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


  • S. Majumdar Ph.D.,

    Corresponding author
    1. Magnetic Resonance Science Center & Musculo-Skeletal Section, Department of Radiology, University of California, San Francisco, California, U.S.A.
    • Department of Radiology, University of California–San Francisco, 1 Irving Street, MRSC, Box 1290, San Francisco, CA 94143 U.S.A.
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  • H. K. Genant,

    1. Magnetic Resonance Science Center & Musculo-Skeletal Section, Department of Radiology, University of California, San Francisco, California, U.S.A.
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  • S. Grampp,

    1. Magnetic Resonance Science Center & Musculo-Skeletal Section, Department of Radiology, University of California, San Francisco, California, U.S.A.
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  • D. C. Newitt,

    1. Magnetic Resonance Science Center & Musculo-Skeletal Section, Department of Radiology, University of California, San Francisco, California, U.S.A.
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  • V.-H. Truong,

    1. Magnetic Resonance Science Center & Musculo-Skeletal Section, Department of Radiology, University of California, San Francisco, California, U.S.A.
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  • J. C. Lin,

    1. Magnetic Resonance Science Center & Musculo-Skeletal Section, Department of Radiology, University of California, San Francisco, California, U.S.A.
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  • A. Mathur

    1. Magnetic Resonance Science Center & Musculo-Skeletal Section, Department of Radiology, University of California, San Francisco, California, U.S.A.
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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.


Current assessment of osteoporotic status is based on bone densitometry techniques such as quantitative computed tomography (QCT) and dual-energy X-ray absorptiometry (DXA). Although trabecular bone density is a widely used method for assessing fracture risk and therapeutic efficacy, it does not always predict the risk of individual fractures, explain the pathophysiology of osteoporotic changes, or assess the impact of a particular intervention completely.1–8 Thus, the quantitative analysis of trabecular bone structure and the elucidation of relationships between structural parameters and bone strength have been important topics of research in the area of osteoporosis. Recent efforts have been directed toward quantifying trabecular bone structure noninvasively, and imaging modalities such as ultrasound and magnetic resonance (MR) have emerged as potential methods for determining both bone density and structure.

High resolution MR images that resolve trabecular bone structure can be obtained in vitro at high magnetic field strengths9,10 and in vivo using clinical scanners at 1.5 T.11,12 The in-plane spatial resolution achievable in vivo is similar to the dimensions of trabeculae (78–200 μm), while it may be lower in the slice direction (400–1000 μm).11,12 As a result of these limits to the achievable resolution, partial volume effects occur, and the depiction of trabeculae in MR images may represent an integrated projection of a trabecular plate or an average over several trabeculae. While extensions of standard stereological techniques13 may provide a means of quantifying trabecular bone structure depicted in MR images, the MR-derived measures differ from those obtained at ∼20 μm resolution (such as those available in histomorphometric sections).14 Despite limitations in resolution, it has been demonstrated in vitro, using cubes from human distal radii14 and vertebral bodies,15 that structural indices derived from these images correlate with biomechanical properties such as the elastic modulus.

In this study, we extended the standard techniques of stereology and texture analysis to analyze the trabecular network in high resolution in vivo MR images (156 × 156 × 700 μm resolution) of the distal radius in normal and osteoporotic subjects. We derived parameters such as apparent trabecular bone volume fraction, apparent trabecular width, apparent trabecular spacing, and apparent trabecular number, and quantitative measures of texture such as a fractal-based box-counting dimension of the trabecular network. Since the spatial resolution in MR is sufficiently high that it does not merely depict a pattern or textural variation due to the presence of trabeculae, such as those seen in projection radiographs or routine computed tomography scans, we have chosen not to adopt the nomenclature for parameters such as “thickness texture” or “spacing texture” as previously done for computed tomography images.16 This study was not designed as a clinical trial and evaluation nor as a means of establishing the efficacy of MR in specific settings for studying osteoporosis. It represents one of the first studies using MR to evaluate differences in bone structure between normal and osteoporotic subjects with atraumatic vertebral fractures and is a forerunner to a larger case control study.


We studied healthy female subjects in accordance with the regulations of the Committee of Human Research at UCSF. The three different groups consisted of 10 premenopausal (group I, age 31 ± 8.4), 9 postmenopausal (group II, age 58.5 ± 8.6), and 11 osteoporotic postmenopausal (group III, age 70.4 ± 7.6). The presence of osteoporosis was determined by qualitative assessment of morphologic changes in the thoracic or lumbar spine by lateral conventional radiographs (an approximate decrease in height of more than 20% at the anterior, medial, or posterior section at one or more vertebral bodies).17

Peripheral QCT measurements were made with a Stratec XCT 960 scanner at 47 kVp and 0.3 mA (Stratec GmbH, Birkenfeld, Germany). A coronal scout view of the forearm was obtained and the ulnar length determined. An axial slice (2.5 mm slice thickness) was imaged in the distal radius, at a distance 4% of the ulnar length and proximal to the joint line. A thresholding and peeling algorithm was used to define the outer boundary of the radius to calculate the total trabecular bone region (threshold level 0.5 mg/cm3). The trabecular bone mineral density (BMD) was measured over this region of interest (ROI). The cortical ROI was defined through a thresholding algorithm detecting bone with high density in the outer rim and eliminating all voxels with a lower attenuation coefficient than the given threshold of 0.7 mg/cm3; the cortical BMC was then measured. The thresholding levels were kept constant for all subjects. The T-score for the pQCT trabecular BMD was also calculated for the postmenopausal women (groups II and III), where the T-score was defined as:

equation image(1)

Both groups of postmenopausal subjects were then stratified into two groups: those with T-scores <−2.5, or osteoporotic, in accordance with the World Health Organization definition of osteoporosis,18 and those whose T-scores >−2.5.

A subset of the patients (n = 6 in each group) had QCT exams on a GE 9800 scanner. A scout view was used to obtain 10-mm-thick midaxial sections through vertebral levels L1–L4 at a pixel resolution of 0.78 mm. The images were obtained at 80 kVp and 140 mA, and BMD was calculated from the Hounsfield units using a simultaneously scanned solid calibration phantom. The mean BMD at each level was assessed using an elliptical ROI within the trabecular bone area,19 and the mean lumbar BMD calculated from the average of L1–L4.

MR images through the distal radius were obtained using a 1.5 T Signa system (General Electric Medical Systems, Waukesha, WI, U.S.A.), and a dedicated wrist coil. A coronal localizer was used to identify axial regions of interest starting at the medial part of the joint line, which was identified as the demarcation of the epiphyseal growth plate and was clearly depicted in the MR scout view for all adult subjects. A modified fast gradient echo imaging sequence,20 with a short echo time to minimize artifacts, was used to obtain a volumetric data set in the axial plane. The imaging field of view was 8 × 8 cm, the matrix size was 512 × 512 pixels, the repetition time (TR) was 31 ms, the echo time (TE) was 7.8 ms, the flip angle was 30°, and all images were acquired at a bandwidth of ±8 kHz. A total of 60 slices, 700 μm thick, were acquired in a total imaging time of ∼16 minutes. The spatial resolution, Vres, of the MR images thus obtained was 156 × 156 × 700 μm, where the in-plane spatial resolution was comparable to the dimensions of trabecular bone but the slice thickness was greater.

The MR images were median filtered (kernel size 3 × 3) to decrease single pixel noise and then displayed and analyzed in reverse gray scale to ease the visualization of the trabecular network and the cortical rim (Fig. 1). In the reverse gray scale image, trabecular bone has a very high intensity, comparable to that of the cortical rim, while bone marrow has a low signal intensity. Muscle tissue has an intermediate signal intensity. The ROIs in each axial slice were manually defined using a graphics cursor. The high intensity cortical rim, as seen in Fig. 1, was used to define the boundary of the ROI, and care was taken to ensure that the analyzed ROI consisted only of the trabecular bone and bone marrow.

Figure FIG. 1.

Representative MR image through an axial section in the distal radius. The image is shown in reverse gray scale. The ROI is outlined and the intensity mean (Ir) over this ROI was measured. The histogram for this ROI is also shown. A slice proximal to the joint line was used to measure the mean intensity of cortical bone, Ib. The lower intensity value (IL) at which the height of the histogram reached half the maximum value is shown (Eq. 2).

To extend the standard stereological techniques and quantify the trabecular bone network, the images were thresholded and divided (or segmented) into a trabecular bone and a bone marrow phase. We used a standardized method of image thresholding based on the intensity histogram of a selected region of interest to ensure consistency in the image thresholding across all subjects studied.14 The rationale for selecting the different intensity values in our thresholding scheme is explained below. In this standardized method, the mean signal intensity (Ir) of the ROI to be analyzed was obtained, and a histogram of the distribution of signal intensities in the ROI was plotted (Fig. 1). Since the spatial resolution of the image, particularly in the slice direction, exceeds the dimensions of trabecular bone, each pixel in the image may not correspond to just one kind of tissue, i.e., either bone or marrow, but may contain a varying mixture of the two tissues. As a result, the histogram of signal intensities did not have two individual peaks (for bone and for marrow) but a single peak and an asymmetric tail for the lower signal intensities. Using the thick cortical rim as a standard, the intensity of trabecular bone (Ib) was obtained; the intensity value of marrow alone, however, was not readily obtainable. A large trabecular space consisting of bone marrow alone is particularly difficult to identify in young subjects with a dense trabecular network. The peak of the histogram represents the most frequently occurring pixel intensity value in the ROI. Since the slice thickness is a factor of approximately five to seven times greater than the dimensions of trabecular bone, the most frequently occurring pixel in the ROI consists of a mixture of trabecular bone and bone marrow. This peak intensity, since it is a mixture of the two phases, should have a value that is lower than the high intensity trabecular bone but higher than the intensity of pure bone marrow. Using this rationale, the marrow equivalent signal intensity was thus set by IL, the lower signal intensity at which the histogram reached half its peak value (Fig. 1). This is an empirical level and was adopted for the purpose of standardization. The apparent trabecular bone volume fraction, app BV/TV (number of bone pixels/total number of pixels) over the ROI was calculated to satisfy the following equation:

equation image(2)

The intensity value at which the fractional trabecular bone content in the ROI corresponded to the calculated app BV/TV was selected as the threshold, and the images were binarized into a bone and a marrow phase.

Standard stereological methods were then extended to quantify the trabecular structure in the binarized images.13 The total number of trabeculae-bone-marrow boundaries that cross a set of parallel rays at a given angle θ through the binarized image were counted to obtain PL(θ). The mean intercept length (MIL) was then computed as:

equation image(3)

In the past, we have defined the average value of MIL over all angles as a measure of trabecular thickness, Tb.Th; however, in keeping with the definitions of Parfitt et al.21 we have adopted the nomenclature that the apparent trabecular thickness width measure, app Tb.Th = ½ average value of MIL(θ). From these measures, apparent measures of app BV/TV and app Tb.Th, the apparent trabecular number app Tb.N, and trabecular spacing (app Tb.Sp) were derived.14 In addition, the images were analyzed to obtain texture parameters such as the fractal geometry-based box-counting dimension.22 A grid consisting of box sizes ε was superimposed on the boundary of the trabecular bone network to be quantified. The number of boxes of a given size ε containing the boundary points, N(ε), was computed. This procedure was repeated for different box dimensions, ε, with sides ranging from 2–128 pixels. The logarithm of ε versus the logarithm of N(ε) was plotted. After careful assessment of the technical factors23,24 the linear portion of this curve was carefully identified, and the dimension, D, was defined to be the negative slope of the linear portion of this curve.

Regional variations in the MR-derived structure parameters of the three groups were assessed. The trabecular BMD at the distal radius was measured at a single slice, but from the MR images, the trabecular bone structure was measured over a 3 cm length of the radius. An average value of the structural measures over the 3 cm range was used for statistical comparisons. Differences in trabecular structure and density in the postmenopausal normal and postmenopausal osteoporotic groups (based on the presence of vertebral fractures, i.e., groups II and III) were assessed using a one-tailed t-test. These differences were also assessed in the two groups stratified according to the radial trabecular bone BMD T-score (T-score <−2.5 compared with group I, osteoporotic). Although the small sample size limits the significance of the results, to examine the trend of the results, logistic regression was used to determine odds ratios for differences of 1 standard deviation (SD) for each measure in the postmenopausal subjects (groups II and III).


Representative slices from the distal joint line down to the radial shaft are shown for two subjects in Fig. 2. Cortical and trabecular bone are depicted as the lower or darker signal, while marrow that contains mobile protons is depicted as the higher or brighter signal intensity. As seen in Fig. 2, the premenopausal normal subject had a dense trabecular network extending from the joint line into the shaft of the radius, whereas the postmenopausal osteoporotic subject (group III) had fewer trabeculae both at the distal and proximal sites with considerable reduction in the proximal shaft. The decrease of trabecular bone in the proximal shaft compared with the distal radius that is seen in both subjects is in agreement with anatomic studies25 and has been previously shown in normal subjects using MR.26

Figure FIG. 2.

Axial images starting at the distal joint line (identified by the epiphyseal line seen in the MR locator) and going into the radial shaft in a subject from group I and in a subject from group III. The images depict cortical and trabecular bone as a signal void and marrow as the higher intensity component. There is considerable variation in trabecular structure along the length of the radius in both subjects.

In Fig. 3, the mean trabecular area fraction for all three groups are plotted for comparison to show that the app BV/TV along the whole radius was greatest in group I and lowest in group III and decreased from the joint line into the proximal shaft. There was considerable variation between subjects as a function of the distance along the radius. The maximum SD was approximately ± 0.2 for all three groups. The app BV/TV decreased rapidly over the first 1.5 cm, but was constant between 1.5–3 cm. The mean trabecular spacing was greatest for group III, lowest for group I (Fig. 4), and increased in the proximal radial shaft. Although the mean value for the three groups shows differentiation, trabecular spacing showed a great deal of biological variation. The maximum SD occurred in the proximal shaft of the radius and was 0.25, 4, and 1.25 mm in groups I, II, and III, respectively. These regional and subject-dependent variations, evident in all subject groups, may have considerable impact when assessing skeletal integrity using a single slice technique as in the case of single slice pQCT, where estimates of trabecular BMD may be affected significantly by a slice displacement of 2.5 mm.

Figure FIG. 3.

The mean value of the apparent trabecular bone area fraction in each of the groups I, II, and III are shown for comparison.

Figure FIG. 4.

The mean value of the apparent trabecular spacing in each of the groups I, II, and III are shown for comparison.

Analysis of covariance showed that age-related changes in groups I, II, and III were not significantly different. Age-related changes and correlation with BMD and trabecular bone structure are presented for all subjects in Table 1. Spinal BMD showed the highest correlation and highest percent decrement with age; however, these results were based on a subset of patients from each group (n = 6 from each group). The cortical BMC and trabecular BMD at the distal radius decreased with age and showed moderate correlation. The apparent trabecular bone area fraction, app BV/TV, decreased with age, although it showed lower correlation with age, while the app Tb.N and fractal dimension showed moderate correlation and decreased with age. The app Tb.Sp showed the greatest increase and moderate correlation with age. The correlation coefficient and the level of significance for age versus app Tb.Th was low, and the trend of variation of trabecular thickness with age was thus inconclusive.

Table Table 1. Linear Regression Model (n = 30) to Determine the Change in Bone Mineral Density and the Indices of Trabecular Bone Structure as a Function of Age
original image

The mean and the SD of the indices of trabecular bone structure in each group are shown in Table 2. Trabecular bone BMD in the spine and in the distal radius, BMC in the distal radius, app BV/TV, app Tb.Th, app Tb.N, as well as D had the expected trend, i.e., the mean values were highest in group I subjects, decreased progressively in the postmenopausal group (group II), and were lowest in the postmenopausal osteoporotic group (III). The app Tb.Sp was highest in group III, lowest in group I. A one-tailed t-test was used to determine the level of significance of the differences between the density and structure parameters in the postmenopausal groups (groups II and III). Significant differences existed between the fracture and the nonfracture groups in the measured spinal BMD, trabecular BMD, trabecular bone area fraction, trabecular spacing, and trabecular number. Although the sample size was small, and the effectiveness of age-adjusted t-tests were limited, age-adjusted results are shown in parenthesis in Table 2.

Table Table 2. Mean ± Standard Deviation of the Measures of BMD and Radial Trabecular Structure Indices
original image

The postmenopausal subjects were stratified into two groups; those with radial trabecular BMD T-scores greater than −2.5, and those less than −2.5 (osteoporotic according to the WHO definition of osteoporosis).18 In the postmenopausal group (groups II and III), 13 women had radial trabecular BMD T-scores greater than −2.5, and 7 had T-scores less than −2.5. The mean ± SD of the trabecular bone structure parameters between these two groups are shown in Table 2. Significant differences, even after age adjustment, was seen in the app Tb.Sp, app Tb.N, and D between these two groups.

The correlation between BMD, BMC, and the trabecular structure parameters are shown in Table 3. The app Tb.Sp and app Tb.N showed moderate correlation with radial trabecular BMD but showed considerably less correlation with radial cortical BMC. The trabecular bone structure parameters such as app Tb.Th and app Tb.Sp were derived from app BV/TV and app Tb.N explaining the good correlation between these parameters. The two independent measures app BV/TV and app Tb.N showed good correlation. As expected from previous studies,22 the box counting dimension showed good correlation with apparent trabecular spacing and trabecular number.

Table Table 3. Correlation (r) and Significance (p) Between Bone Density and Indices of Trabecular Bone Structure
original image

Logistic regression was used to calculate odds ratios for differences of 1 SD for each measure in groups II and III. The odds ratio was 2.44 (p < 0.13) for trabecular BMD in the radius, 1.43 (p < 0.09) for spinal BMD (n = 6 in each group), 1.01 (p < 0.09) for app BV/TV, and 2.46 (p < 0.09) for app Tb.N. The p value for all other parameters were not significant. The age-adjusted odds ratio was considered marginally significant (p < 0.14) only for app Tb.N (3.66), although in this small population size the effectiveness of such age-adjusted odds ratios is limited.


The results of this study indicate that high resolution MR images of trabecular bone structure may be useful for quantifying differences in trabecular structure. The moderate correlation between trabecular bone structure measurements and BMD measures was not surprising because the structure measures were averaged over a 3 cm length of the heterogenous distal radius, while BMD was measured at a single slice. Furthermore, density and structure, while related, are two different characteristics of trabecular bone. The poor correlation between structural parameters and trabecular BMD in the distal radius and cortical BMC in the distal radius was also expected. Trabecular bone changes may be related to cortical bone changes but may not follow identical trends in osteoporosis.

Although differences were seen in the indices of trabecular bone structure between the subjects in groups II and III (postmenopausal nonfracture and postmenopausal fracture subjects), the progression of osteoporosis is not necessarily uniform and may be nonparallel in axial and perpendicular parts as demonstrated previously.27–30 Keeping in mind this study's small sample size in which spinal BMD was assessed, marked differences in spinal BMD (n = 6) between groups II and III were not reflected in differences of the same magnitude in the distal radial density or structural parameters. Depending on whether osteoporosis was defined as a condition characterized by the occurrence of vertebral fractures or by stratifying subjects according to their radial trabecular BMD (the definition proposed by the WHO18, statistics for the trabecular bone structure indices (Table 2) showed differences. In fact, of the subjects who had no vertebral fractures (group II), 2 had T-scores (radial BMD) <−2.5, while of the fracture subjects (group III), 6 had T-scores >−2.5. As a result, the stratification of subjects according to their radial trabecular BMD identifies a different subset of patients.

In in vivo MR images, when the image resolution leads to partial volume effects, segmentation of the image into bone and marrow phases may be difficult. In this context, apparent trabecular bone area fraction and trabecular width are the most affected, not only by the limitations of spatial resolution, but also by the dependence on the specific thresholding criterion used to generate the binary image.

It is not suggested that MR techniques are a replacement for using histomorphometry, the gold standard for assessing trabecular bone structure. However, these techniques in conjunction with current histomorphometric methods may provide a measure of bone structure at several different sites in addition to the iliac crest. The clinical role and specific applications for the use of MR in the study of osteoporosis will depend on the specific requirements for reproducibility, accuracy, resolution, imaging time, and cost. The total imaging time is currently 12–16 minutes and with the development of specialized imaging coils, this may be further reduced. Currently, MR imaging can be applied to the distal radius, calcaneus, and phalanges. Further, imminent improvements in both hardware and software will lead to imaging of the proximal femur. Applications at each of these sites, reproducibility, and technical limitations are currently being conducted. Although technically demanding, it is anticipated that high resolution in vivo MR imaging may play a potentially significant role in the study of osteoporosis.


We acknowledge funding from the NIAMS grants, ROI AR-41226 and KO4 AR-01908.