Individual trabecula segmentation (ITS)–based morphological analysis of microscale images of human tibial trabecular bone at limited spatial resolution

Authors


Abstract

Individual trabecula segmentation (ITS), a rigorous model-independent 3D morphological analysis, has been developed to assess trabecular plate and rod microstructure separately based on micro–computed tomographic (µCT) images. We examined the influence of the limited spatial resolution, noise, and artifact of high-resolution peripheral quantitative CT (HR-pQCT) on ITS measurements of human tibial trabecular bone. In comparison with measurements from “gold standard” µCT images (25 µm), decreased spatial resolution (40, 60, and 80 µm) of µCT had minimal influence on the correlations of the scale of trabecular plates (ie, plate bone volume fraction, thickness, and surface area) and the orientation (ie, axial bone volume fraction) and structural type (ie, plate tissue fraction) of the trabecular network. ITS measurements of HR-pQCT images correlated significantly with those of µCT images at a similar voxel size (80 µm, r = 0.71–0.94); correlations were stronger for plate-related parameters, suggesting that measurements of trabecular rods are more subject to noise and artifact associated with HR-pQCT imaging technology. In comparison with measurements of “gold standard” µCT images, the percent absolute errors of HR-pQCT measurements such as axial and plate bone volume fraction, plate number and tissue fraction, and plate and rod thickness (3.5% to 10.3%) were comparable with those of bone volume fraction (9.3%). For both HR-pQCT and µCT images, measurements of the scale and junction densities of trabecular plates and orientation and structural type were strong and positive indicators of the elastic modulus of trabecular bone (r = 0.59–0.95). We conclude that ITS measurements of HR-pQCT images are highly reflective of trabecular bone microarchitecture from a biomechanical perspective. © 2011 American Society for Bone and Mineral Research

Introduction

Osteoporosis is characterized by low bone mass and microarchitectural deterioration of trabecular bone1 with dramatic changes of trabecular structure from platelike to rodlike.2–5 Micro–computed tomographic (µCT) image–based individual trabecula segmentation (ITS) is a rigorous model-independent 3D morphological analysis that is capable of segmenting trabecular bone microstructure into individual trabecular plates and rods. Based on measurements of each individual trabecula, ITS-based morphological analyses enable separate assessments of trabecular plate and rod microstructure6 and have been used to elucidate the important but distinct roles of trabecular plates and rods in determining mechanical properties and failure mechanisms of trabecular bone.6–12

Recent advances in computed tomography (CT) and magnetic resonance imaging (MRI) techniques have made it possible to image human trabecular bone microstructure in vivo using commercially available scanners.13–15 Great interest has been focused on detecting bone microarchitectural changes despite the limited image resolution of these scans. The initial clinical application of the ITS analysis was on micro–magnetic resonance (µMR) images with limited spatial resolution.16 We successfully demonstrated the ability of ITS analysis to detect trabecular bone microstructural abnormalities in hypogonadal men, as well as subtle microarchitectural improvements following testosterone replacement in these men.16 High-resolution peripheral quantitative computed tomography (HR-pQCT) is a recently developed clinical modality that can assess the volumetric bone mineral density (vBMD) and 3D microstructure of cortical and trabecular bone at the distal radius and tibia.13, 14, 17–26 ITS-based morphological analyses overcome several limitations associated with the standard analysis provided by the HR-pQCT manufacturer. For example, several HR-pQCT standard parameters are derived rather than measured directly.27 The Tb.N* parameter is defined as the inverse of the mean distance between the midline of trabeculae. Tb.Th and Tb.Sp are derived based on Tb.N* and BV/TVd [ie, Tb.Th = (BV/TVd)/Tb.N* and Tb.Sp = (1 – BV/TVd)/Tb.N*] by analogy to standard histomorphometry.28 Therefore, since these parameters are all highly dependent on BV/TV, they may provide only limited additional information beyond BV/TV. In contrast to a statistical average at a global level, ITS parameters are based on measurements of each individual trabecula and are stratified by trabecular structural types, plate or rod, the two fundamental microstructural elements in the trabecular bone network. HR-pQCT-based finite-element (FE) analyses have been shown to provide valuable quantifications of mechanical competence such as elastic stiffness or estimated strength of bone.17, 29 One of the important values of ITS analysis is to provide insight and understanding of mechanisms by which bone quality and microstructure contribute to the mechanical competence of bone,6, 30 which can be evaluated by image-based FE analysis.

Our recent study using HR-pQCT and ITS-based morphological analyses of trabecular bone showed the potential of the combined techniques as sensitive tools to distinguish osteoporotic and healthy subjects and detect subtle differences in trabecular plate and rod microstructure between groups; these data suggest that ITS-based analysis of clinical HR-pQCT scans can accurately assess bone quality.30 Moreover, HR-pQCT and ITS analysis techniques were used recently in a clinical investigation of bone microarchitectural differences in premenopausal Chinese-American and white women.31 This study showcased the significance of trabecular types assessed by ITS analysis in determining mechanical competence of bone. It was shown that Chinese-American women have a more platelike trabecular structure but similar rodlike structure to white women and that these microstructural differences account for greater mechanical competence in Chinese-American women. These microstructural differences could help to explain the lower fracture rate of Chinese-American women.

With the growing use of imaging modalities such as HR-pQCT in clinical research, application of ITS analysis to clinical images has great potential for providing insights into the skeletal effects of aging and other disorders of mineral metabolism. However, it is possible that the low spatial resolution of clinical HR-pQCT images may influence microstructural measurements of trabecular plates and rods by ITS analysis. Moreover, the influence of image resolution on the relationships between ITS measurements and mechanical properties of trabecular bone is unknown.

In this study, the first goal was to determine the influence of image resolution on the ITS measurements of human trabecular bone. Second, we investigated the influence of the limited spatial resolution and image quality of the HR-pQCT imaging technique on ITS measurements. Third, the influence of the image resolution and noise of HR-pQCT and ITS measurements on the clinical detection of ethnicity- and disease-related bone changes was investigated and discussed. The specific objectives were (1) to examine the influence of image resolution on ITS measurements by comparing the measurements of coarsened µCT images (40, 60, and 80 µm) with “gold standard” µCT measurements (25 µm), (2) to validate ITS measurements of HR-pQCT images by correlation analysis with “gold standard” µCT measurements (25 µm) and coarsened µCT measurements (80 µm, similar to HR-pQCT voxel size), (3) to quantify the absolute measurement error associated with HR-pQCT and ITS technologies by comparison with “gold standard” µCT measurements (25 µm), (4) to provide a frame of reference for how these errors compare with clinically observed differences in case-control studies, and (5) to assess the ability of ITS measurements of HR-pQCT images and coarsened µCT images to predict the mechanical properties of trabecular bone.

Materials and Methods

Specimen preparation and HR-pQCT and µCT imaging

Nineteen freshly frozen human cadaveric tibiae from 13 donors (6 pairs and 7 singles, 10 males and 3 females) were obtained from the International Institute for the Advancement of Medicine (Scranton, PA, USA). The age of subjects ranged from 55 to 84 years, with an average of 70.6 years. The subjects' medical histories were screened to exclude metabolic bone diseases or bone cancer. A soft-tissue-equivalent gelatin phantom32 was built into the shape of human leg, and each tibia was scanned inside the phantom first by HR-pQCT (Xtreme CT, Scanco Medical AG, Bassersdorf, Switzerland) with the same settings used clinically (60 kVp, 1000 µA, 100-ms integration time, 82-µm voxel size). A reference line was placed manually at the endplate of the tibia to select the region of interest in the anteroposterior scout view. The HR-pQCT measurement of the tibia included 110 slices corresponding to a 9.02-mm section along the axial direction. Using a band saw, a 25-mm section centered in the scanned area from each distal tibia was obtained by two cuts along the transverse plane of the tibia. The central 10-mm section along the axial direction then was scanned by µCT (µCT 80, Scanco Medical AG) to encompass the same region scanned by HR-pQCT. An ex vivo scanning setting (70 kVp, 114 µA, 700-ms integration time) was used for µCT scanning, resulting in an isotropic 25-µm voxel size.

Image registration and thresholding

A pyramid, three-step registration approach was employed using a landmark-initialized mutual information-based registration toolkit33, 34 of an open-source software (National Library of Medicine Insight Segmentation and Registration Toolkit, Kitware, Inc., Clifton Park, NY, USA)35 to register the grayscale images achieved by HR-pQCT and µCT.16 All the µCT images were registered successfully to the corresponding HR-pQCT images to encompass the same volume of interest (Fig. 1). Then the registered µCT images were downsampled to 40-, 60-, and 80-µm isotropic voxel size. All the µCT images (25-, 40-, 60-, and 80-µm voxel size) were processed by Gaussian filtering and specimen-specific adaptive thresholding to extract the mineralized phase using the standard protocol of Scanco software for µCT analysis. The mineralized phase of HR-pQCT images was thresholded automatically by using a Laplace-Hamming filter followed by global threshold using a fixed value of 40% of maximal grayscale value of the images, a standard clinical protocol.18 Subsequently, a 70 × 70 × 70 voxel cubic subvolume was extracted from the center of the trabecular bone compartment of the thresholded HR-pQCT image (Fig. 1), equivalent to a physical size of 5.74 × 5.74 × 5.74 mm3. The corresponding subvolume also was extracted from each of the thresholded µCT images with different voxel sizes.

Figure 1.

The 3D reconstruction of whole-bone segment (left) and decomposed trabecular bone subvolume by ITS technique (right) based on registered (A) µCT and (B) HR-pQCT images of human distal tibiae. Color indicates different individual trabeculae.

Individual trabecula segmentation (ITS)–based morphological analyses

All the trabecular bone subvolumes of the distal tibia of HR-pQCT and µCT images were subjected to ITS-based morphological analyses. A complete volumetric decomposition technique was applied first to segment the trabecular network into individual plates and rods.8 Based on the evaluations of dimension and orientation of each individual trabecula, as well as junctions of surface and curve skeletons, a set of ITS-based morphological parameters were derived and divided into three categories: scale, topology, and orientation.36 ITS parameters of scale include plate and rod bone volume fraction (pBV/TV and rBV/TV), plate and rod number density (pTb.N and rTb.N, 1/mm), plate and rod thickness (pTb.Th and rTb.Th, mm), plate surface area (pTb.S, mm2), and rod length (rTb.ℓ, mm). The topologic description of the trabecular bone network includes structural-type measurement: plate and rod tissue fraction (pBV/BV and rBV/BV; percentage of plate/rod bone tissue over the total volume of bone tissue) and the connectivity measurements rod-rod, plate-rod, and plate-plate junction density (R-R, P-R, and P-P Junc.D, 1/mm3). Lastly, the orientation of the trabecular bone network is characterized by axial bone volume fraction along the longitudinal axis (aBV/TV). The definition of these ITS measurements can be found in Table 1. Detailed methods of the complete volumetric decomposition technique and ITS-based measurements can be found in the recent publications.6, 8

Table 1. Definition of the ITS-Based Microstructural Parameters
pBV/TVPlate bone volume fraction—the total volume of trabecular plates divided by the bulk volume
rBV/TVRod bone volume fraction—the total volume of trabecular rods divided by the bulk volume
aBV/TVAxial bone volume fraction—the total volume of trabeculae aligned with the longitudinal axis divided by the bulk volume
pBV/BVPlate tissue fraction—the total volume of trabecular plates divided by the total bone volume
rBV/BVRod tissue fraction—the total volume of trabecular rods divided by the total bone volume
pTb.N (1/mm)Trabecular plate number density—the cubic root of the total number of trabecular plates divided by the bulk volume
rTb.N (1/mm)Trabecular rod number density—the cubic root of the total number of trabecular rods divided by the bulk volume
pTb.Th (mm)Mean trabecular plate thickness—the average thickness of trabecular plates
rTb.Th (mm)Mean trabecular rod thickness—the average diameter of trabecular rods
pTb.S (mm2)Mean trabecular plate surface area—the average surface area of trabecular plates
rTb.ℓ (mm)Mean trabecular rod length—the average length of trabecular rods
P-P Junc.D (1/mm3)Plate-plate junction density—the total number of junctions between plate and plate divided by the bulk volume
P-R Junc.D (1/mm3)Plate-rod junction density—the total number of junctions between plate and rod divided by the bulk volume
R-R Junc.D (1/mm3)Rod-rod junction density—the total number of junctions between rod and rod divided by the bulk volume

Micro–finite element (µFE) analyses

Each thresholded µCT image at 40-µm voxel size, corresponding to a 143 × 143 × 143 voxel cubic subvolume, was converted to µFE models by converting each image voxel to an 8-node elastic brick element. A convergence study was conducted and suggested that the maximum difference between the models constructed at 40 and 25 µm was less than 2%. For each µFE analysis, bone tissue was modeled as an isotropic, linearly elastic material with a Young's modulus (Es) of 15 GPa and a Poisson's ratio of 0.3.37 Using a customized element-by-element preconditioned conjugate gradient solver,38 µFE analyses were performed for each model to derive axial Young's modulus E33 along the principal direction of orthotropic axes of the tibia.39 Detailed procedures also can be found in previously cited publications.16, 17

Statistical analyses

Statistical analyses were performed using NCSS software (NCSS 2007, NCSS Statistical Software, Kaysville, UT, USA). All data are expressed as mean ± SD. ITS measurements based on µCT images at 25 µm resolution were taken as “gold standard” measurements, against which measurements of coarsened µCT (40, 60, and 80 µm) and HR-pQCT images were compared. The effect of resolution (25, 40, 60, and 80 µm) on each ITS measurement of µCT images was examined by one-way analysis of variance (ANOVA) with repeated measures. If the resolution effect was significant, Bonferroni tests were conducted to compare measurements at each resolution (40, 60, and 80 µm) against the “gold standard” (25 µm). Since BV/TV of registered HR-pQCT and µCT images were significantly different, analysis of covariance (ANCOVA) with repeated measures and BV/TV as a covariate was performed to compare ITS measurements of HR-pQCT scans against “gold standard” and coarsened (80-µm) µCT measurements after adjustment of difference in BV/TV. Furthermore, if an HR-pQCT measurement was significantly correlated with its “gold standard” (25 µm µCT) by linear regression, the percentage of absolute error of the HR-pQCT measurement was calculated as 100 times the absolute value of the residual (difference between the “gold standard” and the prediction based on HR-pQCT) divided by the “gold standard” measurement. Finally, each of the ITS measurements of HR-pQCT and µCT images at different resolutions was correlated individually with the axial elastic modulus derived from the µCT-based µFE model by linear regression.

For correlation analyses, Pearson correlation coefficients are provided if both parameters were normally distributed, and Spearman correlation coefficients are provided if results of one or both parameters were not normally distributed based on a Shapiro-Wilk test. A p value of less than .05 was considered significant.

Results

Analysis of variance indicates that there is a significant effect of image resolution on most ITS measurements of coarsened µCT images, except for BV/TV, aBV/TV, pBV/TV, pTb.N, and R-R Junc.D (Table 2). However, significant correlations were found for most ITS measurements of µCT images at coarsened resolutions against “gold standard” measurements (Fig. 2). The correlations were strongest at 40 µm (r = 0.89–1.00) and decreased but remained significant at 60 µm (r = 0.54–1.00) for all the ITS measurements (Fig. 2). At 80 µm, correlations diminished for rTb.ℓ, P-P Junc.D, and P-R Junc.D, whereas the rest remained significant (r = 0.55–1.00; Fig. 2). Compared with the “gold standard” µCT at 25 µm, image resolution had minimal influence on correlations of trabecular orientation–related measurements (aBV/TV; r = 1.00 at all resolutions); plate-related measurements of scale, including pBV/TV (r = 1.00 at all resolutions), pTb.Th (r = 0.98–1.00), and pTb.S (r = 0.84–0.97); and structural-type measurement pBV/BV (r = 0.92–1.00; Fig. 2). In contrast, major degradations were observed in correlations for rTb.ℓ and trabecular network junction density measures P-P, P-R, and R-R Junc.D following image voxel downscaling (Fig. 2).

Table 2. ITS Measurements (Mean ± SD) of HR-pQCT Images at Voxel Size 82 µm and µCT Images at Voxel Sizes 25, 40, 60, and 80 µm
ParametersµCT 25 µmµCT 40 µmµCT 60 µmµCT 80 µmHR-pQCT 82 µm
  • a

    Significant difference between measurements of µCT images at voxel sizes 40, 60, and 80 µm and those of µCT images at 25 µm.

  • b,c, b

    Significant difference between measurements of HR-pQCT images and those of µCT images at 25 µm after adjustment for BV/TV.

  • c

    Significant difference between measurements of HR-pQCT images and those of µCT images at 80 µm after adjustment for BV/TV.

BV/TV0.136 ± 0.0480.142 ± 0.0480.138 ± 0.0500.134 ± 0.0520.245 ± 0.057b,c
aBV/TV0.112 ± 0.0410.109 ± 0.0430.096 ± 0.0520.088 ± 0.0420.120 ± 0.039b,c
pBV/TV0.118 ± 0.0490.112 ± 0.0500.099 ± 0.0440.082 ± 0.0510.109 ± 0.054b,c
rBV/TV0.018 ± 0.0040.030 ± 0.006a0.042 ± 0.008a0.052 ± 0.009a0.136 ± 0.019b,c
pTb.N (1/mm)2.03 ± 0.121.88 ± 0.141.64 ± 0.141.52 ± 0.181.44 ± 0.17b,c
rTb.N (1/mm)1.49 ± 0.191.57 ± 0.18a1.55 ± 0.15a1.55 ± 0.14a1.68 ± 0.11b,c
pTb.Th (mm)0.124 ± 0.0200.128 ± 0.0200.135 ± 0.0200.144 ± 0.018a0.211 ± 0.016b,c
rTb.Th (mm)0.116 ± 0.0130.129 ± 0.014a0.145 ± 0.015a0.159 ± 0.015a0.226 ± 0.009b,c
pTb.S (mm2)0.110 ± 0.0260.127 ± 0.0280.148 ± 0.031a0.143 ± 0.029a0.162 ± 0.015b
rTb.ℓ (mm2)0.470 ± 0.0230.539 ± 0.027a0.631 ± 0.024a0.662 ± 0.037a0.672 ± 0.030b,c
P-P Junc.D (1/mm3)7.10 ± 1.415.45 ± 1.23a3.36 ± 0.79a2.02 ± 0.65a1.75 ± 0.59b,c
P-R Junc.D (1/mm3)6.67 ± 1.745.92 ± 1.454.69 ± 0.96a3.36 ± 0.70a3.38 ± 0.79b,c
R-R Junc.D (1/mm3)1.13 ± 0.691.39 ± 0.831.33 ± 0.591.44 ± 0.522.02 ± 0.49b,c
pBV/BV0.847 ± 0.0670.763 ± 0.0960.660 ± 0.127aa0.564 ± 0.147a0.426 ± 0.111b,c
Figure 2.

Correlations between ITS measurements of µCT images at 25 µm and those at 40, 60, and 80 µm. *Significant correlations with p < .05.

Compared with “gold standard” µCT images, HR-pQCT significantly overestimated the bone phase in that BV/TV was almost double that of µCT images. After adjusting for the variance attributable to BV/TV, ITS measurements based on HR-pQCT images still were significantly different from those based on registered “gold standard” µCT measurements (25 µm), as well as from those based on registered 80 µm µCT measurements, the only exception being pTb.S (Table 2). Linear regression analysis revealed that HR-pQCT-based ITS measurements correlated significantly with those based on µCT images at a similar voxel size (80 µm, r = 0.71–0.95; Fig. 3) and that plate-related measures had particularly high correlations (r = 0.84–0.94; Fig. 3). In comparison with “gold standard” µCT measurements (25 µm), strong correlations were found for HR-pQCT measurements of aBV/TV, pBV/TV, pTb.Th, and pBV/BV (r = 0.82–0.93) and moderate correlations for rBV/TV, pTb.N, rTb.Th, and pTb.S (r = 0.44–0.66; Fig. 3). However, there was no correlation between HR-pQCT and “gold standard” µCT measurements for rTb.N, rTb.ℓ, P-P Junc.D, P-R Junc.D, and R-R Junc.D.

Figure 3.

Correlation between ITS measurements of HR-pQCT images and those of µCT images at 25 and 80 µm. *Significant correlations with p < .05.

Based on the linear correlations between the “gold standard” µCT measurements (25 µm) and HR-pQCT measurements, mean percentages of absolute errors were calculated for the eligible ITS measurements with exception of rTb.N, rTb.ℓ, and Junc.D, for which the correlations were not significant (Table 3). BV/TV of HR-pQCT had a 9.3% absolute error compared with that of µCT at 25 µm voxel size. The absolute errors associated with aBV/TV, pBV/TV, pTb.N, pTb.Th, rTb.Th, and pBV/BV were comparable with that of BV/TV, ranging from 3.5% to 10.3%. Larger errors were found for pTb.S (14.2%) and rBV/TV (17.2%). To provide a frame of reference for how these errors compare with clinically observed differences in case-control studies, percentages of absolute differences in ITS parameters found in two clinical studies are also listed in Table 3. In a study comparing bone microarchitecture of healthy and osteoporotic young women, the most significant differences were found in pBV/TV, rBV/TV, aBV/TV, and pTb.N (15.6% to 31.3%) and were much greater than the corresponding absolute error associated with each parameter (3.8% to 17.2%). Moreover, in our recent study of microarchitectural differences between Chinese-American and white women, significant differences were found in pBV/TV, aBV/TV, pTb.N, and pBV/BV (15.8% to 47.4%). The difference in each of these parameters was much greater than its associated absolute error (3.8% to 10.3%). A significant difference also was observed in pTb.Th between Chinese-American and white women (4.5%) that was similar to the measurement error (4.4%). In addition, a significant difference was found in pTb.S in both studies (10.2% and 10.8%); however, the measurement error associated with pTb.S was greater (14.2%).

Table 3. Mean Percentage Absolute Errors of ITS Measurements Based on HR-pQCT Images in Comparison with “Gold Standard” µCT-Based Measurements (Voxel Size 25 µm) and Percent Difference in HR-pQCT-Based ITS Measurements Between Healthy and Osteoporotic Young Women30 and Between Premenopausal Chinese-American and White Women31
ITS parametersMean percent absolute error (%)Percent absolute difference between healthy and osteoporotic young women30Percent absolute difference between premenopausal Chinese-American and white women31
  • *

    Significant differences.

BV/TV9.329.5*12.5*
aBV/TV9.617.5*25.6*
pBV/TV10.323.4*47.4*
rBV/TV17.231.3*10.5
pTb.N3.815.6*15.8*
pTb.Th4.40.64.5*
rTb.Th6.31.30.6
pTb.S14.210.2*10.8*
pBV/BV3.52.540.1*

For µCT images with voxel sizes between 25 to 80 µm, ITS measurements of aBV/TV (r = 0.98–1.00), pBV/TV (r = 0.99–1.00), pTb.N (r = 0.56–0.94, except for 25 µm), pTb.Th (r = 0.84–0.87), rTb.Th (r = 0.75–87), pTb.S (r = 0.78–0.86), and pBV/BV (r = 0.89–0.93) were significantly and positively associated with axial elastic modulus E33 of trabecular bone (Table 4). In contrast, rTb.N (r = –0.47 to –0.75) and R-R Junc.D (r = –0.62 to –0.82) of µCT images significantly and negatively correlated with E33 at each voxel size. rBV/TV correlated negatively with E33 at 25 and 40 µm voxel size. rTb.ℓ of µCT images had no significant correlation with E33 at 25 or 40 µm but correlated negatively and significantly with E33 at 60 and 80 µm (Table 4). Owing to the change of image voxel size, relationships between E33 and P-R Junc.D changed significantly from negative correlations at 25 and 40 µm (r = –0.66 and –0.59) to a positive correlation at 80 µm (r = 0.58). In addition, relationships between E33 and P-P Junc.D also changed from no correlation at 25 and 40 µm to significant and positive correlations at 60 and 80 µm (r = 0.64 and 0.90; Table 4).

Table 4. Pearson Correlation Coefficient (r) Between Axial Elastic Modulus E33 and ITS Measurements (Mean ± SD) of HR-pQCT Images at Voxel Size 82 µm and µCT Images at Voxel Sizes 25, 40, 60, and 80 µm
ParametersµCT 25 µmµCT 40 µmµCT 60 µmµCT 80 µmHR-pQCT 82 µm
  • Note: The significant correlations are given in bold.

  • a

    p < .001.

  • b

    p < .01.

  • c

    p < .05.

BV/TV0.99a0.99a0.99a1.00a0.78a
aBV/TV1.00a1.00a1.00a0.98a0.93a
pBV/TV1.00a0.99a0.99a0.99a0.95a
rBV/TV−0.55a−0.54a0.370.060.06
pTb.N (1/mm)0.390.56c0.78a0.94a0.86a
rTb.N (1/mm)−0.72a−0.75a−0.73a−0.47c0.17
pTb.Th (mm)0.86a0.84a0.87a0.84a0.77a
rTb.Th (mm)0.75a0.81a0.83a0.87a0.35
pTb.S (mm2)0.86a0.84a0.78a0.78a0.63b
rTb.ℓ (mm2)0.120.35−0.69b−0.46c0.39
R-R Junc.D (1/mm3)−0.75a−0.82b−0.76b−0.62b0.32
P-R Junc.D (1/mm3)−0.66b−0.59c0.200.58b0.76a
P-P Junc.D (1/mm3)0.060.210.64b0.90b0.85a
pBV/BV0.89a0.91a0.93a0.93a0.89a
rBV/BV−0.89a−0.91a−0.93a−0.93b−0.89a

For HR-pQCT images, ITS measurements of aBV/TV, pBV/TV, pTb.N, pTb.Th, pTb.S, P-R Junc.D, P-P Junc.D, and pBV/BV (r = 0.63–0.95) were positively associated with E33, consistent with the corresponding relationships for µCT images at 80 µm voxel size (Table 4). rBV/TV had no correlation with E33, which also was consistent with findings for µCT images at 80 µm. In addition, four rod-related measurements of HR-pQCT images—rTb.N, rTb.Th, rTb.ℓ, and R-R Junc.D had no significant correlation with E33, whereas the corresponding measurements of µCT images at 80 µm were significantly correlated with E33.

Discussion

The goal of this study was to examine the influence of spatial resolution and image quality associated with HR-pQCT imaging technique on ITS measurements of human tibial trabecular bone. In general, we found that the limited spatial resolution and image quality of clinical images had minimal influence on measurements of the scale of trabecular plates and the orientation and structural type of the trabecular bone network; these HR-pQCT measurements were associated with very small absolute errors and correlated significantly and strongly with their corresponding µCT measurements at a much higher image resolution and reduced noise level. Moreover, ITS measurements of HR-pQCT images correlated significantly with those of µCT images at similar voxel sizes; plate-related parameters correlated more strongly than rod-related parameters, suggesting that measurements of trabecular rods are more subject to noise and artifact associated with HR-pQCT imaging technology. For both µCT and HR-pQCT images, even at limited spatial resolution, measurements of the scale and junction densities of trabecular plates and measurements of orientation and structural type of trabecular bone network were strong and positive indicators of mechanical competence of trabecular bone.

pBV/TV, a measure of the amount of platelike trabecular bone, and aBV/TV, a measure of the amount of axially aligned trabecular bone, were not influenced by spatial resolution; these measures at 40, 60, and 80 µm correlated perfectly with those at 25 µm. Moreover, pBV/TV and aBV/TV based on HR-pQCT images had similar percent absolute errors as BV/TV, correlated strongly with “gold standard” measurements, and were the strongest indicators of axial elastic modulus. Our previous studies have shown that pBV/TV and aBV/TV represent those aspects of trabecular bone microarchitecture with the most significant implications for bone strength.6, 7, 40 Thus their application to clinical HR-pQCT images should provide more insight into mechanistic studies of metabolic bone diseases and their treatment and potentially could improve fracture risk assessment.

pTb.Th, rTb.Th, and pTb.S were overestimated and pBV/BV was underestimated when images were coarsened. Despite this, however, at 40, 60, and 80 µm, these measures correlated highly with those at 25 µm. pTb.Th, rTb.Th, and pTb.S are measurements of mean size of individual trabeculae and positive indicators of the elastic modulus of trabecular bone. Furthermore, these measurements based on HR-pQCT images correlated significantly with “gold standard” µCT measurements. Likely owing to the image noise and artifact associated with HR-pQCT imaging, rTb.Th of HR-pQCT scans did not reflect elastic modulus. One of the major structural changes in osteoporotic bone is the conversion of platelike to rodlike trabecular bone, which weakens bone strength to a greater extent than can be accounted for by the loss of bone volume. ITS parameter pBV/BV is a measure of the “platelikeness” of trabecular bone structure. The strong correlation between pBV/BV of HR-pQCT images and “gold standard” µCT measures and a minimal absolute error associated with pBV/BV of HR-pQCT suggested that measurement of pBV/BV on clinical HR-pQCT scans accurately reflects the amount of platelike bone. Furthermore, its high correlation with E33 indicates that it is a significant predictor of bone's mechanical competence.

rBV/TV and rTb.N were overestimated and pTb.N was underestimated when image voxel size was coarsened. While these measurements at 40 and 60 µm still correlated strongly with “gold standard” measurements, the correlations were much weaker for HR-pQCT images or when µCT image voxel was coarsened to 80 µm. The negative correlation between E33 and rTb.N of µCT images suggests that increased rod number is associated with reduced elastic modulus of trabecular bone. However, similar to rTb.Th, the correlation with E33 diminished for rTb.N of HR-pQCT images, suggesting that the image noise and artifact associated with HR-pQCT imaging have major effects not only on the accuracy of rod-related measurements but also on their relationship with elastic modulus of bone. In contrast, pTb.N measurements by both HR-pQCT and µCT were highly associated with E33, indicating that increased number of trabecular plates contributes to bone's mechanical competence.

Reduced spatial resolution had the most significant impact on ITS measurements of junction densities and rTb.ℓ. At 60 µm, they were only weakly correlated with 25 µm measurements. For both HR-pQCT and µCT images with approximately 80 µm voxel size, these measurements differed dramatically from those measured at 25 µm. Especially for R-R Junc.D, ANOVA testing indicated that there was no significant influence of image voxel size on the measurements; however, the correlations of R-R Junc.D, based on the coarsened images, with the “gold standard” measurements decreased significantly. This suggests a significant decrease in precision of the measured R-R Junc.D with decreasing image resolution. Measurements of junction densities and rTb.ℓ are highly dependent on the skeletonized and classified trabecular bone network. Certain details of trabecular bone microarchitecture apparent at a high spatial resolution cannot be represented at a reduced resolution. Thus bone images with coarsened voxel size represent a trabecular bone network with reduced complexity. Furthermore, reduced image resolution also makes it more difficult to distinguish a trabecular plate from a rod, therefore resulting in overestimation of rodlike structure. This is so because the classification of trabecular structural type is based on an iterative skeletonization process, and coarsened voxel size reduces the number of required iterations. In other words, the procedure to identify plate or rod structural type is simplified when image voxels are coarsened. With greater voxel size, more trabecular plates were identified as rods, and rTb.ℓ was overestimated and correlated less strongly with “gold standard” measurements. Similarly, based on a much more simplified trabecular bone skeleton associated with increased voxel size, all the junction density measurements were underestimated and less correlated with “gold standard” measurements.

Although P-R and P-P Junc.D of HR-pQCT and µCT images at limited spatial resolutions were not consistent with their “gold standard” measurements, surprisingly, they were positively and highly correlated with E33. It is intriguing that based on high-resolution µCT images, P-P Junc.D had no correlation and P-R Junc.D had a negative correlation with E33, suggesting that these parameters are substantially affected by image resolution and noise. Whether the significant correlations between these parameters of HR-pQCT images and elastic modulus are artifactual or reflect true relationships of trabecular microarchitecture and mechanical competence is unclear but is a worthy topic of investigation in the future studies.

To evaluate the performance of ITS analyses of HR-pQCT images in detecting bone microarchitectural abnormalities, a comparison between the measurement error and the differences that occur in aging or metabolic bone disease is essential (Table 3). As a novel clinical image analysis tool, there have only been two published studies using the combined HR-pQCT and ITS techniques. However, these two studies clearly showed that the measurement error owing to the limited image resolution and noise of HR-pQCT did not affect the performance of ITS analyses in detecting the significant differences associated with the disease/ethnicity. Since there are dramatic changes in trabecular microstructure from plates to rods in aging and osteoporosis, ITS measurements of HR-pQCT images may offer unique microstructural measures that are independent of bone mass yet detect subtle but important changes in trabecular types and numbers at the onset of bone loss and during progression toward osteoporosis. As demonstrated by previous studies,7, 41 microarchitectural changes such as loss of trabeculae or changes from plates to rods have far greater impact than decreases in bone mass on the mechanical competence of trabecular bone.

There are several limitations associated with this study. HR-pQCT imaging of cadaver bone is not affected by patient motion artifacts commonly encountered under in vivo situations. Although a soft-tissue-equivalent gelatin phantom was scanned with cadaver bone, noise associated with the acquired bone image could be different from that in in vivo situations. Owing to computational costs associated with ITS analysis of high-resolution µCT images, we used approximately 6 mm cubic subvolumes for this validation study. While we do not expect any major change in conclusions by extending the current analyses to a larger region of interest, in future HR-pQCT studies, we will apply ITS analyses to the entire trabecular bone compartment in order to reduce sampling error associated with regional variations.42 Results and conclusions of this study were based on images of human distal tibial bone from an older cohort. Confirmation for bone images from other anatomic locations and younger cohorts will be required. However, given the wide range of bone volume fraction and microarchitecture of bone specimens used in this study and the robustness of the ITS technique, our findings should apply to other skeletal sites and other types of cohorts. In this study, we used the FE model–derived elastic modulus as a representative of trabecular bone's mechanical competence. Other properties, such as yield strength, ultimate stress, and toughness, are also critical to define bone's mechanical properties. We did not examine the relationship between ITS parameters and experimentally determined mechanical properties, which is another limitation of this study. A more extensive study focusing on these relationships is currently being conducted in our laboratory.43 Furthermore, we and others have shown that the elastic modulus derived from FE models is highly correlated with both elastic modulus and yield strength from mechanical testing.44–46

In conclusion, we have tested the accuracy of ITS measurements based on HR-pQCT and µCT images of the human distal tibia at limited spatial resolutions with reference to high-resolution µCT measurements. The high correlations we observed for measurements of the scale of trabecular plates, trabecular bone orientation, and structural types suggest that ITS analyses can adequately quantify most microstructural aspects of bone quality even at a limited spatial resolution. Moreover, high correlations between these ITS measurements of HR-pQCT images and elastic modulus suggest that measurements based on coarsened trabecular bone images with clinical imaging noise reflect the biomechanical characteristics of trabecular bone microarchitecture.

Disclosures

Drs Liu and Guo are inventors of the ITS analysis software used in the study, and they may or may not benefit from results of this study. The other authors state that they have no conflicts of interest.

Acknowledgements

This work was supported in part by grants from the National Institutes of Health (AR051376, AR055968, and AR052661) and the Thomas L Kempner and Katheryn C Patterson Foundation. We would like to thank Dr X Henry Zhang for acquisition of the HR-pQCT and µCT images used in this study.

Author's roles: Study design: XEG and XSL. Study conduct: XSL. Data analysis: XSL and DJM. Data interpretation: XSL, ES, DJM, and XEG. Drafting manuscript: XSL. Revising manuscript content: ES, DJM, and XEG. Approving final version of manuscript: XSL, ES, DJM, and XEG. XSL takes responsibility for the integrity of the data analysis.

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