A HYDROXYAPATITE PHANTOM MATERIAL FOR THE CALIBRATION OF IN VIVO X-RAY FLUORESCENCE SYSTEMS OF BONE STRONTIUM AND LEAD QUANTIFICATION by

A HYDROXYAPATITE PHANTOM MATERIAL FOR THE CALIBRATION OF IN VIVO X-RAY FLUORESCENCE SYSTEMS OF BONE STRONTIUM AND LEAD QUANTIFICATION Doctor of Philosophy 2017 Biomedical Physics Ryerson University Eric Da Silva A hydroxyaptite [HAp; Ca5(PO4)3OH] phantom material was developed with the goal of improving the calibration protocol of the 125I-induced in vivo X-ray fluorescence (IVXRF) system of bone strontium quantification with further application to other IVXRF bone metal quantification systems, particulary those associated with bone lead quantification. It was found that calcium can be prepared pure of inherent contamination from strontium (and other elements) through a hydroxide precipitation producing pure Ca(OH)2, thereby, allowing for the production of a blank phantom which has not been available previously. The pure Ca(OH)2 can then be used for the preparation of pure CaHPO4 ⋅ 2H2O. A solid state pure HAp phantom can then be prepared by reaction of Ca(OH)2 and CaHPO4 ⋅ 2H2O mixed as to produce a Ca/P mole ratio of 1.67, that in HAp and the mineral phase of bone, in the presence of a setting solution prepared as to raise the total phosphate concentration of the solution by increasing the solubility CaHPO4 ⋅ 2H2O and thereby precipitating HAp. The procedure can only be used to prepare phantoms in which doping with the analyte does not disturb the Ca/P ratio substantially. In cases in which phantoms are to be prepared with high concentrations of strontium, the cement mixture can be modified as to introduce strontium in the form of Sr(OH)2 ⋅ 8H2O as to maintain a (Ca + Sr)/P ratio of 1.67. It was found by both X-ray diffraction spectrometry and Raman spectroscopy studies that strontium substitutes for calcium as in bone when preparing phantoms by this route. The necessity for iii the blank bone phantoms was assessed through the first blank bone phantom measurement and Monte Carlo simulations. It was found that for the 125I-induced IVXRF system of bone strontium quantification, the source, 125I brachytherapy seeds may be contributing coherently and incoherently scattered zirconium X-rays to the measured spectra, thereby requiring the use of the blank bone phantom as a means of improving the overall quantification methodology. Monte Carlo simulations were employed to evaluate any improvement by the introduction of HAp phantoms into the coherent normalization-based calibration procedure. It was found that HAp phantoms remove the need for a coherent conversion factor (CCF) thereby potentially increasing accuracy of the quantification. Further, it was found that in order for soft tissue attenuation corrections to be possible using spectroscopic information alone, HAp along with a suitable soft tissue surrogate material need to be employed. The HAp phantom material was used for the evaluations of portable X-ray analyzer systems for their potential for IVXRF quantification of lead and strontium with a focus on a comparison between tungsten, silver and rhodium target systems. Silver and rhodium target X-ray tube systems were found to be comparable for this quantification.


LIST OF TABLES
keV. The direct measurement collected over a 12 hour live time period shows the presence of rubidium, strontium and zirconium characteristic X-rays presumed to be emitted from the brachytherapy seeds themselves. . . 91 4.3 Qualitative X-ray fluorescence spectrometry measurement of the three 125 I brachytherapy seeds used as a source for in vivo XRF bone strontium measurements (12.6 µCi total activity at the time of measurement) made on a portable X-ray analyzer known to be void of zirconium. Measurement made of the seeds after they were allowed to sufficiently decay using a portable X-ray analyzer (see Section 4.3. 3) The spectrum shows the presence of the zirconium as well as several other light elements (not of interest to this work). The higher energy lines are those of the the Rh K-series as well as the 125 I γ-ray, Te, Ag characteristic X-rays and associated Compton peaks. The inlay shows the zirconium K-series (see Table 4 The simulation is of a finger phantom that does not contain any strontium. . 95 4.5 Intensities of zirconium contributions for various fractional proportions of the zirconium K-series to the total source fluence. Once below a 1 % contribution, the simulations indicate that the zirconium contributions become negligible. . 95 4.6 A preliminary measurement of a blank hydroxyapatite phantom made for a 20 minute live time using an SDD detection system and an off-centre source backscatter geometry. The spectrum is poor statistically due to the use of cold seeds but may indicate the presence of the dominant zirconium Compton scattered X-ray (*), although this peak may be due to strontium contamination that is system dependent as seen from the direct measurement of this system (Figure 4.2). Rubidium is also shown as a contaminant of the system. 97 4.7 Total reflection X-ray fluorescence spectrum of the clean phantom material.
There is no indication of strontium in the material at levels of less than 0.7 µg/g Ca. . There is only a slight decrease in intensity as a function of ρ b for the Kα 1 and thus the Kα 1,2 line (see Table 6.2). . . . . . . . . . . . . . . . . . . . . . . . . 133 6.2 Effect of ρ b on the observed coherent peak intensity from the 35.5 keV 125 I source γ-ray, for a cortical bone phantom containing 400 µg/g strontium. The "physiological range" is between 1.5 and 2.2 g/cm 3 26 resulting in a 14% increase in intensity. The range of densities evaluated in this figure extends further from the physiological range to include the density of pure HAp. . . . 135 6.3 Quantification of strontium for a 400 µg/g cortical bone sample, using either the Kα 1,2 line alone or the Kα 1,2 /coh ratio against a cortical bone-based calibration curve. A larger bias is observed in the case of using the Kα 1,2 /coh ratio as the analytical measure due to introduction of the density dependence of the coherent scattered photon. The close match in results when using the Kα 1,2 alone is due to the match in geometry between sample and phantoms and a match in the total mass attenuation coefficients of the sample and phantoms/calibrators. . 8.1 X-ray fluorescence spectra of a strontium (60 µg/g Ca)-and lead (100 µg/g Ca) containing HAp bone phantom measured using the tungsten target pXA system. Spectrum acquired for a real time of 180 s. The spectrum is void of any characteristic lines from tungsten with the background being composed of largely scattered bremsstrahlung source photons. . . . . . . . . . . . . . . . 184 8.2 Spectra of a strontium (60 µg/g Ca)-and lead (100 µg/g Ca)-containing HAp phantom collected with A) the silver target pXA system; and B) the rhodium target pXA system over a 30 s real time measurement. Spectra C) and D) are the same spectra corresponding to A) and B), respectively, zoomed into the region of interest containing the lead L-series and the strontium K-series. For B) and D) the various spectra correspond to those collected with different primary filtration arrangements order according to

Strontium and bone
Strontium is a group II alkaline Earth metal (Z = 38) and thus shares similar chemistry, and by extension biochemistry, to the most abundant of the alkaline Earth metals in the human body, calcium (Z = 20). Strontium can substitute for calcium in most of calcium's biological roles (including similar uptake and excretion rates and routes), with some minor favour towards calcium which is generally attributed to strontium's size relative to calcium's. 1 Although excellent reviews on the biological role of strontium in a general sense are provided elsewhere, 1,2 in general, the main interest in strontium, and its study in biological systems, is its effect on bone health. [1][2][3][4] Strontium has been shown to be both detrimental to bone health as well as beneficial to overall bone health. For this latter reason, there has been a significant renewed interest in strontium and investigation into the element's possible essentiality to humans in the context of overall bone health.
Strontium is a bone seeking element, like calcium, with the majority of accumulated strontium being found in bone tissue. 1,2 Strontium is an ubiquitous element to calcium and is acquired through the diet of all humans, thus every person will present some strontium in 1 their calcified tissue in the microgram-per-gram range-nominal values in the average human being on the order of approximately 350 ppm, with this value being highly dependent on diet (with grains and seafood presenting some of the highest concentrations of strontium). 1,2 Large excess bone strontium concentrations have been shown to cause bone disorders in both children and adults including rickets and osteomalacia, respectively. [5][6][7][8] Strontium at low levels has however been shown to be beneficial to bone health. 3,4 Although the true biochemical/molecular mechanism of strontium's action on osteocytes is still not fully understood: strontium has been shown to increase the rate of bone formation while suppressing bone resorption, thus having a direct action on the osteocytes in bone. [1][2][3] Given this finding, and the fact that strontium seems to have an anti-osteoporotic effect, strontium has been proposed as a possible therapeutic agent in the treatment of osteoporosis, and the drug, strontium ranelate, has been developed and applied to the treatment of osteoporosis for this purpose. 3,4 Similarly, individuals have also begun self-supplementing with various strontium salts for the purpose of either osteoporosis treatment or prevention. 9,10 Regardless of the strontium salt used for the purpose of osteoporosis treatment and/or prevention (i.e. ranelate versus citrate), strontium has been shown to accumulate in bone with similar kinetic behaviour. 9,10 Osteoporosis is a bone disorder which is characterized by a decrease in bone mineral density (BMD) and an increased risk of various fractures. 11 The use of strontium ranelate as an anti-osteoporotic drug presents some significant challenges in terms of the evaluation of its effectiveness against osteoporosis which is quantified against changes in BMD over time. Although several other biochemical markers can be used to monitor the effectiveness of anti-osteoporotic drugs, an individual's BMD remains the standard marker of the effectiveness of a given osteoporosis therapy as it relates directly to fracture risk. 4,11,12 A major concern with the use of BMD as a marker of drug effectiveness, in the context of evaluating strontium ranelate therapy (as well as the effectiveness of any other strontium salt used for the same purpose), is that strontium itself, which integrates into bone tissue, will positively bias the determined BMD, determined by the gold standard technique, dual energy X-ray absorptiometry (DXA), presenting higher BMD readings in comparison to true BMDs (see section 1.2). This strontium-induced bias has been well established and it is well known that changes in the Sr/Ca mole ratio in bone results in linear changes in observed/apparent BMDs. 13 As such, it is hard to judge the current work on strontium's effect on BMD as most, if not all, studies report uncorrected DXA-determined BMDs. Given that such a correction for bone strontium content would in theory require that a piece of bone be excised to make such corrections based on a quantitative assessment of the excised bone tissue, it is thus desirable to have a method which can determine bone strontium concentrations in vivo rapidly and accurately for the purpose of making such corrections, monitoring strontium uptake in bone over time, as well as to have available as a general method of determining the concentration of strontium in bone for general epidemiological and population studies.
The latter application may be of significant interest as the effect strontium displays on bone health when present at low levels may indicate a possible essential role for strontium in human bone health-a matter to be further studied and defined but requiring large populations studies on bone strontium content.

The influence of bone strontium concentration on BMD determinations
DXA can be well considered the gold standard method for bone mineral density determinations and is often employed to assess BMDs clinically as well as in academic studies assessing anti-osteoporotic therapies. 14 In the case of strontium-based osteoporosis therapies, bone strontium concentrations have been clearly shown to bias DXA-determined BMD. 13 This section briefly discusses the reasoning behind this trend.
The physical basis of DXA, and the standard method of determining BMD is provided by the International Commission on Radiation Units & Measurements (ICRU). 14 A DXA measurement is based on the simple exponential law of photon attenuation. A DXA scan consists of acquiring attenuation measurements at two photon (X-ray) energies, and, in this way, the effect of soft tissue attenuation is accounted for and BMDs can be determined unhindered. If we consider a DXA measurement of some arbitrary sample composed of soft tissue (s) and bone (b), then, if the photons of each energy have an initial intensity I 0 , the intensity of the photons of each energy after passing through the sample [I(t)] is given by where (µ ρ) is the total mass attenuation coefficient of the material, t the thickness (mass thickness, g/cm 2 ) and H and L denote high and low energy photons as per the ICRU 14 convention.
The BMD determination is in fact an areal BMD (BMD a ) which is quoted in units of g/cm 2 versus the true BMD (per unit of volume) which can be determined by other methods such as quantitative X-ray computed tomography. 14 The DXA determined BMD is also an average BMD along the path of the X-rays. The BMD a is thus the total thickness of the sample (t tot = t s + t b ) multiplied by the weight fraction of bone within the sample, which cannot be easily determined directly from a DXA scan, A DXA determined BMD a reading is thus determined by a re-arrangement of the system of equations shown in Eqns. 1.1 and 1.2 with knowledge of Eqn. 1.3 resulting in an expression for the BMD a which allows for its determination directly from attenuation measurements, where in this case (µ ρ) b is the total mass attenuation coefficient of bone.
Assigning a soft tissue correction term R which can be made at an area in which no bone which allows for an experimentally determined BMD a .
The influence that strontium substitution for calcium has on the BMD a determination 5 can be seen by considering that a BMD a determination must assume that (µ ρ) b is a constant term, spatially and temporally, as it is impossible to know the true bone composition of each individual site of measurement. Although this in itself may very well be a source of error in the BMD a determinations, the issue with strontium incorporation can be more easily observed by expanding (µ ρ) b through the additivity law of mass attenuation coefficients for a specimen containing N elements where (µ ρ) i is the mass attenuation coefficient of element i and w i its weight fraction.
In the case that strontium substitutes for calcium, the attenuation of that particular bone specimen begins to increase, as, strontium is a higher Z element than calcium and has a larger mass attenuation coefficient at all energies relevant to DXA scans. As such for a given degree of attenuation of the primary photons, if the mass attenuation of bone is not considered with the inclusion of strontium it will seem as if the bone attenuated more of the photons and thus has a higher BMD than is truly present.
Nielsen et al. 13 have found that the percentage variation in BMD (a) as a function of the mole fraction of strontium in bone relative to the mole fraction of calcium follows a positive linear function. As such, the correction model has been proposed where BMD(adj) is the adjusted, or true, BMD of the bone, BMD(n) is the true DXAdetermined BMD of the bone, C Sr is the concentration of strontium in the bone and m is the calibration factor determined on the DXA instrument relating the variation in BMD to strontium concentration.
The limiting factor here is the determination of C Sr of which, to be done effectively clinically, should be estimated as non-invasively as possible. Although the problem of DXA correction is outlined here, bone strontium determinations are not limited to this problem alone. From a clinical viewpoint, uptake of the element in bone and modelling kinetics 9,10 is also of importance in which reliable concentration estimations are necessary, further necessitating in vivo methods of bone strontium assessment.

X-ray fluorescence spectrometry
A full description of the fundamentals of XRF calibration can be found elsewhere which is generally described in the context of flat infinitely thick samples. [15][16][17][18] XRF, in a more general sense, is an analytical methodology which is based fundamentally on the measurement of characteristic X-rays emitted from an excited sample. XRF systems consist of a source which impinges on a sample. The source needs to emit radiation with sufficient energy as to cause photoelectric excitation of the elements in the specimen. When photoelectric excitation has occurred, the atoms relax and emit characteristic X-rays which can be detected using a photon detector. The intensity of these X-rays relate to the concentration of the element in the sample. The relationship between X-ray intensity and concentration is however not a simple relationship. The intensity becomes a complex function of the total sample matrix composition and as a result it is often necessary to be able to quantify the total composition of the sample. An exception to this general rule is one in which the sample composition is relatively constant and one wants to quantify a trace element. In this case, if the analyte composition does not change the mass attenuation coefficient of the sample significantly then the relationship with respect to composition is linear. This is a fundamental assumption in in vivo applications of XRF.
X-ray fluorescence spectrometry (XRF) has been successfully applied to the measurement of various trace and minor elements of toxicological and epidemiological interest, namely lead, uranium and strontium, in the bone tissue of human subjects in vivo. [19][20][21][22][23] Such measurements can be divided into two categories defined by the energy of the characteristic X-ray series measured; namely, those based on the detection of hard characteristic X-ray series, as is the case of the K-XRF measurement of bone lead and uranium, 19,[21][22][23] and those based on the use of soft characteristic X-rays series, as is the case of the L-XRF measurement of lead 24,25 and the K-XRF measurement of strontium. 26 The calibration of in vivo XRF systems of bone metal quantification has traditionally been, and remains, a challenge, largely due to the need for calibrators (phantoms) which are matched to the sample in regards to both composition and geometry.
It is well established-particularly in the context of soft X-ray-based XRF analysis common to conventional XRF spectrometry-that calibration should be performed against calibrators which match the overall composition of the sample matrix as closely as possible. [15][16][17][18] Matrix matching of the calibrators being critical in order to account for the so-called "matrix effects" (absorption/attenuation and in some cases enhancement) which ultimately influence the observed characteristic X-ray intensities, and which form the basis of the Sherman equations and most calibration and quantification algorithms/protocols; [15][16][17][18] if the aim is to estimate concentration values in relation to the mass of the matrix as a whole. The quantitative analysis of bone tissue for trace and minor elements by XRF is however complicated by the fact that the sample, bone, is variable 27 in its composition and that the majority of the matrix is not measurable by XRF (a "dark matrix") and thus there is no way of knowing the total composition of the specimen as measured through XRF. This was a hindering fact 8 at the early onset of in vivo XRF system development for bone lead determinations which required complicated calibration procedures. 28,29 1.4 Applications of XRF to the in vivo quantification of lead and strontium in bone From a historical standpoint, it can be argued that the earliest in vivo X-ray fluorescence spectrometry (IVXRF)-based system of bone metal quantification was developed for the quantification of bone lead in response to concerns of occupational exposure to the element.
The system consisted of a 57 Co induced K-IVXRF system which is fully described by Ahlgren et al. 28 and Ahlgren and Mattsson 29 . The system was originally designed alongside a calibration protocol which was intended to provide concentrations on the basis of total mass of bone.
The calibration of this IVXRF bone lead system was found to be complicated by several factors, including inter-subject variations in bone geometry and bone mineral concentration (i.e., gross bone composition). 29 Proper calibration, and ultimately the estimation of bone lead concentrations, required that the bone size of the subject be determined via imaging at the measurement site. Phantoms (calibrators) were then either developed or sampled from a preexisting set composed of bone ash and silica wax to mimic both the bone size and the bone mineral concentration of the subject's bone. The estimation of the bone size and bone mineral content for each subject was estimated from the scattered source radiation (both coherently scattered radiation and incoherently scattered radiation) from the subject's IVXRF spectrum. 29 Given these difficulties in IVXRF system calibration as determined by Ahlgren et al. 28 and Ahlgren and Mattsson 29 , subsequently developed IVXRF-based methods of bone lead and strontium quantification [30][31][32][33][34] were either hindered by the complete absence of a calibration procedure, or, employed calibration against bone specimens which had been previously assessed for their bone metal concentrations by secondary method of analysis (instead of the currently employed phantom sets). [30][31][32][33][34] Such an approach resulted in limited concentration ranges included in the calibration and lacked a blank calibrator, which are both undesirable features of a robust and reliable calibration protocol. [30][31][32][33][34] A major improvement to the K-IVXRF analysis of bone lead, and by extension to other elemental quantifications, was developed after the introduction of a 109 Cd source as a replacement for the 57 Co source in the context of an IVXRF bone lead measurement. 35 Somervaille et al. 36 introduced a normalization procedure for the calibration of the 109 Cdinduced K-IVXRF system of bone lead quantification. This coherent normalization-based calibration procedure has become standard to IVXRF bone lead analysis and by extension to other IVXRF bone metal analyses-the normalization procedure being based on the coherently scattered 109 Cd source photon which has an energy equivalent to the K-edge of lead.
In the context of an IVXRF bone lead measurement, it was found that the majority of the coherently scattered 109 Cd γ-rays had origins from scattering events within the bone mineral (namely the calcium). [36][37][38] By normalizing the characteristic X-ray intensity of the analyte to that of the coherently scattered 109 Cd γ-ray intensity, various factors, including variations in source activity, source-to-detector distance, soft tissue thickness attenuation, variations in bone shape, size and orientation, subject bone mineral concentration, and minor subject movement during measurement were normalized out. [36][37][38] This thus greatly simplified the in vivo quantification of bone lead as it removed the need for imaging and thus allowed for quantification based on spectroscopic data only. This method of calibration is however de-pendent on normalization to signal which is predominately originating from the bone mineral only. As a result, concentrations are quoted on a mass of analyte per mass of bone mineral basis. Although this method of calibration does not allow one to estimate the analyte concentration on a mass of bone basis, without a priori knowledge of the bone mineral content, concentrations quoted in this fashion are the most clinically relevant given that these bone seeking elements target the mineral phase of bone only. As such, coherent normalization also acts as a means of providing clinically relevant bone metal concentrations with one less step than previously reported (i.e. as per Ahlgren et al. 28 and Ahlgren and Mattsson 29 ).
Given that coherently scattered 109 Cd γ-rays originate predominately in bone mineral, and more specifically predominately from calcium in the bone mineral, the use of single For IVXRF bone strontium measurements, the coherent normalization procedure developed for the K-IVXRF bone lead system, has been largely adapted with modifications including the use of poP-based calibrators/phantoms. From a system design viewpoint, work has been accomplished over the years as to identify a suitable source and system geometry for IVXRF bone strontium measurements. Given that the energy of the strontium K-series is in the 14-16 keV range, the hyper-pure germanium (HPGe) detection system used for the K-IVXRF bone lead system has been replaced by a silicon-drifted lithium [Si(Li)] detection system more efficient at the detection of soft characteristic X-rays. The use of a Si(Li) de-tection system also allows one to avoid the presence of Ge escape peaks which overlap with the strontium K-series. 20 Although initial work on source development in the context of an IVXRF bone strontium measurement focused on the application of a 109 Cd excitation source, which provides a sufficient fluence of silver X-rays next the K-edge of strontium for IVXRF bone strontium measurements, 26 it was later identified that 125 I in the form of brachytherapy seeds acted as a more suitable source for the excitation of strontium in bone. 20,45 125 I in the form of brachytherapy seeds produce an emission spectrum with an isolated 35.5 keV γ-ray from 125 I which may be useful for coherent normalization while also emitting a series of silver and tellurium X-rays (from the silver beads in the brachytherapy seeds and the decay of 125 I) near the K-edge of strontium ensuring higher efficiency of strontium excitation. Geometrically, various source-sample arrangements have been evaluated, mainly, a 90 ○ geometry and a 180 ○ geometry. 45 The evaluation of geometrical arrangements being made as a means of assessing possible background reduction by removal of background signal from Compton scattered source photons as well as allowing for ease and reproducibility in patient positioning.
Currently, the clinical system used for IVXRF-based bone strontium measurements is composed of a Si(Li) detection system with 125 I seeds as an excitation source positioned in a 180 ○ backscatter geometry (Figure 1.1). Measurements on this system are made for a period of 30 minutes, resulting in an effective dose to subjects within the range of (64 − 76) × 10 −6 mSv. 46 Minimum detectable limits (2σ) have been reported on the order of 23 µg Sr/g Ca. 46 This clinical system being used for human measurements. 9,10,46 Quantification is still a limiting factor for this system of IVXRF bone strontium quantification. Coherent normalization (normalization of the strontium Kα X-ray to the coherently scattered 125 I γ-ray) has been evaluated through both simulation and in conjunction with human data and has shown that it is able to partially correct for factors such as bone size and geometry but is not a high fidelity normalization procedure. 46,52 The major effect observed by applying the coherent normalization procedure is the reduction in the total measurement variance which allows one to make inter-subject comparisons of variations in bone strontium concentrations (apparent through normalized intensities), but not quantification. 46 Coherent normalization and general quantification protocols still remain an area of investigation.
One of the limiting factors to the quantitative power of the in vivo bone strontium system is the lack of a suitable phantom/calibration material. Although the use of poP as a phantom material has been rather successful in the case of K-XRF bone lead quantification, several issues remain with its use. The coherent normalization procedure requires that a conversion factor be applied between the data obtained from humans in order to be comparable to calibration data acquired from poP phantoms (or vice versa) given the different scattering properties of the two materials. This correction factor is simply the ratio of the relativistic form factors for each of the two materials, a compositionally dependent factor, whereby bone mineral is assumed to be pure HAp and poP pure calcium sulphate hemihydrate. 36,38 This is a feature of the calibration protocol currently used for the in vivo quantification of bone strontium. 48 Concerns have arisen as to the accuracy of this correction factor given inherent contamination in the poP and given assumption to the phantom's true composition. 38,53 A more severe issue with the use of poP phantoms, in the context of bone strontium quantification, is the extensive degree of contamination from the analyte itself. Strontium, being an ubiquitous element to calcium is present in calcium compounds, including poP, at levels which are near those expected in the bone of human subjects (several hundred parts per million); this is a fact which has been shown to be independent of the quoted degree of purity of calcium compounds. 26 With such a high level of contamination from the analyte, no true blank can be produced limiting the ability to determine accurate analytical figures of merit for the system, and, this also limits calibration in the low strontium concentration range. 20,26 It is thus desirable to have available a pure HAp phantom which can be used as a phantom material for the calibration of in vivo XRF-based systems of bone metal quantification. Such a material would allow for the proper determination of analytical figures of merit as well as possibly remove the need for the introduction of a phantom-bone conversion factor between the calibration and measurement. This work aims at first developing calibrators to attempt to remedy these issues while also evaluating the use of the blank phantom for the purpose of system background assessment.
In regards to analyte quantification, it is generally desirable that the concentration of the analyte is represented with respect to calcium, as is necessary for DXA correction (see section 1.2); however, there is no calcium signal due to soft tissue attenuation. 26 The coherent normalization procedure does however normalize analyte concentrations to the amount of bone mineral, and by extension calcium, in the bone being measured, and thus is desirable in the case of extracting clinically relevant concentrations of strontium. 20,36 The application of the coherent normalization procedure to in vivo bone strontium measurements using the 125 I induced system has shown that it is applicable yet with some limitations as it only provides a partial normalization when overlaying soft tissue is present. [46][47][48]52 For this reason, this work only assessed the coherent normalization procedure in the context of a bare bone measurement to assess the HAp material's suitability for this purpose in contrast to poP-based calibrations. Soft tissue attenuation of the signal was ignored in this work as to ensure that the assessment was specific to calibration material and not to any other confounding factors affecting the analytical signal, namely, issues with soft tissue attenuation corrections. Although soft tissue attenuation was not considered in the simulation work here from a quantitative viewpoint, Compton-based methods of soft tissue thickness estimations, as first described by Nie et al. 24 were evaluated in this work as a means of identifying a possible spectroscopic means of improving the coherent normalization procedure in future system developments. This work also further assessed portable X-ray analyzers for in vivo bone strontium and lead quantification on the basis of their analytical figures of merit. This assessment was completed in this work using the newly developed phantom material as a means of assessing new systems which may provide a more portable, rapid and inexpensive means of performing bone strontium and lead quantification in humans.

Outline of dissertation
The overall outline of this dissertation is as follows: Chapter 2: This chapter describes the preparation of a hydroxyapatite phantom material which is chemically free of any interfering analyte concentration. This chapter presents, to the author's knowledge, the first description of the preparation of a bone mineral surrogate material which is free of analyte (namely strontium) contamination. The material being designed such that the final solid phantom material is free of the analyte, thus allowing one to prepare phantoms with a true blank as a means of performing a background assessment, as well as to determine analytical figures of merit properly. This chapter describes the preparation of the phantoms as well as their general chemical assessment.
Chapter 3: This chapter describes the preparation of phantoms which contain a high concentration of the analyte strontium, strontium being the only discernible analyte which would be present in bone mineral at concentrations which would reach the mole-percentage concentration levels. In this chapter, a phantom material is described and assessed which contains high concentrations of strontium and which is prepared using a tertiary mixture of salts as to maintain the (Ca + Sr)/P ratio at 1.67. The high concentrations of strontium in these phantoms also allowed for an assessment of the chemical structure of the apatite which allowed for an assessment of the substitution behaviour of the analyte.
Chapter 4: This chapter demonstrates the necessity of the blank phantom prepared in chapter 2 in the context of an in vivo bone strontium measurement by XRF using the current clinical system. The need for this phantom in the context of a background assessment is discussed and described given excitation source and/or system contamination which has not be assessed in previous system developments.
Chapter 5: This chapter assesses the possible need for the phantoms described in chapter 3, that is, phantoms with high concentrations. This particular work focuses on the assessment of non-linearity as a function of strontium concentrations while also assessing the possibility of analyte enhancement in the context of a bone lead measurement made using the lead Lseries. This chapter thus provides a critical step in the further development of quantification methodology as it assesses the need for phantoms of high strontium concentration while also assessing the possible reality that bone lead quantification (via the L-series) may need to be completed only with bone strontium quantification. Chapter 8: This chapter applied the new HAp phantom material in a system comparison study of portable X-ray analyzers potentially suitable for bone strontium measurements. The focus of this work was the assessment of these portable X-ray analyzers for possible future work in in vivo bone strontium and lead quantification using X-ray tube based spectrometers which would make the system much more portable than the current clinical system. This study also focused on a comparison on system performance as a function of X-ray tube target material selected as well as an assessment of performance as a function of measurement time.

Introduction
Human bone is used as a biomarker of cumulative exposure to various elements including lead and strontium. In vivo X-ray fluorescence spectrometry (IVXRF) is an analytical methodology which allows one to quantify the concentration of such elements in bone non-destructively and with minimal radiation dose to the subject. IVXRF-based bone metal quantification has traditionally been complicated by the complex nature of the analyte's characteristic X-ray intensity which influences the calibration protocol. By extension, a major hindrance to the calibration of IVXRF systems of bone metal quantification is the availability of suitable calibrators, otherwise and hereby referred to as phantoms, to be used for the purpose of system calibration.
The earliest IVXRF-based system of bone metal quantification is the 57 Co induced K- A major improvement to the K-IVXRF analysis of bone lead was the introduction of a 109 Cd source as a replacement for the 57 Co source. 8 After this major development, Somervaille et al. 9 introduced a normalization procedure to the calibration protocol of the 109 Cd-29 induced K-IVXRF system of bone lead quantification which has become standard to IVXRF bone lead analysis and by extension to other IVXRF bone metal analyses. It was found that the majority of the coherently scattered 109 Cd γ-rays had origins from scattering events within the bone mineral. [9][10][11] By normalizing the characteristic X-ray intensity to that of the coherently scattered source radiation intensity, it became possible to determine the quantity of lead per unit mass of bone mineral. This normalization procedure corrected the observed response for various factors, including variations in source activity, source-to-detector distance, soft tissue thickness and associated signal attenuation, variations in bone shape, size and orientation, subject bone mineral concentration, and minor subject movement during measurement. [9][10][11] The fact that coherent scattered 109 Cd γ-rays originate predominately in bone mineral The use of poP as the phantom material raises some concerns about its purity and chemical composition in comparison to the matrix being measured. In the case of bone lead analysis, contamination in the poP used for the preparation of phantoms has been insinuated as a problem due to assumptions of the purity of the material when computing the CCF. 11,30 It has been proposed that the level of contamination may influence the reliability of the applied CCF given that poP used for phantom preparation is generally not pure poP and does present some contamination, which is not necessarily accounted for. 11,30 The problem with contamination in poP is much more severe in the case of in vivo bone strontium analysis. 20,30 Strontium, being a ubiquitous element to calcium, is generally present in calcium compounds at levels which are near those of the levels expected in human bone. This is a feature which is independent of the quoted degree of purity of calcium compounds. 20,31 The fact that strontium is present in poP at high concentrations does not allow for the development of a proper calibration procedure. Strontium contamination does not allow for the preparation of a blank phantom, making the true analytical figures of merit of the system difficult to determine. 31 The chemical difference between the poP, a calcium sulfate [albeit also containing other species of calcium 11,30 ], and bone mineral, a calcium phosphate, also presents some general concerns. The application of a CCF inherently introduces some uncertainty in the quantification while the chemical difference between the two materials, in the context of 109 Cd induced K-IVXRF bone lead measurements, results in different high-energy tails from the Compton scattering profile for calcium, sulfur and phosphorous. [32][33][34][35] As such, having a phantom material composed of a calcium sulfate and a sample of calcium phosphate results in different spectral features, which require different data analysis procedures. It is desirable to have a phantom material that mimics bone mineral (HAp) as closely as possible while also being chemically pure. This chapter describes a simple method of preparing pure HAp phantoms as a more suitable phantom material for bone strontium and lead quantification using IVXRF.

Preparation of pure calcium compounds
All of the reagents used for the preparation of phantoms and/or the purification of calcium were assessed for purity by total reflection X-ray fluorescence spectrometry (TXRF).  Kingstown, RI, USA). The analyte solution was added to the 1 mol/dm 3 NaHPO 4 setting solution, which resulted in the formation of a fine and well-dispersed precipitate. The powders were added immediately to the analyte-containing setting solution and the phantom prepared as described previously. Standard curves were prepared and measured by EDXRF.

Total reflection X-ray fluorescence spectrometry
High-purity quartz reflectors were used as the sample carriers (Bruker-AXS

Energy dispersive X-ray fluorescence spectrometry
All EDXRF measurements were performed on an S2 Ranger™ spectrometer equipped with a Pd anode X-ray tube and an SDD detection system positioned with an incident angle of 45 ○ and a take-off angle of 45 ○ (Bruker-AXS, Madison, WI, USA). The X-ray tube was operated with a potential of 40 kV and current of 250 µA and the distribution hardened using a 500 µm Al filter. Measurements were made for 1200 s live time. Total integrated peak areas of the characteristic X-rays of interest were determined using an in-house trust-region reflective least-squares curve-fitting algorithm.

Powder X-ray diffraction spectrometry
The crystal phase of the prepared Ca(OH) 2 , CaHPO 4 ⋅2H 2 O, phantoms and NIST bone meal were assessed by powder X-ray diffraction spectrometry. The materials were finely ground prior to analysis in a tungsten carbide ball mill. The measurements were made using a Co X-ray source (λ = 1.79021 Å) operating at a potential of 40 kV and a current of 40 mA (Rigaku Geigerflex, Danvers, MA, USA). The diffractograms were collected over the range of 5.00 to 90.00 ○ 2θ at a sampling interval of 0.05 ○ and scan speed of 4 ○ /min.

Results and discussion
Commercially available calcium compounds used for preparing phantoms were assessed for purity by TXRF after the method was validated against a suitable standard reference material ( -Sr 442 ± 20 286 ± 6 773 ± 241 < 0.7 Pb 6 ± 1 9.8 ± 0.3 21 ± 6 < 0.3 § In all cases, calcium compounds were contaminated with both strontium and lead, the analytes of interest, as well as various transition metals and halides. Elements either not listed or accompanied by (-) indicates that the element was present at/or below the limit of detection of the spectrometer. Limits of detection are listed for strontium and lead * TXRF limits of detection (3σ), † Prepared from the CaCl 2 ⋅2H 2 O, ‡ Prepared from the purified Ca(OH) 2 One of the major problems associated with the use of poP as the phantom material for IVXRF-based methods of bone metal quantification is that of purity. Two major sources of contamination have been identified: contamination of the whole material by the analyte and other metals and contamination of the material with other chemical species of calcium. 11,20,30 Such contamination makes it difficult to accurately calculate the CCF or to properly determine the analytical figures of merit of IVXRF systems given the inability to produce a true, well-characterized blank phantom. 11,30,31 The contamination of calcium compounds with strontium is far more severe than contamination from lead ( Table 2.2). 20,30 Pure calcium compounds are required in order to have complete control over the composition of the proposed HAp phantoms.
The purification of calcium from strontium is a known challenge given the chemical similarity between the two elements. In the case in which the concentration of calcium is far greater than that of strontium, the calcium must be removed from solution, given the difficulty in removing very small masses of strontium reliably. The selective precipitation of calcium from a strontium-containing solution with 8-hydroxyquinline has been shown to be quite successful at greatly reducing the strontium content of calcium compounds. 37,38 However, the process is time consuming, expensive, and requires the use of large quantities of solvent and acid for the preparation of relatively small amounts of pure calcium. That method of purification is not particularly well-suited to the preparation of a set of phantoms that require large masses of calcium compounds.
The separation of calcium from strontium has been shown to be possible by hydroxide precipitation of calcium from a strontium containing solution. 36,39,40 This method of separation is successful due to the differential solubility of calcium and strontium hydroxide. 36 The method is quite simple, requiring only that an aqueous Ca 2+ solution be treated with . This observation may be due to the higher probability of coprecipitation of strontium when higher numbers of equivalents are used. In order to maximize the yield of high purity calcium, it was found that when using a calcium concentration of 1 mol/dm 3 , the addition of 0.5 equivalents of OH − produces Ca(OH) 2 with a strontium concentration of <0.7 µg/g Ca (p = 0.05) ( Table 2.2), which is below the limit of detection of the current IVXRF system of bone strontium quantification. 20,21,31 A striking feature of this method of separation is the high efficiency for not only the removal of strontium but all other elements which were originally present in the CaCl 2 ⋅2H 2 O (Table 2.2), thus producing Ca(OH) 2 of high purity (Figure 2.2).
The Ca(OH) 2 produced by this method was found to be free of all metals and was used for the purpose of preparing phantoms after using the compound to prepare metal-free The preparation of phantoms for IVXRF calibration requires that the phantoms be prepared in various shapes and sizes. The use of poP for the purpose of phantom preparation was thus ideal as, being a plaster, it can be molded and shaped to virtually any geometry.   The purification protocol was found to free the calcium of all metals in comparison to the metal content found in the reagent. This may allow for the use of this phantom material as calibrators for other elements for both in vivo and ex vivo XRF applications and for general calcified tissue analysis.

Acknowledgements
The

Abstract
The current in vivo X-ray fluorescence spectrometry (IVXRF)-based method of bone stron- setting solution (to increase phosphate concentration) produced a phantom composed of (Ca 1-x Sr x ) 5 (PO 4 ) 3 OH of known strontium concentration. The final phantom material was found to be a strontium-substituted product (through X-ray diffraction and Raman spectroscopy measurements) to the degree of substitution expected. This work thus describes the preparation of a bone phantom material which can be used for the calibration of IVXRF systems of bone strontium quantification, as well as for other modalities (i.e. dual energy X-ray absorptiometry and quantitative ultrasound) in the case that bone strontium concentrations are expected to be high such as in the case of individuals taking strontium salts for the treatment/prevention of osteoporosis.

Introduction
In vivo X-ray fluorescence spectrometry (IVXRF) has been applied to the quantification of various elements in bone tissues as it offers a non-destructive method for the quantification of various elements in bone which allows for long term monitoring and with modest radiation dose to the subjects. [1][2][3][4][5][6][7] The calibration of IVXRF systems for bone metal quantification can be quite complicated as various factors, such as the inter-subject variations in bone geometry, bone mineral concentration and overlaying soft-tissue thickness, can influence the analytical signal (the characteristic X-ray intensity of interest). 8,9 As a result, a coherent normalization procedure is generally employed and has been shown to correct for such influence. 10 The procedure being dependent on the assumption that bone mineral is composed of hydroxyapatite [HAp; Ca 10 (PO 4 ) 6 (OH) 2 ] and concentrations determined on a mass of analyte per unit mass of bone mineral basis. 10 The success of the coherent normalization procedure developed in the context of a 109 Cd-induced K-XRF bone lead measurement 10-16 has thus led to its application, in whole or in part, to other IVXRF systems of bone metal quantification, either by use of the coherent normalization procedure as a whole, or, the use of plaster of Paris [poP; as a surrogate for bone mineral in the calibration. [4][5][6][7][17][18][19][20][21][22][23][24] Several concerns have arisen as to the use of poP as a phantom material for IVXRF systems of bone metal quantification, namely, its chemical dissimilarity to bone mineral, the need to apply a coherent conversion factor (CCF) to the calibration procedure to account for the different scattering properties of poP versus HAp and various issues with contamination by the analyte. 2,17,25,26 In the case of a bone strontium measurement, commercial poP has been shown to contain rather large levels of strontium contamination, resulting in the inability to produce a true blank phantom and difficulty in determining analytical figures of merit. 2,17 In response to these concerns, a new HAp phantom material, which is chemically pure and similar to bone mineral, has been proposed to provide a means of preparing bone mineral-like phantoms as a substitute for poP and removing the concerns which arise from poP's use as a phantom material in IVXRF calibration. 27 .
The shown that this approach allows for the preparation of analyte free phantoms (blanks), in particular, phantoms clean of strontium, and also that it is possible to prepare standard curves when the analyte is introduced in this fashion.
The case of strontium in bone presents a certain analytical challenge particularly in the context of preparing phantoms. In the case of most other metals (e.g. lead), the expected concentrations in bone tissue are in the part-per-million concentration range 1,3 which lends the phantom preparation to a simple doping procedure in the context of adding the analyte.
Strontium is however a ubiquitous element to calcium and is naturally present in human bone in the part-per-million range. Strontium compounds are used as a treatment for osteoporosis and thus it is expected that in some populations the bone strontium concentration may reach the mol-percentage concentration range. 28 This is evident from the concerns already raised in the context of dual energy X-ray absorptiometry measurements. 29,30 As a result, the addition of strontium to an IVXRF phantom through doping, whether poP or the HAp phantoms, 27 is not a feasible route as it is necessary to keep the (Ca + Sr)/P mole ratio at 1.67.
This work thus evaluates the feasibility of preparing HAp bone phantoms which are high in strontium concentration and which are maintained at a (Ca + Sr)/P mole ratio of 1.67 and thus preparing a strontium-substituted HAp phantom material This is of particular importance in the case phantoms are to be prepared with strontium concentrations in the mole-percentage concentration range, and thus, the addition of the analyte may introduce a non-trivial deviation from the 1.67 (Ca + Sr)/P mole ratio. The procedure evaluated in this work being based on a CaHPO 4 whereby the analyte is introduced as a heavy hydroxide hydrate to reduce analytical uncertainty in computed phantom concentrations. This work thus evaluates the feasibility of preparing phantoms by this route, in which the final product is a substituted strontiumhydroxyapatite. It also provides an assessment of the reaction (given the varying solubilities of the two hydroxides) for any possible contamination issues that are of analytical importance to calibration protocol of bone strontium analysis.

Phantom preparation
Phantoms were prepared using the method described by

Powder X-ray diffraction spectrometry
The phantoms were finely ground in a tungsten carbide ball mill prior to analysis and loaded into an aluminium sample holder for XRD analysis. The measurements were made using a

Raman spectroscopy
Raman measurements were made on a Renishaw confocal Raman microscopy (Renishaw Ramascope 2000, Gloucestershire, UK) equipped with an energy dispersive CCD detector (resolution better than 2.5 cm −1 ) and a 782 nm laser. Measurements were made using a 20× objective on finely ground samples mounted on optically flat quartz sample carriers.

Results and discussion
The preparation of the HAp phantoms is based on the solubility properties of calcium phosphates as well as the common ion effect. [31][32][33][34] Within a pH range of 4.5 to 14, HAp is the least soluble of all calcium phosphate compounds. 31,34 As a result most calcium phosphates will tend to dissolve and precipitate as HAp. 31,34 The setting mechanism for CPC systems has been proposed to be similar to that of poP. 32 The precipitated phase tends to grow in clusters and the cluster mass tends to set via entanglement. 31,32,35 The rate at which this conversion to HAp occurs is rather slow and the phosphate ion concentration in the setting solution becomes critical in the formation of an HAp product through the common ion effect. [32][33][34] The rate of formation has a direct impact in the overall physical qualities of the phantoms, in particular, the material strength.
As with poP, the CPC system used to prepare phantoms 27 takes advantage of the common ion effect in order to increase the rate of formation of HAp and thus improve its physical properties. When considering the setting behaviour of poP, potassium salts, namely K 2 SO 4 , are often used as setting accelerants. 35 Commercial poP is often employed as a phantom material in the context of IVXRF measurements; the unknown proportion of these accelerants being a known form of contamination in the final phantoms. 26 Given that current IVXRF calibration protocols require the application of a CCF-that is material dependent-preparing phantoms with commercial poP in which the concentration of these accelerants (and other additives) are unknown may result in added uncertainty to the measurement. 10,26 Removing these accelerants to produce phantoms from pure CaSO 4 ⋅ 1 allow for the complete removal of the CCF from the calibration protocol. 27 In the case of HAp cements, a high free phosphate ion concentration is required in the system in order to ensure a rapid setting time which ultimately improves the physical qualities of the final phantom. [32][33][34] This has been shown to be achievable by either including an anion of phosphoric acid 27,34 or free hydroxyl ions 34 to the setting solution. In the case of a CaHPO 4 ⋅ 2 H 2 O based HAp cement, the hydroxyl ion can increase the overall free phosphate ion concentration in the system by increasing the solubility of CaHPO 4 ⋅ 2 H 2 O, thereby inducing the so-called "common ion" effect. 34 The use of this type of CPC system for the preparation of HAp phantoms, more specifically, by increasing the phosphate concentration using an anion of phosphoric acid in the setting solution, was found to be successful when the analyte was added directly to the phosphate-containing setting solution. 27  More specifically, addition of strontium as its hydroxide was investigated.
With regards to a CaHPO 4 ⋅ 2 H 2 O CPC system, the reaction does require that all reagents be present in their respective proportions for the formation of HAp to occur. Considering  37,38 in this study in which the powder-to-liquid ratio is 2:1, the system was prone to losing water rather rapidly, but no HAp was formed (3.1). The

For the CaHPO
and/or Sr(OH) 2 ⋅ 8 H 2 O did more than just increasing the (Ca + Sr)/P mole ratio to that of 1.67 as previously suggested. 34 Such a mixture is desirable as a means of introducing the analyte into the phantom as it allows for maintaining the total (Ca + Sr)/P ratio at 1.67.
The results of the CaHPO 4 ⋅ 2 H 2 O reaction with the setting liquids alone suggests that the presence of all reactants need to be present in this calcium phosphate cement system in order for HAp to be produced ( Figure 3.1).
In the case of a saturated solution of Ca(OH) 2 , which has a solubility of 0.160 g/100 g 36 the equilibrium and reaction in Scheme 3.2 would be expected to occur.
Here, an interfering reaction when the phantom mixture is produced at ambient is expected due to integration of ambient CO 2 from the air. In this case CaCO 3 would form as a phantom contaminant given the pH of the solution. In the case that a OHcontaining setting solution is used, the common ion effect would dictate a push towards the formation The difference in the diffraction pattern observed for the unreacted CaHPO 4 ⋅ 2 H 2 O in the region of 2θ < 32 ○ may be due to a difference in the particle size of the powders after the sample preparation as well as minor pH dependant structure changes.
of Ca(OH) 2 in this system. The production of CaCO 3 would then be expected to be rather low, but, is present at low quantities when this setting solution is used (Figure 3.2). In the case of using a HPO 2 -4 containing setting solution traces of Ca 10 (PO 4 ) 6 (OH) 2 are observed but no CaCO 3 (Figure 3.2).
When the Sr(OH) 2 ⋅ 8 H 2 O is mixed with either of the setting solutions, the final product in both cases was nearly pure SrCO 3 (Figure 3.3). This is an expected result as with this degree of solubility, the CO 2 integrated into the mixture with mixing is likely to react to form

Conclusions
This work assessed the feasibility of preparing strontium-substituted HAp bone phantoms with inherently high concentrations of strontium for the purpose of calibration of IVXRF systems of bone strontium quantification. These phantoms to be used in cases in which strontium concentrations are sufficiently high that doping of the setting solution in the phantom preparation protocol previously reported 27  "Assessing spectral background interference in the in vivo bone strontium system using a blank phantom." † † E. Da Silva designed and carried out the experiments, performed the data analysis and wrote this manuscript/chapter. M. Moise and D. R. Chettle made similar observations to be included in future drafts of this work (see Figure 4.2) with regards to a direct seed measurement, but on the clinical system (not included in this draft). A. Pejović-Milić financed this project, provided critical feedback as to its contents and the experiments, assessed the manuscript/chapter critically and brought both research groups together.

Abstract
Analytical blanks are routinely used in spectrochemical analysis as a means of assessing spectral background, the presence of spectral interferences and for the determination of analytical figures of merit. In the context of an in vivo X-ray fluorescence spectrometry (XRF)-based bone strontium determination, a true blank measurement has not been possible to date given the lack of a suitable blank phantom. The absence of a suitable blank being due to the fact that calcium compounds (including plaster of Paris typically used to make bone phantoms) are heavily contaminated with the analyte strontium. In this work, we investigate the need for the blank hydroxyaptite phantom recently developed for the purpose of XRF-based bone strontium quantification. 1 It was found that the 125 I brachytherapy seed excitation source used in the clinical system emits a spectrum containing the zirconium K-series The presence of zirconium on/in the seeds was confirmed after their decay and qualitative assessment using a portable X-ray analyzer. Monte Carlo simulations demonstrated that in the 180 ○ backscatter geometry, used for clinical bone strontium measurements, the most probable scattering interaction into the detector is Compton scattering of the zirconium K X-rays; thus, presenting a possible spectral interference beneath both the strontium Kα 1,2 and Kβ 1,3 lines. A blank measurement using a blank hydroxyaptite phantom and silicon drift detector (SDD)-based detection system in an off-centre backscatter geometry showed the presence of rubidium and possible strontium (believe to be system contamination) and Compton scattered zirconium photons. This work thus demonstrates the need for a blank measurement in the context of an in vivo XRF-based bone strontium measurement as a means of quantifying these interferences further and implementing them in future system

INTRODUCTION
developments as well as refinements to the overall calibration protocol.

Introduction
Spectrochemical methods of quantitative analysis generally include an analytical blank measurement as part of their calibration protocols. Analytical blank measurements serve various important functions. For wet chemical methods, in which a sample is to be digested and samples and calibrators prepared as solutions, an analytical blank will generally be composed of all of the reagents used to prepare the samples and calibrators with the exception of any added analyte. A measurement of an analytical blank then provides a measure of any signal which may arise due to contamination from the analyte as well as provide an assessment of any spectral interferences which may hinder the ability to measure the given analyte-produced signal reliably. Analytical blank measurements thus allow the analyst to devise background subtraction methods in the case any inherent contamination is present to the system and/or reagents or if sufficiently minor spectral interferences are present. Aside from simple background and spectral interference assessments, one of the more important applications of an analytical blank measurement is to assess the statistical distribution of the spectral background and associated system noise without the inclusion of any signal from the analyte. This allows one to properly compute analytical figures of merit for the system (i.e. the signal-to-noise ratio, limit of detection and limit of quantification)-a critical component of any calibration procedure. Although not a wet chemical method, for in vivo methods of bone metal quantification, blanks are employed for the determination of the minimum detectable limit (MDL) which is an analogous parameter to the limit of detection for the same reasons as for wet chemical methods.
For solid state, in situ, methods of quantitative metals analysis, such as X-ray fluores-

INTRODUCTION
cence spectrometry (XRF), it is desirable to make an analytical blank measurement as a means of assessing for any spectral interferences as well as for any contamination that may arise from any sample preparation pretreatments. Sample pretreatment as a source of contamination is not relevant for the case of in vivo XRF (IVXRF) measurements which are in situ measurements void of a sample preparation.
The determination of true background noise is however more complicated for in situ methods, such as XRF, in comparison to wet chemical methods of metals analysis, as wet chemical methods generally present the analyte in solution at low concentrations, whereby, XRF measurements are routinely used to assess total sample composition, or, as is the case of an in vivo bone metal measurement a single element with assumptions about total sample composition. By the measurements very nature it becomes difficult, if, at all possible, to produce true analytical blanks for many cases of XRF calibration.
From a practical viewpoint, XRF, in its most general sense and not only considering the in vivo case, is a method in which a blank calibrator is not available for assessment of spectral background. Given that XRF is used to quantify the total composition of samples, thereby, as a requirement for calibration procedure all analyte lines are present, 2-4 and thereby, blanks are often not available, estimates of the background are often performed using background information adjacent to the analytical peak of interest, while, spectral interferences from system components can be estimated using selected pure materials which act as scatterers (i.e. graphite). 5 IVXRF bone metal measurements offer a scenario in which a blank can be produced (see Chapter 2). Given that the analyte, say, strontium, is only present in small concentrations (at trace or minor levels) then it is possible to produce a blank in which the matrix (bone mineral) is free of the analyte, although, in the case of strontium, such a material has

INTRODUCTION
traditionally been unavailable. 1,6 IVXRF methods of bone lead and bone uranium quantification have been shown to be calibrated against sufficiently pure materials such that blanks are produced adequately. [7][8][9][10][11] This is not however the case for bone strontium analyses as there has been no available analytical blank for the system until this work. 1,12 The lack of a blank being due to endogenous contamination of the plaster of Paris (poP) used for the preparation of phantoms with the analyte strontium. 12,13 One of the most important functions of an analytical blank is its critical role in the determination of the minimum detectable limit (MDL) of the system/method. Determination of the MDL inherently involves assessing sources of noise in the analytical/spectral region associated with the signal produced by the analyte. In the case of an IVXRF bone strontium determination, if one ignores any other sources of background/interference, background and associated noise would include electronic noise as well as the background due to Compton scattering of source photons into the energy region of the strontium K-series. In reality however, sources of background may include spectral interference from other overlapping characteristic X-rays, which could influence the data reduction (curve fitting) procedures used to extract the analytical signal (integrated peak areas) as well as the MDL. If these spectral interferences-notably peak overlaps-are severe enough, they may not be perfectly visible on any collected spectrum. In this case, the blank serves the function of assessing sources of noise and possible exogenous analyte contamination from the system, that will influence the MDL as well as the determined analytical signal in any given spectrum collected for analysis, if spectral interferences are present.
The current IVXRF system of bone strontium measurement uses phantoms which are heavily contaminated with strontium. 12,13 The current "blank" (i.e. the 0 ppm phantom) is simply a poP phantom with no additionally added strontium but which contains an inherently large amount of the strontium due to endogenous contamination. 12,13 In this case, by use of a heavily contaminated blank phantom possible spectral interferences cannot be assessed as even the "blank" phantom produces a In this chapter we provide the first blank phantom measurement for bone strontium quantification and discuss possible sources of spectral interference which inherently demonstrate the necessity for the material which is suitable for a true blank measurement to assess for spectral interferences.

Blank Bone Phantom
The blank phantom was prepared as previously described 1 (Chapter 2) using the same listed reagents and methodologies. The phantom was prepared with a diameter of 10 mm and a height of 20 mm. The presence of strontium in the blank bone phantom was assessed by total reflection X-ray fluorescence spectrometry (TXRF) as previously described. 1

Brachytherapy Seeds
The excitation source used for the purpose of IVXRF bone strontium measurements was 125 I in the form of brachytherapy seeds. This type of excitation source is what is typically used as the excitation source for said measurements. [14][15][16] The seeds used in this study were Advantage 125 I interstitial brachytherapy seeds (Model No. IAI-125A; IsoAid, Port Richey, FL, USA). Each seed consisted of a laser welded titanium capsule which contained 125 I chemically affixed onto a silver rod. In the context of the actual application of these seeds, prostate brachytherapy, the silver rod acts as an X-ray marker. Each seed had a total length of 4.5 mm, a thickness of 0.8 mm and a titanium wall thickness of 0.5 mm.
The batch of brachytherapy seeds consisted of three seeds in total. The weighted average activity per seed was determined by the manufacturer to be 0.638 mCi (range of 0.632-0.644 mCi) and the total activity of all three seeds was 1.91 mCi. The emission spectrum assumed for these seeds in the simulation work was that as determined by . 6,17

Qualitative elemental analysis of brachytherapy seeds
The seeds were assessed for their overall composition, on a qualitative level by XRF. This measurement was performed as to assess the composition of the seeds without fear of exciting surrounding features of the silicon drift detector-based in vivo XRF unit. The seeds were allowed to decay for a period of 430 days prior to the measurement which amounts to 7.24 half-lives of 125 I (t 1 2 = 59.4 days). The total activity at the time of the measurement for all three seeds was calculated to be 12.6 µCi.
The XRF measurement was performed using a portable X-ray spectrometer (Tracer-III SD, Bruker-AXS, Madison, WI, USA). The spectrometer was equipped with a miniaturized rhodium target X-ray tube operating at 40 kVp and 30 µA. The primary beam was hardened for this measurement using a multilayer filter composed of 12 mil Al + 1 mil Ti + 1 mil Cu as to improve the background at the zirconium K-series energy region. Photon detection was achieved using a 10 mm 2 XFlash® silicon drift detector system (Bruker-AXS, Madison, WI, USA). The resolution of the detector was quoted by the manufacturer as being on the order of 145 eV.
The measurement was made by placing the seeds directly onto the measurement window and a 300 s real time measurement acquired. Although the seeds were still relatively active, the measurement did not exceed a dead time of 2.1 % (total raw count rate of 8947 cps). The system is routinely monitored for contamination using a series of standard alloys and glasses.
No inherent zirconium contamination is known of this system as a whole, as determined routinely using various scatterers.

Direct Source and Blank Phantom Measurement
The direct seed measurement and the blank phantom measurement was performed on the SDD detector-based detection system which was selected due to availability. This system was a test system for the first blank measurement and is not currently the clinical IVXRF bone strontium system which was selected for the simulation study. The clinical system being based on a Si(Li) detection system and a true 180 ○ backscatter geometry as described elsewhere. 6,15,16 The detector used for our measurements, due to availability for a preliminary assessment, was an 80 mm 2 active area Vitus H80 single-element SDD detector with an associated AXAS-A module (KETEK GmBH, Munich, Germany). A tungsten collimator was place at the head of the detector, which reduced the total area of the detector and acted as a mount for the tungsten collimator used to house the brachytherapy seeds. This

Monte Carlo Simulations
Monte Carlo simulations were made as per Zamburlini et al. 17 as to mimic a human bone strontium measurement. 6,15,16 The simulations were completed using the EGS5 (Electron Gamma Shower) Monte Carlo simulation package using 10 12 incidence particles. 10 12 incident particles was selected as it was found that this was an optimal number to balance computation time and statistical variation at the strontium Kα 1,2 (not greater than approximately 5 % at 400 ppm). The emission spectrum used for the 125 I brachytherapy source was that described by Zamburlini et al. 6 Simulations were carried out on a finger phantom modelled as a 9 mm cylinder of cortical bone tissue with a 2 mm shell of soft tissue which models the average geometry of a human finger adequately. 17 The detector window-to-phantom surface distance was maintained at 5 mm for all simulations. The detector arrangement was simulated as to mimic a Si(Li) detection system, with a tungsten collimator housing the 125 I brachytherapy source which allows for a 180 ○ backscatter geometry to the detector relative to the sample. 17 A schematic of the geometry used for the simulations is shown in

Results and Discussion
One possible source of spectral interference/system contamination may be the excitation source itself, which, in the context of an in vivo bone strontium measurement, consists of brachytherapy seeds. These seeds, being prepared for a therapeutic application, have not been specifically prepared for such an analytical application and may be a source of contamination to the system.  apparent that the system is prone to possible spectral contamination from rubidium, the analyte strontium and zirconium. Provided that this is a direct measurement, it is likely that these X-rays are emanating directly from the source, but may be due to excitation of system components which necessitated a secondary assessment of the source external to the detection system. Based on the direct seed measurement, the rubidium can be of concern in the case in which it is present in large concentrations as the rubidium Kβ line overlaps with the high energy side of the strontium Kα 1,2 line which is often used for the purpose of quantification (Table 4.1). Zirconium contamination may be an issue when the strontium Kβ line is to be used for quantitative purposes (Table 4.1). With regards to the degree of contamination, from the direct measurement, the total measured fluence of the zirconium K-series was estimated to be less than 1 % of the total fluence from the source, as normalized to the full emission spectrum.
Although characteristic X-rays from elements which produced characteristic X-rays within the strontium energy region were observed during a direct seed measurement (Figure 4.2), this does not necessarily mean that their origins were from the excitation source. For this reason, the brachytherapy seeds themselves were subjected to a qualitative assessment by XRF after a sufficient time was allowed for the seeds to decay to an appropriate level of  activity, in order to assess their composition. This decay was implemented as a means of ensuring that the fluence rate from the γ-radiation emitted by the brachytherapy seeds to the X-ray spectrometer's detector was not exceedingly high. The spectrum showed the expected X-ray series from the 125 I decay as well as the presence of zirconium (Figure 4.3).
There was no evidence of rubidium or strontium in the spectrum obtained from the direct seed measurement (Figure 4.3) which would indicate that the rubidium and strontium were likely from internal components of the SDD detection system or from surrounding contamination. The qualitative assessment of the cold brachytherapy seeds thus indicates that the only spectral interference to be considered as emanating from the source is in fact zirconium and not any rubidium or strontium (Figure 4.3).
The presence of zirconium in the brachytherapy seeds in not unexpected. The main application of the seeds is for permanent implantable brachytherapy for the treatment of prostate cancer. The seed capsules are composed of titanium (Section 4.3.2); however, as a means of reducing the corrodibility of the titanium, biomedical grade titanium is often either coated with, or an alloy of, zirconium. It is thus reasonable to conclude that the brachytherapy seeds used as a source for the IVXRF system for bone strontium quantification are contaminated directly with zirconium, which presents a possible spectral interference within the analyte's energy region (Table 4.1).
The consequence to the presence of zirconium in/on the seeds is relatively clear when inspecting If this were to occur however, the contribution to the spectrum from zirconium would be due to scattering back into the detector and not from a direct measurement contribution as  Qualitative X-ray fluorescence spectrometry measurement of the three 125 I brachytherapy seeds used as a source for in vivo XRF bone strontium measurements (12.6 µCi total activity at the time of measurement) made on a portable X-ray analyzer known to be void of zirconium. Measurement made of the seeds after they were allowed to sufficiently decay using a portable X-ray analyzer (see Section 4.3. 3) The spectrum shows the presence of the zirconium as well as several other light elements (not of interest to this work). The higher energy lines are those of the the Rh K-series as well as the 125 I γ-ray, Te, Ag characteristic X-rays and associated Compton peaks. The inlay shows the zirconium K-series (see Table  4.1). measured in Figure 4.2.
The clinical IVXRF system for bone strontium measurements is dependant on measurements made in a 180 ○ backscatter geometry whereby the source is facing the finger used as the measurement site (or the phantom) and the detector is placed behind the seeds as sources. 6,15,16 If we presume that the tungsten collimator holding the seeds is acting such that all photons are attenuated by the backing of the collimator, then, the only zirconium signal that would be observed from the seeds would be coherently and incoherently scattered zirconium X-rays scattered from the soft tissue and bone in the phantom/finger being measured. Photons in this energy region demonstrate the highest probability for coherent scatter. It would then be easy to assume that the spectral contribution of greatest proportion would be coherently scattered zirconium X-rays. From the point of view of the directional scattering probability coherent scattering is highly forward directed. As a result a further investigation was made, using simulations, to assess contributions from source contamination by zirconium in the backscatter geometry.
Monte Carlo simulations were performed on a finger phantom using the geometry described by Zambrulini et al. 22 Here, the simulation was of a finger with a source with varying zirconium K-series contributions to the total source fluence to simulate cases in which the total zirconium contribution to the emission spectrum varies. A typical spectrum is shown in   were sufficiently significant to produce a contribution above the uncertainty of the fitting routine. This may also have an influence on the computation of other parameters, such as the Kα 1,2 /Kβ 1,3 ratio which has been proposed as an analytical measure in human data with mixed success experimentally. 6,23,24 The effect is however suppressed greatly as the the zirconium characteristic X-ray contribution to the total source fluence decreases, which would be apparent through a reduction in the total activity of the source (Figure 4.5). It would thus be required that the contribution from the zirconium backscatter be assessed throughout measurements using a suitable blank phantom. A preliminary measurement of a blank hydroxyapatite phantom made for a 20 minute live time using an SDD detection system and an off-centre source backscatter geometry. The spectrum is poor statistically due to the use of cold seeds but may indicate the presence of the dominant zirconium Compton scattered X-ray (*), although this peak may be due to strontium contamination that is system dependent as seen from the direct measurement of this system (Figure 4.2). Rubidium is also shown as a contaminant of the system.  There is no indication of strontium in the material at levels of less than 0.7 µg/g Ca.
Although the simulation work was performed and showed the possibility of interference from scattered zirconium X-rays when considering an in vivo bone strontium measurement using brachytherapy seeds as sources, the actual total fluence from the zirconium in the source is rather low representing less than 10 % of the total fluence. The actual contribution to the spectrum being small when the total relative fluence is 1 % or less (Figure 4.5) and this type of backscatter may, or may not, be a true concern depending on the activity of the source which will influence the zirconium contribution and can only be evaluated with a blank phantom on a measurement-by-measurement basis, thus necessitating a blank bone phantom.
To assess the possibility of this type of interference in a real measurement, a blank phantom was prepared as per Da Silva et al. 1 which has been found to be void of strontium (concentrations less than 0.7 µg/g Ca) (Figure 4.7). The blank measurement is shown in  the strontium may be from exogenous system contamination as previously shown through the direct measurement (Figure 4.2). There also seems to be a small peak which would correspond in energy to the zirconium Compton for the angle used in the measurement of approximately 180 ○ with the SDD detection system. This Compton peak is very minor and buried in uncertainty, which indicates that the backscatter issue from zirconium is in fact rather minor. This measurement does however indicate, in conjunction with the simulations, that the use of an analytical blank for IVXRF systems is needed in order to investigate experimentally the possibility of spectral interferences, which may be influencing the measurements in humans. Although the problem with zirconium is source dependent, the consistent presence of both strontium and rubidium in the measured spectra throughout this work may indicate the need to move towards a new closed system for IVXRF bone strontium analysis, namely and potentially, commercially available portable X-ray analyzers, the focus of Chapter 8, or the use of other custom X-ray tube-based sources which can be design to counter these issues of spectral interferences.

Conclusions
In Given that this work also demonstrated a consistent source-independent contamination from rubidium, the presence of scattered zirconium X-rays may be responsible for the observed issues with the accounting of rubidium K X-rays within the analytical curve fitting procedure used for in vivo bone strontium measurements 23 due to an inflation of the rubidium Kβ line by Compton scattered zirconium photons. The first true blank measurement using 125 I brachytherapy seeds is presented and showed the possible presence of zirconium Compton peaks in an experimentally measured blank. All measurements showed the presence of strontium and rubidium contamination which indicates room for improvement in the measurements by investigated more closed systems for measurement including those provided through the use of portable X-ray spectrometers (tube-based, custom or portable X-ray analyzers). This is the focus of Chapter 8 which evaluates the suitability of portable X-ray spectrometers for IVXRF bone strontium measurements. This work is however limited to the fact that measurements were not made on the clinical system presently used for the bone strontium IVXRF measurements, which presents a different resolution in comparison to the SDD detection system as well as source-phantom geometry. The blank measurement being made on relatively cold seeds, also necessitates a more thorough and statistically valid assessment of measured blank spectra prior to any firm conclusions being made as to the real effect this type of interference may have on human measurements and other analytical measures, namely, the strontium Kα 1,2 /Kβ 1,3 ratio which has been proposed as a means of assessing strontium homogeneity in humans. 6,23,24 The observations made in this work were also step-wise, requiring decay of the source and thus low count rates when producing

Acknowledgements
The

Abstract
In vivo X-ray fluorescence (XRF)-based methods of bone metal quantification ignore the possibility of secondary excitation in their calibration protocols. Ignoring the possibility of secondary excitation of certain analytes is not generally detrimental as the analytes are present in matrices in which the analyte is either of the highest atomic number within the mixture and/or they are often present in trace quantities, furthermore the difference in energy between emitted characteristic X-rays and the K-or L-edges of other elements is typically large. In all of these case, the system is not conducive to secondary excitation by definition. One exception to this would be the case of quantifying bone lead in the presence of a high concentration of strontium when the lead L-series is to be used as the analytical signal. Strontium is not a trace, but rather a minor element, and has been well established to bias dual energy-X-ray absorptiometry (DXA) measurements given its concentration in bone reaching the mole-percentage level relative to calcium. [1][2][3][4][5] This bias being introduced due to strontium's ability to increase the mass attenuation coefficient of the bone, reported at even fractional mole percentages of strontium in the case of DXA studies. Given the fact that it has been observed for DXA measurements that relevant bone strontium concentrations can alter the mass attenuation coefficient of bone, and the fact that the strontium K-series is just above the L 3 edge for lead, secondary excitation is at least theoretically possible. If secondary excitation does occur this would require a priori knowledge of bone strontium content in order to quantify lead via its L-series. In this work, we employed Monte Carlo simulations to evaluate the possibility of secondary excitation of lead in bone matrices with high bone strontium concentration-within the 0-10 % mol/mol range [Sr/(Sr + Ca)], using a 125 I source excited system currently used for in vivo bone strontium measurements. No evidence of secondary excitation was observed which indicates that lead can be freely quantified using its L-series without a priori knowledge of bone strontium concentrations. Unlike the case of DXA, it was found that the mass attenuation coefficient of bone changes by less than 5 % within the strontium concentration range observed in humans. Coupled with the low concentration of lead to be expected in humans (much less than 1000 ppm, selected in this study as a higher upper theoretical limit), secondary excitation becomes negligible and can be ignored in the case of in vivo bone lead determinations using the lead L-series.

X-ray fluorescence spectrometry (XRF)-based analyses by definition considers various forms
of fluorescence which can occur within a specimen when irradiated with a source and which may result in the emission of analyte characteristic X-rays. [6][7][8] Fluorescence caused solely by the interaction of the primary beam, being known as primary fluorescence, is the major source of characteristic X-ray emission in specimens. 6 In cases in which various elements are present within a matrix in sufficiently large concentrations, which is often the case for most matrices, characteristic X-rays emitted by one element may be of sufficiently high fluence and of sufficient energy to cause excitation of another element on its passage out of the specimen. This is known higher order, or more specifically, secondary excitation/fluorescence, that is, when a photon being emitted from an element within the specimen causes fluorescence of another, thus, fluorescence being created due to interactions not created by the primary beam fluence alone. 6 In cases in which secondary excitations are probable, it is then necessary to quantify not only the analyte, but all elements which may result in secondary fluorescence-, which is the basis of the so-called Sherman equations. 7,8 In order for secondary excitation to be probable, the product of the excitation probabilities, which are a function of concentration as well as proximity of the photon's energy to a K-or L-edge energy, must be substantial; therefore, both the exciting element and analyte need to be present a sufficiently high concentrations, and, the energy of the photon causing secondary fluorescence must be sufficiently close in energy to that of the K-or L-edge of the element begin fluoresced. The term "high concentrations" defined here as being a concentration of an element sufficiently large as to have a substantial influence on the total mass attenuation coefficient of the specimen. [6][7][8] In the context of an in vivo XRF (IVXRF) bone metal quantification, secondary excitation has been ignored in the calibration protocols. Ignoring this effect is quite reasonable as the analytes of interest are often at low concentrations in bone (that is, their concentration and changes thereof do not affect the total mass attenuation coefficient of the specimen) and there are no other elements present in the bone sample which would fulfill the condition of secondary excitation, largely due to the fact that the emitted characteristic X-ray energy is far from either the K-or L-edge of the analyte of interest. This is the case for bone lead, strontium and uranium analysis which all use the K-series of the analyte for quantitative purposes. [9][10][11][12][13][14][15][16][17][18][19] In the case of bone strontium, the element cannot be considered a trace element. In fact, dual energy X-ray absorptiometry (DXA) measurements are well established to be biased by bone strontium concentrations, whereby, bone strontium content results in an overestimation of the DXA determined areal bone mineral density. [1][2][3][4][5] This overestimation being due to strontium's influence on the mass attenuation coefficient of bone and being apparent at concentrations of even a fraction of a mole percentage of strontium being present in bone. 1,2 DXA is a transmission-based method of analysis, and uses higher energy X-rays than does XRF; however, this effect would indicate that even small quantities of strontium in bone can produce a sufficiently significant change in the bone's mass attenuation coefficient as to Given the fact that strontium seems to be able to substantially change the total mass attenuation coefficient sufficiently such that DXA measurements are influenced through a measured bias, 1-5 it would follow that at these clinically relevant levels of bone strontium the secondary excitation may be probable for certain analytes. This would be the case in the context of a bone lead measurement when the L-series is employed as the analytical signal which has gained recent and further interest given advancements in the development of field portable X-ray analyzers 20-23 after some preliminary work in the area. [24][25][26][27][28] This work thus evaluates possible secondary excitation in the context of a bone lead measurement, when the L-series is used as the analytical signal, in the presence of high strontium levels.
If present, this would indicate that both strontium and lead would need to be quantified simultaneously, in order to accurately obtained bone lead determinations in the presence of high bone strontium concentrations.

Monte Carlo Simulations
Monte Carlo simulations were performed using the EGS5 system using code as per Zamburlini et al. 29 Although portable X-ray analyzers are most often used for in vivo XRF measurements of bone lead when employing the L-series as the analytical measure, 20-23 simulations were performed in this work using the validated code used for simulations that mimic a 125 Iinduced bone strontium measurement (schematic in Figure 1.1). 13,[29][30][31] This difference was not deemed as of concern as the source spectrum from an 125 I brachytherapy seed has a fluence that is most produced from the silver in the seeds, thus, mimicking the major line used for excitation in tube-based systems. [20][21][22][23] The source was simulated as to emit 10 12 incidence particles found to produce sufficient uncertainty in the simulated net peak areas of interest (less than 5 %), each particle being sampled from a source spectrum that of a 125 I brachytherapy source as described elsewhere. This source spectrum accounted for the emission spectrum of the 125 I as well as emitted silver and tellurium X-rays due to 125 I decay and excitation of the silver beads. 13 To simulate a human finger bone (the phalanges) adequately, the simulations were performed a bare bone finger phantom modelled as a 9 mm cylinder of cortical bone tissue. 29 A bare bone phantom was selected as to avoid any confounding of the results from overlaying soft tissue attenuation. The sample-to-detector window distance was maintained at 5 mm for all simulations in this work. The detector arrangement was simulated as to mimic a Si(Li) detection system, with a tungsten collimator housing the 125 I brachytherapy source which allows for a 180 ○ backscatter geometry to the detector relative to the sample. 29 A schematic of the simulation geometry is shown in Figure   1

Results and Discussion
Higher order fluorescence is a concern in XRF-based analyses, as if probable and present, the determined intensity of an analyte's characteristic X-ray is not only a function of the pri-mary beam fluence, but also a function of the concentration of other, higher atomic number elements within the sample being measured. [6][7][8] Quantification in this case becomes complicated and requires various iterative approaches to calibration/quantification which stem from the so-called Sherman Equations. 6 Aside from the introduction of higher order fluorescence into the calibration procedure and quantification methodology, if the condition of higher order fluorescence is met such that concentrations of various elements are sufficiently high as to change the mass attenuation coefficient as a function of concentration, then calibration against linear standard curves, which is customary in the context of in vivo bone metal analyses, [9][10][11][12][13][14][15][16][17] is not possible.
Expressions for the secondary excitation term under various conditions have been well developed. [6][7][8] In general, the effect can only occur if the product of the excitation probabilities between both elements is significant which is generally apparent only if the fluorescing element produces characteristic X-rays which are close in energy to either the K-or L-edge of the analyte of interest. [6][7][8] Given that the excitation probability term is highly dependant on the product of both elements' weight fractions (which translates to the bulk number density of both elements), it would follow that secondary excitation can only occur if the weight fraction of each element is sufficiently large as to make a marked change in the total mass attenuation coefficient of the specimen. In the case of in vivo bone metal analyses, secondary excitation has largely been ignored as a possible factor in the calibration protocol as this condition is often not met.
One possible case in which secondary excitation may occur when considering methods of in vivo bone metal analysis, is in the case of a bone lead measurement when the lead L-series is to be used as the analytical signal and when the bone strontium content is sufficiently high. Strontium emits its most intensity K-lines at 14.1 keV (Kα 1,2 ) and 15.8 keV (Kβ 1,3 ). 33 The L 3 edge of lead is at 13.0 keV. 33 As such, the strontium K-series are able to cause photoelectric emission at the L 3 level of lead. Given that the most prominent lines in a bone lead spectrum are the Lα 1,2 (L 3 M 5 and L 3 M 4 transitions, respectively) 33   a concentration which is expected to be higher than that expected in humans in modern days. 34 The absence of any change in characteristic line intensities for these lead lines, which are the analytically relevant lines, indicates the absence of any enhancement as well as no real influence with changes in the mass attenuation coefficient of the specimen. Even in cases in which the bone lead concentration is orders higher than what would be expected in a human subject, 34 selected here as a hypothetical extrema to observe any possible effect given the enhancement effect's dependence on concentration, there was no observable effect as seen through the simulation. This is attributed to the fact that even at concentration of lead and strontium which far exceed the clinically relevant concentrations, no enhancement needs to be considered. This also indicates that calibration protocols may be produced without the need to account for total mass attenuation coefficient changes in the specimen at these high strontium concentrations. This observation thus indicates that calibration protocols can proceed for lead analysis in bone using the L-series without the need to account for strontium concentrations and that traditional approaches to calibration may be sufficiently suitable. [9][10][11][12][13][14][15][16][17][20][21][22][23] The lack of enhancement of the lead Lα 1,2 and Lβ 1,3 lines can be attributed largely to the fact that even when the strontium concentration increases, the concentration of lead remains sufficiently low as to negate the probability of secondary excitation. Even if the probability of secondary excitation is high due to the proximity of the strontium X-rays to the L 3 edge of lead, the concentration of lead remains so negligible that the probability of secondary excitation vanishes. This was observed even when selecting a concentration range for strontium which is expected to far exceed the concentration in human populations as well as selecting a concentration of bone lead that is orders higher in concentration than that expected in exposed populations. The mass attenuation coefficient changes for bone in the energy region relevant to XRF were found to be minimal, being less than 5 % over an energy range relevant to XRF analysis ( Figure 5.3), and for this reason, demonstrates little effect due to attenuation for either the elemental lines with varying strontium concentration. The total mass attenuation coefficient changed more substantially only for photon energies surpassing the K-edge of strontium.
Although in the context of DXA measurements, even small fractional percent changes have been shown to change the mass attenuation coefficient sufficiently as to show a marked difference in determined bone mineral densities, 1-5 in the case of an in vivo bone lead determination, these changes are negligible and allow for quantification without the need to resort to iterative methods. The differences in the mass attenuation coefficient which would become relevant to DXA measurements are only seen to occur at energies which are greater than the K-edge of strontium and this may be the reason why DXA, a transmission-based method, becomes more sensitivity to strontium content in bone.

Conclusions
In this work we assessed the possibility of secondary excitation of lead, as would be apparent in the L-series, in the case in which bone strontium concentrations are sufficiently high in the matrix being measured. This theoretical study being carried out given the known effect strontium concentration, even at fraction mole percentage levels, has on DXA-determined bone mineral densities. It was found that in cases whereby strontium concentrations reach as high in concentration as 10 %mol/mol [Sr/(Sr+Ca)], which corresponds to approximately 5 % w/w, that secondary excitation of lead is not of concern in the context of a bone lead measurement via the lead L-series. This study thus demonstrates that although high bone strontium concentrations seem to have an effect on the mass attenuation coefficient in the context of a DXA measurement, [1][2][3][4][5] in the context of an in vivo L-XRF bone lead determination, lead can be determined irrespective of any a priori knowledge of bone strontium concentration. to the amount of calcium in the specimen, which is, the most useful quantity in a clinical sense. Determining concentrations on a per-mass-of-material basis, that is, a concentration not normalized to the calcium content of the phantom/bone, results in large biases in estimated bone strontium content. The use of an HAp phantom material was found to remove the need for a CCF but it was also found that variations in the degree to which the phantom material truly converts to HAp has little influence on the differential coherent cross-section and thereby the calibration protocol.

Introduction
The calibration of in vivo X-ray fluorescence systems (IVXRF) of bone metal quantification are heavily dependant on a coherent normalization procedure as central to the calibration protocol. [1][2][3][4][5][6][7][8][9] The coherent normalization procedure being developed by Somervaille et al. 1 in the context of a bone lead analysis using a 109 Cd source and later extrapolated to other IVXRF systems of bone metal quantification. The coherent normalization procedure developed by Somervaille and colleagues 1 was found to correct for various measurement-based factors, including variations in source activity, source-to-detector distance, soft tissue thickness/signal attenuation, variations in bone shape, size and orientation, the subjects bone mineral concentration, and minor subject movement during the measurement. 1,12,13 The total procedure thus allowed the analyst to determine the concentration of lead in the bone sample being measured in vivo from a single measurement, making this a great advancement in the context of in vivo bone metal analysis.
It is not thus surprising that this method of calibration has extended to most other methods of bone metal quantification including those for bone uranium quantification, 2,3 bone strontium quantification, 4-8 bone lead quantification via L-IVXRF 14-17 and 57 Co-induced K-IVXRF bone lead quantification. 9 Coherent normalization is based on the premise that calcium is the major coherent scatterer in bone mineral, and thus, a surrogate for bone mineral can be used for calibration. For this reason, plaster of Paris (poP, calcium sulphate) was selected as the calibration/phantom material given its availability. 1,[4][5][6][7][8][16][17][18][19] Several factors do however have to be met for coherent normalization to be applicable. The cadmium-109 source emits a γ-ray which is Although bare bone measurements are by their very nature not possible in the context of an in vivo bone strontium quantification, and, counter to their purpose, they are presented here as to evaluate the suitability of the hydroxyapatite phantom material, 21 as signal from bare bone is in fact the desired corrected signal for the quantification.

Methods
Monte Carlo simulations were performed to assess the HAp phantom material as a suitable calibrator for the purpose of calibrating the 125 I-induced IVXRF system of bone strontium quantification used for the purpose of measuring human populations as described elsewhere. 6,23-25 Monte Carlo simulations were performed using the EGS5 (Electron Gamma Shower) system using bench-marked code for the 125 I-induced IVXRF system of bone strontium quantification. 23 The simulations were performed on bare phantoms without the addition of any overlaying soft tissue composed of various compositions including that of cortical bone, 26 plaster of Paris (poP) and hydroxyapatite (HAp) ( Table 6.1). Cortical bone was selected as the material type as it is presumed that on average the cortical layer can be considered infinitely thick for these in vivo measurements. In order to assess compositional influence only, all phantoms were simulated to be of a diameter of 9 mm as to mimic the second phalanges of the finger: the measurement site for an in vivo bone strontium measurement and the system geometry is described elsewhere. 23 An assumption is made as to the substension of the primary beam in all cases with relation to any IVXRF quantification methodology. In the context of this study it was assumed that the beam completely subtended around the bone, thus all photons interacted with the phantom/bone material. This is assumed to be an ideal case and was selected as a means of investigating material dependence only. No further assessment as a function of bone size was evaluated as such effects have already been established by Zamburlini et al. 23 Simulations were performed using the following parameters: 10 12 incident particles; in-  The effect of various matrix compositions on the quantification was evaluated by producing calibration curves with varying strontium concentrations at the expense of a calcium substitution. Standard curves being prepared against the concentration of strontium and either the Kα 1,2 alone, or, the Kα 1,2 peak normalized to the intensity of the coherently scattered 125 I γ-ray at 35.5 keV. 7 From these calibration curves, recovery analyses were produced as to assess the analytical bias of the measurements when different phantom materials are used for quantification. Recovery was determined by using the intensities from cortical bone phantoms with known strontium concentrations and those determined when quantification was performed against either poP or HAp. In all cases, calibration was presumed to follow a linear model as is customary for the calibration of IVXRF bone strontium systems. [4][5][6][7][8] For this reason, the concentrations of strontium in bone were maintained to a maximum concentration of 1000 µg/g phantom material as a means of ensuring that no effects on the linearity would be observed.
Differential coherent cross-sections were computed using a custom computer program written for this purpose in GNU Octave. Elemental form factor data was taken from Hubbell and Øverbø 27 and extrapolations made on this data in order to compute the differential coherently scattered cross-section. The computation of the differential coherent cross-section for mixtures was performed by determining the differential coherent cross-section at an elemental level and performing weighting by each element's weight fraction within the mixture.
For the purpose of this study, differential coherent cross-sections were computed for various hydroxyapatite mixtures with varying degrees of reaction completeness (conversion ratios).
Differential coherent cross-sections where thus calculated for mixtures of hydroxyapatite, brushite and calcium hydroxide.

Results and Discussion
In practice it is not possible to prepare a phantom for IVXRF purposes which matches the human bone matrix exactly for all factors including composition as well as geometry. This was a concern which was presented by Ahlgren et al. 10  can be resolved when employing a coherent normalization procedure and using a surrogate for bone mineral such a poP; however a matrix correction is still required. When poP is used as a calibration/phantom material, the sulphur presents a coherent scattering profile which is different than that of phosphorous which is found in the bone matrix. As a result, a coherent conversion factor (CCF) needs to be applied, which is simply defined as the ratio of the differential coherent cross-sections between poP and bone mineral (presumed to be HAp). 1,13 Application of the CCF to poP-based calibration curves adjusts the determined poP calibration factor/sensitivity to a calibration factor/sensitivity, which is usable against hydroxyapatite/bone mineral-based signal.
Bone mass density is known to be variable depending on various factors such as sex, age and health status. The effect of variations in subject bone mass density was evaluated at the level of both the strontium characteristic X-rays and the normalizing signal-the 125 I coherently scattered photon. In the case of bone mass density (ρ b ) variations which can occur in human subjects, 26 a marginal influence was observed for the K lines for strontium  Table 6.2).
For an arbitrary infinitely thick specimen, which one would presume to be the case of the cylindrical bone phantom simulated in this study, one would expect the characteristic X-ray intensities to be independent of sample mass density (or in the case of this study ρ b ). This is 132 bone density (g/cc)  Table  6.2). only the case when the primary beam is treated as a pencil beam, which is well established and is one of the attractive features when employing XRF for quantitative analysis as it simplified both calibration and quantification greatly. [28][29][30] Therefore the fluorescent X-ray intensity becomes a direct function of only the total mass attenuation coefficient of the sample matrix and is density independent. 30 The decrease in characteristic X-ray intensity as a function of sample mass density (ρ b ) which was observed in this simulation study is thus contrary to the expected trend for infinitely thick specimens. The relatively minor decrease in the analytical signal was only observed for the Kα 1 line which is the less energetic of the characteristic X-rays. This decrease in analytical signal is likely attributed to the signal emanating and being self attenuated at the edges of the cylindrical phantom/bone in which the beam substends which would not be considered necessarily infinitely thick for this X-ray energy.
The coherently scattered photon from the 125 I source does however show a strong dependence in its intensity with relation to bone mass density (Figure 6.2). This can be attributed simply to the increase in the total number density of potential scattering targets for the same probed volume and thus simply a larger number of scatterers. The total coherently scattered photon intensity thus follows a trend which may result in an issue with regards to strontium quantification via coherent normalization, given that the fluorescence X-ray intensity is independent of density while the coherently scattered photon intensity is dependant on density. Quantification for strontium using the Kα 1,2 X-ray relative to the coherently scattered X-ray, thus results in strong biases, given that no normalization has been made for the number of scatterers for which the coherently scattered photon intensity depends A larger bias is observed in the case of using the Kα 1,2 /coh ratio as the analytical measure due to introduction of the density dependence of the coherent scattered photon. The close match in results when using the Kα 1,2 alone is due to the match in geometry between sample and phantoms and a match in the total mass attenuation coefficients of the sample and phantoms/calibrators. coherent normalization. 1 The dependence on density alone thus becomes a potential factor in the quantitative power of the coherent normalization procedure, even when the calibration material is perfectly matched to the sample matrix as is the case for Figures 6.1 -6.3 and Table 6.2.
In the case of any sample of a given composition, the fluorescence intensity becomes a function of the total mass attenuation coefficient as previously described. [28][29][30]  This simulation study thus indicates that quantification relative to the total mass of bone is not possible using either direct characteristic X-ray intensities or the Kα 1,2 -to-coherent ratio, and this observation is independent of which calibration/phantom material is used.
The total mass attenuation coefficient and the density of the calibrators/phantoms must be matched to that of the patients bone in order for quantification to be achievable. In      0% Conversion 100% Conversion Figure 6.10: Differential coherent cross-sections for an HAp phantom with either a 0 % of 100 % conversion ratio to the reaction. A 100 % conversion ration corresponds to pure HAp, while a conversion ratio of 0 % corresponds to a mixture of brushite and calcium hydroxide in a proportion as to produce a Ca/P mole ratio of 1.67.
In the case of the HAp phantom materials designed for the purpose of calibration IVXRF bone strontium and lead system 21,22 , one aspect that has not been evaluated thoroughly has been the possibility that the conversion ratio for the reaction does not tend to unity, the conversion ratio being defined as the percentage of material actually produced by the pseudo-solid state reaction. That is, that the starting materials do not fully convert to HAp. Figure 6.10 shows the computed differential coherent cross-sections for the two extrema of this scenario: when the conversion ratio is 100 %, that is the phantom material is pure HAp, and when the conversion ratio is 0 %, that is that the phantom is composed of a mixture of brushite and calcium hydroxide as to make a Ca/P mole ratio of 1.67. As can be seen, the influence in the differential cross-section is minor, amounting to 20 % difference between the extreme cases of complete and fully incomplete reactions, at the 180 ○ backscatter mark The ratio of the cortical bone cross-section to that of soft tissue at 180 ○ is 6.2.
( Figure 6.10). This would indicate that the removal of the CCF is achievable when applying an HAp phantom material, in that uncertainty is removed from the protocol by removing any uncertainty on a compositional basis, but this also indicates that even if the HAp phantom is not completely pure HAp, that there will be little effect on the calibration protocol and the accuracy of any determined concentrations.
This work is however limited by two factors. Only the 35.5 keV 125 I coherently scattered γ-ray was evaluated for the purpose of normalization although various coherently scattered photons exist which are produced by interactions of the silver and tellurium X-rays emitted by the source with the sample being measured. The 35.5 keV 125 I coherently scattered γ-ray has been previously selected as the optimal photon for the purpose of coherent normalization. 6,23 This photon was selected as it is the highest energy photon within the spectrum and is an isolated peak. As a result, the degree of influence that soft tissue attenuation would have on this photon is minimized in comparison to other coherently scattered X-rays from the emission spectrum as degree of attenuation is inversely proportional to the energy of the photon. Selection of the 35.5 keV 125 I coherently scattered γ-ray as the normalizing photon thus reduces any effects due to photon attenuation by the overlaying soft tissue, if only by a small fraction. The isolation of this peak also allows for a better ability to extract net intensities as there is no complication from overlapping Compton peaks in comparison to the location of the silver and tellurium coherent scattered X-rays which fall on top of Compton continua. This thereby results in a reduction in the total uncertainty brought into the measurement during the data reduction phase of the quantitative analysis.
This study was further limited as the influence of soft tissue was not evaluated on the coherent normalization procedure. This was the intention of this work as the effect of phantom material and a perfectly corrected signal was the intention of the evaluation. In reality, there is a coherent contribution from soft tissue to the total net intensity of the 35.5 keV 125 I coherently scattered γ-ray observed of human measurements which cannot be necessarily ignored. In a real human measurement then, the 35.5 keV 125 I coherently scattered γ-ray intensity will have contributions from both the bone and the overlaying soft tissue. At 180 ○ the ratio of the differential coherent cross-sections between cortical bone and soft tissue is approximately 6 ( Figure 6.11). That is, that the probability of scattering from the bone rather than the soft tissue is approximately one order of magnitude higher (Figure 6.11).
This would thus inherently necessitate that in order to perform a quantification, the soft tissue thickness would need to be known, as this would influence the total number of coherent scattered photons, and a further normalization would have to occur in which the contribution of the soft tissue scattering to the net 35.5 keV 125 I coherently scattered γ-ray intensity is accounted for. This work thus shows that if this procedure is introduced, which requires further development, then, the application of HAp phantoms allows for a direct quantitative measure of bone strontium through the application of the coherent normalization procedure.

Conclusions
This study employed Monte Carlo simulation as a means of investigating the effect of using a HAp phantom material 21 within the calibration protocol of the IVXRF system of bone strontium quantification. Simulations were performed on bare phantoms and the emanating signal used for the assessment would be equivalent to an IVXRF determination in which overlaying soft tissue attenuation has been accounted for. It was found that bone density does have a minor influence on the intensity of the of the Kα line and a major influence on the coherently scattered 125 I γ-ray at 35.5 keV. Calibration against either poP, HAp or an cortical bone phantom resulted in major sensitivity differences and biases in the quantification which resulted from variations in the total mass attenuation coefficients between materials.
Quantification against the mass of strontium to the total mass of bone was found not to be possible without knowledge of the bone density and bone mass attenuation coefficient which is not possibly known in a clinical environment for each patient. Coherent normalization was found to be successful in the case in which the strontium concentration was normalized to the mass of calcium in the sample and thereby the mass of bone mineral. In this case, calibration against this normalized concentration allows one to directly determine the concentration of strontium relative to calcium content in patients without the need to have a measure of the patients bone mineral content/density. Both HAp and bone phantoms produced standard curves which agreed well, while poP did not, resulting in excellent agreement of quantified results with minimal bias. This is attributed to the difference in differential cross-sections between the materials. This also indicates that it may be likely that the type of calcium phosphate used for calibration purposes is irrelevant and thus the removal of the CCF from the calibration protocol by the introduction of an HAp phantom material allows for the removal of a large area of uncertainty in the protocol. This study demonstrates that if a suitable soft tissue correction procedure is employed, that quantification is possible without the need of added matrix correction terms if an HAp calibrator is used. Further work however, must assess the coherent normalization procedure when overlaying soft tissue is present as a means of delineating the contributions from soft tissue and bare bone must be established for the normalization procedure to be useful.

Abstract
In vivo bone strontium measurements require that the characteristic X-ray intensity from strontium be corrected for attenuation due to the overlaying soft tissue at the measurement site. This allows for the extrapolation back to a bare bone signal intensity which can be used

Introduction
In vivo X-ray fluorescence (IVXRF) measurements of bone strontium (and by extension lead, when considering the L-series as the analytical measure) requires that the measured intensity from the characteristic X-ray of interest (e.g. the strontium Kα 1,2 line), acquired from a human subject, undergo a series of corrections. The calibration protocol of this system being based on the measurement of bare phantoms. [1][2][3][4][5][6][7] For the calibration factors determined from phantom measurements to be useful, the analytical measure of interest is the intensity of characteristic X-rays as if they were emanating from a bare bone. Given the energy of these X-rays, for the case of strontium, 14.1 keV for the Kα 1,2 and 15.8 keV for the Kβ 1,3 , 8 one of the more important required corrections is that for attenuation of the characteristic X-rays is the overlaying soft tissue around the bone being measured. 5 Calibration is performed against a series of bare phantoms in order to determine the system's sensitivity factor, and thus, the measured intensities must undergo a correction to a bare bone, unattenuated intensity; the unattenuated intensity, thus being equivalent to the expected intensity if the measurement was made on bare bone. 1,6,7 The calibration function in this case is however developed against the intensity of the Kα 1,2 line normalized to the intensity of the 125 I source γ-ray (35.5 keV), which also requires an attenuation correction. 4,6,7 In the practical sense then, for a human measurement, the measured coherently scattered peak must also be corrected for soft tissue attenuation given the energy of this photon. Proper calibration and quantification in the context of an IVXRF bone strontium measurement requires that the overlaying soft tissue thickness be known in order to make the an attenuation correction using Lambert's law.
Soft tissue thickness estimates for the purpose of this correction are currently made using medical imaging procedures in order to estimate soft tissue thickness. 5-7 Several imaging modalilties have been evaluated for this purpose, 5 with ultrasound imaging currently the modality employed for soft tissue thickness estimates in human subjects 6,7 due mostly to its simplicity and no need for any additional ionizing radiation exposures. Although imaging- Paris and lucite phantom measurements). As such, the intensity of the Compton scattered radiation for any given collected human measurement can be used to extrapolate an estimate of soft tissue thickness from a suitably prepared calibration function produced using suitably prepared phantoms. This procedure of estimating soft tissue thickness has been further applied to phantom and human measurements. 10,11 Undoubtedly, this proposal offers the potential for introducing a simple and elegant method of soft tissue thickness estimation and thus soft tissue attenuation correction which could be extrapolated to the IVXRF system of bone strontium quantification.
Nie et al.'s 9 approach was however made in the context of a portable X-ray analyzer-based analysis of bone lead using a silver target X-ray tube. IVXRF bone strontium measurements are made using an 125 I source in the form of brachytherapy seeds, which offers an array of Compton scattered photons due to the emission of the 125 I, the silver beads that act as the support for the 125 I (thus emitting the silver K-series) and the tellurium X-rays (the daughter product of 125 I β − decay). For this reason, it is possible that this Compton-based method of t st estimation could be extended to the IVXRF bone strontium measurement system as the energy of the strontium K-series is similar to that of the lead L-series and the silver Kα 1,2 line emitted from the brachytherapy seeds offers a identical photon to that produced by a silver target X-ray tube for scattering.
This work thus evaluates, via Monte Carlo simulation, the potential of employing Comptonbased soft tissue thickness estimations in the context of 125 I-induced IVXRF measurement made in the conventional 180 ○ geometry. This work focuses on this evaluation using the most prominent peak in the measured spectrum, the silver Kα 1,2 Compton scattered peak, 3 which is identical to that proposed by Nie et al. 9 for this purpose.

Methods
Monte Carlo simulations were carried out using the EGS5 (Electron Gamma Shower) system using code developed as to simulate the the IVXRF bone strontium system with measurements made in a 180 ○ backscatter. 3,6,7,12 To assess the Compton intensities as a function of soft tissue thickness simulations were made for cylindrical bone phantoms of various sizes ranging from a diameter of 0.5 cm to 1.5 cm which was considered to encompass cases of extrema; a diameter of 9 mm being a nominal diameter for the human phalanges. 12 The inner bone core of the bone phantom used for simulations was composed of either bone or a phantom material (Table 7.1). The bone phantom materials evaluated were either plaster of Paris (poP), currently used for the purpose of calibrating IVXRF systems of bone strontium quantification, [1][2][3][4][5][6][7] or HAp as has been proposed as an alternative. 13,14 Chemical and physical parameters for each of the materials used in the simulations are found in Table 7.1.
To evaluate the influence of soft tissue thickness variations, soft tissue thicknesses were varied from 0 to 10 mm, which was also expected to encompass extreme as nominal soft tissue thickness at the finger can be expected to be on the order of 5 mm. 12 Calibration of any system for soft tissue thickness estimations requires that the a series of external calibrations/phantoms be used. 9 The effect of soft tissue surrogate material on the ability to perform soft tissue thickness estimations based on calibration data was performed by simulating phantoms using either soft tissue International Commission on Radiological Units (ICRU) 15 as the tissue layer, or, lucite, as proposed by Nie et al. 9 Physical and chemical parameters used for each soft tissue material within the simulations are shown in Table   7.1. For each soft tissue thickness and bone diameter combination, the samples-to-detector window distance was maintained at 5 mm. A schematic of the simulation geometry can be found in Figure 1.1 and is intended to simulate a human measurement using the 125 I-induced in vivo bone strontium system.
Simulations consisted of 10 12 incident particles with a previously defined emission spectrum used for the 125 I brachytherapy seed source. 3 The surface-to-detector window distance was maintained at 5 mm throughout all simulations. The backscatter geometrical arrange-

Results and Discussion
The proposed method of estimating overlaying soft tissue thickness using Compton scattered radiation requires the preparation of a calibration function based on phantoms composed of an inner-core of a bone surrogate material and an outer core of a soft tissue surrogate material. According to Nie et al.'s 9-11 original preparation this is prepared using plaster of Paris, of one given size, which are subsequently enveloped in various thicknesses of lucite which was proposed as the surrogate material for soft tissue. poP was likely selected as the inner core bone surrogate material given its extensive use as a phantom material in the context of most IVXRF bone metal quantification systems. [1][2][3][4][5]9,[18][19][20][21] From measurements of these phantoms, with variation in the soft tissue thickness only, a non-linear relationship can be expected 9 and a calibration function constructed between the soft tissue thickness and the intensity of the Compton scattered photons. From this calibration function, it is proposed that the soft tissue thickness from a human measurement can be extrapolated.
Compton scattering intensity in the context of an IVXRF bone strontium measurement is a function of various parameters, one, being the geometry of the sample, which is made apparent given the differential incoherent scattering cross-section that is scattering angle dependent. Considering even the simple case simulated here of concentric cylindrical fingers with only two material phases, if the bone diameter changes, then, for the broad-beam source which is produced from a collimated collection of 125 I brachytherapy seeds, the effective scattering angle also changes given the change in the overall curvature of the bone sample.
For very large bone diameters, the source photons may be effectively observing a flat surface.
This would also be the case if a portable X-ray analyzer is equipped with a highly focused primary beam, whereas for small bone diameters, the curvature relative to the primary beam becomes more apparent. In this regard, the actual angular values sampled through the differential incoherent cross-section would vary greatly, depending on bone geometry, and the Compton intensity would be expected to change as a function of bone size. Preparation of a calibration function based solely on soft tissue thickness variations without considerations for variations in bone diameter will thus likely bias the calibration function, or, limit its use greatly. Nie et al. 9 , who employed a silver target portable X-ray analyzer for measurements, the analyzer may have been equipped with a highly focused beam, and thus, does not represent the case of a broad beam geometry in which bone geometry may influence greatly the Compton intensity. With a focused beam, the samples surface would seem virtually flat regardless of size and shape. In the case of broad beam excitation as with the IVXRF system of bone strontium, or, the portable XRF systems evaluated by our group for bone strontium measurements (see Chapter 8), Compton-based normalization is hindered simply by the fact that bone and phantom geometries are not static and are not known and controllable factors.
Variations in bone size or discrepancies between phantom and sample geometry will thus not allow for reliable Compton based soft tissue thickness estimations.
If we consider the hypothetical case that geometries can be perfectly matched, which cannot be done in practice, other than by the method of taking orthoplanar X-rays of the finger, 22 then, the other factor which may hinder the ability to perform a soft tissue thickness estimation based on Compton scattered radiation comes from the differences in materials used between the phantoms and the bone being measured. In the case of producing a calibration function for soft tissue thickness estimation using phantoms with a poP core, what is ignored is the material dependence of Compton scattering which is apparent through the incoherent cross-sections' dependence on total electron density and through the incoherent scattering function. Given that is inevitable that some Compton contribution will be coming from the bone itself, this variation may produce calibration functions which are also dependent on the composition of the human bone. Calibration against poP or HAp phantoms may then produce calibration functions that are not transferable to human bone measurements given this material dependence.  be used for this purpose instead of lucite, then combined with a HAp phantom material as core, 13,14 a soft tissue thickness estimation may be determined using Compton intensities as long as the bone size can be ascertained, which may be possible using a coherent normalization procedure. 12 The consistency in the biases also does seem to suggest that the similar to the coherent conversion factor (CCF) that is required in order to traditionally correct for the differences in scattering properties between poP phantoms and human bone, it may be necessary to make a similar correction factor to account for incoherent scattering differences between the soft tissue equivalent material and the overlaying soft tissue. Development of such a material is however a focus of future work as the actual composition of soft tissue in humans, and whether more global incoherent scattering correction need to be made, needs to be assessed.

Conclusions
Monte Carlo simulations were employed to evaluate the feasibility of employing the intensities of Compton scattered source radiation for the estimation of soft tissue thickness in order to provide a means of performing soft tissue attenuation corrections for 125

Acknowledgement
There has been a growing interest in the application of portable X-ray analyzers (pXAs) for in vivo bone metals analysis, namely, that of bone lead and bone strontium. Such

Introduction
The in vivo X-ray fluorescence (XRF)-based measurement of bone strontium and lead has traditionally been performed using radioisotope-induced ( 125 I and 109 Cd, respectively) K-XRF using either a liquid nitrogen cooled Si(Li) or HPGE detection system, respectively. [1][2][3] Although in vivo measurements have been made with such systems, 4-6 their cost, size and the need for liquid nitrogen as a coolant for the detector can limit their portability, and thereby, their use under certain circumstances. This becomes of particular importance when large scale epidemiological studies are desired (i.e. for bone lead as a biomarker for cumulative exposure), 7,8 or, in the case of a bone strontium measurement, if clinical use is desired and portability becomes a convenient feature (i.e. to monitor patients undergoing strontium therapy for osteoporosis). 5,6 In response to the need for a smaller and more portable means of performing in vivo XRF of bone lead, portable X-ray analysers (pXA) have been evaluated for this purpose. 9,10 Similar to initial attempts by others, such a method requires the use of the L-series of lead as the analytical measure and the use of X-ray tube sources. [11][12][13][14] Modern pXAs generally consist of a miniaturized X-ray tube as a source, in contrast to the radioisotope induced systems, and a miniaturized Peltier cooled solid state detector (e.g. an SiPiN or SDD). This allows for great flexibility with regards to their use as they are battery (or outlet power) operated and do not require any coolant at the level of either the detector or X-ray tube. Such systems are however designed for the measurement of inanimate objects.
One limitation to such systems, in the context of a human measurement, then becomes one of radiation dosimetry as the X-ray tube may provide either a highly focused or broad source beam, and, they usually produce a significantly higher source fluence rate in comparison to radioisotope sources.
Another consideration that needs to be made when applying a pXA to a human measurement, aside from the dosimetric aspects of such system applications, is which X-ray tube to select for the given measurement. This has an influence on both the potential sensitivity of the measurement (and system overall), which ultimately has an impact on the dosimetry due to necessary fluctuations in measurement counting time. Further, the selected source may produce a bremsstrahlung continuum as its main spectrum (as is the case of a higher Z target material such as tungsten), or, the main excitation may originate from interactions with the characteristic lines from the tube target material. In such cases whereby a lower Z material such as silver or rhodium are used as the X-ray tube target material, one must consider which tube to apply to the measurement to further increase sensitivity and reduce the measurement time thus the radiation dose received by the subject. This selection needs to be performed carefully to also include primary filtration options as a means of eliminating any superfluous radiation and as such reducing surface radiation dose.
In the context of in vivo applications of pXAs for bone metal analysis either tungsten (Z = 74) or silver (Z = 47)-based X-ray tubes have been used. 9,10 Another quite common anode material is rhodium (Z = 45) which is available in commercial pXRF systems. In the case of bone lead measurements in which the L-series is measured and for bone strontium measurements in which the K-series is measured, rhodium target X-ray tubes produce a characteristic X-ray series which are closer to the L-edge of lead and the K-edge of strontium, and thereby offer the potential of being an ideal source for both a bone strontium and bone lead measurements.
In this work, we compare the system performance of three commercially available pXAsystems in the context of a bone lead and bone strontium measurement using bare bone phantoms. The systems include a tungsten target system, a silver target system and a

Portable X-ray Analysers
The rhodium target pXA system consisted of a Tracer-  (Table 8.1).
The silver target pXA system consisted of a Niton-XL3t 950 system (Thermo Scientific).
The system consisted of a miniaturized silver target X-ray tube operating at 50 kVp and 40 µA. Photon detection was achieved with an SDD system. The detector had a resolution of <180 eV at the iron Kα. The primary beam had an static aluminum primary filter with unknown thickness.
The tungsten target pXA system used in this work was that used previously for the assessment of arsenic and selenium in biological specimens 15 and also for that assessed for the possible quantification of lead in bone. 10 The system was an Innov-X Alpha-4000S model portable X-ray analyzer (Innov-X Systems Canada, Mississauga, Ontario). The system con-

Phantom preparation and measurements
Phantoms used in this study were bare bone phantoms composed of hydroxyapatite as to mimic a bone mineral measurement more closely. Phantoms were prepared by the method Measurements were made for 180 s real time for both strontium and lead phantoms on the tungsten target system. Measurements were made for 180 s real time for the lead measurements on the rhodium and silver target systems. Additionally, measurements were made for 1 s, 10 s and 30 s real time for the strontium phantoms on the rhodium and silver target systems. All measurements were made with five replicates re-positioning the phantom after each measurement to also assess phantom homogeneity.

Data processing
All spectra were processed using an in-house program for determining integrated peak areas written in GNU Octave. From these integrated areas, calibration curves were prepared as to determined the sensitivity for the element, S. the systems were compared based on the minimum detectable limit (MDL) calculated using the 3σ criteria (Eqn. 8.1) where σ 0 is the standard deviation of the 0 ppm phantom and S is the sensitivity for the given element determined from the linear calibration prepared from the phantoms. MDLs were determined for the strontium Kα and lead Lα lines only. The MDL was selected as the figure of merit of choice in this study as it provides for the minimum concentration detectable for the given measurement conditions and thus acts a a measure of the feasibility of using the pXA system for an in vivo measurement.

Results and Discussion
All pXAs where compared on the basis of the MDL for the given conditions of the measurement. All MDLs were determined using the same HAp bone phantoms as to mimic the bone mineral matrix more closely 16 in comparison to the traditional calibration material, plaster of Paris (poP). 9,10 MDLs for all systems and conditions of interest, for strontium and lead, are presented in Table 8.2 and have been determined on the basis of bare bone measurements.
In the context of an in vivo XRF measurement the selection of a suitable pXA system requires various considerations. The system must be able to provide adequate analytical sensitivity while minimizing the radiation dose to the subject being measured, which may be reduced by controlling exposure via the measurement time and by filtering the primary beam of any superfluous radiation.
At the level of the excitation source, further consideration should be given to the presence or absence of scattered radiation from the characteristic lines emitted from the target.
Such scattered radiation may render themselves useful within the calibration protocol as coherent and Compton scattered radiation may be useful for global matrix corrections and/or  production would suggest that a heavy target such as tungsten would produce a sufficient fluence above the strontium K-edge and lead L-edge, which may result in adequate analytical sensitivity for in vivo measurements, the lack of any scattered source characteristic X-rays was considered undesirable given the possible use of such radiations within the calibration protocol. Dead times in this case did not exceed 10 %. The two target materials presented markedly lower atomic numbers in comparison to tungsten, yet, the intensity of the bremsstrahlung component (as scattered radiation) was found to be comparable for a much shorter measurement time (Figures 8.1 & 8.2). This greater fluence also demonstrates the potential for a great reduction in the radiation dose to the subject being measured as it may allow for a large reduction in the measurement times. In the case of a bone lead measurement, the concentration and thus signal from lead is low (Figure 8.2) and thus a 180 s live time measurement was maintained when comparing all pXA systems. The decrease in radiation dose to the subject would be much more apparent in the case of a bone strontium measurement which is one of the reasons the application of a pXA for such purposes is desirable. Given that strontium is naturally present in bone at several hundred parts-per-million, being classified as a minor element, it may be possible to reduce radiation dose allowing for the safer long-term monitoring of individuals, such as  those supplementing with strontium for the prevention/treatment of osteoporosis. 5,6 For this reason, the analytical performance of the systems was evaluated for various counting times in the case of strontium as the analytical signal was found to be potentially useful even as low as a 1 s measurement time (Figures 8.3 & 8.4). The measurement time did have a direct effect on the MDL in the case of a strontium measurement (Table 8.2) as one would expect given that the signal-to-noise ratio would increase as a function of time. In the case of both the silver target and rhodium target pXA system, although it seems that it would be possible to make an in vivo bone strontium measurement with as low as a 1 s measurement, such measurements may be hindered by not taking into consideration subtle subject movement during the measurement which would be averaged out over an extended measurement period.
Although the fluence rate does play a role in the selection of the pXA system for the aforementioned reasons, a consideration that needs to be made when selecting a pXA system for an in vivo measurement is the primary filtration arrangement which has an influence on the ultimate dosimetry. Given that most modern pXA systems are X-ray tube based, a bremsstrahlung component to the emission spectrum will likely always be present unless care has been taken to monochromatize the primary X-ray beam. The primary filtration in the silver pXA system, also a thick aluminum primary filter, was found to reduce the background considerably near the strontium and lead regions providing good analytical performance (Table 8.2) as well as a large reduction in the low energy photons, which would only deposit radiation dose to the subject.
The rhodium tube pXA system is unique amongst the systems evaluated in this work, as it is provided to the user with no added primary filtration other than the inherent filtration provided by the X-ray tube window. For this reason, it is potentially advantageous for in vivo applications of various different analytes as primary filtration arrangements can be custom designed. Three filter combinations were evaluated in this work (provided by the manufacturer, Table 8.1) as an initial assessment and prior to the design of any custom primary filters. From the point of view of dosimetry, however, the greater the hardening of the beam, the greater reduction in radiation dose, as one will remove the majority of the lower energy photons not useful for the excitation of the analyte of interest, in this case lead and strontium. The addition of primary filters was however found to have a minimal effect when it came to the MDL for strontium and lead (Table 8.2). The addition of the filter with the highest half-value layer (red filter, Table 8.1) did show an increase in the MDL which is attributed to a compensatory effect. In this case, the reduction of background is counteracted by a reduction in sensitivity due to the hardening of the photons above the edges of interest. In any case, the limits of detection for strontium and lead, for as low as a 1 s long measurement in the case of strontium, are sufficient for an in vivo measurement when considering no soft tissue attenuation. In the average strontium content in humans naturally is approximately 350 ppm, 17,18 whereby, any of the systems evaluated would be sufficient for clinical measurements, even if soft tissue attenuation reduces the overall sensitivity. Although beam hardening was achievable for the rhodium pXA system using the primary filtration arrangements, given the operating potential of the pXA, and thus, the location of the bremsstrahlung mean energy, the heaviest of the filtrations still produced a background approximately one order of magnitude larger than the silver pXA system in the low energy region (Figure 8.3). For this reason, the silver X-ray tube system performed marginally better than the rhodium pXA system (Table 8.2) however every system seems to be sufficient for a clinical measurement when considered strictly on the basis of the determined MDLs. This feature may also have consequences dosimetrically, which needs to be further assessed.
When comparing the silver target versus rhodium pXA systems, the rhodium target system becomes potentially attractive given that the rhodium Kα line is closer to the Kedge of strontium and L-edge of lead. However, the total spectral output of an X-ray tube is known to follow the relation in Eqn. 8.2, where I is the intensity, k a constant and V the applied voltage.
Thus, from the point of view of the target material, for the same applied voltage, there is a linear relationship to total spectral output with the atomic number of the target material.
In this case, even though the Rh line is closer in energy to the strontium and lead edges, this physical feature (Eqn. 8.2) will always result in a higher total number of silver photons which likely compensates for the distance in energy. In this particular study, the silver system was operating at 50 kVp. The rhodium target system was limited in its operation, given Ontario regulations with regards to pXA spectrometers, to 40 kVp. The square dependence on total output would suggest that increasing this voltage to 50 kVp would result a 36 % increase in the total spectral output. Coupled with the spread in energy distribution, the MDLs could be comparable. Aside from the lower MDLs the shape of the bremsstrahlung distribution also results in a larger amount of radiation below the edges which will impart dose to the subject in the case of a rhodium target system. Dosimetry was not completed in this work however and remains a point of investigation. Although dosimetry was not performed in this study as it was intended to evaluate performance strictly in the context of the analytical figures of merit, dosimetry must be considered carefully. For the clinical in vivo XRF system of bone strontium quantification effective doses have been determined to be on the order of (64 − 76) × 10 −6 mSv for a 3600 live time measurement. 19 Specht et al. 7 have reported an effective dose for an in vivo bone lead determination using a portable silver target system of 2 µSv for a 180 s live time measurement. Although one can thus apply these spectrometers such that it allows for greater portability, the dosimetric aspects must be considered given that such systems deliver dose much higher than those expected of isotope-induced systems.

Conclusions
Three pXA spectrometers were evaluated as potential candidates for the in vivo quantification of bone strontium and lead: a tungsten target pXA, a rhodium target pXA and a silver target pXA. It was found that the tungsten target pXA, which presented no characteristic CHAPTER NINE

CONCLUSIONS AND FUTURE DIRECTIONS
This work aimed at designing and evaluating a hydroxyapatite (HAp) phantom material for the purpose of calibrating in vivo X-ray fluorescence (IVXRF) systems of bone metal quantification. 1,2 Although the HAp phantom material can potentially be used for the preparation of phantoms for any particular metal to be quantified in bone via IVXRF, this work focused on its application to IVXRF bone strontium quantification using the 125 I-induced clinical IVXRF bone strontium system [3][4][5][6][7][8][9] and its application to the assessment of portable X-ray analyzers (pXAs) for the purpose of bone strontium and lead quantification. This chapter provides a review of conclusions drawn and recommendations for future work. This results in the inability to prepare a blank phantom and thus does not allow for a true system contamination assessment or the determination of the analytical figures of merit of the system properly. 10 This is due to the fact that any signal which is present from the inherent contamination brings about another source of uncertainty to the background which is not purely due to the system itself. This work itself found that for the calcium compounds used, which were purchased as high purity compounds, the strontium concentrations ranged from approximately 286-773 µg Sr/g Ca. The calcium compounds were also found to contain contamination from various other elements including lead in lower concentrations of contamination (see Chapter 2 1 ). It was found to be possible to prepare purified calcium by simply precipitating calcium from a calcium chloride solution in the case in which the number of equivalents of hydroxide ions were much small than those of the calcium. In this case, the solubilities of the calcium hydroxide which is formed and in equilibrium with a solution containing a high concentration of calcium are different than those for strontium hydroxide.

Development of Phantom Materials
As a result, pure calcium can be prepared at a great sacrifice for calcium in solution. The resultant calcium hydroxide was free from the contaminants found in the original reagent (calcium chloride used for the precipitation). As assessed by total reflection X-ray fluorescence spectrometry, the calcium hydroxide produced after precipitation was found to contain <0.7 and <0.3 µg/g Ca for strontium and lead, respectively. This purified calcium hydroxide can then be used for the preparation of strontium-free brushite which can be produced by the dissolution of the calcium hydroxide and reaction with a solution of Na 2 HPO 4 and NaH 2 PO 4 ⋅H 2 O. The calcium hydroxide and brushite formed by these reactions were found by powder X-ray diffraction to be identical to those of purchased precipitated reagents. The phantoms can thus be prepared pure by using these reagents to prepare a hydroxyapatite cement to form the final phantom.
By mixing the calcium hydroxide and brushite as to prepare a powdered mixture with a Ca/P mole ratio of 1.67, that of HAp, the reaction can proceed by the addition of a suitable setting solution. The calcium phosphate cement mixture being based on the solubility properties of calcium phosphates. In the case in which a high phosphate ion concentration is maintained in the setting solution, the solubility of the brushite increases. The result is a precipitation to hydroxyapatite whereby the calcium hydroxide is added as to maintain the stoichiometry of the final product. The phantoms can thus be prepared by mixing the powered mixture with the a setting solution consisting of 1 M HPO 2 -4 . It was found that a 2:1 mass ratio of powder mixture-to-liquid was ideal for the preparation of a cement which was sufficiently fluid for moulding of phantoms. The analyte can be added directly by doping to the setting solution mixture. The phantoms, when suitably set, were found to have a crystal phase similar to that of the mineral phase of bone as compared to NIST bone meal though a powder X-ray diffraction assessment. The reaction was found to produce a phantom with a mass density of (2.0±0.6) g/cm 3 . The phantom density was lower than that of pure hydroxyapatite (3 g/cm 3 ) but close to that of bone, 11 of 1.9 g/cm 3 (nominal). The reaction is, however, not 100 % efficient whereby contamination was observed as unreacted brushite. It is anticipated that the conversion ratio (a measure of the degree of the reaction) can be to some degree assessed by mass difference given that the calcium hydroxide seemed to be the limiting reagent in the reaction and from a preliminary assessment, the amount of brushite left after reaction seems small. This should however be assessed through a proper conversion ratio assessment.
The phantoms produced by this route seem to be suitable for the calibration of IVXRF systems of bone metal quantification as they are more suitable to mimicking bone mineral than plaster of Paris (poP), and become further more so suitable in the context of a coherent normalization-based calibration procedure. By the addition of the analyte into the phantom through doping linear calibration curves were produced for both lead and strontium with intercepts through the (0,0) point which indicates that the phantoms seem to be taking up the analyte in a predictable fashion (Figure 2.5). This thus suggests that the phantoms are suitable for IVXRF system calibration and is also the first, to the author's knowledge, production of a true analytical blank for strontium. The phantoms produced by this method are however not truly bone equivalent and should be used with caution outside of a coherent normalization-based calibration protocol. The phantom produced here are bone mineral phantoms and were designed as a replacement for poP in the context of a coherent normalization-based calibration procedure. The mass attenuation coefficient of the material in comparison to bone is different and this may have an influence in the case that XRF quantification is to be employed in a more general sense (i.e. through the application of fundamental parameters approaches). This was the focus of a separate part of the work.
This portion of this work thus demonstrates the suitability of a method for the preparation bone mineral equivalent phantoms as discussed in Chapter 2.
The pure HAp phantoms as well as the purified calcium compounds can also be used for other purposes outside of general calibration of IVXRF systems of bone metal quantification.
Although the method of preparing phantoms here does present the possibility of removing a correction factor from IVXRF systems based on calibration through a coherent normalization procedure (the coherent conversion factor or CCF, see Chapter 6), their use has not yet been fully established. As such, in the case that poP-based calibrations are to continue, this method of calcium purification can be used for the preparation of strontium-free poP.
Although not the focus of this work, this can likely occur by the formation of gypsum from reaction of the pure calcium hydroxide which can then be dehydrated to plaster of Paris.
Caution should be used if this method is employed. Like the CPC system, the common ion effect holds for poP 12 and care should be taken to evaluate a suitable methodology for the preparation of purified poP phantoms as it is likely that the addition of a common ion be required for the preparation of phantoms suitable for long term calibration of IVXRF systems of bone metal quantification.
Further the purified HAp material can be potentially used for a purpose outside of calibration, and this is validation. Currently, validation of IVXRF bone metal systems requires that animal bone be used as a means of performing the validation after cross-validation with secondary methods of analysis. [13][14][15][16][17][18][19] The major problem associated with this route becomes and limited range of concentrations which are attainable with animal or human bone whereby a true validation should use a matrix reference material with as wide a concentration range as possible. This is possible if the HAp phantoms are used for this purpose.
Although it is possible to prepare HAp phantoms using commercially available reagents, one of the areas that requires further work is the scaling up of the procedure for the purification. In order to prepare pure calcium hydroxide in sufficient quantities as to prepare a full set of phantoms, a very large loss of calcium is required and the time commitment is vast. Future work within the area of purification should thus focus largely on procedures to scale up the purification while re-using as much of the calcium as possible. Without such future work, the cost of producing a phantom set from purified calcium compounds is rather large. The alternative of preparing phantoms using commercially available calcium compounds and reserving the purified calcium compounds for a blank along would also require further quantitative confirmation of the true concentrations in each phantom as to account for the contamination levels, which, to some degree, removes the point of producing pure calcium compounds. Proceeding with calibration using phantoms with confirmed concentrations necessitates the need to introduce uncertainty into the concentration direction of the calibration curve, which, complicates the analysis substantially. Future work thus should focus on either alternative methods of purification, or, methods of preparing pure calcium compounds by precipitation while salvaging more calcium and reducing total time of production.
Chapter 2 of this work focuses on the preparation of phantoms which are pure of the analyte, namely, strontium; however, this is only one extrema of the problem in phantom preparation in the context of IVXRF for bone strontium. Unlike lead, strontium levels in bone can, theoretically, reach the percentage mass levels, whereby, lead will generally only be present in bone mineral in the parts-per-million level. This is due to the fact that strontium is ubiquitous to calcium from dietary sources but also is used as a supplement/medication for therapy against osteoporosis. 20  This indicated the potential for a large amount of residual contamination as strontium carbonate. Another concern was the possibility that the phantom would set by first creating Sr 5 (PO 4 ) 3 OH with the available brushite given the solubility of Sr(OH) 2 ⋅ 8 H 2 O relative to Ca(OH) 2 and then the formation of pure hydroxyapatite after the exhaustion of the added Sr(OH) 2 ⋅ 8 H 2 O. This would then result in not a strontium-substituted phantom but an undesirable biphasic phantom. It was however found that as a whole system, the phantom does in fact set into a strontium-substituted hydroxyapatite and there was no evidence of a large degree of contamination from carbonate of either species. Further, a vibrational spec-troscopy study (Raman spectroscopy) found that the phosphate groups stretching behaviour indicates an overall strontium substitution resembling that expected of a strontium substitution hydroxyapatite with formula (Ca 1-x Sr x ) 5 (PO 4 ) 3 OH (as seen through an energy shift in the phosphate group ν 1 mode) which is that which would be expected in bone if strontium is substituted for calcium in the mineral phase when bone mineral is forming. Chapter 3 thus demonstrates that it is possible to prepare high strontium concentration phantoms while maintaining a (Ca + Sr)/P mole ratio at 1.67; and that it can be presumed that even in cases in which low concentrations of divalent metals are used for phantom preparation that they likely integrate into the apatite lattice.
Chapter 3 thus introduces a case in which the HAp phantom material may be a necessity in comparison to the poP phantoms given the flexibility in their preparation while maintaining a mineral phase component which is similar to that in bone. In cases in which high strontium phantoms may be needed for calibration/validation purposes, the HAp series may be recommended. This requires further investigation as to their suitability as well as a more thorough study of the general integration behaviour of divalent metals (and possibly trivalent metals such as gadolinium ions) into the hydroxyapatite lattice. This was hindered in this study by the sensitivity of the powder X-ray diffraction spectrometry system which would not allow for the visualization of say lead apatites. The substitution of lead into the system as a lead hydroxide was also complicated as lead hydroxide is not generally stable in the solid phase. † As a result, this chapter leaves the question open as to whether or not lead and other divalents also integrate in the expected fashion as this would require a much more sensitive spectrometer to what was available and it was not possible to produce phantoms of high lead concentration with the same substitution for the hydroxide fraction. † Generally present as lead basic carbonate and lead oxide mixtures.

Application to quantification methodology
The design and production of the hydroxyapatite phantom material as described in Chapter 2 was largely focused on the development of a blank phantom material. A blank being necessary for the purpose of determining analytical figures of merit while also allowing one to assess spectral interferences with the analyte signal. Chapter 4 of this work demonstrates the need for a blank phantom in the context of an IVXRF 125 I-induced bone strontium measurement. The excitation source for the current clinical system being brachytherapy seeds which are not intended for the purpose of analytical spectrometry but rather for radiation therapy. Given that these seeds are composed of titanium capsules, which, as is well established, are generally either coated with, or formed into an alloy of, zirconium, as a means of ensuring a minimum of corrosion when implanted. Indeed, a direct measurement of the excitation source was found to include the characteristic K-series of zirconium which overlaps directly with the Kβ line of strontium and is thus a spectral interference that needs to be assessed via a blank phantom as a means of controlling the interference during the calibration protocol. Monte Carlo simulations demonstrated however that in the 180 ○ backscatter geometry used for measurements, that scattering back into the detector is largely due to Compton scattering rather than coherent scatter-expected result given the heavy forward directedness of coherent scatter. As a result, the main zirconium peaks which would be Further work should thus focus not only on the application of a blank for the assessment of spectral interferences and background but also on the impact the availability of a true blank phantom will have on the assessment of analytical figures of merit. This was not assessed in this work as the topic becomes complicated given the observed spectral interference. The ultimate result would be the ability to determine σ 0 without the contribution of the counting statistics from the K-lines of strontium as currently present. This would result in a reduction in the limit of detection and quantification. That being said, the current limit of detection of the clinical system, determined with contaminated phantoms, is already sufficient for human measurements. 8,9 The limit of detection also being dependant on scatter from the soft tissue component in humans and phantoms would also require further development in this area to calculate, if anything, the limit of detection on a subject-by-subject basis, which is customary in the context of XRF analyses in a general sense. Although Compton-based global matrix corrections are known to make these corrections for variations in mass attenuation coefficients in cases with large dark matrices, this was ignored in this context as the Compton scattering signal also arises, in a significant way, from interactions of photons within the soft tissue. 31 Coherent normalization, which is currently applied within the context of a bone strontium measurement calibration, 8,9 was found to be successful in normalization of the signal if the concentration of strontium is represented on a mass of bone mineral basis. This is a well established mode of calibration in the context of IVXRF which arises from early work on the K-XRF bone lead system ( 109 Cd-induced). 13 This work did however find that the application of HAp as a phantom material does remove the need to apply the CCF to the calibration protocol as the sensitivity determined for both bone and HAp were similar. The application of HAp as a phantom material thus removed the need to apply a factor to the calibration protocol and thus allows for direct transferability of the calibration sensitivity factor between calibrator and the matrix-a factor which has been known to be a source of uncertainty when applied to poP-based calibrations. 32 It was also found that the sensitivity was, by default, to be independent of the phantom conversion ratio. That is, even if the material produced as per Chapter 2 were to be the product of an incomplete reaction, the sensitivity factors are not influenced. This is attributed to the fact that the coherent scatter, being predominately from calcium, normalized signal sufficiently well that any calcium phosphate material can be used as a calibration material as long as coherent scatter is used as a normalization factor in the calibration protocol. Thus, the phantom material developed in this work is suitable for calibration of IVXRF bone strontium systems without the need for worry about incomplete reaction and also allows one to remove the CCF simplifying the calibration protocol as well as reducing the introduction of uncertainty given that the true composition of poP materials is unknown, thus, introducing uncertainty into the CCF.
Chapter 7 of this work expanded on Chapter 6 whereby soft tissue attenuation correction was evaluated, more specifically, the use of spectroscopic information alone for the determination of the overlaying soft tissue thickness-a required piece of information in order to correct for signal attenuation. In the context of an IVXRF bone strontium measurement employing the current 125 I-induced clinical system, 8,9 Compton intensities of scattered source photons were evaluated as a means of determining the soft tissue thickness. This method being previously proposed by Nie et al. 31 in the context of measurement made using a portable X-ray analyzer. It was found, via Monte Carlo simulation, that the choice of calibration material used as to mimic the bone as well as the soft tissue plays a significant role in the applicability of this method of soft tissue thickness determination. Lucite, a proposed soft tissue surrogate in the context of a IVXRF measurements, 31 when coupled with poP as a calibration material was found to produce standard curves which were non-linear and nontransferable to soft tissue and bone. If HAp were to be used as a phantom material, similar Compton intensities were observed to that of bone. Compton scattering was found to be heavily dependant on the bone surrogate used as well as the soft tissue phantom material used. With this regard, if a soft tissue equivalent material can be developed to be used in conjunction with the HAp material developed in this work, it does seem to be possible to be able to use the Compton intensity as a means of determining the soft tissue thickness directly from spectroscopic data. This fact, coupled with the fact that the coherent normalization can be applied for matrix correction/normalization, indicates the possibility of producing direct bone strontium quantification using spectroscopic data alone. Further work however would be needed in order to devise this quantification algorithm, as it would need to be iterative by its very nature in the sense the Compton scattered intensity is also a function of bone size.
Thus, given that coherent normalization can correct for bone size, this may become another unknown parameter which would render Compton-based soft tissue correction unusable and this thus remains an area of future work alongside the design of more suitable soft tissue equivalent materials for in vivo XRF applications.
Chapters 4 through 7 of this work focus on applications using the current clinical IVXRF system of bone strontium when discussing quantification and calibration. Although the system has been well applied to human subjects, 8,9 and is, in theory, portable, it does require liquid nitrogen cooling and by extension a large dewar making it cumbersome. Chapter 8 of this work evaluates the potential of applying portable X-ray analyzers for the purpose of bone strontium and lead quantification. The chapter was a comparison of commercially available portable X-ray analyzers for this purpose. It was found that the target material applied does play a role in the sensitivity of the system and may have an impact on the dosimetry.
Commercially available silver target X-ray tube systems seem to produce a sufficiently high fluence such that heavier filtration can be applied while maintaining good sensitivity in comparison to rhodium tube-based systems. The result is a high fluence of photons in the region below the strontium K-edge of lead L-edge which will only result in added dose to the subject. The systems were found to be rather equivalent when considering strontium as the analyte with sensitivity sufficient to produce measurements with a 30 s real time measurement. In the case of lead, the silver target X-ray tube system out performed the rhodium system which is largely attributed to the higher background in the strontium and lead characteristic X-ray energy region. Although rhodium is slightly closer to the K-edge of strontium and L-edge of lead, the lower atomic number results in sufficiently lower fluence such that the silver target X-ray tube system does outperform and will likely result in a smaller dose to subjects. Either the silver target or rhodium target X-ray tube systems seem suitable for the purpose, however, and dosimetric studies are needed in future work.

Future Recommendations
As a point for future investigation, quantification methodology and associated algorithms should be considered more carefully. Namely, within this work and within the framework of a coherent normalization procedure, various assumptions need to be taken into account including those associated with sample homogeneity. As was found in this work, issues with soft tissue thickness correction remain and it was found that the coherently scattered 125 I γ-ray carries significant contributions from both the bone as well as the overlaying soft tissue, as does Compton scattered radiation from the sample, which in turn complicates quantification. It is thus difficult to delineate contributions from each tissue as a means of extrapolating to an analytical measure determined directly from bone tissue in this case. Two possible methods can potentially be investigated as a means of improving the quantification methodology for the in vivo bone strontium system in particular. Both of these methods, however, would require future development alongside novel instrumentation as a means of acquiring the required data, in the required form, for quantification to be possible. In both cases, this may mean a re-evaluation of the broad-beam geometries suggested, as with the current clinical in vivo XRF bone strontium system and the portable X-ray analyzers evaluated in this work.
It may be possible, with suitable instrumentation, to perform tomographic analysis of the site being measured, if sufficiently small, such as the finger. In this case, acquired spectra, taken at various angles throughout the finger, can be used to develop a series of Radon transforms based on not only the strontium K-series intensities but also those of the coherent and Compton scattered radiation. In this case, it may be possible to reconstruct both soft tissue thickness and concentration information from the sample performing a more robust quantification which can take into account true sample geometry as well as any inhomogeneities present in the sample being measure-both at the soft tissue and bone level. This method carries the inherent limitation that instrumentation would need to be fully developed for this purpose, likely requiring a tomographic system to be designed using pencil beam sources rather than the broad beam sources used throughout this work. Further, the fact that the bone sample is infinitely thick for strontium K X-rays would inherently result in a series of incomplete Radon transforms which would complicate the quantification, if it would even be possible. Such an approach would however potentially allow for quantification in a more robust sense.
The second proposed future investigation would be to the development and application of Monte Carlo-based procedures for quantification. In this case, it may be possible to develop a system in which imaging information can be used to model the geometry of the sample while applying a Monte Carlo procedure as to perform quantification. In this way, quantification can proceed using an iterative approach as to match spectral intensities of not only the strontium K-series but also that of the scattered radiation to measured spectra. The total space of unknowns with this approach, however, would require future work in evaluating the feasibility of a Monte Carlo-based procedure for this purpose, as there may be far too many unknown parameters to allow for a convergence of concentration information. This method would however be more akin to what is currently been applied to radiation therapy treatment planning. If sufficient information is obtained via imaging of the measurement site, it may be possible to delineate tissue types which would aid in the Monte Carlobased quantification procedure as a means of both defining tissue composition regions as well as direct implementation of geometrical information into the algorithm. The Monte Carlo package used throughout this work, EGS5, is a predecessor to EGSnrc which is used for the purpose of evaluating radiation therapy treatment planning. Both Monte Carlo code packages are suitable to the Monte Carlo simulation of radiative transport within the photon energies of interest and can also be modified to perform dose calculations by suitably following any released charged particles. In this case, application of either code, with modification and suitable system design, may allow for quantification to proceed while also allowing for a direct computation of radiation dose to the subject on a measurement by measurement basis. Although this work developed phantom materials as well as evaluated quantification in the context of the current in vivo XRF system of bone strontium quantification future work may require a re-consideration of quantification algorithms which should be performed