acquire the data, the high dead
time did not compromise the peak resolution (Bateman et al 2000, Pejovi´ c-Mili´ c et al 2004).
The Kαand Kβareas were corrected for tissue attenuation, using the value of soft tissue
thickness obtained from the ultrasound measurement. The soft tissue correction included the
correction for the attenuation of both the incoming beam and the Sr signal. The factor to
correct for the primary beam attenuation was obtained for each subject using the formula:
where ?iis the flux of photons of energy Eiemitted by the source, piis the probability of
emission for a photon of energy Ei(table 1), N is the total flux of photons emitted by the
source (hence ?i=N·pi), µiistheabsorption coefficient ofskinattheenergy Ei, disthesoft
correction for the primary flux is limited by the fact that it does not take into account those
photons that interact with soft tissue through inelastic scattering and subsequently can excite
Sr to fluorescence.
3. Results and discussion
3.1. Phantom measurements
The pooled MDL for the finger phantom measurement was equal to 22.9 ± 0.6 µg Sr/g
Ca. The pooled MDL for the ankle phantom measurement was 27.3 ± 0.4 µg Sr/g Ca.
These values may be compared with the MDL reported by Pejovi´ c-Mili´ c et al (2004) (110 µg
Sr/g Ca) or the one reported by Zamburlini et al (2006) (44.6 ± 0.9 µg Sr/g Ca). In this
work, the calibration lines were not used to extract the Sr concentration from the measured
patient spectra because the built phantoms are not representative of a normal untreated bone.
In particular, we believe that in the measured population the Sr distribution is not uniform
along the bone radius and therefore using phantoms with uniform Sr distribution as a means
of calibration would produce misleading results. However, we included the MDL, as obtained
with the phantom measurements, as a means to compare the system used in this work to other
Table 2 shows the average measured LiF chip dose at each site. The error was calculated as
the standard deviation of the three measurements performed at the same site. The background
dose was subtracted from the readings.
Table 2 shows also the simulated LiF chip dose at the two sites where the simulation
was performed. The simulated and measured doses agree within error, at the two sites for
which the comparison was possible. This gives us confidence that the simulation was able to
reproduce realistically the source positioning and spectrum.
The simulated skin- and bone-absorbed doses during a finger measurement are (1.011 ±
0.002) × 10−3mGy MBq−1min−1and (2.603 ± 0.003) × 10−3mGy MBq−1min−1,
respectively. The simulated skin- and bone-absorbed doses during an ankle measurement are
(11.05 ± 0.02) × 10−3mGy MBq−1min−1and (11.206 ± 0.009) × 10−3mGy MBq−1min−1,
In vivo study of an x-ray fluorescence system to detect bone strontium non-invasively2115
Table 2. Measured and simulated absorbed dose at different sites. The error of measured absorbed
dose is given by the standard deviation of the three measurements performed at the same location.
The error in the simulated absorbed dose is given by the statistical error.
Measured absorbed dose
Simulated absorbed dose
Skin surface—in front of source
Skin surface—1 cm above
Bone surface in front of source
Bone surface 1 cm above
40 cm away from source
(1.03 ± 0.20) × 10−2
(2.39 ± 0.17) × 10−3
(1.80 ± 0.20) × 10−2
(1.12 ± 0.05) × 10−2
(1 ± 4) × 10−5
(1.122 ± 0.012) × 10−2
(2.25 ± 0.05) × 10−3
Table 3. Coefficient of variation of the Kα and Kα/coherent when the bone diameter varies
between 10 and 16 mm.
variation of Kα
Coefficient of variation
respectively. The error reported is the statistical error. It is therefore an underestimation of the
sectional data and in the estimation of the number of photons emitted by the source at each
energy. The calculated whole body effective dose for a 30 min measurement with a 30 MBq
source is (49.08 ± 0.05) × 10−6mSv and (87.32 ± 0.09) × 10−6mSv, during a finger and an
ankle measurement, respectively. This effective dose can be put in context by recalling that
the annual natural background in North America is about 3 mSv/year and that the effective
dose associated with a standard chest x-ray is about 0.1 mSv.
3.3. Normalization of Sr measurement
The effect of the change in the bone diameters for different skin thicknesses on the normalized
Sr net area (Kα/coherent) was assessed using the coefficient of variation. Table 3 shows, for
each skin thickness, the coefficient of variation of the normalized Sr area as the bone diameter
varies. As it can be seen, the coefficient of variation is poorest when the soft tissue thickness
is equal to 1.5 mm or 4 mm. The worsening of the coefficient of variation when the skin
thickness is 1.5 mm was found to be due to geometrical factors, while the worsening with
the increasing skin thickness is probably due to the increased fraction of coherently scattered
photons origination from the skin as thickness increases.
To estimate the accuracy with which the Sr concentration can be estimated, we calculated
the coefficient of variation for all 20 simulated cases (five skin thicknesses, each with four
bone diameters). Inthiscase, theSrnetpeak areawascorrected fortheskinattenuation before
dividing it by the coherent net peak area. The coefficient of variation for all the simulated
cases was 12%. This result needs to be compared with the coefficient of variation obtained
when the Sr net peak area was not normalized (but still corrected for skin attenuation), which
was 28%. The normalization with the 35.5 keV coherent peak, therefore, is not perfect but
2116M Zamburlini et al
5 101520 25 3035
Number of Counts
Number of Counts
Figure 3. (a) Typical Sr spectrum for an in vivo measurement in logarithmic scale. (b) Finger Sr
spectra from two subjects with the same soft tissue thickness of 2.1 mm. SN: subject number.
it represents a considerable improvement over the Sr net area. The normalization worked
the best when the skin thickness was between 2 and 3 mm, in which case the coefficient of
variation was 8%. This is a promising outcome, because this thickness range was observed
most frequently in the human population participating in this study (14 and 18 people out of
22 had skin thickness between 2 and 3 mm in the ankle and the finger, respectively). The
coherent normalization with the 35.5 keV peak is just an initial attempt at normalization and
more work is needed to find a more robust way to correct the data for geometrical factors,
including bone size and shape and overlying soft tissue thickness.
3.4. In vivo measurements
Figure 3(a) shows a typical in vivo spectrum in logarithmic scale. Figure 3(b) shows two
Sr finger spectra, one from a subject with high Sr concentration (subject number 4) and one
In vivo study of an x-ray fluorescence system to detect bone strontium non-invasively2117
101214 16 18 2022
Figure4. Kα/coherentforthefinger. Theuncertaintyreportedrepresentsthestatisticaluncertainty.
10 1214 1618 2022
Figure5. Kα/coherentfortheankle. Theuncertaintyreportedrepresentsthestatisticaluncertainty.
from a subject with low Sr concentration (subject number 5), both having the same soft tissue
thickness. In both cases, the Sr Kαand Kβpeaks are clearly distinguishable from background.
These spectra demonstrate that the system sensitivity is high enough to detect, in some cases,
inter-subject differences of natural bone Sr concentrations.
and the ankle, respectively. The error reported in the figures is the statistical error arising from
the number of recorded photons. For a quantitative comparison between people a 12% error
should be added in quadrature to the statistical error to account for inter-subject differences.
2118M Zamburlini et al
0.00.20.4 0.6 0.8 1.01.21.41.6
Y = (0.21±0.02) * X + (0.059 ±0.017)
Figure 6. Correlation between Sr Kα and Kβ in the finger measurement. The correlation is
significant (p < 0.0001). Note: the intercept is bigger than zero. The error on the X and Y is given
by the statistical uncertainty.
It is interesting to note that the Kα/coherent values cluster into two groups: one having
much higher Sr concentration than the other. The fact is particularly interesting because the
people who belong to the cluster of high bone Sr concentrations are all continental Asian
people, who have been shown to have a smaller prevalence of osteoporosis (Barrett-Connor
et al 2005). A two-sample t-test (assuming unequal variances) shows that the normalized
Sr concentration is significantly higher for continental Asian (p < 0.001 and p = 0.003, for
finger and ankle, respectively). This result is in agreement with that reported by Schroeder
et al (1972), who showed a higher Sr concentration in ex vivo bone samples from Far Eastern
than from American people.
Figure 6 shows the correlation between Kαand Kβin the case of the finger measurements
(the result for the ankle measurements is comparable). As expected the correlation between
Kαand Kβis significant (p < 0.0001, R2= 0.84). It is interesting to note that the intercept is
greaterthanzerowithintheerror. Apossibleexplanationforthisisasfollows. Theprobability
of emission for a Sr Kαphoton is seven times larger than the probability of emission for a
Sr Kβphoton, therefore the theoretical Kα/Kβratio is 7. If we assume Sr to be uniformly
distributed in hydrated cortical bone, it can be calculated that the expected Kα/Kβratio (under
the assumption that the bone thickness is infinite at this energy) is 5.2. Figure 7 shows the
Kα/Kβratio in the case of the ankle after the correction for soft tissue attenuation has been
performed. Interestingly, most of the values are lower than 5.2 within the error. The fact
that the intercept of the Kαversus Kβline is greater than zero and that the Kα/Kβratio is, in
many cases, smaller than expected suggests that the Sr depth distribution in normal bone is
non-uniform, i.e. there might be a gradient or a step in the magnitude of the Sr concentration.
The variability of the Sr Kα/Kβratio between subjects also means that the possibility of using
this ratio to correct for soft tissue attenuation is not feasible. Unfortunately, there is little data
in the literature with which to compare our result. Zoeger et al (2005) studied the distribution
of Pb and Zn in human bone and showed one profile of Sr depth distribution in hip bone.
In vivo study of an x-ray fluorescence system to detect bone strontium non-invasively2119
Figure 7. Ratio of Sr Kαto Kβin the case of the ankle measurements of 22 human subjects. The
error is given by the statistical error (dominated by the error in the Sr Kβpeak). The Sr Kα/Kβ
ratio in the case of uniformly distributed Sr in cortical bone is 5.2.
However, the authors do not discuss this distribution and it is difficult to draw any conclusions
from the graph presented. Boivin et al (1996) reported a uniform Sr distribution in untreated
monkey iliac bone; however, the detection limit was comparable to the Sr concentration in
untreated monkey. In conclusion, we could not find in the literature any works that address
further studies are warranted to address this issue.
Figure 8 shows the correlation between the normalized Sr Kαin the finger and the ankle.
The error reported is the statistical error. It can be seen that the correlation is significant
(p < 0.0001, R2= 0.88) and that the intercept is equal to zero within the error.
result is important because it demonstrates the ability of our system to provide a quantitative
measurement. A paired t-test was performed to determine whether the bone Sr concentration
at the two sites is equal. The result of the test shows that the bone Sr concentrations at the
finger and ankle are not statistically different (p = 0.14). This result is in agreement with the
finding reported in the literature of a uniform Sr distribution within the skeleton in untreated
people (Hodges et al 1950, Thurber et al 1958). However, since Sr seems not to distribute
uniformly after Sr administration, more work is needed to identify whether a finger or an ankle
measurement would be more clinically relevant to follow up a person under Sr treatment.
The normalized Sr signal in female and male (two-sample t-test) was not significantly
different (p = 0.54 and p = 0.35 for the finger and the ankle, respectively) in our population.
This result is in agreement with that reported by Zaichick (2004), who measured the Sr
concentration in the cortical part of the human femoral neck in 78 cadavers.
The correlation between the normalized Sr signal and age was also found to be not
significant (p = 0.27, R = 0.25) in our population. In the literature, the correlation between Sr
and age is controversial. Schroeder et al (1972) found that Sr increases with age, while other
does not depend on age.
2120M Zamburlini et al
0.00.2 0.40.6 0.8 1.01.21.4 1.6
Y = (0.88±0.07) * X + (0.01 ±0.06)
K /coherent - Ankle
K /coherent - Finger
Figure 8. Correlation between the Sr Kα/coherent signal in the ankle and the finger. The error
reported represents the statistical error. The correlation of the Sr signal between the two bone sites
is significant (p < 0.0001). Note: the intercept is equal to zero within the error.
This pilot study demonstrates that bone Sr levels in the general population can be detected in
the finger and ankle bone with an125I based XRF system delivering a maximum effective dose
of 64 × 10−6and 76 × 10−6mSv in a 30 min measurement.
We tested the validity of normalizing the Sr signal to the coherent peak at 35.5 keV to
correct for the effect of the bone size and geometrical factors. It was found that the method
thedata. However, thenormalizationwiththe35.5keVpeakdecreasestheuncertaintyto12%,
and therefore allows for a quantitative inter-subject comparison, even if to a limited extent.
Moreover, both precision and accuracy are expected to be more than adequate to distinguish
raised bone Sr levels from normal levels.
This study identified an intriguing result that needs further investigation. We noticed
a difference in the normalized Sr signal between continental Asian and non-Asian people
in bone might not be uniform, when Sr intake is only through diet.
Future work on the described system will include improving the positioning accuracy and
establishing the measurement reproducibility. Calibration curves will also be obtained using
ex vivo cadaver fingers in order to quantify the Sr concentration.
This work was supported by an OGS scholarship to MZ, through NSERC research grants to
DRC and AP-M and a CFI/OIT grant to AP-M We thank Jason Falladown for help in the
design of the source holder. We are indebted to the volunteers who participated in the study.
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