A physical phantom for the calibration of three-dimensional X-ray microtomography examination

Authors

  • E. PERILLI,

    1. Laboratorio di Tecnologia Medica, Istituti Ortopedici Rizzoli, Via di Barbiano 1/10, 40136 Bologna, Italy
    2. Department of Electronics, Computer Science and Systems, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
    Search for more papers by this author
  • F. BARUFFALDI,

    1. Laboratorio di Tecnologia Medica, Istituti Ortopedici Rizzoli, Via di Barbiano 1/10, 40136 Bologna, Italy
    Search for more papers by this author
  • M. C. BISI,

    1. Second Faculty of Engineering, University of Bologna, Via Venezia 52, 47023 Cesena, Italy
    Search for more papers by this author
  • L. CRISTOFOLINI,

    1. Laboratorio di Tecnologia Medica, Istituti Ortopedici Rizzoli, Via di Barbiano 1/10, 40136 Bologna, Italy
    2. Dipartimento di Ingegneria delle Costruzioni Meccaniche, Nucleari, Aeronautiche e di Metallurgia, Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
    Search for more papers by this author
  • A. CAPPELLO

    1. Department of Electronics, Computer Science and Systems, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
    Search for more papers by this author

Egon Perilli. Tel: +39-051-6366858; fax: +39-051-6366863; e-mail: perilli@tecno.ior.it

Summary

X-ray microtomography is rapidly gaining importance as a non-destructive investigation technique, especially in the three-dimensional examination of trabecular bone. Appropriate quantitative three-dimensional parameters describing the investigated structure were introduced, such as the model-independent thickness and the structure model index. The first parameter calculates a volume-based thickness of the structure in three dimensions independent of an assumed structure type. The second parameter estimates the characteristic form of which the structure is composed, i.e. whether it is more plate-like, rod-like or even sphere-like. These parameters are now experiencing a great diffusion and are rapidly growing in importance. To measure the accuracy of these three-dimensional parameters, a physical three-dimensional phantom containing different known geometries and thicknesses, resembling those of the examined structures, is needed. Unfortunately, such particular phantoms are not commonly available and neither does a consolidated standard exist. This work describes the realization of a calibration phantom for three-dimensional X-ray microtomography examination and reports an application example using an X-ray microtomography system. The calibration phantom (external size 13 mm diameter, 23 mm height) was based on various aluminium inserts embedded in a cylinder of polymethylmethacrylate. The inserts had known geometries (wires, foils, meshes and spheres) and thicknesses (ranging from 20 µm to 1 mm). The phantom was successfully applied to an X-ray microtomography device, providing imaging of the inserted structures and calculation of three-dimensional parameters such as the model-independent thickness and the structure model index. With the indications given in the present work it is possible to design a similar phantom in a histology laboratory and to adapt it to the requested applications.

Introduction

X-ray microtomography (microCT) (Feldkamp et al., 1984, 1989; Sasov, 1987) has become an important method for the inspection of small objects, thus having a wide spectrum of applications, e.g. in the field of orthopaedics (Rüegsegger et al., 1996; Müller & Rüegsegger, 1997), dentistry (Hubscher et al., 2002) and biomaterial research (Lin et al., 2003). It permits the three-dimensional (3D), non-destructive investigation of the sample with a spatial resolution of up to a few micrometres, without special preparation of the specimen.

Appropriate 3D indices for the quantitative characterization of the examined structure were introduced, such as the model-independent thickness (Tb.Th*) and the structure model index (SMI). The Tb.Th* calculates the thickness in three dimensions, independent of an assumed structure type (Hildebrand & Rüegsegger, 1997a). This method evaluates a volume-based local thickness by fitting maximal spheres to every point contained in the 3D structure. The arithmetic mean value of the local thicknesses (i.e. of the diameters of the maximal spheres), taken over all points of the structure, gives the mean thickness of the structure. The SMI is a topological index that gives an estimate of the characteristic form in terms of plates and rods composing the 3D structure (Hildebrand & Rüegsegger, 1997b). It is calculated using a differential analysis of the triangulated surface of the structure under examination. The SMI assumes integer values of 0, 3 and 4 for ideal plates, rods and spheres, respectively. For a structure containing both plates and rods the SMI value lies between 0 and 3. (Please see the Appendix for the formal description of Tb.Th* and SMI.)

Since their introduction, these 3D parameters have rapidly gained importance for the study of a priori unknown or changing structures, as occurs for trabecular bone (Hildebrand et al., 1999; Ding & Hvid, 2000; Mittra et al., 2005). To determine the accuracy of these 3D parameters, a 3D object of a priori well-known material, shape and linear dimensions has to be investigated, i.e. a 3D calibration phantom is needed. The phantom should contain a number of physical elements of known geometries and thicknesses, to allow a number of measurements within a single microCT scan.

To our knowledge, such phantoms are not commonly available. Anthropomorphic phantoms for medical computed tomography are not useful for microCT because of their large size, being bigger than the maximum size allowed for typical microCT scanners or having inserts not designed for accuracy measurements of thin structures in the micrometer range (Kalender, 1992; Royle & Speller, 1992; Rüegsegger & Kalender, 1993). Phantoms dedicated to microCT applications are currently available but their use principally concerns the calibration of density values or general quality assurance (QRM GmbH, 2005). Because of the growing importance of the 3D microCT examination technique in the investigation of trabecular bone samples (Ding & Hvid, 2000; Mittra et al., 2005), we decided to design and construct a dedicated 3D microCT calibration sample using available aluminium objects. The sample contained geometrical elements, such as spheres, rods, plates and meshes, embedded in polymethylmethacrylate (PMMA), with tolerances (5–15%) and thicknesses (20–1000 µm) declared by the manufacturer.

This study describes how to construct a calibration phantom for microCT using aluminium objects and reports an application example, together with measurements of Tb.Th* and SMI using a microCT scanner.

Materials and methods

Design of the phantom

Choice of the material.  Anthropomorphic phantoms for medical computed tomography (CT) are typically composed of water- and bone-equivalent materials, built of polyethylene-based and epoxy-resin-based plastics. However, they were not designed specifically for microCT applications. Their external size [e.g. the European Forearm Phantom (Rüegsegger & Kalender, 1993), 40 × 60 × 100 mm; upper thigh phantom (Royle & Speller, 1992), diameter 165 mm, height 130 mm and European Spine Phantom (Kalender, 1992), 180 × 260 × 120 mm] is larger than the typical maximum size allowed for microCT scanners, although microCT scanners having a field of view of about 80 × 100 mm have recently become available. Moreover, their inserts were not designed for measurements of thicknesses in the micrometre range [e.g. in the European Forearm Phantom (Rüegsegger & Kalender, 1993) the thinnest insert has an inner diameter of 5 mm].

A microCT phantom should contain structures of material, shape and dimensions resembling those of the usually examined objects, i.e. trabecular bone in the present case, as this is the main microCT application in our laboratory. The bone biopsies typically examined have the shape of cubes or cylinders, with a side length or diameter in the order of 10–15 mm (Feldkamp et al., 1989; Rüegsegger et al., 1996; Müller & Rüegsegger, 1997; Hildebrand et al., 1999). The structure of human trabecular bone can be represented as a mixture of rods and plates (Parfitt et al., 1983; Fazzalari et al., 1989), having mean thicknesses that can range from below 100 µm to 300 µm (Hildebrand et al., 1999). Consequently, the thicknesses of the contained structures have to be in this range. An easy-to-handle material with an attenuation coefficient (µ) similar to bone and already used for calibration scopes in radiology is aluminium (µAl(30 keV) = 3.04 cm−1, µcortical bone(30 keV) = 2.56 cm−1) (Kalebo & Strid, 1988; Hubbel & Seltzer, 1995; Brodt et al., 2003).

Aluminium was chosen as the appropriate material in the design of the present phantom. As the phantom has to be used for quantitative measurements, the contained elements have to be of previously established morphologies and dimensions. The introduction of plate-like, rod-like and sphere-like geometries of known size in the phantom is useful to control the measurement of the thickness in 3D and of the SMI. Small aluminium objects with dimensions and tolerances declared by the manufacturer (Goodfellow Cambridge Limited, Huntingdon, U.K.) were used in the phantom as ‘ideal structures’. Table 1 describes the characteristics of the used foils (which were used to resemble plate-like structures), wires (to resemble rod-like structures), meshes (to resemble connected rod-like structures) and spheres. In order to verify the nominal thicknesses, 10 repeated measurements were performed in the laboratory on other specimens deriving from the same batch. Physical measurements were not made on the samples themselves, which had to be used in the calibration sample, so as not to alter their geometry and thicknesses. A micrometer (1-µm resolution, screw-thread micrometer with digital display, Mitutoyo, Kawasaki, Kanagawa, Japan) was used for the measurements of the foils and spheres, whereas an optical microscope (magnification on screen 400×, 0.346 µm pixel size, DC300, Leica Microsystems, Wetzlar, Germany) was used for the wires and mesh. These measurements confirmed that the average thickness values were within the tolerances declared by the manufacturer.

Table 1.  Specifications of the aluminium objects used for the realization of the phantom, with material purity, nominal thicknesses and tolerances declared by the manufacturer (Goodfellow Cambridge Limited, Huntingdon, U.K.).
ObjectMaterial (purity)DescriptionNominal value ± toleranceMeasured value ± SD
  1. The last column reports mean values and SDs obtained by 10 repeated measurements with a digital micrometer (for the foils and spheres) and an optical microscope (for the wires and mesh) on other samples deriving from the same batch.

SphereAl (95.2%)Thickness (µm)1000 ± 501009 ± 3
Foil (250 µm)Al (99.0%)Thickness (µm) 250 ± 25 256 ± 5
Foil (100 µm)Al (99.0%)Thickness (µm) 100 ± 10 102 ± 1
Foil (50 µm)Al (99.0%)Thickness (µm)  50 ± 7.5  48 ± 1
Foil (20 µm)Al (99.0%)Thickness (µm)  20 ± 3  21 ± 1
Wire (250 µm)Al (99.99%)Thickness (µm) 250 ± 25 247 ± 1
Wire (125 µm)Al (99.5%)Thickness (µm) 125 ± 12.5 125 ± 1
Wire (50 µm)Al (99.5%)Thickness (µm)  50 ± 5  51 ± 1
Wire (20 µm)Al (99.99%)Thickness (µm)  20 ± 2  21 ± 1
MeshAl (99.0%)Thickness (µm) 100 ± 10 102 ± 3
Aperture (µm) 110 ± 10 109 ± 5
Wires per mm  4.7 × 4.7 4.7 ± 0.1 × 4.7 ± 0.1

Scheme of the phantom.  The spatial positioning of the single aluminium structures was performed to fit a field of view of 15-mm side length. Because of the rotational geometry of the image acquisition procedure in microCT, one way to design a suitable phantom is to force the phantom to match a hypothetical cylinder having the axis common with the rotation stage. Therefore, a cylindrical geometry was chosen for the external shape of the phantom, with the base of the phantom parallel to the scan plane (Fig. 1).

Figure 1.

Scheme of the phantom (measures in mm). PMMA, polymethylmethacrylate.

The aluminium wires and foils were posted orthogonally to the base of the phantom. As the object turns during the image acquisition process, there is a rotation position at which the foils are aligned parallel to the path of the X-rays, causing a high attenuation of the photons. This phenomenon could be a problem for the wires if they were posted in the plane of one of the foils because they would be covered by the whole length of the foil, which is of several millimetres. To overcome the problem, each foil was positioned on different parallel planes, with the four wires in a separate plane parallel to the foils (Fig. 1).

Two small meshes of 4 × 4 mm were posted one parallel and one orthogonal to the scan plane. The mesh posted parallel to the scan plane, having 110-µm thick wires and 4.7 wires per mm, was assumed to resemble the typical total thickness encountered by an X-ray along its path during a microCT scan of a trabecular bone biopsy [i.e. assuming a scan of a human trabecular bone biopsy of d = 10 mm diameter, having a direct trabecular number (Tb.N*) of about 1.4 mm−1 and Tb.Th of 150 µm, the total thickness encountered by an X-ray would be in the order of d × Tb.N* × Tb.Th* = 10 mm × 1.4 mm−1 × 0.150 mm = 2.1 mm; histomorphometric data taken for the iliac crest (Hildebrand et al., 1999)]. A larger mesh (7 × 7 mm) was posted parallel to the scan plan. The spheres, because of their large diameter (1 mm), cause a high attenuation of the X-rays. They were positioned on a different plane with respect to the other objects.

Arrangement of the aluminium objects and embedding in polymethylmethacrylate

Wires and foils of small dimensions (thickness 20–250 µm) are brittle. Embedding them in a resistant material results in a phantom that is easy to handle and preserves its integrity with time. The embedding material should be relatively radiotransparent to limit the attenuation of the crossing X-rays. PMMA, commonly used in histology for the embedding of bone biopsies, was chosen for this purpose. PMMA has an attenuation coefficient similar to that of water [µPMMA(30 keV) = 0.36 cm−1, µwater(30 keV) = 0.38 cm−1 (Hubbel & Seltzer, 1995)], so its use with the aluminium objects can simulate the acquisition conditions of trabecular bone submerged in water. Methylmethacrylate is liquid before polymerization. A glass cylinder with an internal diameter of 13 mm, normally used for embedding bone biopsies, was chosen to contain the aluminium objects during the embedding process. It was necessary to find a method of keeping the aluminium structures separated from each other and in determined positions during the embedding process (Fig. 1). After various trials, the most appropriate method was found to be the gluing (glue Technovit 7210 VLC, Heraeus Kulzer, Wehrheim, Germany) of the aluminium objects onto microscope slides made of PMMA (Exact Apparatebau, Norderstedt, Germany).

Construction of the phantom

Cutting of the microscope slides.  The PMMA microscope slides (initial dimensions 75 × 25 × 1.5 mm, length × height × thickness) were ground down to a thickness of 1.1 mm (Exact grinding system, Exact Apparatebau). They were then cut to suitable dimensions using a diamond saw (Remet TR 60, Casalecchio di Reno, Bologna, Italy). The final dimensions of the cut slides were 25 × 5 × 1.1 mm for those to contain the aluminium foils (five slides), 25 × 9 × 1.1 mm for those to contain the wires (two slides) and 8 × 8 × 1.1 mm for those to contain the spheres and large mesh (three slides).

Cutting of the aluminium foils, wires and meshes.  The aluminium foils, wires and meshes were cut by hand with scissors. Great care was needed not to deform the objects during this process.

The foils (20, 50, 100 and 250 µm thick, respectively) were cut to dimensions of 25 × 5 mm and the wires (20, 50, 125 and 250 µm diameter, respectively) were cut into 25-mm-long segments. Two meshes were cut into 4 × 4-mm squares and one was cut into a 7 × 7-mm square.

Gluing the aluminium objects.  A glue layer was put on a microscope slide and subsequently covered by an aluminium foil. The next glue layer was then applied, followed by the second microscope slide. This procedure was repeated with the other foils and slides, thus obtaining a multilayered sandwich (Fig. 2a and b).

Figure 2.

(a) Top view and (b) side view of the four aluminium foils glued between five microscope slides.

The four aluminium wires were all glued together between two microscope slides, trying to keep them as taut as possible without causing breakage (Fig. 3).

Figure 3.

The four aluminium wires glued between two microscope slides.

The four aluminium spheres (1 mm diameter) were glued between two PMMA microscope slides. The 7 × 7-mm mesh was glued onto the external side of one of these slides and then covered by a third slide (Fig. 4a and b).

Figure 4.

(a) Top view and (b) lateral view of the four spheres and the large mesh glued between three microscope slides.

Finally, one of the two small meshes (4 × 4 mm) was glued onto the external side of the microscope slides containing the large mesh (becoming the ‘mesh parallel to the scan plane’), whereas the second small mesh was glued onto an external side of the slides containing the wires (becoming the ‘mesh orthogonal to the scan plane’), respectively. The positioning of the objects on the microscope slides had to be performed rapidly and carefully because the glue quickly formed a consistent film on the microscope slides.

The objects were then put under a blue light for polymerization of the glue (Adhesive press Exact 402, Exact Apparatebau).

Embedding in polymethylmethacrylate.  The methylmethacrylate (Merck-Schuchardt, Hohenbrunn, Germany) was first destabilized and then benzoyl peroxide (3.5%) (Sigma-Aldrich Chemie, Steinheim, Germany) was added to start the polymerization. The aluminium objects glued on microscope slides were put in a glass cylinder to which the methylmethacrylate was added using a pipette. Subsequently, the cylinder was closed with a plastic plug and placed in an oven at 26 °C for polymerization. After curing (4 days), the glass was manually broken and the calibration phantom embedded in the PMMA cylinder was extracted. The cylinder was then cut with a diamond saw to a final length of 23 mm (Fig. 5a–c).

Figure 5.

Final calibration phantom: (a) frontal view, (b) top view and (c) bottom view.

Application example

X-ray microtomography imaging and calculation of the parameters model-independent thickness and structure model index.  The microCT scanner used in the present work was a Skyscan 1072 (Skyscan, Aartselaar, Belgium). It consists of a microfocus X-ray source, a rotatable specimen holder and a detector system, which has a 1024 × 1024-pixel charge-coupled device (CCD) camera. The scanning geometry is of the cone-beam type (Sasov, 1987; Feldkamp et al., 1989; Sasov & Van Dyck, 1998). The X-ray projections are obtained as 12-bit greylevel images, stored in 16-bit file format. The scan settings used are the typical settings for microCT examination of trabecular bone samples in our laboratory. The microCT operated at 50 kVp, 200 µA, rotation step 0.45°. An aluminium filter (1 mm thick) was used for beam-hardening reduction. The exposure time was set at 5.9 s, averaged by two frames. The magnification was set at 20× with a pixel size of 15 µm and a field of view of 15 × 15 mm. The system is supplied with a computer equipped with a 1.7-GHz Intel Xeon double processor (1 GB RAM). The cross-section reconstruction was performed using the program cone-rec V2.9 (Skyscan), which is based on the cone-beam reconstruction algorithm (Feldkamp et al., 1984). The reconstructed tomographic images were stored in 8-bit format (256 greylevels).

The calibration phantom was microCT imaged five times, keeping the same scan settings. Each scan was performed on different days, repositioning the phantom in the microCT each time. A global threshold was used for the segmentation of the reconstructed images (software 3d calculator V0.9, Skyscan). Separate volumes of interest were chosen to each contain one single object entirely to allow the calculation of the Tb.Th* (Hildebrand & Rüegsegger, 1997a) and SMI (Hildebrand & Rüegsegger, 1997b) (software 3d calculator V0.9, Skyscan). (Please see the Appendix for the formal description of these parameters.) Therefore, there was one separate volume of interest for the 250-µm foil, one for the 125-µm foil and one for the 50-µm foil, etc. Various threshold levels were applied on the reconstructed images of the first scan. The threshold level that minimized the root mean square error in Tb.Th* from the nominal thicknesses was chosen as the unique threshold for all inserts. This threshold was then applied on the reconstructed images of the five scans.

Results

The phantom was successfully constructed and microCT imaged. The single objects were visually clear in the frontal X-ray images of the phantom (Fig. 6a and b). The tomographic images contained sections of the spheres, meshes, wires and foils surrounded by the PMMA (grey halo), as can be seen in Fig. 7(a–e). In particular, the four spheres, the 250-, 100- and 50-µm-thick foils and the 250- and 125-µm-thick wires were clearly visible. The 50-µm diameter wire had a greyvalue that was higher (brighter) than that of the other wires but was still visible, whereas the 20-µm wire was visually not distinguishable from the PMMA (Fig. 7d and e). The 20-µm-thick foil was less visible than the thicker ones, but still evident.

Figure 6.

(a) Frontal X-ray projection of the calibration phantom. (b) Frontal X-ray projection of the calibration phantom, obtained with the phantom rotated by 90° with respect to (a).

Figure 7.

Cross-section images of (a) spheres, (b) large horizontal mesh, (c) small horizontal mesh, (d) wires and small vertical mesh, and (e) wires and foils. The measures are nominal and expressed in mm. Each image is of 15 mm side length, 15 µm pixel size.

The threshold value used for the binarization of the reconstructed images did not allow segmentation of the thinnest structures, such as the 20- and 50-µm wire and the 20-µm foil, because of their high greyvalue. Therefore, only the calculation results of the segmented objects will be reported, i.e. the spheres, wires of 125 and 250 µm diameter, foils of 50, 100, 250 µm and three meshes (Fig. 8a–f).

Figure 8.

Binarized cross-section images of (a) spheres, (b) foils, (c) wires, (d) large mesh, (e) small horizontal mesh and (f) small vertical mesh.

The basic descriptive statistics of the structural parameters Tb.Th* and SMI calculated over five repeated scans and their deviations from the nominal values are shown in Table 2. Images of the 3D reconstructions of the segmented aluminium phantom are shown in Fig. 9(a and b) (software ant, Skyscan).

Table 2.  Measurements of model-independent thickness (Tb.Th*) and structure model index (SMI) obtained by X-ray microtomography on the calibration phantom after five repeated scans (pixel size 15 µm).
ObjectTb.Th*
Nominal value ± toleranceTolerance (%)Mean measured value ± SD (µm)Error (%)
Sphere1000 ± 50 51025.4 ± 4.0 2.5
Foil (250 µm) 250 ± 2510 264.5 ± 1.4 5.8
Foil (100 µm) 100 ± 1010 105.1 ± 0.8 5.1
Foil (50 µm)  50 ± 7.515  50.3 ± 1.1 0.6
Foil (20 µm)  20 ± 315Not segmented 
Wire (250 µm) 250 ± 2510 250.1 ± 0.7 0.04
Wire (125 µm) 125 ± 12.510 111.7 ± 1.5 −10.6
Wire (50 µm)  50 ± 510Not segmented 
Wire (20 µm)  20 ± 210Not segmented 
Mesh (small horizontal) 100 ± 1010  89.1 ± 0.7 −10.9
Mesh (large horizontal) 100 ± 1010  74.4 ± 1.0 −25.6
Mesh (small vertical) 100 ± 1010 100.9 ± 0.9 0.9
ObjectSMI
Nominal valueMean measured value ± SDError
Sphere43.90 ± 0.05 −0.10
Foil (250 µm)00.69 ± 0.02 0.69
Foil (100 µm)00.28 ± 0.01 0.28
Foil (50 µm)00.19 ± 0.04 0.19
Foil (20 µm)0Not segmented 
Wire (250 µm)32.88 ± 0.01 −0.12
Wire (125 µm)32.90 ± 0.01 −0.10
Wire (50 µm)3Not segmented 
Wire (20 µm)3Not segmented 
Mesh (small horizontal)32.66 ± 0.12 −0.34
Mesh (large horizontal)33.09 ± 0.02 0.09
Mesh (small vertical)32.48 ± 0.16 −0.52
Figure 9.

(a) Three-dimensional (3D) images obtained from the segmented X-ray microtomography (microCT) images: wires of 125 and 250 µm diameter, foils of 50, 100 and 250 µm thickness, small vertical mesh, small horizontal mesh, large horizontal mesh and four spheres (nominal scan resolution 15 µm pixel size). (b) 3D images obtained from the segmented microCT images: wires of 125 and 250 µm diameter, small vertical mesh and small horizontal mesh.

Discussion

Details of the design of a physical 3D calibration phantom for microCT are presented, together with an application example reporting images and structural measurements obtained using a microCT scanner. The phantom was based on aluminium inserts of various known geometries and dimensions, embedded in PMMA. These included spheres (diameter 1 mm), foils (thickness 250, 100, 50 and 20 µm), wires (diameter 250, 125, 50 and 20 µm) and meshes (wire diameter 100 µm, separation 110 µm). The phantom was designed to have the inserts contained in a small space, i.e. in a PMMA cylinder of 13 mm diameter and 23 mm high. This had the advantage of allowing a microCT examination of all of the structures within a single scan, as is shown in the figures (Fig. 7a–e). The single inserts of various sizes and geometries were visually distinguishable, except for the 20-µm wire, probably due to its transverse diameter, which was close to the pixel size used (15 µm). Quantitatively, the phantom allowed the calculation of 3D parameters such as the Tb.Th* and SMI. The small SDs reported in Table 2 show that the results were minimally influenced by the repositioning of the phantom into the scanner.

The largest deviation in thickness from the nominal value was found for the large horizontal mesh (−26%) and was probably due to its large size (7 × 7 mm) together with its spatial position parallel to the scan plane, which caused a high attenuation of the X-rays along that path. This was confirmed by the two smaller meshes (4 × 4 mm), which were correctly resolved in the reconstructed images but showed position-dependent deviations in thickness from the nominal values (−10.9% for the horizontal mesh and 0.9% for the vertical mesh, respectively). The calculated thicknesses of the other objects, such as wires with diameters of 125 and 250 µm, foils with thicknesses of 50, 100 and 250 µm and spheres with a diameter of 1000 µm, had deviations ranging from −10.6 to 5.8%. However, a deviation from the nominal thickness of 10% over 100 µm is equivalent to 10 µm, which is smaller than the pixel size used. This can be considered as an acceptable deviation for thickness measurements obtained by microCT. The 20- and 50-µm wires and the 20-µm foil were not segmented because of their high greyvalue in the reconstructed images. This was due, especially for the wires, to their small transverse diameter, which was one to three times the pixel size, thus also being close to the limit for the segmentation. Trying to segment these structures by forcing the threshold to a higher value also led to overestimations of the order of 30% in the calculated thicknesses of the remaining objects (data not shown). We chose the global threshold value that gave the smallest deviations in thickness from the nominal thicknesses, which consequently did not permit segmentation of the thinnest structures.

The global threshold method is widely used (Hildebrand et al., 1999) and needs only one parameter (i.e. the greylevel value) to be set by the user. Additional segmentation trials were also performed by using a local adaptive threshold algorithm (Waarsing et al., 2004), which is supplied as a plug-in with the software 3d calculator (data not shown for brevity). This plug-in needs several parameters to be adjusted (e.g. pre-threshold low, high, gradient cut-off factor low, high, etc.). Although a comparison between threshold algorithms was not the aim of this study, preliminary trials using the adaptive local threshold algorithm yielded results close to those reported for the global threshold method (deviations from the nominal values in a maximum range of −25 to 5%). It could be expected that, with a fine tuning of the various threshold settings as described in the work of Waarsing et al. (2004), an improvement in the segmentation of the thinner structures could be obtained.

The SMI is a topological parameter, having values of 0, 3 and 4 for structures of ideal plates, wires and spheres, respectively. The measured values of 0.19–0.69 for the foils (assumed to resemble plate-like structures), 2.88–3.09 for the wires (assumed to resemble rod-like structures) and 3.90 for the spheres reflected with good approximation the ideal values and permitted correct identification of the examined structure. The meshes, being built of connected wires, had SMI values of 2.48–3.09 and were thus identified as mostly rod-like structures.

From a practical point of view, the small size of the presented calibration phantom (13 mm diameter, 23 mm height) allows its use with commonly used microCT systems, which can be of commercial type, custom made (Rossi et al., 2002) or based on synchrotron sources (Nuzzo et al., 2002). Moreover, considering the thin structures contained in it, embedding in PMMA makes the phantom easy to handle and preserves it over time. This also allows the phantom to be applied for periodic measurements to monitor the performance of the system. As a general comment, a special application-dedicated phantom is certainly the most suitable, depending on the particular microCT examination and the type of measurement involved. The presented phantom is built of inserts with simple geometries, which obviously cannot represent the complex architecture of a cancellous bone sample. However, as the morphology of cancellous bone in three dimensions can be represented as a mixture of rods and plates, the used inserts are appropriate for comparisons with nominal values of 3D parameters such as Tb.Th* and SMI. A further development of the phantom could be the positioning of these inserts in different tilted planes, e.g. parallel to the scan plane, or the introduction of bent wires and plates. This work reports the details of the development, construction and application of a microCT phantom dedicated to quantitative measurements in three dimensions, giving simple suggestions that could be helpful for laboratories interested in replicating similar reference samples.

In conclusion, the designed object worked successfully as a 3D calibration phantom for microCT. Its application enabled a microCT examination of the different physical inserts within a single scan and the calculation of 3D quantitative parameters, such as the Tb.Th* and SMI, on the examined structures.

Acknowledgements

The authors would like to thank Manuela Visentin and Roberta Fognani for their constant support during the realization of the phantom, Luigi Lena for the pictures and Keith Smith for checking the language of the manuscript.

Appendix

The following descriptions of the parameters Tb.Th* and SMI (calculations implemented as plug-ins in the software 3d calculator V0.9, Skyscan) are based on the original works of Hildebrand & Rüegsegger (1997a,b).

Description of model-independent thickness (Tb.Th*) (Hildebrand & Rüegsegger, 1997a)

The Tb.Th* is based on the estimation of volume-based local thicknesses, calculated independently of an assumed structure type. From these local thicknesses, the volume-weighted mean thickness of the structure is calculated.

Let Ω ⊂ R3 be the set of all points constituting the spatial structure under examination, with p∈Ω an arbitrary point in this structure. Then consider a set of points constituting a sphere defined as sph(x, r), having centre x and radius r, which contains the point p and is completely contained inside the structure. The diameter of the largest sphere that contains the point p is defined as the local thickness τ(p):

image((A1))

As an example, in the case of an ideal cylinder with infinite length, all points in the structure will have the same local thickness value corresponding to the diameter of the cylinder.

The arithmetic mean value of the local thicknesses, taken over all points in the 3D structure, gives the mean thickness + of the structure (Eq. A2), which is also noted as Tb.Th* (model-independent trabecular thickness or direct thickness) in the examination of trabecular bone:

image((A2))

Description of structure model index (SMI) (Hildebrand & Rüegsegger, 1997b)

The SMI estimates the characteristic form in terms of plates and rods composing the 3D structure, assuming the values 0, 3 and 4 for ideal plates, rods and spheres, respectively. Mixed structures composed of both rods and plates have SMI values between 0 and 3.

Given the structure volume V and the structure surface S, the SMI is calculated as:

image((A3))

where S is defined as the structure derivative of the volume with respect to a linear measure r and S′ denotes the structure surface area derived with respect to r:

image((A4))

For the implementation, the surface area S(r) is found by triangulation of the structure surface using the Marching Cube method (Lorensen & Cline, 1987). Structure thickening is then simulated by displacing the triangulated surface by a small distance Δr in its normal direction and recalculating the surface area S(r + Δr). The derivative of the surface area is then calculated as:

image((A5))

where the magnitude of the displacement Δr, i.e. the thickening of the structure, is chosen so that it is more than an order of magnitude smaller than the voxel side length.

Ancillary