Published online before print April 3, 2003, 10.1148/radiol.2273020420
(Radiology 2003;227:708-717.)
© RSNA, 2003
Trabecular Bone Structure of the Calcaneus: Preliminary in Vivo MR Imaging Assessment in Men with Osteoporosis1
Nathalie Boutry, MD,
Bernard Cortet, MD,
Patrick Dubois, PhD,
Xavier Marchandise, MD, PhD and
Anne Cotten, MD
1 From the Departments of Bone Radiology (N.B., A.C.), Rheumatology (B.C.), and Biophysics (P.D., X.M.), Hôpital Roger Salengro, CHRU de Lille, Boulevard du Pr. J Leclercq, 59037 Lille Cedex, France. Received April 30, 2002; revision requested July 10; revision received August 12; accepted September 25. Address correspondence to N.B. (e-mail: nboutry@chru-lille.fr).
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ABSTRACT
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PURPOSE: To use magnetic resonance (MR) imaging to evaluate potential differences in bone structure between men with and men without osteoporosis.
MATERIALS AND METHODS: Sagittal MR images of the calcaneus were obtained in 50 men (26 patients with osteoporosis and 24 age-matched healthy control subjects). Osteoporosis was defined as a low bone mineral density (at least 2.5 SDs below the normal value for young adults at either the lumbar spine or proximal femur) as measured with dual-energy x-ray absorptiometry. Seventeen patients had a history of osteoporotic fractures. For each participant, 10 consecutive sagittal three-dimensional gradient-echo MR sections were analyzed by using a rectangular region of interest. Twenty structural measurements were obtained from these images. Additionally, density measurements at the calcaneus were obtained in 46 participants. The significance of differences between the two groups was calculated by using the unpaired Student t test. The odds ratios for fracture per 1 SD decrease in the control group were calculated with logistic regression analysis. Adjustment for participant weight and height was performed if necessary.
RESULTS: Thirteen of 20 structural parameters, especially connectivity parameters, showed significant differences between control subjects and patients (P < .05). Differences between the two groups were more significant (P < .001) for apparent bone marrow skeleton length, apparent node count, apparent node-to-node strut count, and apparent terminus-to-terminus strut count. Odds ratios for 11 of 13 structural parameters but not for calcaneus density were significant (P < .05). After adjustment for calcaneus density, these parameters were still significant predictors of osteoporotic fracture.
CONCLUSION: Structural measurements derived from MR images of the calcaneus may be used in vivo to characterize trabecular bone architecture in men with osteoporosis.
© RSNA, 2003
Index terms: Bones, MR, 4642.121412 • Calcaneus, fractures, 4642.41 • Magnetic resonance (MR), three-dimensional, 4642.12117 • Osteoporosis, 40.56
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INTRODUCTION
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Osteoporosis is a common metabolic disorder characterized not only by a reduction in bone mineral density but also by changes in bone trabecular structure with propensity for atraumatic fractures (1). Bone mineral density is assessed routinely with dual-energy x-ray absorptiometry. A considerable overlap in density measurements between patients with and those without fractures exists, however, and it is now well established that microarchitecture plays an important role in cancellous bone strength. Since postmenopausal osteoporosis in women is viewed as a major public health problem, many studies have focused on in vivo evaluation of trabecular architecture with noninvasive techniques, including computed tomography (CT) and magnetic resonance (MR) imaging. Results of these studies have indicated that structural measurements derived from CT (2–4) and MR (5–7) images may be used in vivo to better differentiate patients with and those without osteoporotic fractures.
In contrast, there is little information on osteoporosis in men. However, morbidity, mortality, and health care costs related to male osteoporosis are far from negligible. In theUnited States, the estimated lifetime risk of developing any fracture is 13% in 50-year-old white men (compared with 40% in similarly aged women): 6% for hip fracture, 5% for vertebral fracture, and 2.5% for distal forearm fracture (8).
In the study of Davies et al (9), men in their 50s and 80s have 29% and 39% prevalence of vertebral fracture, respectively. It also has been reported that the mortality associated with hip fractures in men is at least twice that in women (10). Investigators in many studies have shown that bone mineral density decreases substantially with age in both men and women, which consequently increases the risk of osteoporotic fractures. The cutoff level of 2.5 SDs as defined in white postmenopausal women by the World Health Organization (11) is still being investigated in men. Some study results (12,13) suggest, however, that the same threshold of 2.5 SDs below the normal mean for young men could be the better choice.
Whatever it is, bone mineral density alone does not provide reliable estimates of bone strength and fracture risk in men either. Few histomorphometric studies have been conducted to investigate trabecular architecture variations in male osteoporosis. Moreover, results are conflicting. Initial reports (14–17) indicated that trabecular structural disorder occurred less frequently in men with osteoporosis than in women with osteoporosis. Legrand et al (18) reported significant differences in bone trabecular microarchitecture, as determined with the use of bone biopsy, when one compares vertebrae with and those without fracture in middle-aged men with osteopenia. Thus, noninvasive and nonionizing structural analysis with MR imaging may have applications for evaluation of skeletal changes related to male osteoporosis. The purpose of the present study, therefore, was to use MR imaging to evaluate potential differences in bone structure between men with and men without osteoporosis.
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MATERIALS AND METHODS
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Patients
From February 1998 to April 2000, 252 men were referred to our rheumatology department for measurement of bone mineral density because they had a history of low-energy fracture, risk factors for osteoporosis, or apparent osteopenia on radiographs of the spine.
Twenty-six consecutive patients with a decrease in bone mineral density (at least 2.5 SDs below the normal value for young adults at either the lumbar spine or proximal femur) were enrolled in our prospective study. Their ages ranged from 40 to 60 years (mean, 50.3 years). Of these 26 patients, 13 (50%) had relevant medical disorders associated with osteoporosis, including alcohol abuse (n = 2), hypercalciuria and/or moderate phosphate diabetes (n = 7), hypogonadism (n = 1), and use of glucocorticosteroid therapy (n = 3). The remaining 13 (50%) patients had no cause for bone fragility and were considered to have idiopathic osteoporosis.
A subset of 17 patients had osteoporotic fractures that resulted from a fall from standing height or that occurred without history of trauma. Eleven patients had vertebral fractures. These spinal fractures were defined according to the criteria proposed by Genant et al (19) as a decrease in height of more than 20% at the anterior, medial, or posterior aspect of one or more vertebral bodies in the thoracic or lumbar spine on conventional lateral radiographs. Vertebral fractures were isolated in seven patients and were associated with appendicular fractures in four.
Patients with osteoporosis were compared with age-matched healthy control subjects (mean age, 48.2 years; age range, 37–59 years). This control group was recruited through medical staff members and their relatives and through patients hospitalized for disorders not related to bone metabolism and malignant disease. None of the volunteers had a history of fracture or metabolic bone disease (hyperparathyroidism, osteomalacia, or renal osteodystrophy). All of the control subjects underwent anteroposterior and lateral spine radiography to ensure that they had no vertebral fractures.
Neither the patients nor the control subjects were receiving treatment that could influence bone mass or bone metabolism. Our study was approved by the ethics committee of our institution. Informed consent was obtained from all participants.
In this study, we examined the nondominant calcaneus. In patients with osteoporotic fractures of the nondominant extremity (hip, leg, and calcaneus) or a history of foot or ankle trauma, we examined the contralateral calcaneus.
Bone Densitometry
Dual-energy x-ray absorptiometry was performed by using a QDR 2000 scanner (Hologic, Waltham, Mass). For all participants, areal (integral) bone mineral density (in grams per square centimeter) was determined at the lumbar spine from L2 to L4 in the anteroposterior view and at the upper left femur. Fractured vertebrae were excluded from the analysis. Bone mineral density at the calcaneus was also assessed in the lateral view for 46 of 50 participants with a manually selected region of interest (ROI) placed in the whole calcaneus. The coefficient of variation of dual-energy x-ray absorptiometry was <1.5% for the lumbar spine and <2% for the upper femur.
MR Imaging
MR images of the calcaneus (Fig 1) were obtained by using a standard clinical 1.5-T whole-body imaging system (Vision; Siemens, Erlangen, Germany) equipped with 22 mT/m gradients and a flexible surface coil (Flex Small; Siemens). Participants lay supine on the scanning bed with legs outstretched. The flexible coil was wrapped around the calcaneus, and the foot was placed in a U-shaped polystyrene block. The foot was secured in position by placing weighted bags on each side of the heel. We used straps to secure the whole assembly and to perform motion-free MR imaging in this position. A small pad was also placed under the knee for the duration of the examination.
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Figure 1. Sagittal three-dimensional MR images obtained with a fast imaging with steady-state precession, or FISP, sequence (repetition time msec/echo time msec, 24/12) show the calcaneus in a 50-year-old male control subject (C, left) and a 50-year-old male patient with osteoporosis (OP, right). Images are shown in reverse gray scale (the trabecular bone is hyperintense, while the bone marrow is hypointense). Note the decrease in trabecular bone in the patient compared with that in the control subject.
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A series of transverse and coronal gradient-echo MR sequences were used to locate the calcaneus. Once localized, a set of sagittal images of the calcaneus was obtained by using a three-dimensional gradient-echo MR sequence (fast imaging with steady-state precession). The imaging parameters were 24/12; flip angle, 25°; field of view, 88 x 100 mm; section thickness, 0.7 mm; two signals acquired; and matrix, 439 x 512. Spatial resolution was 172 x 172 x 700 µm. Overall examination time was 19 minutes.
Structural Analysis
One author (N.B.) selected 10 consecutive central sections in each participant. The data set was then transferred from the MR imaging system to a personal computer for image texture analysis. A reverse gray-scale display was used to ease visualization of the trabecular network. After the cortical rim was excluded, a rectangular ROI was placed manually by the postprocessing technician (P.D.) in the superior part of the calcaneus (Fig 2). The ROI was chosen to be the largest possible rectangle that fit the inner perimeter of the calcaneus. Structural analysis was masked—that is, it was not indicated whether the participant was a patient or control subject. The algorithms used for characterization of the trabecular bone texture were developed in our biophysics department. The average time to perform the structural analysis in an individual was about 10 minutes.
Structural analysis consisted of trabecular network characterization. First, the boundary between cortical bone and soft-tissue background was defined by using an automatic contour detection algorithm. Trabecular bone was then extracted from the bone marrow by using a laplacian-Gaussian filter (20,21). This scheme generated a binary representation of the trabecular structure in which the dark regions represent bone marrow and the light regions represent the trabeculae (Fig 3).
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Figure 3a. Corresponding (a) ROIs and (b) binary images resulting from trabecular network extraction in the same control subject (C, left) and patient with osteoporosis (OP, right) as in Figure 1. In b, the trabeculae are shown in white, and the bone marrow spaces in black.
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Figure 3b. Corresponding (a) ROIs and (b) binary images resulting from trabecular network extraction in the same control subject (C, left) and patient with osteoporosis (OP, right) as in Figure 1. In b, the trabeculae are shown in white, and the bone marrow spaces in black.
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We took into account the regional heterogeneity of trabecular bone structure in the calcaneus (strong overestimation of the hyperintense regions) and adjusted the postprocessing as described previously for the distal radius (4). Therefore, the laplacian-Gaussian filter was applied first to the original image and then to the thresholding one. This thresholding scheme was achieved by selecting pixels with a signal intensity above the mean increased by 25% of the SD. The two resulting binary images were finally combined. This procedure permitted the pixels coming from the two resulting images to be kept and excluded the "false-positive finding" of trabeculations in the dark regions. An additional pruning step was also applied to the resulting image to remove the residual small artifacts.
From the binary image, we measured the following parameters derived from histomorphometric studies (Table 1): (a) ratio of apparent bone volume to tissue volume (percentage); (b) ratio of apparent trabecular bone perimeter to ROI area (per millimeter); (c) apparent trabecular thickness (in millimeters); (d) apparent trabecular number (per millimeter); (e) apparent trabecular separation (in millimeters); (f) ratio of apparent trabecular partition to ROI area (in square millimeters), defined as the number of trabecular bone "islands" for each ROI selected (4) (Fig 4); (g) ratio of apparent bone marrow partition to ROI area (in square millimeters), defined as the number of bone marrow islands for each ROI selected (4) (Fig 4); (h) trabecular bone pattern factor (per millimeter), as proposed by Hahn et al (15)—briefly, many concave surfaces indicate a well-connected structure (corresponding to low values of trabecular bone pattern factor), whereas numerous convex surfaces indicate a badly connected structure (high values of trabecular bone pattern factor) (Appendix, Fig 5); (i) ratio of Euler number to ROI area (in square millimeters), according to the method described by Compston (22)—the more connected the trabecular network, the smaller the Euler number (Appendix, Fig 6); and (j) star volume of the marrow space (in cubic millimeters), obtained with the chord method described initially by Levitz and Tchoubar (23) for porous glasses or cements and adapted to bone by Chappard et al (17) (Appendix, Fig 7)—with this method, a decrease in trabecular bone connectivity is characterized by an increase of star volume of the marrow space.
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Figure 4. Apparent trabecular partition is defined as the number of islands of trabecular bone (in red) for each ROI selected. These islands are more numerous when disconnection of trabeculae is present, as in the patient with osteoporosis (OP, right). Conversely, islands of bone marrow (in blue) are more numerous if the trabecular network is well connected, as in the control subject (C, left).
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Figure 5. Drawing illustrates the trabecular bone pattern factor method. P1 (in yellow) is the perimeter of the original image. P2 (in red) is the perimeter of the dilated image. The bone area is increased in both cases, while bone perimeter is increased only with the convex structure.
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Figure 6. Drawing illustrates the three-dimensional concept of Euler number in a control subject (C, left) and a patient with osteoporosis (OP, right). The enclosed medullary cavities are shown in yellow (m), the connected trabeculae in red (n). In the control subject (with a well-connected trabecular network), enclosed medullary cavities and connected trabeculae are abundant in comparison to those in the patient with osteoporosis (with a disconnected trabecular network). This provides low values of Euler number in highly connected systems.
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The binary image was thereafter skeletonized and pruned. On the skeletonized representation, several parameters derived from histomorphometric studies were also measured (4) (Table 2): ratio of apparent trabecular network skeleton length to ROI area (per millimeter) (Fig 8), ratio of apparent bone marrow skeleton length to ROI area (per millimeter) (Fig 9), ratio of apparent node count to ROI area (in square millimeters) (Fig 10), ratio of apparent terminus count to ROI area (in square millimeters) (Fig 10), ratio of apparent node-to-node strut count to trabecular strut length (per millimeter), ratio of apparent node-to-terminus strut count to total strut length (per millimeter), ratio of apparent terminus-to-terminus strut count to trabecular strut length (per millimeter), apparent node-to-node strut length (in millimeters), apparent node-to-terminus strut length (in millimeters), and apparent terminus-to-terminus strut length (in millimeters).
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Figure 9a. Bone marrow skeleton. (a) Binary images in the same participants as in Figure 1 have been inverted: The trabeculae are shown in black and the medullary spaces in white (the image of marrow spaces is the complementary set of the trabeculae within the cancellous space). (b) The skeleton of the bone marrow spaces is shown. C = control subject (left), OP = patient with osteoporosis (right).
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Figure 9b. Bone marrow skeleton. (a) Binary images in the same participants as in Figure 1 have been inverted: The trabeculae are shown in black and the medullary spaces in white (the image of marrow spaces is the complementary set of the trabeculae within the cancellous space). (b) The skeleton of the bone marrow spaces is shown. C = control subject (left), OP = patient with osteoporosis (right).
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Figure 10. Corresponding skeletonized images in the same control subject (C, left) and patient with osteoporosis (OP, right) as in Figure 1. Trabecular skeleton is shown in blue. A node is defined as a trabecular junction (shown in yellow), a terminus as a free end (shown in green), and a strut as part of the skeleton that connects some combination of nodes and termini: Alteration of trabecular bone connectivity is seen in the patient, as indicated by a decrease in node count and an increase in terminus count.
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Statistical Analysis
All statistical computations were performed with Statview 5 software (SAS Institute, Cary, NC). Means and SDs of bone mineral density and structural measurements were calculated for the patients and control subjects. The significance of differences between the two groups was calculated by using the unpaired Student t test at the 95% significance level. Correlations between architectural parameters and bone mineral density were assessed by means of linear regression analysis. Additionally, correlations were investigated between the ratio of apparent bone volume to tissue volume and other morphologic texture parameters (linear correction analysis with the Pearson r test, based on the model y = ax + b, where y is the dependent variable, x is the predictor variable, a is the slope, and b is the intercept of the regression line). When nonlinear relationships between the ratio of apparent bone volume to tissue volume and other texture measurements appeared evident at graphic examination, polynomial, logarithmic, and exponential models were computed.
Patients were categorized according to the presence (n = 17) or absence (n = 9) of osteoporotic fracture. Odds ratios (and 95% CIs) per SD were calculated by means of logistic regression analysis to provide an estimate of the discriminatory capability of each of the variables for osteoporotic fracture. Finally, calcaneus odds ratios adjusted for bone mineral density were also determined to examine the relationship between morphologic parameters and fracture status at the same skeletal site. For all data, adjustment for participant weight and height was performed if necessary (analysis of covariance).
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RESULTS
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Demographic data and results of dual-energy x-ray absorptiometry and MR imaging are shown in Tables 3 and 4. Participant weight and height were found to be significantly different between patients and control subjects (Table 3). After adjustment for weight and height, densities of the spine, hip, femoral neck, and calcaneus showed significant differences between the two groups (Table 3). Thirteen of 20 morphologic parameters were significantly different between patients and control subjects (Table 4). Differences in structural parameters between the two groups were more significant (P < .001) for apparent bone marrow skeleton length, apparent node count, apparent node-to-node strut count, and apparent terminus-to-terminus strut count.
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TABLE 3. Demographic Data and Results of Dual-Energy X-ray Absorptiometry in Patients with Osteoporosis and Control Subjects
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TABLE 4. Significantly Different Morphologic Parameters between Patients and Control Subjects after Adjusting for Weight and Height
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Statistically significant (P < .05) but moderate correlations between morphologic parameters and calcaneus bone mineral density were found only for the ratio of apparent bone volume to tissue volume (R = 0.31) and apparent terminus-to-terminus strut count (R = 0.29). The relationship between texture measurements and bone mineral density at other sites (spine and hip) showed similar results—that is, few and poor correlations (data not shown). Significant correlations between the ratio of apparent bone volume to tissue volume and other morphologic texture parameters are shown in Table 5. Nonlinear relationships were found between the ratio of apparent bone volume to tissue volume, apparent node count, apparent node-to-node strut count, and star volume. Use of polynomial regression was found to best delineate relationships between the variables.
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TABLE 5. Significant Correlations between the Ratio of Apparent Bone Volume to Tissue Volume and Other Morphologic Parameters
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Odds ratios were assessed after adjustment for participant weight and height and are shown in Table 6. They were found to be significant for bone mineral density at the spine, hip, and femoral neck and for all the morphologic parameters reported previously, except for apparent trabecular partition and Euler number. Adjustment for calcaneus bone mineral density did not modify odds ratios for the measurements of structure (Table 7). The ratio of apparent bone volume to tissue volume, apparent node count, apparent node-to-node strut count, and apparent node-to-terminus strut length were the strongest discriminators (P < .001) between patients with osteoporotic fractures and control subjects.
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TABLE 6. Association between Bone Mineral Density, Morphologic Parameters, and Fracture Status (after adjustment for weight and height)
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TABLE 7. Association between Morphologic Parameters and Fracture Status (after adjustment for weight, height, and calcaneus bone mineral density)
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DISCUSSION
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Results of this preliminary study indicate that measurements of trabecular structure derived from MR images of the calcaneus can be used in vivo to differentiate male patients with osteoporosis and healthy male control subjects. In this study, we used a standard clinical MR imager and its dedicated surface coil. Trabecular bone structure was assessed by using gradient-echo MR images with a spatial resolution of 172 x 172 x 700 µm.
A previous report (24) indicated that gradient-echo MR imaging typically results in an artifactual enlargement of the trabeculae, whereas spin-echo MR imaging does not. This magnetic susceptibility effect has been shown to decrease with shorter echo times (24). In the gradient-echo MR sequence we used, 12 msec was the shortest echo time possible. However, the artifactual trabecular thickening that resulted from our gradient-echo MR sequence applied equally to both control subjects and patients and should not adversely affect the structural differences between the two groups with respect to most measurements we obtained. Furthermore, Majumdar et al (24) indicated that standard parameters, such as apparent trabecular thickness and apparent trabecular separation, could be affected by the susceptibility effect, whereas connectivity parameters were less dependent on this artifact.
Because of its weight-bearing role, the calcaneus is an important site for predicting the risk of osteoporotic fracture. Majumdar et al (6) showed that structural measurements derived from MR images of the calcaneus may provide better differentiation of postmenopausal women with and those without osteoporotic fractures of the lower extremity than do MR images of the distal radius. In our study, we also chose to study the calcaneus because of the ease of performing MR imaging free of motion.
The trabecular structure of the calcaneus, however, is known to exhibit important regional variations (25). Inhomogeneity in structure and density of trabecular bone complicates both the segmentation process and ROI selection. However, Link et al (7) found no significant differences in structural parameters between postmenopausal women with and those without fractures according to the location of the ROI within the calcaneus (anterior, central, or posterior). We decided to place the ROI in the superior part of the calcaneus.
In the present study, 13 of 20 morphologic parameters were significantly different between patients and control subjects. As would have been expected with standard histomorphometry, the ratio of apparent bone volume to tissue volume was lower, and apparent trabecular separation was higher in patients than that in control subjects. In women with osteoporosis, in vivo (5–7) and in vitro (26) studies provided similar results. Investigators in those studies observed that parameters derived from MR images of the distal radius (5,6) and calcaneus (7), such as the ratio of apparent bone volume to tissue volume, apparent trabecular separation, and apparent trabecular number, were statistically different between postmenopausal women with and those without fractures. Studies in human bone specimens (26) have also shown that the ratio of apparent bone volume to tissue volume, apparent trabecular separation, and, to a lesser degree, apparent trabecular number derived from high-spatial-resolution MR images were highly correlated with bone biomechanical properties.
In our study, differences between the two groups were not significant for apparent trabecular number. Although a marked reduction in trabecular number is observed in women with osteoporosis, observations in men are conflicting. Chappard et al, with use of bone biopsy, showed that trabecular thickness was reduced significantly, while trabecular number was not modified in men with alcoholism-related osteoporosis (27) and men with corticosteroid-induced osteoporosis (17). Conversely, Francis et al (28) observed a reduction in trabecular number in men with primary osteoporosis. To explain our results, we must consider that a variety of disorders (alcohol abuse, hypercalciuria, hypogonadism, and use of glucocorticosteroid therapy) may have promoted premature male osteoporosis, resulting in a more heterogeneous population. In the present study, apparent trabecular thickness could not be used to differentiate patients and control subjects.
Similar results were observed by Majumdar et al (5,6) and Link et al (7) in women. As previously assumed by these authors, the section thickness used in vivo is still substantially thicker than the size of individual trabeculae (100–300 µm). Hence, the accuracy of the assessment of small trabeculae is subject to partial volume averaging.
In contrast to the extensive data available in women, there is relatively little information on the changes in trabecular network connectivity in men. Compston et al (14) and Hahn et al (15), by using a computerized method and the trabecular bone pattern factor technique, respectively, investigated age-related changes in men and women with use of bone biopsy findings. Both showed that men and women exhibited age-related bone loss, but changes in trabecular bone connectivity were less prominent in men than in women. Chappard et al (17) compared patients with corticosteroid-induced osteoporosis and control subjects by performing bone biopsy and showed that the trabecular network remained well connected as long as the ratio of bone volume to tissue volume was above 11%. More recently, Legrand et al (18) evaluated the trabecular microarchitecture in bone samples in a large and heterogeneous cohort of men with osteoporosis with vertebral fractures and those without fractures. These authors found a marked alteration of trabecular bone connectivity in patients with fractures compared with those without fractures. The morphologic texture parameters that provided the best results were trabecular number, trabecular separation, node-to-node strut count, terminus-to-terminus strut count, and interconnectivity index of the marrow cavities.
Interconnectivity index is a combination of several connectivity parameters derived from the bone marrow skeleton. The higher the index, the higher the level of connectivity of the bone marrow cavities, and conversely, the higher the fragmentation of the trabecular network. It is noteworthy that we observed similar findings, since parameters related to trabecular bone connectivity were significantly different between patients and control subjects. In our study, increased Euler number, trabecular bone pattern factor, and star volume of the marrow space in osteoporotic patients also showed loss of bone connectivity. In contrast, Legrand et al (18) found no significant differences between presence and absence of fractures in men with osteoporosis with respect to star volume of the marrow space. The potential to measure such structural parameters on MR images, however, clearly warrants further investigation.
In general, we found a few low correlations between bone mineral density measurements and trabecular bone microarchitecture. In the study of Legrand et al (18), hip density was weakly correlated with interconnectivity index and the number of struts joining two free ends (the ratio of apparent terminus-to-terminus strut count to trabecular strut length), whereas spinal density was correlated only with the ratio of apparent terminus-to-terminus strut count to trabecular strut length. In contrast to the results of Legrand et al (18), it must be noted that in our study, measurements of bone mineral density and estimation of the bone architecture concerned the same skeletal site. Similar trends, such as scarce and weak correlations between bone mineral density and trabecular structure parameters, were also observed by Majumdar et al (5) and Link et al (7) in women with osteoporosis. Such results might signify that bone mass and bone architecture are independent factors that contribute to osteoporotic fractures (5–7,18). Moreover, the ratio of apparent bone volume to tissue volume and some architectural descriptors were not correlated linearly, as previously reported by Chappard et al (17) and Legrand et al (18).
The present study does have limitations. First, it has a cross-sectional design. Second, the number of patients is small. Third, the group of male patients constitutes a heterogeneous series, as a result of the heterogeneity of the patient population developing male osteoporosis. Thus, Legroux-Gerot et al (29) evaluated causative factors in male osteoporosis. Of the 160 patients included in their study, only 28.1% had idiopathic osteoporosis. Alcoholism-related osteoporosis (22.5%), glucocorticoid-induced osteoporosis (19.4%), moderate idiopathic proximal tubule dysfunction (12.5%), and senile osteoporosis (8.8%) were identified in the remaining patients. In our study, a separate analysis could not be performed as a result of the small sample size in each subgroup.
Fourth, we measured many trabecular parameters and did not fully assess the relationships between the variables. However, all of these parameters do not relate to the same architectural changes. Standard measurements, such as trabecular number, thickness, or separation, do not provide valuable information on trabecular bone connectivity. In contrast, with the development of image analysis, new methods that focus on trabecular bone connectivity have been developed. When applied to bone biopsy, results are promising, but, presently, data about noninvasive techniques are scarce.
In summary, although our results are preliminary, they indicate that structural measurements derived from MR images of the calcaneus may be used in vivo to characterize trabecular bone architecture in men with osteoporosis. In addition, changes in trabecular bone connectivity are likely to be an important determinant of male osteoporosis in future investigations.
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APPENDIX
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Trabecular Bone Pattern Factor
The concept of trabecular bone pattern factor is supported by the fact that concave surfaces are abundant in a highly connected trabecular network. In contrast, convex surfaces are more numerous in patients with osteoporosis because of perforations in the trabecular network. Trabecular bone pattern factor is defined as (P1 - P2)/(A1 - A2), where P1 is the perimeter of the original image, P2 is the perimeter of the dilated image (dilation of one pixel), A1 is the area of the original image, and A2 is the area of the dilated image (Fig 4). As shown in Figure 5, the dilation process results in an increase of bone area whether the structure is convex or concave but an increase of bone perimeter only with convex structures (15). Thus, low values are obtained for trabecular bone pattern factor in a well-connected trabecular network, whereas high values are obtained in a disconnected network.
Euler Number
The Euler number method consists of counting the number of enclosed medullary cavities (m) and the number of connected trabeculae (n) in the cancellous space (Fig 6). Euler number (E) is defined as E = n - m. Negative values can be obtained in case of a highly connected trabecular network.
Star Volume of the Marrow Space
Star volume of the marrow space is defined as the mean volume of all the parts of the marrow space that can be seen unobscured in all possible directions from a random point (30). Thus, star volume was determined with use of the sampling point method in the original description (Fig 7a). In the present study, we used the chord length distribution method adapted by Chappard et al (17) for the study of bone (Fig 7b). Grids of parallel lines (with angles from 
to 2) are superimposed on the binary image of the marrow spaces. For each angle 
, the grid of parallel lines is intersected with the medullary spaces and provides a set of linear segments ("chords"). The cubed length of each overimposed chord (
) is computed on the whole section for a given angle , and the star volume of marrow spaces is defined as /3 ·
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ACKNOWLEDGMENTS
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The authors thank Marnix van Holsbeeck, MD, of the Henry Ford Hospital in Detroit, Mich, for his assistance in reviewing the manuscript.
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FOOTNOTES
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Abbreviation: ROI = region of interest
Author contributions: Guarantors of integrity of entire study, N.B., B.C., P.D.; study concepts, N.B., B.C.; study design, N.B., B.C., P.D.; literature research, N.B., B.C.; clinical studies, B.C., X.M.; data acquisition, N.B., B.C.; data analysis/interpretation, N.B., P.D., X.M.; statistical analysis, B.C.; manuscript preparation, N.B., B.C., A.C.; manuscript definition of intellectual content, X.M., A.C.; manuscript editing, N.B., B.C.; manuscript revision/review and final version approval, all authors.
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ABSTRACT
INTRODUCTION
