Preparation and characterization of calibration standards for bone density determination by micro-computed tomography

Abstract

Phantoms for the calibration of local bone mineral densities by micro-computed tomography (μCT), consisting of lithium tetraborate (Li₂B₄O₇) with increasing concentrations of hydroxyapatite [HAp, Ca₁₀(PO₄)₆(OH)₂] have been prepared and characterized for homogeneity. Large-scale homogeneity and concentration of HAp in the phantom materials was determined using laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS), while homogeneity on the micrometer scale was assessed through μCT. A series of standards was prepared by fusion of pure HAp with Li₂B₄O₇ in a concentration range between 0.12 and 0.74 g cm⁻³. Furthermore, pressed and sintered pellets of pure HAp were prepared to extend the calibration range towards densities of up to 3.05 g cm⁻³. A linear calibration curve was constructed using all individual standard materials and the slope of the curve was in good agreement with calculated absorption coefficients at the effective energy of the μCT scanner.

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Introduction

Micro-computed tomography (μCT) is an established technique to assess three-dimensional bone micro-architecture of cancellous and cortical bone.¹ The amount of X-ray energy that is absorbed by hydroxyapatite in a section of bone reflects the bone mineral content. Bone mineral content divided by the area or volume of the bone estimates the bone mineral density (BMD). Laboratory studies have found a high correlation between BMD and the force needed to break a bone.^2–4 In clinical practice, the availability of bone densitometry has revolutionized the capacity to detect osteoporosis, since it enables a determination of fracture risk and helps to select patients for different treatment measures.⁵ However, little headway has been made to accurately determine bone mineral density (BMD) at the micrometer spatial resolution, due to the fact that only very few suitable calibration standards are available. In order to be useful for calibration of modern μCT scanners, the calibration standards need to fulfil several requirements: (a) their X-ray attenuation needs to reflect the absorbance of bone minerals and they should cover a representative range of mineral densities, and (b) they have to be homogeneous at the spatial resolution of the scanner. Since the main constituents of bone tissue are calcium and phosphate, bound in the form of hydroxyapatite, both criteria would be met if solid samples of hydroxyapatite were available at variable densities and as homogenous phases at a scale of <10 μm.

Currently, solid phantom materials are in use that contain the bone mineral hydroxyapatite for performing BMD measurements in quantitative computed tomography (QCT)^6,7 on millimeter to centimeter scales. Computed tomography is widely used as a diagnostic tool in many medical disciplines.^8–11 Specifically, much research has been aimed at the development of CT-based calibration phantoms to mimic the attenuation profile of various tissue types.^12–16 Commercially available bone phantom materials, such as the epoxy resin-based SB3 introduced by White et al.¹⁷ containing 67% calcium carbonate, allow the accurate calibration for cortical BMD. Several other phantoms have been designed to quantify bone mineral density from CT images,^12,18–24 and effects of temperature,^25,26 imaging resolution²⁷ and radiation dosage²⁷ have been studied in detail for such phantoms. However, the concentration range covered and the homogeneity of these phantoms make them suitable to only a limited extent for μCT measurements. Owing to the spatial resolution of μCT, assessment of the local bone mineral content of individual bone struts, so-called trabeculae, is possible. Thus, the mass attenuation coefficients that need to be quantified by μCT in bones are significantly higher than the averaged values obtained by QCT, reaching bone mineral densities of up to 1.6 g cm⁻³.²⁸ However, higher phantom material densities are desirable to perform μCT calibration, to be able to also measure biomaterials (alone and after implantation in bone). These materials are very often ceramics, HAp or tricalcium phosphate (TCP) based.²⁹

Additionally, a suitable μCT reference material to calibrate the scanner for BMD measurements has to mimic the absorption properties of the underlying bone material.^28,30,31 Increasing mass attenuation coefficients corresponding to an exactly determined concentration of bone mineral have to be attained. Also, the reference material has to be homogenous on a micrometer scale such that the standard deviation of the attenuation coefficient in a given area is reduced to a minimum.

So far, two commercially available μCT phantoms from the CIRS (Computerized Imaging Reference Systems, Inc., Norfolk, USA) and Scanco (Scanco Medical, Bassersdorf, Switzerland) companies and fluid phantoms containing H₂KPO₄ are used for quantitative mineralization analysis of bone specimens. However, they all have limited concentration ranges of up to about 1 g cm⁻³ HAp equivalents only. Higher values of bone volume densities have to be extrapolated, assuming an accurate correction of effects such as beam hardening.³² In addition to their limited concentration range, H₂KPO₄ phantoms have been shown to form air bubbles and were therefore subjected to changing attenuation properties over time. Replenishment and proper service at regular intervals is needed for those phantoms.³³

In this work we describe the preparation and characterization of new phantom materials for the calibration of a μCT scanner for BMD measurements. The materials cover a HAp density range from 0.12 to 3.05 g cm⁻³ and were prepared using two different methods. One set of samples contained HAp dissolved in a flux of lithium tetraborate (Li₂B₄O₇), at densities between 0.12 and 0.74 g cm⁻³. Lithium tetraborate is a traditionally used solid solvent for a wide range of minerals and is commonly used for the production of homogenous glassy samples for mineral bulk characterization in X-ray fluorescence spectroscopy (XRF).³⁴ It has a relatively low X-ray absorption coefficient and low fluorescence yield and is thus an ideal solvent for absorption measurements of a wide range of materials. The mineral concentrations (or densities) can be adjusted very easily and precisely by mixing known weights of the flux and the mineral before the fusion.

A second set of standards was prepared by compaction of HAp directly in a hydraulic press at different pressures. The phantoms were measured in-house and the micro-scale homogeneity was validated on a Scanco μCT scanner (μCT 40, Scanco Medical, Bassersdorf, Switzerland). Large-scale homogeneity and mineral contents were determined using Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICPMS).

Experimental

Instrumentation

μCT measurements were carried out using a Scanco μCT scanner (μCT 40, Scanco Medical, Bassersdorf, Switzerland) using volume elements (voxels) of a size of 10 × 10 × 10 μm, at an intensity of 160 μA. 1000 projections were acquired over a range of 180° using an integration time of 200 ms. The scanner was operated at a peak voltage of 50 kV and absorption was measured by applying a ten-frame averaging mode to improve the signal-to-noise ratio. LA-ICPMS measurements were performed using a GeoLas C laser ablation unit (Microlas GmbH, Göttingen, Germany) in combination with a 7500cs ICPMS unit (Agilent Technologies, Waldbronn, Germany). Analyses were carried out by single spot analysis at a spot size of 40 μm and a laser energy density of 7 J cm⁻². The ablated material was transported into the ICPMS using helium as carrier gas. Calibration of the instrument was performed using the standard reference material NIST 610 (NIST, Gaithersburg, USA). More detailed descriptions of the operating principles of LA-ICPMS can be found, for example, in Günther and Hattendorf (2005),³⁵ Durrant (1999)³⁶ and references therein.

Results and discussion

Hydroxyaptatite fused with lithium tetraborate

Low density HAp samples were prepared by fusion with lithium tetraborate. Variable amounts of the HAp nano-crystals (Berkeley Advanced Biomaterials Inc., USA) were weighed on a precision balance (precision: ±0.1 mg), followed by addition of lithium tetraborate to a final weight of 6 g (Table 1). After thorough mixing, the powders were transferred into platinum crucibles for fusion. The crucibles were heated to a maximum temperature of 1300 °C for 10 min by an oxygen/natural gas flame under constant agitation on a commercial fusion machine (Autofluxer, Breitländer, Germany) for 10 min. After dissolution was complete the melt was poured into pre-heated Pt-moulds and allowed to cool. Using this method, it was possible to prepare concentrations of up to 30 wt% of HAp in lithium tetraborate. At higher concentrations, HAp began to re-crystallize during cooling and no homogeneous samples could be obtained. The samples prepared by this method had a diameter of 32 mm and were approximately 3 mm high. For further analysis by μCT, the samples were broken into smaller pieces.

Table 1 Composition, measured mass attenuation and intra-measurement standard deviations (SD) for the different samples prepared with Li₂B₄O₇

Sample	HAp concentration (wt%) (±1 SD)^a	HAp density/g cm^−3 (±1 SD)^b	Linear attenuation/cm^−1 (±1 SD)^c
a Average concentrations and standard deviations for the entire samples according to LA-ICPMS analyses. b Combined uncertainty from concentration, mass and volume determinations.^37 c Intra-scan standard deviation.
Blank	<0.02	<0.0005	1.10 ± 0.034
L05	4.96 ± 0.19	0.12 ± 0.057	1.46 ± 0.037
L10	9.99 ± 0.28	0.23 ± 0.035	1.71 ± 0.048
L20	19.97 ± 0.31	0.48 ± 0.018	2.33 ± 0.080
L30	30.03 ± 0.95	0.74 ± 0.032	2.85 ± 0.097

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After preparation the fused beads were characterized for large-scale homogeneity by spatially resolved analysis using an established LA-ICPMS method.³⁸ The samples were analyzed at ten equally spaced positions between the center and the rim. There is a slight depletion of HAp towards the inner parts of the samples, which might have been a result of non-congruent solidification of the melt. Nonetheless, the variation of the HAp concentration across the entire sample was less than 10% in all cases (Fig. 1). Blank values were below the instrumental detection limit (0.02 wt% of HAp). Apart from the major constituents of HAp, several potential contaminants were also analyzed. Most trace elements were present at or below the instrumental detection limit, while magnesium [2 mg (kg HAp)⁻¹], aluminium [0.2 mg (kg HAp)⁻¹], manganese [0.015 mg (kg HAp)⁻¹], nickel [0.012 mg (kg HAp)⁻¹], copper [0.008 mg (kg HAp)⁻¹], zinc [0.015 mg (kg HAp)⁻¹], strontium [0.15 mg (kg HAp)⁻¹] and barium [0.01 mg (kg HAp)⁻¹] were detectable at very low levels.

Fig. 1 Concentrations of HAp when fused with lithium tetraborate, at different locations across the samples L05–L30. Analyses were carried out by LA-ICPMS. Error bars indicate one standard deviation of the individual results, based on counting statistics of the ICPMS data for calibration and measurements.

Density measurement of the lithium tetraborate pills

To assess the density of HAp in the pills, a small piece was taken from an intermediate position of each pill, where the concentration matched most closely the desired value, and weighed precisely. The volume of the piece was determined by scanning μCT and the density of HAp was calculated using the volume and mass of the piece and the average concentration of the HAp. The relative standard deviation (RSD) of the volumetric measurements with μCT is 0.5%.³⁷ According to the variation of the HAp concentration across the individual pills, the accuracy of the HAp densities is in the range of 5–10% relative.

Pure HAp pellets

Samples with higher densities of HAp cannot be produced by the fusion method and were realized by compaction of the raw material in a hydraulic press under different pressures (Table 2). For compaction, a circular steel mould (10 mm diameter) was filled with approximately 400 mg of HAp nano-crystals and closed by a steel plunger, which transfers the pressure to the material. The pressure was adjusted manually and was kept constant for ca. 10 min.

Table 2 Conditions for preparation, densities, mass attenuation and corresponding intra-scan variations of the pure HAp pellets

Sample	Press load/tons	HAp density/g cm^−3 (±1 SD)^a	Mass attenuation/cm^−1 (±1 SD)^b
a Uncertainty calculated from readability of the balance and caliper. b Intra-scan standard deviation. c Relative uncertainty of the pycnometer.
Pressed powder samples
P05	0.5	1.24 ± 0.007	3.13 ± 0.16
P10	1	1.41 ± 0.007	3.53 ± 0.19
P20	2	1.61 ± 0.008	4.02 ± 0.20
P30	3	1.77 ± 0.012	4.16 ± 0.21
P50	5	1.95 ± 0.013	4.68 ± 0.23
Sintered powder sample
S50	5	3.05 ± 0.01^c	7.19 ± 0.36

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One sample was additionally sintered in a temperature-controlled electrical furnace (Nabertherm 1750 °C; Eurotherm controller, Nabertherm, Lilienthal, Germany) after pressing. The furnace temperature was ramped from ambient to 800 °C at a rate of 2 °C min⁻¹ and kept constant for 30 min. Subsequently the temperature was increased to 1300 °C at 5 °C min⁻¹ and held constant for another 180 min. After sintering, the sample was allowed to cool to ambient temperature at a rate of 2 °C min⁻¹ again.³⁹ Table 2 lists the conditions and resulting densities obtained for these samples.

Density measurement of the pure HAp pellets

The density of the sintered HAp pellet was determined pycnometrically. The uncertainty of this determination is ±0.001 g cm⁻³ (see ref. 40).

The density of the pressed pellets was determined from their geometrical volume (calculated from five individual measurements of diameter and height) and the weight of the samples.

Micrometer-scale homogeneity characterization and determination of mass attenuation using μCT

Micrometer-scale homogeneity of all samples was characterized by scanning a sub-volume of 207 layers of each material, at an intensity of 160 μA and using a voxel size of 10 × 10 × 10 μm. 1000 projections were acquired over a range of 180° using an integration time of 200 ms. The samples were placed inside a 20 mm cross-section polypropylene vial for the measurement. Absorption data from a volume of 252 × 252 × 100 voxels were used to calculate the linear attenuation values and to estimate the homogeneity of the material. Tables 1 and 2 list the linear attenuation coefficients and the standard deviation of these measurements for the lithium tetraborate samples and the pure HAp pellets, respectively. Fig. 2 shows a typical distribution of the mass attenuation coefficients for the sample P50 corresponding to a linear mass attenuation coefficient of 4.68 ± 0.23 cm⁻¹. The variations in the mass attenuation coefficients are typically 3% RSD for the lithium tetraborate samples and 5% RSD for the pure pellets.

Fig. 2 Histogram of the mass attenuation data for the HAp pellet P50. The solid line represents a fit to a Gaussian distribution.

The distribution of the attenuation coefficients represents the combined uncertainties arising from the homogeneity of the material and the measurement uncertainty during signal acquisition. It thus constitutes an upper limit for the estimate of uncertainty of the homogeneity of the material. Averaging a larger number of frames may reduce the overall uncertainty but will also increase measurement times dramatically. A compromise has to be made with respect to uncertainty and analysis time. By visually inspecting sample homogeneity on a micrometer scale, most phantoms also proved to be homogeneous at a resolution of 10 μm. In Fig. 3, representative samples from the lithium tetraborate pills and the pressed pills are shown. Only sample P05 shows variation of the attenuation coefficient at the resolution of the scanner. This indicates that the pressure applied is insufficient to compact the starting material to below a range of 10 μm. At higher pressures and in the fused material, however, the density of the material shows an even distribution at the spatial resolution of the scanner.

Fig. 3 Representative areas (1 × 1 mm) for samples L10, L20, P05, and P20, scaled to the maximum intensity of the system. The pixel resolution is 10 × 10 μm.

Calibration of mass attenuation coefficients

Fig. 4 displays the relation between the average mass attenuation values and the HAp density of the material for the lithium tetraborate pills. Owing to absorption of the beam by the fusion material, the calibration curve shows an offset. This offset can be corrected by subtracting the absorption caused by the mass fraction of lithium tetraborate present. A linear fit to the data (Fig. 4, left) yields a correlation coefficient (r²) of 0.9954 (0.9967 for the uncorrected data). A numerical simulation of the absorption for the fused pills of the given composition using the Photons software (Hasylab, Hamburg, Germany) yields an X-ray energy of 26.6 keV, which is in agreement with the effective energy of 26–27 keV for the μCT scanner.⁴¹ It needs to be mentioned though that a quadratic fit of the data resulted in a higher correlation coefficient (0.9997), indicating that secondary effects within the sample material, such as beam hardening³² at higher HAp densities, were present.

Fig. 4 Calibration graphs for mass attenuation versus HAp density in the fused pills (left) and pressed pellets (right). Error bars correspond to one standard deviation of the linear attenuation and HAp densities respectively.

The mass attenuation of the pressed and sintered pellets of HAp also shows a linear dependence on the HAp density (Fig. 4, right). Nonetheless, the slope of this fit yields a smaller slope, corresponding to a higher effective beam energy (27–28 keV).

Fig. 5 shows a combined calibration graph for all samples prepared in this study. Despite the different matrix compositions, the correlation of the measured mass attenuation with the HAp density is very high.

Fig. 5 Combined calibration curves for fused and pressed HAp samples. Also given are the corresponding prediction intervals (p = 95%).

Selected regression data are listed in Table 3. The correlation for the combined calibration curve is reasonably good, while the slopes show variations of 12% RSD. According to the regression statistics, the uncertainty of the results obtained against this calibration are in the range of 10% RSD, as indicated by the prediction interval in Fig. 5.

Table 3 Regression data for the individual and combined calibration curves

	Slope	Intercept	r ^2
a Corrected for absorption of the lithium tetraborate.
Fused pills^a	2.81	0.053	0.9970
Pressed pellets	2.24	0.33	0.9966
All samples	2.31	0.20	0.9971

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Conclusion

This study has shown that standards with mass densities covering a wide range from 0.1 to 3 g cm⁻³ can be prepared for calibration of the X-ray absorption of hydroxyapatite. The samples can be considered homogeneous on the scale of current μCT scanners and thus allow a quantitative micro-analytical characterization of bones. The new materials overcome the uncertainty in a calibration, which is introduced by extrapolating the calibration curve obtained from lower density materials towards the actual mineral density values found in trabeculae. The use of hydroxyapatite in the calibration standards is advantageous because its absorption of X-rays is very close to that of bone mineral, which mitigates measurement bias, induced by variation of the X-ray energies and the corresponding changes in absorption cross-sections. Furthermore, the materials contain only low concentrations of other absorbing elements, which might additionally affect the calibration.

The standards allow the calibration of μCT scanners for the density of HAp with an accuracy of better than 10% relative, which enables a spatially resolved quantitative characterization of the bone mineral content.

Furthermore, the newly prepared phantoms are mechanically stable, allowing them to be handled without special care. The phantom weight did not significantly change over a two-year period (differences below 1%). They can be cut and polished when necessary to adjust them to individual sample holders of μCT scanners.

Acknowledgements

Many thanks to Stefan Loher and the group of Professor Stark at the Department for Chemistry and Applied Biosciences at ETH Zurich for their help with the hydroxyapatite nano-crystals. Many thanks also to Dr Elena Tervoort and Urs Gonzenbach from the Department of Materials at the ETH Zürich for their support with the sintering furnace and the density determination of the HAp pills.

The research was funded by the Swiss National Science Foundation (SNF) through the SNF Professorship in Bioengineering (FP 620-58097.99).

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