David C. Newitt

Correlation of Trabecular Bone Structure with Age, Bone Mineral Density, and Osteoporotic Status: In Vivo Studies in the Distal Radius Using High Resolution Magnetic Resonance Imaging

High resolution magnetic resonance (MR) images of the distal radius were obtained at 1.5 Tesla in premenopausal normal, postmenopausal normal, and postmenopausal osteoporotic women. The image resolution was 156 μm in plane and 700 μm in the slice direction; the total imaging time was ∼16 minutes. An intensity‐based thresholding technique was used to segment the images into trabecular bone and marrow, respectively. Extensions of standard stereological techniques were used to derive measures of trabecular bone structure from these segmented images. The parameters calculated included apparent measures of trabecular bone volume fraction, trabecular thickness, trabecular spacing, and trabecular number. Fractal‐based texture parameters, such as the box‐counting dimension, were also derived. Trabecular bone mineral density (BMD) and cortical bone mineral content (BMC) were measured in the distal radius using peripheral quantitative computed tomography (pQCT). In a subset of patients, spinal trabecular BMD was measured using quantitative computed tomography (QCT). Correlations between the indices of trabecular bone structure measured from these high‐resolution MR images, age, BMD, and osteoporotic fracture status were examined. Cortical BMC and trabecular BMD at the distal radius, spinal BMD, trabecular bone volume fraction, trabecular thickness, trabecular number, and fractal dimension all decreased with age. Trabecular spacing showed the greatest percentage change and increased with age. In addition, significant differences were evident in spinal BMD, radial trabecular BMD, trabecular bone volume fraction, trabecular spacing, and trabecular number between the postmenopausal nonfracture and the postmenopausal osteoporotic subjects. Trabecular spacing and trabecular number showed moderate correlation with radial trabecular BMD but correlated poorly with radial cortical BMC. High resolution MR imaging, a potentially useful tool for quantifying trabecular structure in vivo, may have applications for understanding and evaluating skeletal changes related to age and osteoporosis.

High-Resolution Magnetic Resonance Imaging: Three-Dimensional Trabecular Bone Architecture and Biomechanical Properties

The purpose of this study was to use high-resolution magnetic resonance (MR) imaging combined with image analysis to investigate the three-dimensional (3D) trabecular structure, anisotropy, and connectivity of human vertebral, femoral, and calcaneal specimens. The goal was to determine whether: (a) MR-derived measures depict known skeletal-site-specific differences in architecture and orientation of trabeculae; (b) 3D architectural parameters combined with bone mineral density (BMD) improve the prediction of the elastic modulus using a fabric tensor formulation; (c) MR-derived 3D architectural parameters combined with BMD improve the prediction of strength using a multiple regression model, and whether these results corresponded to the results obtained using higher resolution depictions of trabecular architecture. A total of 94 specimens (12 x 12 x 12 mm cubes) consisting of trabecular bone only were obtained, of which there were 7 from the calcaneus, 15 from distal femur, 47 from the proximal femur, and 25 from the vertebral bodies. MR images were obtained using a 1.5 Tesla MR scanner at a spatial resolution of 117 x 117 x 300 microm. Additionally, BMD was determined using quantitative computed tomography (QCT), and the specimens were nondestructively tested and the elastic modulus (YM) was measured along three orthogonal axes corresponding to the anatomic superior-inferior (axial), medial-lateral (sagittal), and anterior-posterior (coronal) directions. A subset of the specimens (n=67) was then destructively tested in the superior-inferior (axial) direction to measure the ultimate compressive strength. The MR images were segmented into bone and marrow phases and then analyzed in 3D. Ellipsoids were fitted to the mean intercept lengths, using single value decomposition and the primary orientation of the trabeculae and used to calculate the anisotropy of trabecular architecture. Stereological measures were derived using a previously developed model and measures such as mean trabecular width, spacing, and number were derived. Because the spatial resolution of MR images is comparable to trabecular bone dimensions, these measures may be subject to partial volume effects and were thus treated as apparent measures, such as BV/TV, Tb.Sp, Tb.N, and Tb.Th rather than absolute measures, as would be derived from histomorphometry. In addition, in a subset of specimens, the Euler number per unit volume was determined to characterize the connectivity of the trabecular network. There were significant differences in the BMD, trabecular architectural measures, elastic modulus, and strength at the different skeletal sites. The primary orientation axes for most of the specimens was the anatomic superior-inferior (axial) direction. Using the fabric tensor formulation, in addition to BMD, improved the prediction of YM (SI), while including some of the architectural parameters significantly improved the prediction of strength. In comparing MR-derived 3D measures with those obtained from 20 microm optical images (n=18; 9 vertebrae, 9 femur specimens), good correlations were found for the apparent Tb.Sp and Tb.N, moderate correlation was seen for the apparent BV/TV, and poor correlation was found for the apparent Tb.Th. Using these higher resolution images, the fabric tensor formulation for predicting the elastic modulus also showed improved correlation between the measured and calculated modulus in the axial (SI) direction. In summary, high-resolution MR images may be used to assess 3D architecture of trabecular bone, and the inclusion of some of the 3D architectural measures provides an improved assessment of biomechanical properties. Further studies are clearly warranted to establish the role of architecture in predicting overall bone quality, and the role of trabecular architecture measures in clinical practice. (ABSTRACT TRUNCATED)

In Vivo High Resolution MRI of the Calcaneus: Differences in Trabecular Structure in Osteoporosis Patients

The purpose of this study was to use high resolution (HR) magnetic resonance (MR) images of the calcaneus to investigate the trabecular structure of patients with and without osteoporotic hip fractures and to compare these techniques with bone mineral density (BMD) in differentiating fracture and nonfracture patients. Axial and sagittal HR MR images of the calcaneus were obtained in 50 females (23 postmenopausal patients with osteoporotic hip fractures and 27 postmenopausal controls). A three‐dimensional gradient–echo sequence was used with a slice thickness of 500 μm and in plane resolution of 195 × 195 μm. Texture analysis was performed using morphological features, analogous to standard histomorphometry and fractal dimension. Additionally, BMD measurements of the hip (dual‐energy X‐ray absorptiometry) were obtained in all patients. Significant differences between both patient groups were obtained using morphological parameters and fractal dimension as well as hip BMD (p < 0.05). Odds ratios for the texture parameters apparent (app.) bone volume/total volume and app. trabecular separation were higher than for hip BMD. Receiver operator characteristic values of texture measures and hip BMD were comparable. In conclusion, trabecular structure measures derived from HR MR images of the calcaneus can differentiate between postmenopausal women with and without osteoporotic hip fractures.

Processing and Analysis of In Vivo High-Resolution MR Images of Trabecular Bone for Longitudinal Studies: Reproducibility of Structural Measures and Micro-Finite Element Analysis Derived Mechanical Properties

Abstract: The authors have developed a system for the characterization of trabecular bone structure from high-resolution MR images. It features largely automated coil inhomogeneity correction, trabecular bone region segmentation, serial image registration, bone/marrow binarization, and structural calculation steps. The system addresses problems of efficiency and inter- and intra-operator variability inherent in previous analyses. The system is evaluated on repetitive scans of 8 volunteers for both two-dimensional (2D) apparent structure calculations and three-dimensional (3D) mechanical calculations using micro-finite element analysis. Coil correction methods based on a priori knowledge of the coil sensitivity and on low-pass filtering of the high-resolution mages are compared and found to perform similarly. Image alignment is found to cause small but significant changes in some structural parameters. Overall the automated system provides on the order of a 3-fold decrease in trained operator time over previous manual methods. Reproducibility is found to be dependent on image quality for most parameters. For 7 subjects with good image quality, reproducibility of 2–4% is found for 2D structural parameters, while 3D mechanical parameters vary by 4–9%, with percent standardized coefficients of variation in the ranges of 15–34% and 20–38% respectively.

Evaluation of technical factors affecting the quantification of trabecular bone structure using magnetic resonance imaging

High resolution magnetic resonance (MR) techniques combined with standard techniques of stereology and texture analysis have been used to quantify trabecular structure. Using dried excised specimens from the tibia (n = 10) and radius (n = 2) we evaluate the impact of using volumetric gradient-echo (GE) and spin-echo (SE) MR imaging sequences, the relative importance of echo time in gradient-echo MR imaging, and the impact of different threshold values to segment the bone and bone marrow on the estimation of trabecular bone structure. We also investigate the inter-relationships between the different structural parameters derived from MR images. Images were obtained using fast gradient-echo and spin-echo imaging sequences, with TE values ranging from 7 to 17 ms using 4.7 and 1.5 Tesla imaging systems. In-plane image resolution ranged from 128 to 156 microns, and slice thickness ranged from 128 to 1000 microns. We derived stereological measures such as the mean intercept length, trabecular width, fractional area of trabecular bone, trabecular number, and trabecular spacing, the fractal dimension as a texture-related parameter and the Euler number as a measure of connectivity from these images. We found that the mean intercept length as a function of angle traced an ellipse with the orientation of the principal axis of the ellipse, a measure of trabecular orientation, identical when measured from the spin-echo or gradient-echo MR images. Absolute measures such as the fractional area, trabecular width, trabecular number, and fractal dimension as measured from gradient echo images were 28%, 30%, 1.3%, and 0.6% greater, respectively, than those calculated from spin-echo images, while the trabecular spacing was 14% less when calculated from gradient-echo images compared to spin-echo images. The structural parameters also depended on the echo time used to obtain the MR image. The choice of the threshold used to segment the high resolution images also affected the estimated structural parameters significantly. Our results indicate that MR may be used to visualize and quantify trabecular bone architecture; however, the different technical factors that could affect the appearance of MR images must be understood and considered in the data analysis and interpretation.

A Comparative Study of Trabecular Bone Properties in the Spine and Femur Using High Resolution MRI and CT

The purpose of this study was to use high resolution (HR) magnetic resonance (MR) and computed tomography (CT) images combined with texture analysis to investigate the trabecular structure of human vertebral and femoral specimens and to compare these techniques with bone mineral density (BMD) in the prediction of bone strength. Twenty‐nine bone cubes were harvested from 12 proximal femur cadaver specimens and 29 from 8 spines. HR MR and CT images were obtained, and texture analysis techniques were used to assess trabecular structure. Additionally, BMD, elastic modulus (EM), and maximum compressive strength were determined. R2 for EM versus texture measures computed in the MR images was higher (R2 = 0.27–0.64, p < 0.01) in the spine than in the femur specimens (R2 = 0.12–0.22, p < 0.05). R2 values were similar in the CT images. R2 for EM versus BMD was 0.66 (p < 0.01) in the spine and 0.61 (p < 0.01) in the femur specimens. In the MR images, texture measures combined with BMD in a multivariate‐regression model significantly increased R2, while improvement was less significant in the CT images. Thus, texture analysis may provide additional information needed to analyze bone strength and quality.

Magnetic resonance imaging of trabecular bone structure in the distal radius: Relationship with X-ray tomographic microscopy and biomechanics

The contribution of trabecular bone structure to bone strength is of considerable interest in the study of osteoporosis and other disorders characterized by changes in the skeletal system. Magnetic resonance (MR) imaging of trabecular bone has emerged as a promising technique for assessing trabecular bone structure. In this in vitro study we compare the measures of trabecular structure obtained using MR imaging and higher-resolution X-ray tomographic microscopy (XTM) imaging of cubes from human distal radii. The XTM image resolution is similar to that obtained from histomorphometric sections (18 µm isotropic), while the MR images are obtained at a resolution comparable to that achievable in vivo (156×156×300 µm). Standard histomorphometric measures, such as trabecular bone area fraction (synonymous with BV/TV), trabecular width, trabecular spacing and trabecular number, texture-related measures and three-dimensional connectivity (first Betti number/volume) of the trabecular network have been derived from these images. The variation in these parameters as a function of resolution, and the relationship between the structural parameters, bone mineral density and the elastic modulus are also examined. In MR images, because the resolution is comparable to the trabecular dimensions, partial volume effects occur, which complicate the segmentation of the image into bone and marrow phases. Using a standardized thresholding criterion for all images we find that there is an overestimation of trabecular bone area fraction (∼3 times), trabecular width (∼3 times), fractal dimension (∼1.4 times) and first Betti number/ volume (∼10 times), and an underestimation of trabecular spacing (∼1.6 times) in the MR images compared with the 18-µm XTM images. However, even for a factor of 9 difference in spatial resolution, the differences in the morphological trabecular structure measures ranged from a factor of 1.4 to 3.0. We have found that trabecular width, area fraction, number, fractal dimension and Betti number/volume measured from the XTM and MR images increases, while trabecular spacing decreases, as the bone mineral density and elastic modulus increase. A preliminary bivariate analysis showed that in addition to bone mineral density alone, the Betti number, trabecular number and spacing contributed to the prediction of the elastic modulus. This preliminary study indicates that measures of trabecular bone structure using MR imaging may play a role in the study of osteoporosis.

Ultrasound velocity of trabecular cubes reflects mainly bone density and elasticity.

Abstract. Studies have indicated that quantitative ultrasound (QUS) variables may be influenced by the mechanical properties of bone which in turn are determined by bones material and structural properties. However, from these studies it is unclear what role density, elasticity, and structure play in determining velocity. Eighteen defatted, 12-mm cubic trabecular bone specimens were cut from cadaveric specimens. Amplitude-dependent speed of sound (SOS) using a single point QUS system was assessed in three orthogonal axes. Magnetic resonance images were obtained, from which measures of apparent trabeuclar structure were derived. The specimens were nondestructively tested in compression along three orthogonal axes defined by the sides of the cubes. The elastic modulus (in the three directions) and the strength (in one direction) were determined. Trabecular BMD was measured by quantitative computed tomography. SOS varied significantly with direction of measurement, with the highest value in the axial direction (axial:1715 m/s, sagittal: 1662 m/second, and coronal: 1676 m/s). SOS of each of the three axes was generally associated with the various mechanical (r = 0.30–0.87), density (r = 0.81–0.93), and bone structural variables (0.3–0.8). However, after adjusting the SOS correlations by density, only the correlation with elasticity remained significant in the coronal direction. BMD alone explained 88–93% of variance in SOS whereas in the multivariate model, BMD plus elasticity and/or anisotropic variables explained 96–98% of the variance in SOS. Variability of SOS is explained mostly by density and to a small extent by elasticity or anisotropy. Since only 2–6% of the variance of the QUS measurement is not explained by density and elasticity, one could conclude that the remaining variance reflects other properties of bone or perhaps simply measurement error. Evidence that these other properties may be structure related is only found in the anisotropy of QUS parameter.

Trabecular Bone Architecture in the Distal Radius Using Magnetic Resonance Imaging in Subjects with Fractures of the Proximal Femur

Abstract:To determine whether magnetic resonance (MR)-derived measures of trabecular bone architecture in the distal radius are predictive for prevalent hip fractures, 20 subjects with hip fractures and 19 age-matched postmenopausal controls were studied. Bone mineral density (BMD) measures at the hip (dual-energy X-ray absorptiometry, DXA) and the distal radius (peripheral quantitative computed tomography, pQCT) were also obtained. We compared the MR-based structural measures derived in the radius with those in the calcaneus of the same patients. In the radius, images were acquired at an in-plane resolution of 156 μm and a slice thickness of 0.5 mm. Stereologic measures such as the apparent trabecular thickness (app. Tb.Th), fractional trabecular bone volume (app. BV/TV), trabecular spacing (app. Tb.Sp) and trabecular number (app. Tb.N) were derived from the images. Measures of app. Tb.Sp and app. Tb.N in the distal radius showed significant (p<0.05) differences between the two groups, as did hip BMD measures. However, radial trabecular BMD measures showed only a marginal difference (p= 0.05). Receiver operating curve analysis was used to determine the diagnostic efficacy of BMD, structural measures and a combination of the two. The area under the curve (AUC) for total hip BMD was 0.73, and for radial trabecular BMD was 0.69. AUC for most of the measures of trabecular bone structure at the distal radius was lower than for hip BMD measures; however, AUC for app. Tb.N at the radius was 0.69, comparable to trabecular BMD using pQCT. The AUC for combined BMD (hip) and structure measures was higher (0.87) when radius and calcaneus structure was included. Measures of trabecular architecture derived from MR images combined with BMD measures improve the discrimination between subjects with hip fractures and normal age-matched controls.

In Vivo Assessment of Architecture and Micro-Finite Element Analysis Derived Indices of Mechanical Properties of Trabecular Bone in the Radius

Abstract: Measurement of microstructural parameters of trabecular bone noninvasively in vivo is possible with high-resolution magnetic resonance (MR) imaging. These measurements may prove useful in the determination of bone strength and fracture risk, but must be related to other measures of bone properties. In this study in vivo MR imaging was used to derive trabecular bone structure measures and combined with micro-finite element analysis (μFE) to determine the effects of trabecular bone microarchitecture on bone mechanical properties in the distal radius. The subjects were studied in two groups: (I) postmenopausal women with normal bone mineral density (BMD) (n= 22, mean age 58 ± 7 years) and (II) postmenopausal women with spine or femur BMD −1 SD to −2.5 SD below young normal (n= 37, mean age 62 ± 11 years). MR images of the distal radius were obtained at 1.5 T, and measures such as apparent trabecular bone volume fraction (App BV/TV), spacing, number and thickness (App TbSp, TbN, TbTh) were derived in regions of interest extending from the joint line to the radial shaft. The high-resolution images were also used in a micro-finite element model to derive the directional Young’s moduli (E1, E2 and E3), shear moduli (G12, G23 and G13) and anisotropy ratios such as E1/E3. BMD at the distal radius, lumbar spine and hip were assessed using dual-energy X-ray absorptiometry (DXA). Bone formation was assessed by serum osteocalcin and bone resorption by serum type I collagen C-terminal telopeptide breakdown products (serum CTX) and urinary CTX biochemical markers. The trabecular architecture displayed considerable anisotropy. Measures of BMD such as the ultradistal radial BMD were lower in the osteopenic group (p<0.01). Biochemical markers between the two groups were comparable in value and showed no significant difference between the two groups. App BV/TV, TbTh and TbN were higher, and App TbSp lower, in the normal group than the osteopenic group. All three directional measures of elastic and shear moduli were lower in the osteopenic group compared with the normal group. Anisotropy of trabecular bone microarchitecture, as measured by the ratios of the mean intercept length (MIL) values (MIL1/MIL3, etc.), and the anisotropy in elastic modulus (E1/E3, etc.), were greater in the osteopenic group compared with the normal group. The correlations between the measures of architecture and moduli are higher than those between elastic moduli and BMD. Stepwise multiple regression analysis showed that while App BV/TV is highly correlated with the mechanical properties, additional structural measures do contribute to the improved prediction of the mechanical measures. This study demonstrates the feasibility and potential of using MR imaging with μFE modeling in vivo in the study of osteoporosis.