The feasibility of K XRF bone lead measurements in mice assessed using 3D-printed phantoms

This article describes the development of a system for in vivo measurements of lead body burden in mice using 109Cd K x-ray fluorescence (XRF). This K XRF system could facilitate early-stage studies on interventions that ameliorate or reverse organ tissue damage from lead poisoning by reducing animal numbers through a cross-sectional study approach. A novel mouse phantom was developed based on a mouse atlas and 3D-printed using PLA plastic with plaster of Paris ’bone’ inserts. PLA plastic was found to be a good surrogate for soft tissue in XRF measurements and the phantoms were found to be good models of mice. As expected, lead detection limits varied with mouse size, mouse orientation, and mouse position with respect to the source and detector. The work suggests that detection limits of 10 to 20 μg Pb per g bone mineral may be possible for a 2 to 3 hour XRF measurement in a single animal, an adequate limit for some pre-clinical studies. The 109Cd K XRF mouse measurement system was also modeled using the Monte Carlo code MCNP. The combination of experiment and modeling found that contrary to expectation, accurate measurements of lead levels in mice required calibration using mouse-specific calibration standards due to the coherent scatter peak normalization failing when small animals are measured. MCNP modeling determined that this was because the coherent scatter signal from soft tissue, which until now has been assumed negligible, becomes significant when compared to the coherent scatter signal in bone in small animals. This may have implications for some human measurements. This work suggests that 109Cd K x-ray fluorescence measurements of lead body burden are precise enough to make the system feasible for small animals if appropriately calibrated. Further work to validate the technology’s measurement accuracy and performance in vivo will be required.


Introduction
Lead is a common environmental toxin that has been found to affect behaviour, learning, and memory in humans [1].Childhood environmental lead exposure, in particular, has been shown to increase antisocial behaviour [2], significantly impact perceptual organisation and concentration [2], decrease IQ [3], and decrease complex language processing [4].Long-term effects of childhood lead exposure continue after exposure has ended: blood lead concentration at age 24 months has been found to correlate with lower IQ 8 years later [5].While urban lead exposure has fallen dramatically in the last thirty years in Europe and North America [6-8], children are still lead poisoned today.In the USA, it is estimated that 2%-3% of children today have blood lead levels above the reference levels that warrant further investigation [9].In addition, lead poisoning is still a concern in China [10], there have been serious lead exposure problems in Zambia [11], and there was a severe incident in Nigeria reported in the last decade where hundreds of children died from lead poisoning [12].
Currently, early treatment for childhood lead poisoning focuses on the lowering of blood lead levels through interventions that include removal of the source of lead, and instruction on hygiene, diet, and nutrition to prevent further exposure [13].Chelation therapy, where lead may complex with a chelate ligand and is more readily excreted from the body [14], may be used when blood lead levels are very high, possibly life-threatening [15].There are no currently approved clinical therapies to mitigate the physiological problems caused by lead poisoning.More understanding of the biological mechanisms underlying lead poisoning effects, and thus the potential for therapies, is required.These will have to be conducted in controlled animal experiments.To date, animal studies have increased our understanding of the problem.Indeed, a recent study linked low-level lead exposure during development with several behavioural changes, including lower interest in social novelty [16].Physiological studies have shown that lead impacts the hippocampal pyramidal neurons through damage to glutamate receptors [1] and causes demyelination of neurons in the peripheral nervous system [17,18].Myelin, constructed from Schwann cells, plays a key role in nerve impulse conduction, increasing conduction speed and contributing to the proper timing of impulses and overall nerve function [19].In addition, some animal studies have researched therapies that may mitigate lead poisoning symptoms, such as administering gallic acid [20] or, as in a recent rat study, investigate the potential for vitamin D to reduce neurotoxic effects [21].
However, cross-sectional animal studies can be costly and involve the sacrifice of multiple animals at different time points to determine the level of both lead exposure and effects such as demyelination.A technology that allows for longitudinal studies by assessing the body burden of lead without sacrificing the animals, such as K x-ray fluorescence (XRF) of whole mice, could be of great utility.Paired with in vivo myelin measurements using MRI [22,23], this could be a powerful combination of tools that could reduce the costs of animal studies and enable some of the long-term effects of lead exposure and/or therapy to be studied in serial measurements of single mice.
The technique of XRF has been used for in vivo analysis of lead in human bone for over forty years [24].The specific XRF technique that uses 109 Cd was first developed in the 1980s [25] and has been the most widely used technology for human studies because it is considered a robust measurement [26].The system employs a normalization of lead characteristic x-rays to a coherent scatter signal: this is considered to make a bone lead measurement independent of bone shape, size, mass, tissue overlay thickness, or subject motion [25].It was argued that since the coherent cross section for soft tissue is a factor of 28 times lower than for bone mineral, and the relative mass of bone to tissue is high, the coherent signal was a measure of bone mineral mass.The normalization, thus meant measurements were in units of μg Pb per g bone mineral.However, the system has not been used for in vivo small animal studies and may not be immediately transferable.The increase in the ratio of soft tissue mass to bone mass in the mouse means that the size of the coherent scatter signal from soft tissue may no longer be negligible when compared to the bone coherent scatter signal.This may impact the normalization, and lead to an underestimation of bone lead levels in mice.It may mean that phantoms that better represent mice must be used in order to obtain an accurate calibration.
In this article, we thus describe the development of a system for the measurement of bone lead (a measure of lead body burden) by XRF in whole mice in vivo using 3D-printed zoomorphic phantoms.The use of 100% PLA printed plastic or PLA plastic with paraffin wax infill as soft tissue analogues were explored.The effects of 3D-printed mouse shape, size, orientation, and source-detector distance on detection limits were investigated.Finally, the contribution of scattering in soft tissue to the coherent scatter signal was studied using phantoms and Monte Carlo modeling, and the possibility of an impact on calibration was explored.The feasibility of the system as a potential technique for use in small animal studies of lead exposure is discussed.

Methods
The 109 Cd K-XRF bone lead measurement system Preliminary studies [27] suggested a second generation 109 Cd bone lead measurement system, initially developed for humans [28,29], would be suitable for this work.Measurements were therefore performed using a cloverleaf detector system composed of four 16mm diameter, 10 mm thick, high-purity germanium (HpGe) detectors from Canberra Industries, Inc. (Meriden, Connecticut, 06 450, USA), each with its own feedback resistive preamplifier (Canberra 2001 CP) and digital signal analyzer (Canberra 2001 CP), as seen in figure 1.The detectors are located behind a 0.5 mm beryllium window.Samples were placed in front of the detectors, approximately 5 mm from the 109 Cd source, which had an activity of 5 GBq as of June 2020.Measurements were performed between December 2020 and August 2022.However, experiments that aimed to determine differences between groups were performed over small time periods, with alternating comparison measurements, to avoid having to perform correction for source decay.
109 Cd emits 88.035 keV γ-rays in only 4% of decays, but the process of electron capture leading to 109 Ag means higher intensities of silver x-rays of energy 22-25 KeV are emitted.The source was thus encased in a tungsten collimator with a 0.5 mm copper window or filter which reduced the silver x-rays to 0.01% of their original intensity while only reducing the γ-ray signal to 76% [25].The detectors are shielded from direct source emission, allowing each detector to measure the backscattered XRF spectrum from the sample independently.The spectra were collected with Genie 2000 Gamma Analysis Software from Canberra.This system had a typical minimum detection limit (MDL) when used for human studies of 1.5-4ppm using a 5 GBq activity source and lead-doped plaster of Paris human tibia phantoms [29].
Material properties of the mouse phantom model PLA plastic ((C3H4O2)n), a standard material for 3D printing, and paraffin wax (CnH(2n+2)), a less expensive material, were selected as possible analogues for soft tissue in the mouse phantom.The linear attenuation coefficients of each of these materials were experimentally determined by us.While the theoretical mass attenuation coefficients for PLA can be calculated, literature reports note that PLA can vary slightly in composition from manufacturer to manufacturer and hence mass attenuation coefficients can vary [30].To reduce the possibility of the determination of the mass attenuation coefficient being inaccurate due to an error in an individual measurement, the mass attenuation coefficients for the 88.035 keV energy used for the fluorescing source in vivo XRF lead measurements were measured by fitting the attenuation curve of each material, i.e. the signal intensity versus material thickness, to an exponential function.The attenuation was measured by placing the 109 Cd source in a support 30 cm in front of the detector with the highest resolution, behind a 3 mm-thick lead collimator with an approximately 1 mm pinpoint opening.The XRF spectrum was then measured for 15 s with blocks of paraffin or PLA ranging from 0.5 cm to 9 cm placed between the source and detector.The magnitudes of the resulting 88.035 keV γ-ray signals were normalized against the γ-ray signal from the unattenuated source to determine the relative intensity.The intensity plot was fitted to an exponential curve in OriginPro 2021, where the experimental attenuation coefficient was determined as the power of the exponent.This experimental attenuation coefficient was compared to the theoretical attenuation coefficient of soft tissue at 88.035 keV, calculated from the mass attenuation coefficient for ICRU-44 soft tissue interpolated from NIST databank [31] data and the average density of ICRU-44 soft tissue as reported by NIST.

Anatomy of the 3D printed zoomorphic mouse phantom
The anatomy of the mouse phantom was based on the Segar et al mouse atlas [32].Major bones which should contribute significantly to measured lead concentrations were selected to be the spine, skull, forelegs and shoulder blades, sternum, and hind legs.Each of these bones was measured and approximated for the 3Dprint design by a simplified geometrical shape.Given that the vertebral column does not have a uniform thickness, measurements were taken along the vertebral column and averaged to approximate the vertebral column using a cylinder with a single width.Similarly, the forelegs, hind legs, and sternum were approximated to cylinders with a radius representing the average radius of the bone.The skull and mandible were approximated with half-cone shapes.
The model was then built in Autodesk Inventor Professional 2020 for 3D-printing.The soft tissue was included as positive space, while the bone was included as negative space, creating channels, such that the model could be printed in tissue-equivalent plastic.For convenience, the model was divided into 8 parts, 4 for the left and 4 for the right side along the sagittal plane.These mirrored pieces represented the head, chest, upper abdomen, and lower abdomen respectively.Phantoms were printed with PLA 3D-printing filament (MG Chemicals, Ontario, Canada) using an Ultimaker 2 Extended 3D printer with 0.15 mm resolution.This print resolution was a factor in the phantom design as it meant that only bones greater than the resolution could be printed in the model.The PLA phantoms were printed at 100% infill, while the paraffin phantoms were printed in 1 mm thick PLA, with the cavities manually filled with molten paraffin wax which was left to set.The bone channels were then filled with Plaster of Paris before final assembly.The development of the model is summarized in figure 2.
The zero concentration mouse phantoms, made from calcium sulfate dihydrate, or plaster of Paris (Merk, Darmstadt, Germanch) with a nominal concentration of 0 μg Pb per g of plaster of Paris were each measured for three time periods: 20 minutes, 40 minutes, and 12 hrs of live time, approximately 30, 60, and 18 hours in real-time respectively.The dead time for all experiments was 50% or below.Our group has tested the proprietary algorithm that estimates dead time and have found it to be accurate with dead times under 50%.In a typical human tibia measurement, a 3 cm portion of the central shaft of the tibia is measured by placing the participant's shin towards the detector, minimizing attenuation from soft tissue as this is an area with a small tissue thickness overlying the bone.However, when measuring a mouse phantom, several orientations are possible.Hence, the PLA mouse phantom was measured in three positions; dorsal, where the spine of the mouse phantom was placed against the detector, ventral, where the front abdomen of the mouse was placed against the detector, and rostral, where the head of the mouse was placed against the detector.An illustration of the experimental mouse positions can be seen in figure 3. The dorsal position was predicted in advance of the measurements to give the lowest detection limit, due to little soft matter attenuation and a relatively large bone contribution from the spine, which was very close to the detector.The ventral position was anticipated to  give the largest detection limit, due to attenuation from the abdominal soft tissue and the approximately 1/r 2 decrease in signal from the spine with distance.
To estimate the uncertainties in a real mouse measurement, a dead mouse suspended in a preservation fluid that was being sent for disposal was obtained from the McMaster University Central Animal Facility, removed from the preservation fluid, and frozen.As with the mouse phantom, the real (frozen) mouse was measured in the dorsal, rostral, and ventral orientations for 40 min live time measurements.

The effects of mouse size and position on detection limit
The effect of mouse size on MDL was investigated using a set of PLA phantoms of nominal concentration 0 μg Pb per g of plaster of Paris.Mouse phantoms dimensions were linearly scaled from 0.75x to 2x the original phantom mouse size.While there is variability in the size of different mouse strains, the 2x mouse is an exaggerated size, probably more reflective of the size of a small rat than a large mouse.These differentsized phantoms were each measured for 40 minutes of live time.
The effect of distance was investigated by measuring the original 0 ppm added lead mouse phantom in the dorsal position for 40 min live time at 1 cm increments from the detector, up to a distance of 5 cm.

Mouse specific calibration standards
Finally, to determine whether mouse-specific calibration phantoms needed to be used to accurately estimate bone lead concentrations in whole mice, a set of mouse calibration standards were created.These phantoms were the same design as the original mouse phantom, but the plaster of Paris used to create the bones was doped with lead.The mouse calibration standards had concentrations of 0, 20, 50, 70, and 100 μg Pb per g of plaster of Paris.
All of the above-described measurements of the mouse and mouse phantoms were repeated 5 times, with the mouse or phantom being removed and repositioned between measurements.

Spectral analysis and fitting methodology
The K XRF spectrum from a bone lead phantom or a person has several significant peaks.Compton scattering is the dominant interaction in low-atomic number materials in this energy range, and this is the largest feature in the backscatter spectrum.The Compton scatter peak is centered at approximately 66 keV because the mean scattering angle of the system is 165°.A coherent scatter peak at 88.035 keV is predominately a result of elastic scattering on higher atomic number materials, such as the calcium found in bones or plaster of Paris.Lead Kα x-ray peaks arise from photoelectric interactions and are characteristic of and specific to the element.The detector reports the number of detected events in the form of a histogram, where each channel has been set to correspond to an approximately 0.05 keV energy window.An example spectrum is shown in figure 4.
The Pb Kα peak and coherent peak portions of the spectrum were fitted with a mathematical model using the Levenburg-Marquart technique in Origin Pro , highlighting the Pb characteristic x-rays and the coherent scatter peak.Due to the greater tissue masses in a human, tibia phantom spectra have a higher count rate compared to mouse phantom spectra, and thus better relative uncertainties in the data.The tibia phantom spectrum is shown for illustration as it is easier to distinguish major features.
2021.The Kβ 1,3 portions of the mouse spectra were not fitted because the signal strengths were too low to make accurate fitting possible.The Kβ 1,3 portions of the spectrum are fitted in human measurements, but the relative uncertainties are higher in mouse measurements, and the background in the region of the Kβ 1,3 x-ray peaks has a series of complicated features that must be included.Attempted fits to the Kβ 1,3 portions of the spectrum resulted in poor statistics and thus negligible improvements to the MDL.In the Kα portion of the spectrum, the lead Kα 1 peak, situated at 74.969 keV, and the lead Kα 2 peak, situated at 72.804 keV, were fitted with Gaussian functions coupled together in terms of position.The background was fitted with a polynomial function, while complimentary error functions below each peak modeled the incomplete charge collection observed to create a step under x-ray peaks in this system.In the coherent peak portion of the spectrum, the coherent peak, centered at approximately 88.035 KeV, and the lead Kβ 2 x-ray peak at 86.6 keV, were fitted with Gaussian functions while incomplete charge collection was modeled by a complementary error function.The background was modeled by a constant value.The goodness of fit was determined using a reduced χ 2 value, which in this work was found to vary between 1.2 and 0.8 indicating that the fitting model was acceptable.

Calibration and minimum detectable limit
Calibration lines were created of the lead Kα x-ray to coherent peak ratio versus concentration using a standard set of human tibia calibration phantoms.Estimates of the Kα x-ray to coherent ratio and the uncertainties on the K α x-ray to coherent ratio were made for each phantom and real mouse measurement.The ratios were converted to concentrations, in units of μg Pb per g of plaster, by dividing by the slope of the calibration line.The coherent cross-section of bone and plaster of Paris are different, and to account for the difference in composition of plaster of Paris and bone a coherent conversion factor (CCF) of 1.46 was used to convert the measured concentrations in the real mouse into units of μg Pb per gram of bone mineral.The CCF was calculated from the ratio of the coherent cross sections in plaster of Paris and bone [33].
In our laboratory, the minimum detection limit is taken to be twice the uncertainty on the zero concentration phantom, as this is the level above which there is a greater than 95% confidence that the signal is truly different from zero [34].To convert the detection limit to units of μg Pb per gram of plaster, the uncertainty is divided by the slope of the calibration line.For initial MDL measurements, the calibration line that was used for this conversion was determined from measurements of an existing set of human tibia calibration standards used for bone lead measurements in humans.These had been constructed by filling cylindrical polyethylene containers of 2.5 cm diameter, 2 mm wall thickness, and 7 cm height (Nalgene, New York, USA) with plaster of Paris doped with lead with concentrations varying from 0 to 100 μg Pb per gram of plaster, as this matches the range of bone lead concentrations generally encountered from nonexposed to exposed people.These phantoms were then measured for 40 and 20 min live time.Human tibia phantom measurements were each repeated three times with the phantom being removed and replaced between measurements.
The uncertainty of the measurement, and therefore the detection limit, decreases with increasing time, such that short measurements of the XRF spectrum will render realistic detection limits for experiments using live mice, while long measurements will render highly precise data, allowing us to determine which mouse orientation will give the lowest detection limit on average.The uncertainty of the measurement was determined using the following equation, where σ i is the uncertainty of the ratio of the K α x-ray peak area to the coherent peak area of detector i, A k is the area of the K α x-ray peak, and sigma Ak the associated error, A c is the area of the coherent peak and sigma Ac the associated error.
The MDL for a single detector was then calculated using the following equation, where MDL i is the minimum detection limit of detector i.
The MDL of the entire system can then be calculated through an inverse variance weighted mean, as described by the equation below.Inverse variance weighting is used because some detectors have better energy resolution than others and hence better precision.
Following the initial MDL measurements, where the detection limit obtained from the mouse phantom was converted to units of μg Pb per gram plaster from the human tibia phantom calibration lines, calibration lines were constructed from the lead-doped mouse calibration phantoms and the slopes compared to the slopes obtained from the set of human tibia phantoms.

MCNP simulation
Monte Carlo N-Particle (MCNP) simulations were used to explore the relative contributions of the soft tissue, bone, and lead to the coherent peak signal in mice.A realistic model of the 109 Cd XRF and cloverleaf HPGe detector system was built in MCNP6 as has been performed in previous K XRF studies [34].Both the human tibia phantom and mouse phantom geometries were translated to MCNP6.As in the physical phantoms, PLA was used in the MCNP model as a soft tissue equivalent, while plaster of Paris was used as a bone analogue.The density of the plaster was set to 2.832 g cm −3 [35], an average density, while the density of the PLA was set to 1.21 g cm −3 [36].
The Kα x-ray peaks and coherent scatter signal were obtained by calling on the .12pphoton library.This library had the necessary cross-section data for coherent scattering but unfortunately does not employ the most recent photoelectric cross-section data sets.The interactions in the detector were simulated by using the pulse height tally, F8.Using this feature, the results are provided in the form of a histogram giving the fraction of particles having interacted in each bin of width 0.8798 KeV.Simulations were run for 5500 million particles.The simulated human tibia and mouse phantoms were run with 0, 20, 50, 70, and 100 μg Pb per gram of plaster concentrations, with the mouse in both dorsal and rostral positions.Additionally, simulations were done with the bone in the model phantom replaced by air, to obtain the contribution of the soft tissue alone to the coherent peak signal.

Attenuation coefficients
Both the PLA plastic and the PLA plastic shell filled with paraffin wax used in these studies were found to be acceptable materials for the simulation of soft tissue in this x-ray energy range.The PLA plastic is, however, a much better match to real tissue as can be seen in figure 5 which compares the experimental attenuation curves for PLA plastic and paraffin wax with the theoretical attenuation curve of soft tissue for a 88 keV source.From the experiments, the mass attenuation coefficient of PLA was found to be 0.186 ± 0.001 cm 2 /g; that of PLA with a paraffin infill was found to be 0.147 ± 0.001 cm 2 /g, while the theoretical attenuation coefficient of soft tissue was calculated to be 0.177 cm 2 /g.This represents a difference in attenuation of signal intensity of approximately 1% over the first 1 cm of tissue for PLA and 4% for paraffin wax compared to soft tissue.

Experimental minimum detectable limits
Effects of orientation on the standard sized mouse MDL figure 6 shows the MDL data for the PLA, paraffin-filled PLA, and real mouse for three different mouse orientations with respect to the detector for the three different measurement times.The rostral position was found to have the best, i.e. lowest, MDL for both phantoms and the real mouse, followed by the dorsal and ventral positions.The MDLs for the three measurement times were found to scale as expected.For both the PLA and paraffin wax mouse, the MDL was statistically significantly different (p < 0.05) between rostral-dorsal or rostral-ventral orientations.In addition, the dorsal orientation was significantly better (p < 0.05) than the ventral orientation.However, the differences in MDL between different orientations in the real mouse were not statistically significant.
While the rostral position was better for both types of phantom in that it provided the best detection limit, it was found to be the hardest position to orient properly.It was also noted that the teeth would contribute significantly to the measurement in this orientation.We concluded that the measurement of mice in the dorsal position may therefore be the best measurement option in a live mouse.The detection limits for the shortest and probably most realistic mouse measurement time of 20 minutes for the dorsal measurement for the PLA mouse and the PLA with paraffin infill mouse were 32.5 ± 0.9 and 47.0 ± 4.7 μg Pb per g of plaster respectively.Converting these detection limits to units of bone using the previously described CCF of 1.46, yields detection limits of 52.0 ± 1.3 and 68.6 ± 6.9 μg Pb per g of bone.
The detection limit for a 20 minute dorsal position measurement in the real mouse was found to be 46.1 ± 2.0 μg Pb per g of bone.The PLA mouse is the better phantom model for a real mouse, as predicted by the better match of the PLA mass attenuation coefficient to that of soft tissue.

MDLs for varying mouse sizes
As expected, the MDL for the dorsal measurement position was found to improve with increasing mouse size as seen in table 1.The MDL for the dorsal position in the largest mouse size (x 2 the original mouse) was found to be 22% better than the MDL of the original mouse, while the MDL of the smallest mouse (X 0.75 the original mouse) was found to worsen to 28 %.
The MDL in the dorsal position was found to vary from 29.6 μg Pb per g plaster in the 0.75 mouse to 18.0 μg Pb per g plaster in the 2x mouse for a 40 minute measurement.These correspond to expected MDLs of 41.7 μg Pb per g plaster in the 0.75 x mouse and 25.4 μg Pb per g plaster in the 2 x mouse for a (possibly more realistic) 20 minute measurement.
The MDLs of the ventral position were found not to change significantly with mouse size and this was attributed to geometry and attenuation effects.The MDLs in the rostral position were found to improve with increasing mouse size, but it was (again) noted that this PLA mouse model did not include teeth which could alter the measurement.

Variation of MDLs with position
MDL was found to worsen with increasing distance from the detector.The MDL of the original PLA mouse phantom measured in the dorsal orientation increased overall as it was moved from 0 to 5 cm, as seen in figure 7. The MDL at 5 cm distance was determined to be 25% larger than the MDL at 0 cm.The MDL varied from 23.1 μg Pb per g plaster to 28.9 μg Pb per g plaster for a 40 minute measurement in the dorsal position.This corresponds to an expected variation of MDL from 0 to 5 cm of 32.6 μg Pb per g plaster to 40.7 μg Pb per g plaster for a 20 minute measurement.

Experimental calibration lines
Calibration lines for the human tibia phantom were determined for each of the four detectors.The slope, intercept, and R 2 values for the four calibration lines can be seen in figure 8.All intercepts are zero to within uncertainties, while all slopes are within the uncertainty of each other, with an average value of 0.002 74 ± 0.00003.These values for slope and intercept are in line with results determined by previous investigators using clover-leaf bone lead systems in our laboratory [37] and were thus confirmation of the system reliability.For all four detectors, the R 2 value of the human tibia phantom calibration line exceeds 0.99.Calibration lines were also determined for the mouse phantom.As expected, because of the small phantom size and low plaster of Paris mass, there was considerably greater variance associated with the mouse phantom measurements.However, the intercept in the mouse phantoms was found to be significantly above 1 μg Pb per gram of plaster.After investigation, it was found that a small but measurable lead fluorescence signal from the room behind the phantoms was observed when these small phantoms were used.The signal was a constant offset: the variance of the average K α-x-ray to coherent ratio for each phantom concentration was similar, with no significant outliers across all five measurements.This lead x-ray signal resulted in an intercept offset of 30.8 ± 5.2 μg Pb per g plaster and a small increase in the measured MDL.In absence of a fluorescence signal in the room, this constant offset on all measurements would not be observed, and the intercepts of calibration lines would be expected to be near zero.
As shown in figure 9, the mouse phantom calibration slopes for the four detectors were found to be within uncertainty of each other.The value for the inverse variance weighted mean (IVWM) mouse lead K α x-ray to coherent calibration line slope was 0.002 30 ± 0.0004 with an R 2 value of 0.93.The data were combined using inverse variance weighting because some detectors have better resolution, and hence better measurement uncertainties, than others.The IVWM slope from the mouse phantoms is a factor of 0.8 ± 0.1 smaller than the human tibia slope, although the difference is not statistically significant.The intercept on the calibration lines reflects the room background signal.In the absence of this signal, calibration line intercepts are expected to be near zero.

MCNP calibration lines
Both the human tibia and mouse phantom calibration lines had been simulated in MCNP.All calibration lines could be fitted using a linear regression model and had R 2 values of 1.A lower Pb Kα x-ray to coherent calibration line slope was found for mouse phantoms compared to human tibia phantoms in MCNP simulations as can be seen in table 2. The ratio of the mouse/human tibia slope determined by MCNP was 0.79 ± 0.02, comparable to the 0.8 ± 0.1 determined experimentally.Both experiment and simulation suggest that the Kα to coherent ratio is approximately 20% smaller in the mouse phantoms than in the human tibia phantoms.

Contributions to the coherent scatter peak
The calibration lines from both experiments and the MCNP model suggested that the Kα to coherent ratio is smaller in the mouse phantom because coherent scattering in soft tissue contributes significantly to the coherent peak signal compared to human tibia phantoms.MCNP simulations were therefore used to obtain the K α x-ray to coherent ratio for both phantom types for concentrations of 1000 μg Pb per g plaster, plus the x-ray to coherent peak ratios for phantoms with no bone.The results were normalized to the K α x-ray peak area to permit easier comparison between mouse and human tibia.Coherent peak signals were then compared.
As seen in figure 10, there is a significant contribution to the coherent signal from the 'soft tissue' in the mouse phantom but not in the human tibia phantom.This increases the coherent signal in the mouse phantom spectra and reduces the x-ray to coherent ratio, lowering the slope of the calibration line.The normalization method used in 109 Cd K XRF bone lead measurements for a robust measurement in humans is incorrect when human tibia calibration standards are used to determine lead concentrations in a mouse.

Discussion
When developing suitable phantoms for XRF studies, accuracy must be balanced with simplicity.In this work, smaller bones in the mouse, such as the rib cage and distal extremities, could not feasibly be printed and filled with plaster.Furthermore, teeth were not considered in this model.That said, the MDL values for a 3D-printed PLA mouse were an extremely good match to the MDLs obtained for a real mouse, and thus the precision of the PLA mouse phantom matches real mice well.This study only investigated precision, and the accuracy of the system will still need to be confirmed in a validation study.
Our study found that 3D-printing soft tissue phantoms for XRF calibration studies of mice is feasible.PLA plastic is an excellent surrogate for soft tissue.However, while PLA is an easily accessible print material, it is higher cost, and printing 3D PLA phantoms with 100% infill takes considerable time.We found that PLA shell phantoms filled with paraffin wax are a more affordable and faster alternative to PLA phantoms, although they are a poorer match for soft tissue than PLA, with detection limits that are 50% larger than those obtained using PLA alone.
These MDLs are being compared against a motionless frozen mouse specimen.While the PLA MDL was an extremely good match in this instance, it was found that there were challenges in aligning the real mouse.These MDLs are most likely an underestimate of the MDL in a breathing anesthetized  mouse as slight motion will increase the MDL.In addition, the MDL was found to depend strongly on the orientation of the phantoms.While the rostral position had the lowest MDL, alignment in this position was the most difficult and the teeth, which would be within the measurement volume, would alter the measurement.Furthermore, while measurements on the real mouse showed the same trends, all positions were within the measurement uncertainties of each other.This is likely due to challenges in properly aligning the real mouse to the detector due to the curvature of the spine and the position of the legs and tail.These may also have increased the bone signal in the ventral measurement.In comparison, the dorsal measurement was more simple to position and would likely be more consistent between mice.Hence, the dorsal position was determined to be more practical, while maintaining an acceptable MDL.
Increasing the mouse size reduced MDL for both the rostral and dorsal measurements, likely due to increased bone signal.The MDL was not affected by mouse size in the ventral position.Bone mass increased with mouse scaling, increasing the bone signal.However, a larger mass of soft tissue separates the spine from the detector in the ventral position, increasing the target-to-detector distance, reducing the signal that reaches the detector an approximate 1/r 2 fashion, and increasing the Compton scatter signal from soft tissue.These factors appear to cancel out and the MDL is not different to within uncertainties.The smaller MDL with increased size in the dorsal position suggests that studies of lead exposure in rodent models will yield better results using larger mouse species or larger rodents, such as rats.Small rats would likely have a 20% advantage in MDL compared to mice, as indicated by the 2× phantom.
The MDL was expected to increase with the distance of the mouse from the detector.There are several factors at play.At close distances, the source collimation means that the whole mouse is not irradiated.Conversely, at large distances, only a portion of the beam irradiates the mouse.The angle subtended by the mouse on the detectors varies, but the detectors are off-axis from the mouse, so 1/r 2 increases in MDL with distance are likely an approximation.Finally, the source holder sits in front of the detectors and at close distances possibly acts as a shield between the mouse and parts of the detector system.The uncertainties on this data mean that a clear function of MDL with distance cannot be discerned, however, the MDL clearly increases with distance.The mouse should, therefore, be placed close to the detectors for measurements.
The MDL of the dead mouse depended strongly on measurement time.It varied as expected, from 37±3 μg Pb per g bone mineral for 20 minutes to 27±2 μg Pb per g bone mineral for 40 minutes to 4.64±1 μg Pb per g bone mineral for 720 minutes.A longer measurement would clearly be better for the estimation of lead, but it is not feasible to measure mice for long periods.The ultimate MDL will depend on several factors including how long animal research ethics boards feel comfortable with investigators anesthetizing mice: we estimate the lowest possible detection limit will be in the 10-20 μg Pb per g bone mineral range for our standard-sized mouse assuming a maximum measurement time of between 2 and 3 hours.However, this length of time may be too long from a logistics point of view in the management of an animal study.Our studies on the effect of mouse size do show that detection limits 20% lower could be obtained by using larger breeds of mice.
Studies of lead levels in mice will require mouse calibration phantoms that accurately represent the real mice being studied.Human tibia phantoms cannot be used without some correction being applied to the measurement.Both experiment and simulation indicate that the different bone-to-soft tissue ratios in mice as compared to humans mean that the contribution to the coherent signal from soft tissue in mice is significantly greater than in the human tibia.The mouse calibration line slope appears to be a factor of 0.8 lower than the tibia calibration line slope, a large enough difference that bone lead estimates in mice will be inaccurate if non-mouse phantoms are used.This finding of a breakdown in the normalization may have implications for wider bone lead studies, including those in humans where there are significant amounts of tissue overlay.There were indications of a breakdown in the normalization in human data sets twenty years ago.For example, one study from 1999 [38] found that bone lead measurements were possibly incorrect in participants with extremely high BMI and recommended that morbidly obese individuals should not be measured.Recent work revisited the data from that study and showed that the reductions in measured lead levels in high BMI individuals were most likely due to increased contributions to the coherent scatter peak from overlying tissue [39].It is an issue that should be studied further.
The altered calibration lines also lead to increased detection limits.Bone lead measurements are reported as the normalized units μ g Pb g −1 bone mineral (or phantom).We measure the ratio of Kα x-ray signal to the coherent signal ratio (Ak/Ac) to create a calibration line with a slope of the Ak/Ac ratio per unit concentration.As previously discussed, and shown in equation (1), the uncertainty of the ratio (σ i ) depends on the uncertainty in the α x-ray signal (σ Ak ) and the coherent signal (σ Ac ) and as shown in equation (2), we define the MDL as 2 × σ i of the zero-concentration phantom.We divide by the A k /Ac ratio per unit concentration to obtain the MDL in units of concentration.
The signal strength of both the Kα x-ray and coherent scatter are reduced in mice.Poisson statistics means that the relative uncertainties, σ Ak /A k and σ Ac /A c , both increase, although not necessarily identically, as the spectral shape in human phantoms differs from mice phantoms.The relative uncertainty of the Ak/Ac ratio thus increases as ( 2 .There are thus two factors that lead to larger MDLs in mice compared to humans.First, uncertainty in the zeroconcentration phantom is increased.Secondly, as the calibration slope is reduced compared to human phantoms when minimum detectable limits are converted to units of μ g Pb g −1 the MDL is further increased.
For bone lead XRF measurements in mice to be viable for animal studies, we assume that they must offer the precision that is able to distinguish between the bone Pb levels in a mouse with sufficient lead exposure to cause observable physiological effects such as demyelination, and a mouse with no exposure.The lead exposure levels which cause behavioural changes in mice may be significantly lower than this [16], but the assumption here is that initial drug development studies would focus on defined physiological changes such as demyelination.However, expected bone lead levels in mice with observable demyelination are not available in the literature and levels must be estimated from other data.One study detected demyelination in rats after 55 days of lead exposure, where the daily dose of lead to the rat was 50mg/g [40].This rat study did not measure bone lead content.However, a study on mice found that administration of 30 mg/dL of lead in the drinking water for 60 days, resulted in an average bone lead content of 43.3 ppm [41].On average, mice that weigh 25 g ingest between 5 and 50 ml of water per day [42].The approximate upper bound of lead ingestion per body mass in this study was 0.6 mg/g.If we assume that lead metabolism in mice is similar to that of rats, the bone lead concentrations of mice exhibiting demyelination could be expected to be well above 100 μg Pb per g bone mineral.This could be measurable even in a 20 minute dorsal XRF measurement of an individual mouse.
However, as with humans, studies are more likely to perform serial measurements of a population of mice, rather than a single specimen.In this case, it is the ability of the system to measure population differences that will matter.The uncertainties of the population estimate of lead level should vary as MDL/ n 1 , where n is the number of mice in the population.Even with small populations of approximately ten mice, differences of 10-15 μg Pb per g could be distinguishable.In our estimation, in vivo bone lead measurements in mice being studied for demyelination due to lead exposure could be feasible and this should be explored further.
While this work suggests that cross-sectional in vivo bone lead studies in mice are feasible, the measurement accuracy will have to be verified in a validation study where XRF mouse bone measurements are compared to a 'gold standard' measure of lead in bone such as inductively coupled mass spectrometry (ICP-MS) of the ashed bone.A direct comparison will require use of ashed bone as the XRF measurements are normalized to the bone mineral signal.The validation studies will also have to be conducted in a manner that ensures that the XRF and the ICP-MS measurements are conducted on the same pieces of bone as in the intact mouse.Bones with different metabolic rates will likely have different turnover and hence different lead levels, so the measured samples must match.This may require Monte Carlo modelling to be able to accurately identify the specific bones interrogated by the XRF system in an intact mouse of a particular mouse strain.
Following verification of measurement accuracy, a longitudinal cohort study, where groups of mice are doped over time with different levels of lead, must be performed.The mice will be measured with XRF at specific time points over the study.This will determine whether the XRF system is capable of distinguishing between: different groups of mice; changes in group bone lead level over time; or, further, bone lead level changes in a single mouse.The outcome of this study will enable power calculations to predict the numbers of mice required in drug testing studies.This will be the final determination of whether this XRF method is feasible.

Conclusion
The present work presents a method that uses 3Dprinted zoomorphic calibration phantoms for the non-invasive in vivo measurement of whole body lead in mice by 109 Cd K XRF.The 3-D printed phantoms were designed using an anatomical mouse atlas and printed using 100% infill PLA plastic as the soft-tissue equivalent material.PLA was found to be an excellent soft tissue phantom material in the 65-80 keV x-ray range.However, if time and cost are factors, 3-D printed PLA shells filled with paraffin wax can be acceptable substitutes.
The study found that measurements of mice require mouse-specific calibration phantoms.Limitations were found in the applicability of the coherent normalization used in 109 Cd K XRF.In human tibia measurements, the soft tissue contribution to the coherent peak has been deemed negligible, but this was found not to be true for measurements of small animals.This information suggests further study of the effect of soft tissue on human in vivo bone lead XRF measurements is required.
Using this PLA phantom method, 109 Cd K XRF measurements of whole body lead in bone in mice are likely feasible and the further work required to move to in vivo measurements can be undertaken.A study to validate the accuracy of the system should be undertaken, prior to tests of the system performance in a small group of animals.

Figure 1 .
Figure 1.A schematic of the (a) 109 Cd XRF system's detector showing the orientations of the four HpGe crystals inside the detector, (b) the 109 Cd source and its collimator, and (c) the backscatter geometry of a phantom measurement.The mean scattering angle is approximately 165 degrees.

Figure 2 .
Figure 2. (a) Development of the zoomorphic mouse phantom, from the Segars et al.mouse atlas [32] to the 3D printed model with plaster of Paris-filled bone channels (sagital cross sections).(b) Transverse cross sections of the Autodesk Inventor model.Important bone-mass contributions are indicated in blue.

Figure 3 .
Figure 3. Position of the phantom and real mouse relative to the detector.

Figure 4 .
Figure 4. Example XRF spectrum of a 100 ppm human tibia bone phantom.The spectrum from 60 to 95 keV, illustrates the dominance of the Compton scatter distribution (a), and the expanded spectrum from 70 to 90 keV (b), highlighting the Pb characteristic x-rays and the coherent scatter peak.Due to the greater tissue masses in a human, tibia phantom spectra have a higher count rate compared to mouse phantom spectra, and thus better relative uncertainties in the data.The tibia phantom spectrum is shown for illustration as it is easier to distinguish major features.

Figure 5 .
Figure 5.The experimental attenuation curves for PLA plastic and paraffin wax, and the theoretical attenuation curve of soft tissue for a 88 keV x-ray source.

Figure 7 .
Figure 7. Relative MDLs for PLA mouse phantom in dorsal position at distances from 0 to 5 cm from the detector for 40 minute measurements.MDLs are normalized to the 0 cm position to show relative change.Each measurement was taken five times.

Figure 8 .
Figure 8. Individual calibration lines for each of the four detectors for the standard tibia phantom.The four detector signals were combined by inverse variance weighting to obtain the mean calibration line which is also shown.Error bars indicate the standard error of the mean value.

Figure 9 .
Figure 9. Individual calibration lines for each of the four detectors for the mouse phantom in dorsal orientation.The four detector signals were combined by inverse variance weighting to obtain the mean calibration line which is also shown.Error bars indicate the standard error of the mean value.

Figure 10 .
Figure 10.Contributions of soft tissue and bone to the coherent peak amplitude in the PLA mouse phantom in dorsal position and the human tibia phantom.Error bars represent the standard deviation between detectors.

Table 1 .
Relative MDLs for PLA mouse phantoms of different sizes for 40 min measurements.MDLs are normalized to the standard mouse MDL to show relative change.Each measurement was taken five times.

Table 2 .
Average slopes, intercepts, and R 2 values of MCNP simulation average calibration lines for PLA mouse and human tibia phantoms.