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

Susanne Schweizer,*a Bodo Hattendorf,b Philipp Schneider,a Beat Aeschlimann,b Ludwig Gauckler,c

Ralph Mullera and Detlef Guntherb

Received 2nd March 2007, Accepted 23rd July 2007

First published as an Advance Article on the web 7th August 2007

DOI: 10.1039/b703220j

Phantoms for the calibration of local bone mineral densities by micro-computed tomography

(mCT), 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 mCT. A series of standards was

prepared by fusion of pure HAp with Li2B4O7 in a concentration range between 0.12 and

0.74 g cm23. Furthermore, pressed and sintered pellets of pure HAp were prepared to extend

the calibration range towards densities of up to 3.05 g cm23. 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 mCT scanner.

Introduction

Micro-computed tomography (mCT) is an established techni-

que 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

mCT 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 mm.

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 contain-

ing 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 mCT measurements. Owing to the

spatial resolution of mCT, 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 mCT in bones are significantly higher than the

averaged values obtained by QCT, reaching bone mineral

densities of up to 1.6 g cm23.28 However, higher phantom

material densities are desirable to perform mCT calibration, to

be able to also measure biomaterials (alone and after implanta-

tion in bone). These materials are very often ceramics, HAp

or tricalcium phosphate (TCP) based.29

Additionally, a suitable mCT 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.

aInstitute for Biomedical Engineering, University and ETH Zurich,Switzerland. E-mail: schweizer@biomed.ee.ethz.chbInstitute of Inorganic Chemistry, ETH Zurich, SwitzerlandcDepartment of Materials, Nonmetallic Inorganic Materials, ETHZurich, Switzerland

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So far, two commercially available mCT 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 cm23 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 characteriza-

tion of new phantom materials for the calibration of a mCT

scanner for BMD measurements. The materials cover a HAp

density range from 0.12 to 3.05 g cm23 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 cm23. 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 mCT scanner

(mCT 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

mCT measurements were carried out using a Scanco mCT

scanner (mCT 40, Scanco Medical, Bassersdorf, Switzerland)

using volume elements (voxels) of a size of 10 6 10 6 10 mm,

at an intensity of 160 mA. 1000 projections were acquired over

a range of 180u using an integration time of 200 ms. The

scanner was operated at a peak voltage of 50 kV and absorp-

tion 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, Gottingen, 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 mm and a laser energy density of 7 J cm22. 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 Gunther 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 trans-

ferred into platinum crucibles for fusion. The crucibles were

heated to a maximum temperature of 1300 uC for 10 min by

an oxygen/natural gas flame under constant agitation on

a commercial fusion machine (Autofluxer, Breitlander,

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 mCT, the

samples were broken into smaller pieces.

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

Table 1 Composition, measured mass attenuation and intra-measurement standard deviations (SD) for the different samples prepared withLi2B4O7

Sample HAp concentration (wt%) (¡1 SD)a HAp density/g cm23 (¡1 SD)b Linear attenuation/cm21 (¡1 SD)c

Blank ,0.02 ,0.0005 1.10 ¡ 0.034L05 4.96 ¡ 0.19 0.12 ¡ 0.057 1.46 ¡ 0.037L10 9.99 ¡ 0.28 0.23 ¡ 0.035 1.71 ¡ 0.048L20 19.97 ¡ 0.31 0.48 ¡ 0.018 2.33 ¡ 0.080L30 30.03 ¡ 0.95 0.74 ¡ 0.032 2.85 ¡ 0.097a Average concentrations and standard deviations for the entire samples according to LA-ICPMS analyses. b Combined uncertainty fromconcentration, mass and volume determinations.37 c Intra-scan standard deviation.

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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)21], aluminium [0.2 mg (kg HAp)21], manganese

[0.015 mg (kg HAp)21], nickel [0.012 mg (kg HAp)21], copper

[0.008 mg (kg HAp)21], zinc [0.015 mg (kg HAp)21], strontium

[0.15 mg (kg HAp)21] and barium [0.01 mg (kg HAp)21] were

detectable at very low levels.

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 mCT 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 mCT 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.

One sample was additionally sintered in a temperature-

controlled electrical furnace (Nabertherm 1750 uC; Eurotherm

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.

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 cm23 (¡1 SD)a Mass attenuation/cm21 (¡1 SD)b

Pressed powder samplesP05 0.5 1.24 ¡ 0.007 3.13 ¡ 0.16P10 1 1.41 ¡ 0.007 3.53 ¡ 0.19P20 2 1.61 ¡ 0.008 4.02 ¡ 0.20P30 3 1.77 ¡ 0.012 4.16 ¡ 0.21P50 5 1.95 ¡ 0.013 4.68 ¡ 0.23

Sintered powder sampleS50 5 3.05 ¡ 0.01c 7.19 ¡ 0.36

a Uncertainty calculated from readability of the balance and caliper. b Intra-scan standard deviation. c Relative uncertainty of the pycnometer.

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controller, Nabertherm, Lilienthal, Germany) after pressing.

The furnace temperature was ramped from ambient to 800 uCat a rate of 2 uC min21 and kept constant for 30 min.

Subsequently the temperature was increased to 1300 uC at

5 uC min21 and held constant for another 180 min. After

sintering, the sample was allowed to cool to ambient

temperature at a rate of 2 uC min21 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 cm23 (see ref. 40).

The density of the pressed pellets was determined from their

geometrical volume (calculated from five individual measure-

ments of diameter and height) and the weight of the samples.

Micrometer-scale homogeneity characterization and

determination of mass attenuation using mCT

Micrometer-scale homogeneity of all samples was charac-

terized by scanning a sub-volume of 207 layers of each

material, at an intensity of 160 mA and using a voxel size of

10 6 10 6 10 mm. 1000 projections were acquired over a range

of 180u 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 6252 6 100 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 cm21. The variations in

the mass attenuation coefficients are typically 3% RSD for the

lithium tetraborate samples and 5% RSD for the pure pellets.

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 homo-

geneous at a resolution of 10 mm. In Fig. 3, representative

samples from the lithium tetraborate pills and the pressed pills

are shown. Only sample P05 shows variation of the attenua-

tion 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 mm. 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.

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 mCT

scanner.41 It needs to be mentioned though that a quadratic fit

of the data resulted in a higher correlation coefficient (0.9997),

Fig. 2 Histogram of the mass attenuation data for the HAp pellet

P50. The solid line represents a fit to a Gaussian distribution.

Fig. 3 Representative areas (1 6 1 mm) for samples L10, L20, P05, and P20, scaled to the maximum intensity of the system. The pixel resolution

is 10 6 10 mm.

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indicating that secondary effects within the sample material,

such as beam hardening32 at higher HAp densities, were

present.

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 composi-

tions, the correlation of the measured mass attenuation with

the HAp density is very high.

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.

Conclusion

This study has shown that standards with mass densities

covering a wide range from 0.1 to 3 g cm23 can be prepared for

calibration of the X-ray absorption of hydroxyapatite. The

samples can be considered homogeneous on the scale of

current mCT scanners and thus allow a quantitative micro-

analytical characterization of bones. The new materials over-

come 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 calibra-

tion 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 mCT scanners for the

density of HAp with an accuracy of better than 10% relative,

which enables a spatially resolved quantitative characteriza-

tion of the bone mineral content.

Furthermore, the newly prepared phantoms are mechani-

cally 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 mCT 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

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.

Fig. 5 Combined calibration curves for fused and pressed

HAp samples. Also given are the corresponding prediction intervals

(p = 95%).

Table 3 Regression data for the individual and combined calibrationcurves

Slope Intercept r2

Fused pillsa 2.81 0.053 0.9970Pressed pellets 2.24 0.33 0.9966All samples 2.31 0.20 0.9971a Corrected for absorption of the lithium tetraborate.

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Zurich 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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