Calibration of trabecular bone structure measurements of in vivo three-dimensional peripheral quantitative computed tomography with 28-μm-resolution microcomputed tomography

Bone Vol. 24, No. 1 January 1999:35–39

Calibration of Trabecular Bone Structure Measurements of In Vivo Three-Dimensional Peripheral Quantitative Computed Tomography With 28-mm-Resolution Microcomputed Tomography ¨ A. LAIB and P. RUEGSEGGER Institute for Biomedical Engineering, University of Zu¨rich and Swiss Federal Institute of Technology (ETH), Zu¨rich, Switzerland

Introduction It has recently been shown that high-resolution computed tomography and magnetic resonance imaging have the potential to assess information about the microarchitecture of bone in a noninvasive way. However, due to the limited spatial resolution of the in vivo measurements, the individual trabeculae are not depicted with their true thickness. Nevertheless, the spacing of the structural elements allows the assessment of trabecular number. In a previous publication, the ridge number density (RND) was introduced as a measure for this structural index. It can be extracted from high-resolution three-dimensional (3D) images of patients and shows a reproducibility of 1.6%. In this work the Ridge extraction procedure is compared to and calibrated with microcomputed tomography (mCT) measurements. Threedimensional measurements of 15 bone biopsies are made with a 28-mm-resolution mCT scanner as well as with a 165-mmresolution peripheral quantitative computed tomography (pQCT) scanner. For the latter, the same settings are used as for patient examinations. The 15 pairs of measurements are analyzed and the resulting structural indices are compared. The results show that structural indices such as trabecular number, mean thickness, and mean separation can be determined from the 3D pQCT data with an r2 of between 0.81 and 0.96 if the mCT data are taken as the gold standard. The calibration equation found for the bone volume fraction has an intercept of 0.04 and a slope of 0.86 (r2 5 0.98), and trabecular number as the main additional structural index shows a nonsignificant intercept and a calibration slope of 0.91 with the mCT. The calibration procedure can be used directly for patient examinations. Applied to time-series measurements it may be of value for monitoring and quantifying microarchitectural changes due to therapy or aging. (Bone 24:35–39; 1999) © 1999 by Elsevier Science Inc. All rights reserved.

Because osteoporosis is characterized by low bone mass and microarchitectural deterioration of bone tissue, it is expected that quantification of microarchitectural indices in addition to bone mass or bone density19 might improve prediction of fracture risk.2,4,9,17,22 A number of procedures such as serial sectioning, micromagnetic resonance imaging, microcomputed tomography (mCT), or synchrotron computed tomography1,7,8,15,21 have recently been introduced, which allow precise description of the structural features of cancellous bone in three dimensions. Few studies have been done to assess such features in patients, the main obstacle being the spatial resolution.12–14 Whereas in vitro examination of cancellous bone can be performed with a resolution of up to 2 mm, in vivo characterization of human bone is complicated by the fact that spatial resolution is not sufficient to describe trabecular thickness. Nonetheless, it seems that some structural indices can be derived quite precisely from in vivo measurements, even though their accuracy is mostly unknown. In a previously published work10 we introduced the Ridge number density (RND) as a precise measure for the number of trabeculae for in vivo cancellous bone examinations. Applied to the distal radius of postmenopausal women, a reproducibility of 1.6% was found in repetitive examinations over a period of 3 months. The question of absolute accuracy, however, was left unanswered. The aim of the present work is to calibrate structural indices derived from the ridge images with indices measured directly from micron resolution images. For this purpose, 15 bone biopsies were measured both with a 3D peripheral quantitative computed tomography scanner (3D pQCT) used for in vivo examinations and with a mCT scanner. The former has a nominal isotropic resolution of 165 mm, the latter of 28 mm. A third data set was artificially created by scaling and averaging the mCT images to a voxel size of 165 mm. Those images are virtually noise-free and unblurred, and are used to study the ideally achievable structural results at the given in vivo voxel size. All data sets were analyzed in a truly three-dimensional way and the resulting structural indices were compared, taking the mCT data as the standard for the lower resolution images.

Key Words: Computed tomography; Bone microarchitecture; Trabecular bone structure; Quantitative bone morphology.

Materials and Methods Specimens Trabecular bone samples were obtained from the BIOMED I project of the European Union’s “Assessment of Quality of Bone in Osteoporosis.”3 Fifteen specimens (seven males, eight fe-

Address for correspondence and reprints: Dr. Andres Laib, Institute for Biomedical Engineering, Moussonstrasse 18, CH-8044 Zu¨rich, Switzerland. E-mail: [email protected] © 1999 by Elsevier Science Inc. All rights reserved.

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8756-3282/99/$19.00 PII S8756-3282(98)00159-8

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A. Laib and P. Ru¨egsegger Calibration of in vivo bone structure measurements

Bone Vol. 24, No. 1 January 1999:35–39

Figure 1. Comparison of matched CT slices. Left: 3D pQCT slice; right: corresponding scaled mCT slice.

Figure 2. Extracted structures from the 3D pQCT (left) and the mCT (right). The same slices are shown as in Figure 1.

males) from the femoral head were selected. These specimens covered a wide range in bone volume to tissue volume (BV/TV from 12% to 34%) and structural type. The latter was quantified by the structure model index (SMI)6 and ranged from very plate-like (SMI 5 0.03) to rod-like (SMI 5 1.91), where perfect plates have an SMI of 0, perfect rods an SMI of 3. The age range of the group was 23– 85 years (mean 1 SD: 69.9 6 16.5). The biopsies had a cylindrical shape with a diameter of 8 mm and a length of 10 –12 mm.

the 3D pQCT scanner. Because the axes of the samples were precisely given by their sample holders, it was not necessary to align the direction of the axes. However, the relative positioning of the slices taken with the two scanners had to be matched. This was done by visual inspection of the 3D pQCT slices and the scaled mCT slices. The matching uncertainty is one slice (i.e., 165 mm). The corresponding slice positions in the 28 mm images were calculated with a scaling factor of 5.89 (5 165 mm/28 mm). An example of two matching slices is shown in Figure 1.

CT Measurements

Structure Extraction

All samples were first scanned with the mCT system,21 which is commercially available (mCT 20, Scanco Medical, Bassersdorf, Switzerland). It is used for the nondestructive imaging of bone biopsies with a diameter of up to 18 mm and a length of up to 50 mm. The spatial resolution of the system is 28 mm and for this comparative study cubic voxels with side lengths of 28 mm were used to represent the objects. The biopsies were measured in sample holders of 10 mm diameter, filled with water. By averaging and scaling the original 28 mm voxels to the voxel size of the 3D pQCT, a scaled mCT data set was obtained for studying the effect of the larger voxel size. The scaled images were unblurred and virtually noise-free due to the averaging of the voxels. Subsequently, measurements were performed with a highresolution 3D pQCT system, which is used for patient examinations.10 This system has a two-dimensional detector array in combination with a 0.2 3 10 mm line-focus X-ray tube, enabling simultaneous acquisition of a stack of parallel CT slices. The protocol for the specimens was the same as the one used for patient examinations: 60 high-resolution slices were measured with a voxel size of 165 mm in all three spatial directions, the effective energy was 40 keV, slice thickness 0.28 mm, field of view 84.48 mm, pixel matrix 512 3 512. For patient examinations, the radiation dose was 0.8 mSv (mean skin dose at measuring site). The samples, still in their sample holders, were placed into the 3D pQCT, with their cylindrical axes aligned with the axis of

The gray-scale images produced by the mCT were segmented using a low-pass filter to remove noise and a fixed threshold to extract the mineralized bone phase. The scaled mCT data sets were segmented using a fixed threshold only, because the noise was already removed by the scaling and averaging of the voxels. For the structure extraction of the 3D pQCT images the ridge technique introduced in a previous work was used.10 Because the data were too “blurred” and the voxel size too large for an accurate representation of the individual trabecular thickness, the ridges (i.e., the “centerpoints” of trabeculae) were extracted from the original 3D gray-level images. This resulted in a skeleton-like binary ridge image. Parameters for the gaussian filter and the ridge threshold were chosen to be the same as for the patient examinations. Such a ridge image is shown in Figure 2, together with the corresponding segmented mCT image. Structure Analysis Structural indices were assessed for both the original mCT data (28 mm) and the scaled mCT data (165 mm) using traditional histomorphometric methods as well as newly developed direct techniques. The volume-of-interest (VOI) was a cylinder of 8 mm in diameter and 9 mm in length. Bone volume BV and bone surface BS were calculated using a tetrahedron meshing technique generated with the marching cubes method.11 The total volume TV was identical to the cylindrical VOI. From BV, BS,

Table 1. Correlation (r2) of structural parameters of the 3D pQCT with the mCT mCT 3D pQCT BV/TV Tb.N* Tb.Th Tb.Sp a

p , 0.0001.

BV/TV a

0.98 0.85a 0.94a 0.93a

Tb.N* a

0.69 0.81a

Tb.Th* a

0.89

Tb.Sp* a

0.71

0.92a

Tb.N

Tb.Th

Tb.Sp

a

a

0.84a

0.80 0.92a

0.92

0.94a 0.81a

0.96a

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A. Laib and P. Ru¨egsegger Calibration of in vivo bone structure measurements

37

Table 2. Calibration equations of the 3D pQCT data with the mCT data mCT

3D pQCT 0.04 1 0.86BV/TV 0.17a 1 0.91 Tb.N* 0.08 1 0.57 Tb.Th 0.33 1 0.62 Tb.Sp 20.32a 1 1.47 Tb.N* 0.04 1 0.56 Tb.Th 20.05a 1 0.92 Tb.Sp

BV/TV Tb.N* Tb.Th* Tb.Sp* Tb.N Tb.Th Tb.Sp

Nonsignificant values (p . 0.01), all other values p , 0.0001.

a

and TV, the mean trabecular number (Tb.N), mean trabecular thickness (Tb.Th), and mean trabecular separation (Tb.Sp) were calculated assuming the plate model16: Tb.N 5 0.5 BS/TV; Tb.Th 5 2 BV/BS; Tb.Sp 5 2 (TV 2 BV)/BS. The structural indices were calculated as well using newly developed direct techniques based on the distance transformation of the binary object,5 and are denoted Tb.N*, Tb.Th*, and Tb.Sp*. They did not rely on an assumed model type and they were assessed directly as metric distances in 3D space. Tb.Th* was the mean thickness of the trabeculae, Tb.Sp* the mean thickness of the marrow cavities, and Tb.N* the mean inverse distance between the mid-axes of the structure. For the 3D pQCT images, the mean trabecular bone density (TBD) was calculated, calibrated with the European forearm phantom in hydroxyapatite (HA) densities.19 In a previous work we showed how a binary ridge image could be created and the ridge number density (RND) assessed as an indirect measure for the number of trabeculae. Applying the distance transformation method5 to the background of the binary ridge image, it was now possible to extract directly the metric parameter Tb.N*. Because the ridge images contained no information regarding bone volume, a mean BV/TV was assessed with the TBD, assuming a constant density of fully mineralized bone of 1.2 g HA/cm3. Even though the individual thickness of trabeculae is not retrievable from 165 mm resolution images, it was possible to calculate a mean trabecular thickness (Tb.Th) from the amount of bone and the mean number of trabecular elements by dividing BV/TV by Tb.N*, similar to methods used in standard histomorphometry. Tb.Sp could be calculated as (TV 2 BV)/TV 4 Tb.N*. These derived indices again assumed a plate model, while Tb.N* was a direct, three-dimensional parameter assessed without model assumptions. The standard histomorphometric parameters based on the volume and the surface of the bone (BV and BS)

Figure 3. Bone volume to tissue volume (BV/TV) from the 3D pQCT vs. BV/TV from the mCT. Quality of fit: r2 5 0.98.

were not available from the ridge images, because the ridges represented the midlines of the trabeculae and from which no information of the original bone volume or surface could be derived. All calculated indices were cross-correlated between mCT and 3D pQCT data sets and, where necessary, multiple ANOVA was performed with SAS/INSIGHT software (SAS Institute, Cary NC). Results Table 1 shows correlations between structural indices from the mCT and the 3D pQCT. Bone volume fraction has an r2 of almost 1 and the structural indices also have a very good quality of fit, with r2 between 0.81 and 0.96. The indices assuming a plate model show higher r2 values with the 3D pQCT data, but also their correlation with bone volume fraction is higher, suggesting that there is less additional information in them. Multiple regression was performed to determine if the correlations between the structural indices could be improved if they were combined with BV/TV. This was not the case for any of the indices.

Table 3. Correlation (r2) of structural parameters of the scaled mCT (with 165 mm voxels) with the original mCT (with 28 mm voxels) mCT Inherent plate-model assumption

Direct metric parameter Scaled mCT BV/TV Direct metric parameter Tb.N* Tb.Th* Tb.Sp* Inherent plate-model assumption Tb.N Tb.Th Tb.Sp a

p , 0.0001.

BV/TV a

Tb.N* a

0.998

0.71

0.82a 0.84a 0.82a

0.93a

0.94a 0.66a 0.71a

0.61a

Tb.Th* a

0.88

Tb.Sp* a

0.73

Tb.N

Tb.Th

Tb.Sp

a

a

0.88a

0.84

0.92

0.93a 0.95a

0.95a 0.95a

0.91a 0.69a

0.83a

0.83a 0.51a

0.83a

38

A. Laib and P. Ru¨egsegger Calibration of in vivo bone structure measurements

Figure 4. Trabecular number (Tb.N*) from the 3D pQCT vs. Tb.N* from the mCT. Quality of fit: r2 5 0.81. The intercept of 0.17 mm is statistically nonsignificant (p . 0.05).

The values of the resulting calibration equations for 3D pQCT are shown in Table 2. As examples, BV/TV and Tb.N* are plotted in Figure 3 and 4. The 90% confidence intervals (CI) for Tb.N* are 20.10 – 0.44 (1/mm) for the intercept and 0.70 –1.12 for the slope; for BV/TV, the 90% CIs are 0.02– 0.05 for the intercept and 0.81 to 0.90 for the slope. A comparison between the full-resolution mCT and the scaled mCT data is shown in Table 3. The model-independent direct indices Tb.N*, Tb.Th*, and Tb.Sp* have a much higher quality of fit (r2 5 0.93– 0.95) than the indirect indices (r2 5 0.69 – 0.83). The voxels of the scaled images seem too coarse for an accurate surface determination (even with the smoothing marching cube method), upon which the derivation of Tb.N, Tb.Th, and Tb.Sp rely (e.g., the mean Tb.N [1/mm] of all biopsies is 1.50 determined with the mCT, but only 0.40 for the scaled data). By directly measuring metric distances, Tb.N*, Tb.Th*, and Tb.Sp* can still be determined with good accuracy; for instance, mean Tb.N* 5 1.31 from the mCT vs. 1.39 from the scaled data. The 3D pQCT indices correlate very well with the direct indices of the scaled mCT with r2 5 0.91 (Tb.N*, Tb.Th*, and Tb.Sp*) to 0.98 (BV/TV). This indicates that, with suitable structure extraction, the effect of the blurring and the noise of the 3D pQCT data can be minimized.

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(Tb.N*, Tb.Th*, and Tb.Sp*) are influenced very little by the coarse voxels (r2 between 0.93 and 0.95). If traditional methods (with the plate model assumption) are used, however, working with 165 mm voxels is less accurate. For the 3D pQCT measurements it is shown that taking the densitometric TBD and deriving a mean BV/TV leads to almost the same results as for the mCT measurements with a quality of fit of 0.98. The structural indices can be calculated with very high r2 values of between 0.81 and 0.92, compared with the standard. Because the structural indices of the 3D pQCT data have a higher quality of fit to their corresponding mCT values than BV/TV, it is demonstrated that the in vivo system allows the accurate assessment of microarchitectural features. The primary additional information content of the structural assessment lies in the trabecular number, which shows a calibration equation with unity within the 90% confidence interval. It is interesting to note that Tb.N* from the mCT shows a lower correlation with BV/TV than Tb.N. This is a consequence of the plate model used to calculate Tb.N. Under the assumption of the plate model, decreasing bone mass can only reduce the number of plates and/or their thickness. In reality, however, the plates are also fenestrated (i.e., they are transformed gradually to rods). This results in a higher dependency of Tb.N on BV/TV. (Performing multiple regression on the mCT data revealed that, while Tb.N correlates with Tb.N*, with r2 5 0.87, also incorporating the structure model index [SMI] in the regression yields Tb.N 5 1.001 Tb.N* 2 0.10 SMI2 1 0.27 with an r2 of 0.99, where SMI is 0 for a plate-like structure and 3 for a rod-like structure; that is, the Tb.N values are influenced exactly according to the varying amount of rods present.) Comparison of the 3D pQCT with the scaled mCT gives correlation coefficients .0.91, indicating that, with a sophisticated structure extraction for the 3D pQCT data and a structure analysis using direct, metric techniques, the ideally achievable results at the given in vivo voxel size can almost be achieved. The 3D pQCT system is currently used for time-series measurements. It is expected that the calibrated in vivo examination will allow improved quantification of microarchitectural changes in the course of disease and/or treatment. Further work will be needed to evaluate the influence of the structural indices of entire bones on bone strength.20,23

Acknowledgment: This work was supported in part by Grant 31-45811.95 from the Swiss National Science Foundation.

References Discussion The purpose of this article was to calibrate measurements of a high-resolution 3D pQCT system with those of a mCT system, where the latter was assumed to have sufficient spatial resolution to produce correct structural images. In a separate study, we had the opportunity to measure some of our samples with a Synchrotron CT with 6 mm resolution.18 The comparison showed very high correlation of the structural indices with r2 5 0.97– 0.99, so the resolution of the mCT is considered adequate for our purposes. To study the influence of the larger voxel size of the in vivo system we used scaled mCT images. A comparison between mCT data with 28 mm voxel size and scaled mCT data with 165 mm voxel size indicates that directly derived indices

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Date Received: March 9, 1998 Date Accepted: August 26, 1998