Long-term stability of hydroxyapatite bone phantoms for the calibration of in vivo x-ray fluorescence spectrometry-based systems of bone lead and strontium quantification

Hydroxyapatite (HAp) phantoms have been proposed as an alternative to plaster of Paris (poP) phantoms for the calibration of x-ray fluorescence-based systems for the in vivo quantification of bone lead and strontium which employ a coherent normalization procedure. The chemical composition of the material becomes critical in the calculation, or omission, of the coherent correction factor (CCF) required in this normalization procedure. This study evaluated the long-term chemical stability of HAp phantoms. Phantoms were prepared and allowed to age for a two week period and over a seven year period in ambient conditions. The chemical composition of the phantoms was then assessed by powder x-ray diffraction. Two week old phantoms were found to be composed of HAp with only a small amount of contamination from CaHPO4·2H2O. Seven year old phantoms were found to have converted nearly completely to a carbonate-bearing apatite in the form of Ca10(PO4)6(CO3)0.75(OH)0.5 indicating that the HAp phantom material likely reacts with carbon dioxide in air over time forming a carbonate-bearing apatite. The influence of this chemical conversion was assessed at the level of relevant cross-sections. Calibration under the assumption that the material is HAp when in fact it is a carbonate-bearing apatite would result in not more than a 0.2%–2% bias in the total mass attenuation coefficient within the photon energy range of 0–100 keV. Differential scattering cross-section for coherent scattering was found to differ between HAp and carbonate-bearing apatite by 0.9%–2% for both a 35.5 keV and 88.0 keV γ-ray. This variation in the differential scattering cross-section for coherent scattering may introduce a ca. 2% bias in the CCF used within the coherent normalization-based calibration procedure. Using HAp phantoms as calibrators thus requires acknowledgement of this conversion in chemical form and possible introduction of uncertainty into the calibration procedure.

The first application of IVXRF can be attributed to the quantification of bone lead using the lead K-series [1,2].The method required the use of a 57 Co source for the excitation of lead in bone and calibration required the use of orthoplanar x-rays [1,2].From the measured spectrum, estimations could be made of the bone mineral concentration of the individual being measured and from all of this information combined calibrators were prepared from wax and bone ash on a subject-by-subject basis [1,2].
The principles associated with the use of a coherent normalization procedure were first assessed in the context of bone lead measurements using the K-series but with the application of a 109 Cd excitation source [8,17].This normalization procedure is based on the normalization of the measured analyte's characteristic x-ray signal to the coherently scattered source γ-ray signal which was found to be able to correct for such factors such as variations in the activity of the excitation source, the attenuation of analytical signal from overlaying soft tissue thickness, variations in bone geometry, variations in the subject's bone mineral concentration as well as minor subject movement during the measurement itself [8,18,19].This method of calibration has since become the standard approach for the IVXRF of not only bone lead but also bone strontium [12-14, 20, 21].
The entire premise around calibration through the coherent normalization procedure is based on the finding that calcium is the major contributor to coherent scattering in bone tissue [8,17].For the purpose of calibration then, phantoms/calibrators need to be prepared with known concentrations of the analyte (i.e.lead, strontium, etc).Given its availability, solidstate phantoms have traditionally been prepared from plaster of Paris (poP; [8,[12][13][14][20][21][22].Using poP (a calcium sulphate) as a phantom material has however been shown to introduce some issues into the calibration procedure for IVXRF systems of bone metal quantification whereby these are large due to the dissimilarity between the bulk composition of the phantom material relative to bone mineral and due to the issues surrounding the purity of commercially available poP [12,19,21,[23][24][25][26].
To mitigate these issues with regards to the availability of a phantom material to be used in the context of the coherent normalization procedure in IVXRF, Da Silva et al [27][28][29] developed a phantom material which can be prepared free of the analyte and sets as hydroxyapatite [HAp; Ca 10 (PO 4 ) 6 (OH) 2 ] which mimics bone mineral more closely than poP.This phantom material was shown to potentially simplify the calibration procedure [29] as well as allow for the determination of suitable system figures of merit and has been applied to various IVXRF cases [30,31].
The HAp phantom material is prepared from a mixture of CaHPO 4 •2H 2 O and Ca(OH) 2 which is doped with the analyte and set using a high phosphate concentration setting solution [27].The resultant material has been shown to be Ca 10 (PO 4 ) 6 (OH) 2 .These phantoms are stored at ambient and being solid state calibrators may be used for quite extended periods of time.As the major impetus to develop such calibrators was to ensure that a material is available to mimic bone mineral closely to be used within the context of the coherent normalization procedure, the chemical stability of these phantoms with time becomes important.This study thus assessed the bulk chemical composition of HAp phantoms after they are freshly prepared and after an extended aging period to to assess their chemical stability.

Preparation of phantoms
Phantoms were prepared following the procedure outline in Da Silva et al [27].Each phantom was prepared independently by mixing CaHPO 4 •2H 2 O (98-102.5%,Sigma-Aldrich, St. Louis Maryland, USA) and Ca(OH) 2 (USP grade, Amresco, Solon, Ohio, USA) to achieve a Ca/P mole ratio of 1.67.To this mixture was added a 1M solution of NaHPO 4 (ACS reagent grade 99%, Sigma-Aldrich, St. Louis, Maryland, USA) in a 2:1 powder-to-liquid ratio.The NaHPO 4 solution was prepared using 18.2 MΩ•cm water drawn from a milliQ water system.The cement mixture was transferred to a 7 mm diameter and 10 cm long glass mould and allowed to set for one week before being removed from the mould.After removal, the phantoms were allowed to cure for two weeks (n = 5 phantoms) and seven years (n = 5 phantoms) prior to being subject to powder x-ray diffraction spectrometry for the determination of the materials' chemical structure.

Powder x-ray diffraction spectrometry
Powder x-ray diffraction spectrometry was performed by first milling the phantoms to a fine powder [27].The powdered phantoms were transferred to aluminum sample holders for measurement and were covered in Kapton film.Measurements were made on a Miniflex600 spectrometer (Rigaku, Tokyo, Japan) equipped with a copper target (λ = 1.5406Å).Measurements were made with the x-ray tube operating at 40 kV and 15 mA.All measurements were made with a scan speed of 5.000 • /min and a step size of 0.02 • .Compound identification was performed using the PDXL 2 Software (Version: 2.7.3.0, Rigaku, Tokyo, Japan) associated with the spectrometer and comparing collected spectra to the International Centre for Diffraction Data (ICDD) database.The quantification of compound mixtures was performed using the reference intensity ratio (RIR) method associated with the spectrometer's software also using the ICDD database.As a means of testing both the identification and quantification methodology, standards were assessed using the starting reagents described in section 2.1 and a hydroxyapatite standard (Alfa Aesar, Mississauga, Ontario, Canada).

Results and discussion
Da Silva et al [27,28].developed HAp phantom material to replace the commonly employed poP phantom material used for the calibration of IVXRF systems of bone lead and strontium quantification (with extension to other bone seeking metals).The impetus for that development was to make available a material that mimics bone mineral more closely in the context of the coherent normalization procedure currently being used by those systems of bone lead and strontium quantification [8,12,15,16,20,29].The material is prepared using a mixture of CaHPO 4 •2H 2 O and Ca(OH) 2 (and/or Sr(OH) 2 •8H 2 O) mixed with a setting solution containing a high phosphate concentration, as NaHPO 4 [27].The use of this HAp phantom material was found to potentially remove the need to apply a coherent conversion factor (CCF) within the context of the same coherent normalization-based calibration procedure for these methods [29].
For solid-state calibrators to be useful over time, one of the fundamental conditions is that they are stable with regards to their chemical composition and physical characteristics in the context of their specific use.In the context of IVXRF applications, one cannot necessarily rely on a calibrator that will change in its composition and physical characteristics such that changes in the attenuation coefficients of the material and scattering cross-sections are large.In the case of the coherent normalization procedure used by IVXRF systems the most critical cross-section being the differential cross-section for coherent scattering [8,29] although changes in the total mass attenuation coefficient can become important in cases where portable x-ray analyzers are employed for IVXRF measurements [31].
Hydroxyapatite phantoms were prepared and were assessed for their composition over time.Fresh phantoms (composition determined after two week of preparation and aging) were found to set as nearly pure hydroxyapatite as determined by powder x-ray diffraction (Figure 1).Phantoms what were left to age at ambient temperature, pressure and humidity for seven years showed the possibility for a complete chemical reactions over this time that resulted in a marked change in their chemical composition.Firstly, no apparent CaHPO 4 •2H 2 O was present as a contaminant indicating that the phantoms take more than two weeks to fully react.In all cases, the phantoms had converted to carbonate-bearing apatites (Figure 1).Of the five samples assessed, all presented a conversion from Ca 10 (PO 4 ) 6 (OH) 2 to Ca 10 (PO 4 ) 6 (CO 3 ) 0.75 (OH) 0.5 which indicates a partial conversion of the apatite to carbonated apatite.This finding is not particularly surprising given the nature of biological apatites.The mechanism for this chemical reaction over time likely depends on the reaction of the hydroxyl moieties within the apatite lattice with carbon dioxide in air forming a carbonate ion in place of the hydroxyl moieties and water as per the following reaction.
Ca 10 (PO 4 ) 6 (OH) 2 (s) + CO 2 (g)→Ca 10 (PO 4 ) 6 (CO 3 )(s) In any case, one thing is certain and that is that the phantoms do react over time with what seems to be carbon dioxide in air and likely change from Ca 10 (PO 4 ) 6 (OH) 2 to Ca 10 (PO 4 ) 6 (CO 3 ) or Ca 10 (PO 4 ) 6 (CO 3 )•H 2 O over long periods of time, this study likely catching the phantoms at a point of incomplete reaction.
The change in the chemical composition of the phantom material from hydroxyapatite to a carbonate-bearing apatite is however not of particular concern if one is aiming to mimic bone mineral closely as apatites found in bone and teeth are generally carbonate-bearing apatites [33].The concern is if calibration procedures depend on the assumption that one is measuring pure hydroxyapatite when in fact the material is either a pure carbonate-bearing apatite or a mixture thereof.
Although not used directly in the calibration protocols of IVXRF systems of bone metal quantification that depend on γ-ray sources [8, 12-14, 18-21], the total mass attenuation coefficient of the material may be of importance to the calibration of IVXRF systems that depend on portable x-ray analyzers [22,31].The total mass attenuation coefficients of Ca 10 (PO 4 ) 6 (OH) 2 and Ca 10 (PO 4 ) 6 (CO 3 ) were however found to not differ by more than 2% over the 0-100keV photon energy range of concern in IVXRF (Figure 2).This small difference in the total mass attenuation coefficients between both materials is attributed to two features: (1) the fact that the hydroxyl moieties only contribute to 3.4% of the mass of HAp while the carbonate moiety only contributes to 5.8% of the mass in carbonate-bearing apatite; and (2) that the majority of the contribution to the mass attenuation coefficient comes from calcium and phosphorous.
The coherent normalization procedure employed within the calibration protocols of most IVXRF systems of bone metal quantification requires knowledge of the scattering behavior of the phantom material relative to bone mineral.Of particular importance is the differential cross-section for coherent scattering which is given in equation (1) [23], where r e is the classical electron radius, θ the scattering angle, F is the relativistic atomic form factor and is the momentum transfer.F 2 (x) was computed for Ca 10 (PO 4 ) 6 (OH) 2 , Ca 10 (PO 4 ) 6 (CO 3 ) and CaSO 4 •2H 2 O as described by Johns and Wismayer [34] using an independent atomic model (IAM) (Figure 3), whereby is the form factor for atoms of the species i (taken from Hubbell and Øverbø [35]), n i is the number of atoms of species i (in stoichiometric units) and Z i is the atomic number of the species i.
The difference in scattering behavior between bone mineral and poP was again one of the main reasons for the development of the HAp phantom material [27].The use of poP as a phantom material requires the application of a coherent conversion factor (CCF) which converts the sensitivity obtained from using poP as a calibrator to the sensitivity one would expect of bone mineral (assumed to be HAp).The CCF is given by equation (3), Figure 2. Total mass attenuation coefficient data for poP, Ca 10 (PO 4 ) 6 (OH) 2 and Ca 10 (PO 4 ) 6 (CO 3 ) as calculated through the NIST XCOM database [32].Calculated mass attenuation coefficients varied between 0.2%-2% between Ca 10 (PO 4 ) 6 (OH) 2 and Ca 10 (PO 4 ) 6 (CO 3 ) which is considered to be marginal.
which is the ratio of the differential cross-section for coherent scattering (equation ( 1)) for both materials, which holds if the mean scattering angle is the same between the calibrators and the actual human measurement.The CCF will tend to 1 if HAp is used as the phantom material [29].If this assumption is then made by using HAp as a phantom material, the concern is that if the phantom material changes, the CCF will not be known.The differential cross-sections for coherent scattering were computed for HAp and carbonate-bearing apatite (Figure 3).These computations were made for a photon energy of 35.5 keV which corresponds to the 125 I γ-ray used for coherent normalization for bone strontium measurements [12-14, 20, 21], and for 88.0keV which corresponds to the 109 Cd γ-ray used for coherent normalization for bone lead measurements [8].The differential cross-sections for coherent scattering varied by 0.9 to 2% for both the 35.5 keV γ-ray and 88.0 keV γ-ray for the entire range of scattering angles.
The consequence of this change in the differential cross-sections for coherent scattering would be apparent in the CCF and would introduce an error at the point of bone metal quantification as the system's sensitivity would potentially not be adequately corrected to that of bone mineral.Figure 4 shows the CCF calculated for poP and carbonate-bearing apatite (CCF for HAp is 1).For both the IVXRF systems of bone lead and bone strontium measurement a 180°back-scatter geometry is used with a broad solid-angle [8,12,13,20,21].For the bone strontium IVXRF system, this results in a CCF that plateaus at approximately 1.02 for carbonatebearing apatite versus 1.30 for poP.For the bone lead IVXRF system, this results in a CCF that plateaus at approximately 1.02 for carbonate-bearing apatite versus 1.50 for poP.The CCF bias introduced from using a carbonate-bearing apatite phantom under the assumption that it is HAp is thus relatively small, but not absent, at approximately 2%.Given that biological apatites in bone and teeth are in fact a mixture of HAp and carbonate-bearing apatite [33] this degree of uncertainty introduced by the conversion of the phantom material from HAp to carbonate-bearing apatite is considered to be inconsequential to the calibration of IVXRF systems of bone metal quantification, but should be noted.
The calculation of the differential cross-sections for coherent scattering by the method employed in this work uses an IAM.This is an estimation especially at low momentum transfer values whereby the differential cross-sections for coherent scattering would be expected to deviate from those calculated using this model significantly [34].A thorough review of this matter is presented by Johns and Wismayer [34] for amorphous materials.In vivo x-ray fluorescence spectrometrybased systems of both bone lead and strontium quantification are designed such that measurements are made Figure 3. Differential coherent scattering cross sections calculated for a) a photon energy of 35.5 keV as would be used in the 125 I system of bone metal quantification [12-14, 20, 21]; and b) a photon energy of 88.0keV as would be used in the 109 Cd system of bone lead quantification [8].
in a 180°backscatter geometry.The coherent scattering of interest is thus measured at 180°with a small variation in angle about the 180° [8,12,13,20,21].As such, at these high momentum transfer values the deviation from our calculation using the IAM and what would be expected from measurement is expected to be minimized [34].It would still be desirable the determine these cross-sections and assess this deviation experimentally as future work.

Conclusions
Hydroxyapatite phantoms were prepared and were assessed for their composition after two weeks and seven years of aging at ambient.Fresh phantoms were found to be nearly pure HAp with only a small amount of contamination from one of the starting reagents.The phantoms that were left to age for seven years were found to have converted to Ca 10 (PO 4 ) 6 (CO 3 ) 0.75 (OH) 0.5 , a carbonate-bearing apatite.The consequence of this conversion from HAp to a carbonate-bearing apatite was assessed at the level of the total mass attenuation coefficient of the materials and the differential scattering cross-section for coherent scattering.It was found that using a phantom under the assumption that it is HAp when it has in fact converted to carbonate-bearing apatite would only introduce a 0.2%-2% bias in the total mass attenuation coefficient within the energy range of 0-100 keV.The differential scattering cross-section for coherent scattering was found to differ between HAp and carbonate-bearing apatite by 0.9%-2% for the 35.5 keV γ-ray used for the calibration of the IVXRF bone strontium system and similarly for the 88.0 keV γ-ray used for the calibration of the IVXRF bone lead system (0°-180°scattering angles).This difference presents a ca.2% bias in the CCF used within the coherent normalization-based calibration procedure when considering the total conversion carbonated-apatite.It is concluded that the use of HAp phantoms still presents an advantage over the use of poP and that the conversion of the phantom from HAp to carbonate-bearing apatite over time introduced marginal uncertainty into the calibration procedure.3)) for (a) a photon energy of 35.5 keV as would be used in the 125 I system of bone metal quantification [12-14, 20, 21]; and (b) a photon energy of 88.0keV as would be used in the 109 Cd system of bone lead quantification [8].
Graduate Studies (Toronto Metropolitan University) for financial support in the form of two Ryerson Graduate Scholarships.S. McFadden and W. Zhang (Department of Chemistry & Biology) are acknowledged for their technical support during the course of this study.

Figure 1 .
Figure 1.Power x-ray diffractograms for phantoms aged at ambient for 2 weeks and for 7 years as well as that for a pure HAp standard, CaHPO 4 •2H 2 O and Ca(OH) 2 used as reagents for phantom preparation.The two week old phantom was found to be composed of Ca 10 (PO 4 ) 6 (OH) 2 with some CaHPO 4 •2H 2 O contamination [27].Phantoms that were aged for seven years showed no signs of CaHPO 4 •2H 2 O contamination and a complete conversion to a carbonate-bearing apatite [Ca 10 (PO 4 ) 6 (CO 3 ) 0.75 (OH) 0.5 shown here].

The
Natural Science and Engineering Research Council of Canada (NSERC) is acknowledged for financial support through a Discovery Grant to EDS.The Faculty of Science at Toronto Metropolitan University (formerly, Ryerson University) is acknowledged for financial support through start-up funds to EDS.EDS further acknowledges The Faculty of Science at Toronto Metropolitan University for support through the Toronto Metropolitan University Faculty of Science Discovery Accelerator program and the Faculty of Science Dean's Discovery Bridging Supplement.MM acknowledges the Yeates School of

Figure 4 .
Figure 4. Coherent conversion factors (equation (3)) for (a) a photon energy of 35.5 keV as would be used in the125 I system of bone metal quantification[12-14, 20, 21]; and (b) a photon energy of 88.0keV as would be used in the109 Cd system of bone lead quantification[8].