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Background: A current challenge in osteoporosis is identifying patients at risk of bone fracture., Purpose: To identify the machine learning classifiers that predict best osteoporotic bone fractures and, from the data, to highlight the imaging features and the anatomical regions that contribute most to prediction performance., Study Type: Prospective (cross-sectional) case-control study., Population: Thirty-two women with prior fragility bone fractures, of mean age = 61.6 and body mass index (BMI) = 22.7 kg/m 2 , and 60 women without fractures, of mean age = 62.3 and BMI = 21.4 kg/m 2 . Field Strength/ Sequence: 3D FLASH at 3T., Assessment: Quantitative MRI outcomes by software algorithms. Mechanical and topological microstructural parameters of the trabecular bone were calculated for five femoral regions, and added to the vector of features together with bone mineral density measurement, fracture risk assessment tool (FRAX) score, and personal characteristics such as age, weight, and height. We fitted 15 classifiers using 200 randomized cross-validation datasets. Statistical Tests: Data: Kolmogorov-Smirnov test for normality. Model Performance: sensitivity, specificity, precision, accuracy, F1-test, receiver operating characteristic curve (ROC). Two-sided t-test, with P < 0.05 for statistical significance., Results: The top three performing classifiers are RUS-boosted trees (in particular, performing best with head data, F1 = 0.64 ± 0.03), the logistic regression and the linear discriminant (both best with trochanteric datasets, F1 = 0.65 ± 0.03 and F1 = 0.67 ± 0.03, respectively). A permutation of these classifiers comprised the best three performers for four out of five anatomical datasets. After averaging across all the anatomical datasets, the score for the best performer, the boosted trees, was F1 = 0.63 ± 0.03 for All-features dataset, F1 = 0.52 ± 0.05 for the no-MRI dataset, and F1 = 0.48 ± 0.06 for the no-FRAX dataset. Data Conclusion: Of many classifiers, the RUS-boosted trees, the logistic regression, and the linear discriminant are best for predicting osteoporotic fracture. Both MRI and FRAX independently add value in identifying osteoporotic fractures. The femoral head, greater trochanter, and inter-trochanter anatomical regions within the proximal femur yielded better F1-scores for the best three classifiers., Level of Evidence: 2 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2019;49:1029-1038., (© 2018 International Society for Magnetic Resonance in Medicine.)

Background Bone remodels in response to mechanical loads and osteoporosis results from impaired ability of bone to remodel. Bone microarchitecture analysis provides information on bone quality beyond bone mineral density (BMD). Purpose To compare subchondral bone microarchitecture parameters in the medial and lateral tibia plateau in individuals with and without fragility fractures. Material and Methods Twelve female patients (mean age = 58 ± 15 years; six with and six without previous fragility fractures) were examined with dual-energy X-ray absorptiometry (DXA) and 7-T magnetic resonance imaging (MRI) of the proximal tibia. A transverse high-resolution three-dimensional fast low-angle shot sequence was acquired (0.234 × 0.234 × 1 mm). Digital topological analysis (DTA) was applied to the medial and lateral subchondral bone of the proximal tibia. The following DTA-based bone microarchitecture parameters were assessed: apparent bone volume; trabecular thickness; profile-edge-density (trabecular bone erosion parameter); profile-interior-density (intact trabecular rods parameter); plate-to-rod ratio; and erosion index. We compared femoral neck T-scores and bone microarchitecture parameters between patients with and without fragility fracture. Results There was no statistical significant difference in femoral neck T-scores between individuals with and without fracture (-2.4 ± 0.9 vs. -1.8 ± 0.7, P = 0.282). Apparent bone volume in the medial compartment was lower in patients with previous fragility fracture (0.295 ± 0.022 vs. 0.317 ± 0.009; P = 0.016). Profile-edge-density, a trabecular bone erosion parameter, was higher in patients with previous fragility fracture in the medial (0.008 ± 0.003 vs. 0.005 ± 0.001) and lateral compartment (0.008 ± 0.002 vs. 0.005 ± 0.001); both P = 0.025. Other DTA parameters did not differ between groups. Conclusion 7-T MRI and DTA permit detection of subtle changes in subchondral bone quality when differences in BMD are not evident.

Purpose To determine if 3-T magnetic resonance (MR) imaging of proximal femur microarchitecture can allow discrimination of subjects with and without fragility fracture who do not have osteoporotic proximal femur bone mineral density (BMD). Materials and Methods Sixty postmenopausal women (30 with and 30 without fragility fracture) who had BMD T scores of greater than -2.5 in the hip were recruited. All subjects underwent dual-energy x-ray absorptiometry to assess BMD and 3-T MR imaging of the same hip to assess bone microarchitecture. World Health Organization Fracture Risk Assessment Tool (FRAX) scores were also computed. We used the Mann-Whitney test, receiver operating characteristics analyses, and Spearman correlation estimates to assess differences between groups, discriminatory ability with parameters, and correlations among BMD, microarchitecture, and FRAX scores. Results Patients with versus without fracture showed a lower trabecular plate-to-rod ratio (median, 2.41 vs 4.53, respectively), lower trabecular plate width (0.556 mm vs 0.630 mm, respectively), and lower trabecular thickness (0.114 mm vs 0.126 mm) within the femoral neck, and higher trabecular rod disruption (43.5 vs 19.0, respectively), higher trabecular separation (0.378 mm vs 0.323 mm, respectively), and lower trabecular number (0.158 vs 0.192, respectively), lower trabecular connectivity (0.015 vs 0.027, respectively) and lower trabecular plate-to-rod ratio (6.38 vs 8.09, respectively) in the greater trochanter (P < .05 for all). Trabecular plate-to-rod ratio, plate width, and thickness within the femoral neck (areas under the curve [AUCs], 0.654-0.683) and trabecular rod disruption, number, connectivity, plate-to-rod ratio, and separation within the greater trochanter (AUCs, 0.662-0.694) allowed discrimination of patients with fracture from control subjects. Femoral neck, total hip, and spine BMD did not differ between and did not allow discrimination between groups. FRAX scores including and not including BMD allowed discrimination between groups (AUCs, 0.681-0.773). Two-factor models (one MR imaging microarchitectural parameter plus a FRAX score without BMD) allowed discrimination between groups (AUCs, 0.702-0.806). There were no linear correlations between BMD and microarchitectural parameters (Spearman ρ, -0.198 to 0.196). Conclusion 3-T MR imaging of proximal femur microarchitecture allows discrimination between subjects with and without fragility fracture who have BMD T scores of greater than -2.5 and may provide different information about bone quality than that provided by dual-energy x-ray absorptiometry. © RSNA, 2018.

Purpose: To use 7T magnetic resonance imaging (MRI) to determine how trabecular bone microarchitecture varies at the epiphysis, metaphysis, and diaphysis of the distal radius., Materials and Methods: The distal radius of 24 females (mean age = 56 years, range = 24-78 years) was scanned on a 7T MRI using a 3D fast low-angle shot sequence (0.169 × 0.169 × 1 mm). Digital topological analysis was applied at the epiphysis, metaphysis, and diaphysis to compute: total trabecular bone volume; trabecular thickness, number, connectivity, and erosion index (a measure of network resorption). Differences and correlations were assessed using standard statistical methods., Results: The metaphysis and epiphysis had 83-123% greater total bone volume and 14-16% greater trabecular number than the diaphysis (both P < 0.0001). The erosion index was significantly higher at the diaphysis than the metaphysis and epiphysis (both P < 0.01). The most elderly volunteers had lower trabecular number (<66 years mean 0.29 ± 0.01; ≥66 years, 0.27 ± 0.02, P < 0.05) and higher erosion index (<66 years mean 1.18 ± 0.17; age ≥66 years, mean 1.42 ± 0.46, P < 0.05) at the epiphysis; differences not detected by total trabecular bone volume., Conclusion: 7T MRI reveals trabecular bone microarchitecture varies depending on scan location at the end-of-bone, being of overall higher quality distally (epiphysis) than proximally (diaphysis). Age-related differences in trabecular microarchitecture can be detected by 7T MRI. The results highlight the potential sensitivity of 7T MRI to microarchitectural differences and the potential importance of standardizing scan location for future clinical studies of fracture risk or treatment response., Level of Evidence: 3 J. Magn. Reson. Imaging 2017;45:872-878., (© 2016 International Society for Magnetic Resonance in Medicine.)

Osteoporosis is associated with increased risk of fractures, which is clinically defined by low bone mineral density. Increasing evidence suggests that trabecular bone (TB) micro-architecture is an important determinant of bone strength and fracture risk. We present an improved volumetric topological analysis algorithm based on fuzzy skeletonization, results of its application on in vivo MR imaging, and compare its performance with digital topological analysis. The new VTA method eliminates data loss in the binarization step and yields accurate and robust measures of local plate-width for individual trabeculae, which allows classification of TB structures on the continuum between perfect plates and rods. The repeat-scan reproducibility of the method was evaluated on in vivo MRI of distal femur and distal radius, and high intra-class correlation coefficients between 0.93 and 0.97 were observed. The method's ability to detect treatment effects on TB micro-architecture was examined in a 2 years testosterone study on hypogonadal men. It was observed from experimental results that average plate-width and plate-to-rod ratio significantly improved after 6 months and the improvement was found to continue at 12 and 24 months. The bone density of plate-like trabeculae was found to increase by 6.5% (p  =  0.06), 7.2% (p  =  0.07) and 16.2% (p  =  0.003) at 6, 12, 24 months, respectively. While the density of rod-like trabeculae did not change significantly, even at 24 months. A comparative study showed that VTA has enhanced ability to detect treatment effects in TB micro-architecture as compared to conventional method of digital topological analysis for plate/rod characterization in terms of both percent change and effect-size.

Purpose: To evaluate the within-day and between-day measurement reproducibility of in vivo 3D MRI assessment of trabecular bone microarchitecture of the proximal femur., Materials and Methods: This Health Insurance Portability and Accountability Act (HIPPA)-compliant, Institutional Review Board (IRB)-approved study was conducted on 11 healthy subjects (mean age = 57.4 ± 14.1 years) with written informed consent. All subjects underwent a 3T MRI hip scan in vivo (0.234 × 0.234 × 1.5 mm) at three timepoints: baseline, second scan same day (intrascan), and third scan 1 week later (interscan). We applied digital topological analysis and volumetric topological analysis to compute the following microarchitectural parameters within the femoral neck: total bone volume, bone volume fraction, markers of trabecular number (skeleton density), connectivity (junctions), plate-like structure (surfaces), plate width, and trabecular thickness. Reproducibility was assessed using root-mean-square coefficient of variation (RMS-CV) and intraclass correlation coefficient (ICC)., Results: The within-day RMS-CVs ranged from 2.3% to 7.8%, and the between-day RMS-CVs ranged from 4.0% to 7.3% across all parameters. The within-day ICCs ranged from 0.931 to 0.989, and the between-day ICCs ranged from 0.934 to 0.971 across all parameters., Conclusion: These results demonstrate high reproducibility for trabecular bone microarchitecture measures derived from 3T MR images of the proximal femur. The measurement reproducibility is within a range suitable for clinical cross-sectional and longitudinal studies in osteoporosis., (© 2015 Wiley Periodicals, Inc.)

Osteoporosis is a disease of poor bone quality. Bone mineral density (BMD) has limited ability to discriminate between subjects without and with poor bone quality, and assessment of bone microarchitecture may have added value in this regard. Our goals were to use 7 T MRI to: (1) quantify and compare distal femur bone microarchitecture in women without and with poor bone quality (defined clinically by presence of fragility fractures); and (2) determine whether microarchitectural parameters could be used to discriminate between these two groups. This study had institutional review board approval, and we obtained written informed consent from all subjects. We used a 28-channel knee coil to image the distal femur of 31 subjects with fragility fractures and 25 controls without fracture on a 7 T MRI scanner using a 3-D fast low angle shot sequence (0.234 mm × 0.234 mm × 1 mm, parallel imaging factor = 2, acquisition time = 7 min 9 s). We applied digital topological analysis to quantify parameters of bone microarchitecture. All subjects also underwent standard clinical BMD assessment in the hip and spine. Compared to controls, fracture cases demonstrated lower bone volume fraction and markers of trabecular number, plate-like structure, and plate-to-rod ratio, and higher markers of trabecular isolation, rod disruption, and network resorption (p < 0.05 for all). There were no differences in hip or spine BMD T-scores between groups (p > 0.05). In receiver-operating-characteristics analyses, microarchitectural parameters could discriminate cases and controls (AUC = 0.66-0.73, p < 0.05). Hip and spine BMD T-scores could not discriminate cases and controls (AUC = 0.58-0.64, p ≥ 0.08). We conclude that 7 T MRI can detect bone microarchitectural deterioration in women with fragility fractures who do not differ by BMD. Microarchitectural parameters might some day be used as an additional tool to detect patients with poor bone quality who cannot be detected by dual-energy X-ray absorptiometry (DXA).

Purpose: To determine how subchondral bone microarchitecture is altered in patients with mild knee osteoarthritis., Materials and Methods: This study had Institutional Review Board approval. We recruited 24 subjects with mild radiographic knee osteoarthritis and 16 healthy controls. The distal femur was scanned at 7T using a high-resolution 3D FLASH sequence. We applied digital topological analysis to assess bone volume fraction, markers of trabecular number (skeleton density), trabecular network osteoclastic resorption (erosion index), plate-like structure (surface), rod-like structure (curve), and plate-to-rod ratio (surface-curve ratio). We used two-tailed t-tests to compare differences between osteoarthritis subjects and controls., Results: 7T magnetic resonance imaging (MRI) detected deterioration in subchondral bone microarchitecture in both medial and lateral femoral condyles in osteoarthritis subjects as compared with controls. This was manifested by lower bone volume fraction (-1.03% to -5.43%, P < 0.04), higher erosion index (+8.49 to +22.76%, P < 0.04), lower surface number (-2.31% to -9.63%, P < 0.007), higher curve number (+6.85% to +16.93%, P < 0.03), and lower plate-to-rod ratio (-7.92% to -21.71%, P < 0.05)., Conclusion: The results provide further support for the concept that poor subchondral bone quality is associated with osteoarthritis and may serve as a potential therapeutic target for osteoarthritis interventions. J. Magn. Reson. Imaging 2015;41:1311-1317. © 2014 Wiley Periodicals, Inc., (© 2014 Wiley Periodicals, Inc.)

Serial reproducibility and reliability critically determine sensitivity to detect changes in response to intervention and provide a basis for sample size estimates. Here, we evaluated the performance of the MRI-based virtual bone biopsy in terms of 26 structural and mechanical parameters in the distal radius of 20 women in the age range of 50 to 75 years (mean=62.0 years, S.D.=8.1 years), representative of typical study populations in drug intervention trials and fracture studies. Subjects were examined three times at average intervals of 20.2 days (S.D.=14.5 days) by MRI at 1.5 T field strength at a voxel size of 137×137×410 μm(3). Methods involved prospective and retrospective 3D image registration and auto-focus motion correction. Analyses were performed from a central 5×5×5 mm(3) cuboid subvolume and trabecular volume consisting of a 13 mm axial slab encompassing the entire medullary cavity. Whole-volume axial stiffness and sub-regional Young's and shear moduli were computed by finite-element analysis. Whole-volume-derived aggregate mean coefficient of variation of all structural parameters was 4.4% (range 1.8% to 7.7%) and 4.0% for axial stiffness; corresponding data in the subvolume were 6.5% (range 1.6% to 13.0%) for structural, and 5.5% (range 4.6% to 6.5%) for mechanical parameters. Aggregate ICC was 0.976 (range 0.947 to 0.986) and 0.992 for whole-volume-derived structural parameters and axial stiffness, and 0.946 (range 0.752 to 0.991) and 0.974 (range 0.965 to 0.978) for subvolume-derived structural and mechanical parameters, respectively. The strongest predictors of whole-volume axial stiffness were BV/TV, junction density, skeleton density and Tb.N (R(2) 0.79-0.87). The same parameters were also highly predictive of sub-regional axial modulus (R(2) 0.88-0.91). The data suggest that the method is suited for longitudinal assessment of the response to therapy. The underlying technology is portable and should be compatible with all general-purpose MRI scanners, which is appealing considering the very large installed base of this modality., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Object: The goal of this study was to determine the feasibility of performing quantitative 7 T magnetic resonance imaging (MRI) assessment of trabecular bone micro-architecture of the wrist, a common fracture site., Materials and Methods: The wrists of 4 healthy subjects (1 woman, 3 men, 28 ± 8.9 years) were scanned on a 7 T whole body MR scanner using a 3D fast low-angle shot (FLASH) sequence (TR/TE = 20/4.5 m s, 0.169 × 0.169 × 0.5 mm). Trabecular bone was segmented and divided into 4 or 8 angular subregions. Total bone volume (TBV), bone volume fraction (BVF), surface-curve ratio (SC), and erosion index (EI) were computed. Subjects were scanned twice to assess measurement reproducibility., Results: Group mean subregional values for TBV, BVF, SC, and EI (8 subregion analysis) were as follows: 8489 ± 3686, 0.27 ± 0.045, 9.61 ± 6.52; and 1.43 ± 1.25. Within each individual, there was subregional variation in TBV, SC, and EI (>5%), but not BVF (<5%). Intersubject variation (≥12%) existed for all parameters. Within-subject coefficients of variation were ≤10%., Conclusion: This is the first study to perform quantitative 7T MRI assessment of trabecular bone micro-architecture of the wrist. This method could be utilized to study perturbations in bone structure in subjects with osteoporosis or other bone disorders.

High-resolution magnetic resonance imaging (MRI) of trabecular bone combined with quantitative image analysis represents a powerful technique to gain insight into trabecular bone micro-architectural derangements in osteoporosis and osteoarthritis. The increased signal-to-noise ratio of ultra high-field MR (≥7 Tesla) permits images to be obtained with higher resolution and/or decreased scan time compared to scanning at 1.5/3T. In this small feasibility study, we show high measurement precision for subregional trabecular bone micro-architectural analysis performed on 7T knee MR images. The results provide further support for the use of trabecular bone measures as biomarkers in clinical studies of bone disorders.

An automatic, simple, and image intensity standardization-based strategy for correcting background inhomogeneity in MR images is presented in this paper. Image intensities are first transformed to a standard intensity gray scale by a standardization process. Different tissue sample regions are then obtained from the standardized image by simply thresholding based on fixed intensity intervals. For each tissue region, a polynomial is fitted to the estimated discrete background intensity variation. Finally, a combined polynomial is determined and used for correcting the intensity inhomogeneity in the whole image. The above procedure is repeated on the corrected image iteratively until the size of the extracted tissue regions does not change significantly in two successive iterations. Intensity scale standardization is effected to make sure that the corrected image is not biased by the fitting strategy. The method has been tested on a number of simulated and clinical MR images. These tests and a comparison with the method of non-parametric non-uniform intensity normalization (N3) indicate that the method is effective in background intensity inhomogeneity correction and may have a slight edge over the N3 method.

There are several medical application areas that require the segmentation and separation of the component bones of joints in a sequence of images of the joint acquired under various loading conditions, our own target area being joint motion analysis. This is a challenging problem due to the proximity of bones at the joint, partial volume effects, and other imaging modality-specific factors that confound boundary contrast. In this article, a two-step model-based segmentation strategy is proposed that utilizes the unique context of the current application wherein the shape of each individual bone is preserved in all scans of a particular joint while the spatial arrangement of the bones alters significantly among bones and scans. In the first step, a rigid deterministic model of the bone is generated from a segmentation of the bone in the image corresponding to one position of the joint by using the live wire method. Subsequently, in other images of the same joint, this model is used to search for the same bone by minimizing an energy function that utilizes both boundary- and region-based information. An evaluation of the method by utilizing a total of 60 data sets on MR and CT images of the ankle complex and cervical spine indicates that the segmentations agree very closely with the live wire segmentations, yielding true positive and false positive volume fractions in the range 89%-97% and 0.2%-0.7%. The method requires 1-2 minutes of operator time and 6-7 min of computer time per data set, which makes it significantly more efficient than live wire-the method currently available for the task that can be used routinely.

Purpose: To produce in vivo high-resolution images of the knee and to determine the feasibility of using 7T MR to detect changes in trabecular bone microarchitecture in elite athletes (Olympic fencers) who undergo high impact activity., Materials and Methods: The dominant knees of four males from the U.S. Olympic Fencing Team and three matched healthy male controls were scanned in a 7T whole-body scanner using a quadrature knee coil with three-dimensional (3D) fast low angle shot (FLASH): 50 axial images at the distal femur (0.156 mm x 0.156 mm) and 80 axial images at the knee joint (0.195 mm x 0.195 mm). Bone volume fraction (BVF) and marrow volume fraction (MVF) images were computed and fuzzy distance transform (FDT) and digital topological analysis (DTA) were applied to determine: trabecular number (Tb.N), trabecular thickness (Tb.Th), and trabecular separation (Tb.Sp); BVF (BV/TV); trabecular and marrow space surface-to-curve ratio (SC, marker of plate to rod ratio); and trabecular and marrow space erosion index (EI, inverse marker for network connectivity). Quadriceps muscle volume (MV) was calculated as well. We calculated group means and performed two-tailed t-tests to determine statistical significance., Results: Compared to controls, fencers had: decreased Tb.Sp (P = 0.0082 at femur, P = 0.051 at joint); increased Tb.N (P < 0.05 at both femur and joint) and BV/TV (P < 0.001 at both femur and joint); increased trabecular SC and decreased marrow space SC (P < 0.01 at both femur and joint); decreased trabecular EI and increased marrow space EI (P < 0.01 at both femur and joint); and increased MV (P = 0.038). There was no difference in Tb.Th at the distal femur (P = 0.92) or joint (P = 0.71) between groups., Conclusion: To our knowledge, this is the first study to perform 7T MRI of the knee in vivo. Elite athletes who undergo high impact activity have increased MV and improved trabecular bone structure compared to controls., ((c) 2008 Wiley-Liss, Inc.)

Unlabelled: In postmenopausal women with a wide range of vertebral deformities, MRI-based structural measures of topology and scale at the distal radius are shown to account for as much as 30% of vertebral deformity, independent of integral vertebral BMD., Introduction: Trabecular bone architecture has been postulated to contribute to overall bone strength independent of vertebral BMD measured by DXA. However, there has thus far been only sparse in vivo evidence to support this hypothesis., Materials and Methods: Postmenopausal women, 60-80 yr of age, were screened by DXA, and those with T-scores at either the hip or spine falling within the range of -2.5 +/- 1.0 were studied with the MRI-based virtual bone biopsy, along with heel broadband ultrasound absorption and pQCT of the tibia. The data from 98 subjects meeting the enrollment criteria were subjected to microMRI at the distal tibia and radius, and measures of topology and scale of the trabecular bone network were computed. A spinal deformity index (SDI) was obtained from morphometric measurements in midline sagittal MR images of the thoracic and lumbar spine to evaluate associations between structure and deformity burden., Results: A number of structural indices obtained at the distal radius were correlated with the SDI. Among these were the topological surface density (a measure of trabecular plates) and trabecular bone volume fraction, which were inversely correlated with SDI (p < 0.0001). Combinations of two structural parameters accounted for up to 30% of the variation in SDI (p < 0.0001) independent of spinal BMD, which was not significantly correlated. pQCT trabecular BMD was also weakly associated, whereas broadband ultrasound absorption was not. No significant association between SDI and structural indices were found at the tibia., Conclusions: Structural measures at the distal radius obtained in vivo by microMRI explained a significant portion of the variation in total spinal deformity burden in postmenopausal women independent of areal BMD.

Osteoporosis is characterized by bone loss and deterioration of the trabecular bone (TB) architecture that leads to impaired overall mechanical strength of the bone. Bone mineral density (BMD) measured by dual-energy x-ray absorptiometry is currently the standard clinical metric assessing bone integrity but it fails to capture the structural changes in the TB. Recent research suggests that structure contributes to bone strength in a manner complementary to BMD. Besides parameters of scale such as the mean TB thickness and mean bone volume fraction, parameters describing the anisotropy of the trabecular architecture play an important role in the characterization of TB since trabeculae are preferentially oriented along the direction of local loading. Therefore, the degree of structural anisotropy is of pivotal importance to the bone's mechanical competence. The most common method for measuring structural anisotropy of TB is the mean-intercept length (MIL). In this work we present a method, based on the three-dimensional spatial autocorrelation function (ACF), for mapping of the full structural anisotropy ellipsoid of both TB thickness and spacing and we examine its performance as compared to that of MIL. Not only is the ACF method faster by several orders of magnitude, it is also considerably more robust to noise. Further, it is applicable at lower spatial resolution and is relatively insensitive to image shading. The chief reason for ACF's superior performance is that it does not require binarization, which is difficult to achieve in the limited spatial regime of in vivo magnetic resonance imaging. MIL and ACF have been applied to high-resolution magnetic resonances images of the tibia in a group of ten healthy postmenopausal women by comparing the structural anisotropy and principal direction of the computed fabric tensor for each method. While there is fair agreement between the two methods, ACF analysis yielded greater anisotropy than MIL for both TB thickness and spacing. There was good agreement between the two techniques as far as the eigenvectors of the fabric ellipsoids were concerned, which parallel the bone's macroscopic axis.

Osteoporosis is the most common degenerative disease in the elderly. It is characterized by low bone mass and structural deterioration of bone tissue, leading to morbidity and increased fracture risk in the hip, spine and wrist-all sites of predominantly trabecular bone. Bone densitometry, currently the standard methodology for diagnosis and treatment monitoring, has significant limitations in that it cannot provide information on the structural manifestations of the disease. Recent advances in imaging, in particular MRI, can now provide detailed insight into the architectural consequences of disease progression and regression in response to treatment. The focus of this review is on the emerging methodology of quantitative MRI for the assessment of structure and function of trabecular bone. During the past 10 years, various approaches have been explored for obtaining image-based quantitative information on trabecular architecture. Indirect methods that do not require resolution on the scale of individual trabeculae and therefore can be practiced at any skeletal location, make use of the induced magnetic fields in the intertrabecular space. These fields, which have their origin in the greater diamagnetism of bone relative to surrounding marrow, can be measured in various ways, most typically in the form of R2', the recoverable component of the total transverse relaxation rate. Alternatively, the trabecular network can be quantified by high-resolution MRI (micro-MRI), which requires resolution adequate to at least partially resolve individual trabeculae. Micro-MRI-based structure analysis is therefore technically demanding in terms of image acquisition and algorithms needed to extract the structural information under conditions of limited signal-to-noise ratio and resolution. Other requirements that must be met include motion correction and image registration, both critical for achieving the reproducibility needed in repeat studies. Key clinical applications targeted involve fracture risk prediction and evaluation of the effect of therapeutic intervention., (Copyright 2006 John Wiley & Sons, Ltd.)

Purpose: To investigate the SNR and image properties of 3D steady-state free precession (SSFP), fast large-angle spin echo (FLASE), gradient-recalled acquisition in steady state (GRASS), and spoiled GRASS (SPGR) for structural imaging of trabecular bone (TB)., Materials and Methods: SNR was examined theoretically and experimentally on phantoms, bone specimens, and in vivo. The bone volume fraction, TB thickness, and echo time (TE) dependence of the thickness were compared. The trabecula was modeled as a cylinder in simulations to examine the intra-voxel spin-dephasing in SSFP and GRASS. Images were acquired on a 1.5 T Siemens Sonata system (40 mT/m maximum gradient, 200 T/m/s peak slew rate)., Results: Within the hardware and safety limit constraints, SNR of FLASE was superior, followed by SSFP, GRASS, and SPGR. The trabecular thickness derived from gradient-echo images was 10-45% greater than that obtained with FLASE. Conversely, SSFP images delineated partial volume trabeculae better than FLASE. Simulations indicated that the artifactual thickening was more severe in SSFP than in GRASS, which was attributed to off-resonance effects from the induced gradients at the bone/marrow interface., Conclusion: FLASE had the highest SNR and was insensitive to susceptibility dephasing. Although SSFP has superior SNR compared to GRASS, off-resonance effects and duty cycle limitations may compromise its practicality in this application. Inc., (J. Magn. Reson. Imaging 2005. (c) 2005 Wiley-Liss, Inc.)

Rationale and Objectives: Quantitative evaluation of cortical bone architecture as a means to assess bone strength typically is accomplished on the basis of images obtained by means of dual-energy X-ray absorptiometry (DXA) or computed tomography. Magnetic resonance (MR) imaging has potential advantages for this task in that it allows imaging in arbitrary scan planes at high spatial resolution. However, several hurdles have to be overcome to make this approach practical, including resolution of issues related to nonlinear receive coil sensitivity, variations in marrow composition, and the presence of periosteal isointense tissues, which all complicate segmentation. The aim of this study is to develop MR acquisition and analysis methods optimized for the detection of cortical boundaries in such complex geometries as the femoral neck., Materials and Methods: Cortical boundary detection is achieved by radially tracing intensity profiles that intersect the periosteal and endosteal boundaries of bone. Profiles subsequently are normalized to the intensity of the marrow signal, processed with morphologic image operators, and binarized. The resulting boundaries are mapped back onto the spatial image, and erroneous boundary points are removed. From the detected cortical boundaries, cortical cross-sectional area and thickness are computed. The method was evaluated on cortical bone specimens and human volunteers on the basis of high-resolution images acquired at a 1.5-Tesla field strength. To assess whether the method is sensitive to detect the expected dependencies of cortical parameters in weight-bearing bone on overall habitus, 10 women aged 46-73 years (mean age, 56 years) underwent the cortical imaging protocol in the proximal femur, and results were compared with DXA bone mineral density parameters of the hip and spine., Results: Reproducibility was approximately 2%. Double oblique images of the femoral neck in the 10 women studied showed that cortical cross-sectional area correlated strongly with height (r = 0.88; p = .0008), whereas cortical diameter versus age approached significance (r = 0.61; p = .06). Measurements in specimens of some cortical parameters indicated resolution dependence. However, note that specimen ranking within each parameter remained constant across all resolutions studied., Conclusion: Data suggest the new method to be robust and applicable on standard clinical MR scanners at arbitrary anatomic locations to yield clinically meaningful quantitative results.

Purpose: To explore the potential role of micro-magnetic resonance imaging (micro-MRI) for quantifying trabecular and cortical bone structural parameters in renal osteodystrophy (ROD), a multifactorial disorder of bone metabolism, traditionally evaluated by bone biopsy., Materials and Methods: Seventeen hemodialysis patients (average PTH level = 502 +/- 415 microg/liter) were compared with 17 age-, gender-, and body mass index (BMI)-matched control subjects. The average dialysis duration for the patients was 5.5 years (range = 0.96-18.2 years). Three-dimensional (3D) fast large-angle spin-echo (FLASE) MR images of the distal tibia (voxel size = 137 x 137 x 410 microm(3)) were processed to yield bone volume fraction (BV/TV). From a skeletonized representation of the trabecular bone network, the topology of each bone voxel was determined providing surface and curve voxel densities (SURF and CURV) and the topological erosion index (EI). Further, high-resolution two-dimensional (2D) spin-echo images were collected at the tibial midshaft for measurement of cortical bone cross-sectional area (CCA), relative CCA expressed as a percentage of total bone area (RCA), and mean cortical thickness (MCT)., Results: The data show both RCA and MCT to be lower in the patients (61.2 vs. 69.1%, P = 0.008, and 4.53 vs. 5.19 mm, P = 0.01). BV/TV and SURF were lower, while EI was increased in the patients, although these differences were not quite significant (P = 0.06-0.09). All of the cortical and trabecular findings are consistent with increased bone fragility., Conclusion: The data suggest that micro-MRI may have potential to characterize the structural implications of metabolic bone disease, potentially providing a noninvasive tool for the evaluation of therapies for ROD., (Copyright 2004 Wiley-Liss, Inc.)

Trabecular or cancellous bone, the type of bone found in the vertebrae and near the joints of long bones, consists of a network of plates and struts. Accurate measurement of trabecular thickness is of significant interest, for example, to assess the effectiveness of anabolic (bone forming) agents of patients with osteoporosis. Here, we introduce a new fuzzy distance transform (FDT)-based thickness computation method that obviates binary segmentation and that can effectively deal with images acquired at a voxel size comparable to the typical trabecular bone thickness. The method's robustness is shown on the basis of micro-CT images of human trabecular bone, resampled at progressively coarser resolution and after application of rotation and addition of noise as a means to simulate the in vivo situation. Reproducibility of the method is demonstrated with micro-CT images by comparing histograms of thickness within and between data sets and with micro-MRI volume data sets of human volunteers imaged repeatedly. Finally, with in vivo micro-MR images from a prior study in rabbits subjected to corticosteroid exposure, it is demonstrated that short-term treatment resulting in trabecular thinning can be quantified with the new method.

Computerized segmentation of 3D tracheobronchial tree is a necessary first step for subsequent registration and analysis of pulmonary airway and vascular magnetic resonance (MR) images obtained by using hyperpolarized 3Helium gas and Gadolinium. The scientific and clinical implications of acquiring these data on the tracheobronchial tree (for studying ventilation, V) and on the coinciding pulmonary arterioles (for studying perfusion, Q), is the next frontier for static and dynamic pulmonary MRI. In this paper, we report an airway segmentation method from 3He MR images based on the scale-based fuzzy connectedness approach. Incorporated in this method are the pre-processing steps of inhomogeneity correction and intensity standardization. The basic sequential steps in the proposed airway segmentation method are: (1) image acquisition, (2) radio frequency field inhomogeneity correction, (3) standardization of MR image intensity scale, (4) seed specification, (5) scale-based fuzzy connected segmentation of airways, and (6) thresholding and binarization. The majority of these steps are automatically executed; others allow interaction through a graphical interface provided in the 3DVIEWNIX software system, in which the algorithms are implemented. The method achieves an overall precision of about 98% in terms of the extent of overlap in repeated segmentations. Its level of accuracy can be described by a true positive volume fraction of about 98% (considering manual delineation as the surrogate of true delineation), and a false negative and positive volume fraction of about 1%. The total operator and computational time required per study are on the average 2 and 20 min.

Intermolecular multiple-quantum coherence (iMQC) MR imaging provides a fundamentally different contrast mechanism. It allows probing tissue microstructure by tuning the direction and strength of the correlation gradient. However, iMQC images of a specific quantum-coherence can easily be contaminated by leakage signals from undesired quantum coherences (zero, single, and triple quantum coherence in this work). Using a modified double-quantum CRAZED imaging sequence, we show that signals originating from various coherence orders (M=0, 1, 2, 3) can be predicted in k-space and effectively isolated by means of a four-step phase cycling scheme and judicious choice of flip angles. Finally, preliminary data suggest the method to be able to provide information on trabecular bone architecture such as regional mean trabecular plate separation.

Under controlled imaging conditions, functional, co-registered ventilation and perfusion images were obtained for quantitative MRI assessment of pulmonary function. Experiments were conducted on 25-35 kg Yorkshire pigs (N = 5) under ketamine/isoflurane anesthesia. Ventilation and perfusion MR images were obtained using laser polarized gas and gadolinium (Gd), respectively. The mutual information-based technique was used to quantify the initial misregistration between the acquired ventilation and perfusion images, to cope with different intensity characteristics. Means and standard deviations (SDs) of misregistrations for the five subjects, in terms of absolute translation and absolute rotations around each of the three coordinate axes, were computed to evaluate the hypothesis. For qualitative illustrations, plots of mutual information values under absolute translations and rotations around each of the three coordinate axes are presented. This preliminary study shows the feasibility of acquiring functional image data that are spatially co-registered. This method has potential applications in the quantitative assessment of regional alveolar ventilation and pulmonary perfusion ratio, in both normal and diseased lung., (Copyright 2003 Wiley-Liss, Inc.)

The strength of trabecular bone and its resistance to fracture traditionally have been associated with apparent density. This paradigm assumes that neither the ultrastructural nor microstructural make-up of the bone is altered during aging and osteoporosis. During the past decade there has been growing evidence from both laboratory and clinical studies against this view. Recent advances in noninvasive imaging technology, notably micro-magnetic resonance imaging (micro MRI) and computed tomography, offer an opportunity to test the hypothesis that architecture is an independent contributor to bone strength. MRI appears to be ideally suited for this task because bone marrow has uniform high signal intensity while bone appears with background intensity, thus yielding a binary system tomographic system. However, in vivo trabecular bone imaging is hampered by the limited signal-to-noise ratio that precludes voxel sizes much smaller than trabecular thickness, which would be required to yield a bimodal intensity histogram for segmentation of the image into bone and marrow. The resulting partial volume blurring leads to fuzzy boundaries. Successful structure analysis thus demands more elaborate processing strategies. This article reviews new approaches conceived in the authors' laboratory toward acquisition, processing, and structural analysis of trabecular bone images in the limited spatial resolution regimen of in vivo micro MRI. These methods are shown to provide detailed insight into the three-dimensional trabecular network topology and scale at the distal radius or distal tibia that typically serve as surrogate sites. The micro MRI-derived structural parameters are shown to be associated with the bone's biomechanical properties and fracture resistance. Further, the technology has advanced to a stage permitting serial studies in laboratory animals and humans as a means to evaluate the effects of treatment. The method currently is confined to peripheral skeletal sites, and its extension to typical fracture sites such as the proximal femur hinges on further advances in detection sensitivity.

We present a new class of approaches for rigid-body registration and their evaluation in studying multiple sclerosis (MS) via multiprotocol magnetic resonance imaging (MRI). Three pairs of rigid-body registration algorithms were implemented, using cross-correlation and mutual information (MI), operating on original gray-level images, and utilizing the intermediate images resulting from our new scale-based method. In the scale image, every voxel has the local 'scale' value assigned to it, defined as the radius of the largest ball centered at the voxel with homogeneous intensities. Three-dimensional image data of the head were acquired from ten MS patients for each of six MRI protocols. Images in some of the protocols were acquired in registration. The registered pairs were used as ground truth. Accuracy and consistency of the six registration methods were measured within and between protocols for known amounts of misregistrations. Our analysis indicates that there is no 'best' method. For medium misregistration, the method using MI, for small and large misregistration the method using normalized cross-correlation performs best. For high-resolution data the correlation method and for low-resolution data the MI method, both using the original gray-level images, are the most consistent. We have previously demonstrated the use of local scale information in fuzzy connectedness segmentation and image filtering. Scale may also have potential for image registration as suggested by this work. Index Terms--Correlation, image analysis, image processing, image registration, image scale, magnetic resonance imaging (MRI), multiple sclerosis, mutual information.

Purpose: Osteoporosis is a bone disease associated with enhanced bone loss, microstructural degeneration, and fracture‐risk. Finite element (FE) modeling is used to estimate trabecular bone (Tb) modulus from high‐resolution three‐dimensional (3‐D) imaging modalities including micro‐computed tomography (CT), magnetic resonance imaging (MRI), and high‐resolution peripheral quantitative CT (HR‐pQCT). This paper validates an application of voxel‐based continuum finite element analysis (FEA) to predict Tb modulus from clinical CT imaging under a condition similar to in vivo imaging by comparing with measures derived by micro‐CT and experimental approaches. Method: Voxel‐based continuum FEA methods for CT imaging were implemented using linear and nonlinear models and applied on distal tibial scans under a condition similar to in vivo imaging. First, tibial axis in a CT scan was aligned with the coordinate z‐axis at 150 μm isotropic voxels. FEA was applied on an upright cylindrical volume of interests (VOI) with its axis coinciding with the tibial bone axis. Voxel volume, edge, and vertex elements and their connectivity were defined as per the isotropic image grid. A calibration phantom was used to calibrate CT numbers in Hounsfield unit to bone mineral density (BMD) values, which was then converted into calcium hydroxyapatite (CHA) density. Mechanical properties at each voxel volume element was defined using its ash‐density defined on CT‐derived CHA density. For FEA, the bottom surface of the cylindrical VOI was fixed and a constant displacement was applied along the z‐direction at each vertex element on the top surface to simulate a physical axial compressive loading condition. Finally, a Poisson's ratio of 0.3 was applied, and Tb modulus (MPa) was computed as the ratio of average von Mises stress (MPa) of volume elements on the top surface and the applied displacement. FEA parameters including mesh element size, substep number, and different tolerance values were optimized. Results: CT‐derived Tb modulus values using continuum FEA showed high linear correlation with the micro‐CT‐derived reference values (r ∈ [0.87 0.90]) as well as experimentally measured values (r ∈ [0.80 0.87]). Linear correlation of computed modulus with their reference values using continuum FEA with linear modeling was comparable with that obtained by nonlinear modeling. Nonlinear continuum FEA‐based modulus values (mean of 1087.2 MPa) showed greater difference from their reference values (mean of 1498.9 MPa using micro‐CT‐based FEA) as compared with linear continuum methods. High repeat CT scan reproducibility (intra‐class correlation [ICC] = 0.98) was observed for computed modulus values using both linear and nonlinear continuum FEA. It was observed that high stress regions coincide with Tb microstructure as fuzzily characterized by BMD values. Distributions of von Mises stress over Tb microstructure and marrow regions were significantly different (p < 10–8). Conclusion: Voxel‐based continuum FEA offers surrogate measures of Tb modulus from CT imaging under a condition similar to in vivo imaging that alleviates the need for segmentation of Tb and marrow regions, while accounting for bone distribution at the microstructural level. This relaxation of binary segmentation will extend the scope of FEA application to assess mechanical properties of bone microstructure at relatively low‐resolution imaging. [ABSTRACT FROM AUTHOR]

Theoretical properties of a multiscale opening algorithm for two conjoined fuzzy objects are established, and its extension to separating two conjoined fuzzy objects with different intensity properties is introduced. In addition, its applications to artery/vein separation in pulmonary CT imaging and carotid vessel segmentation in CT angiograms (CTAs) of patients with intracranial aneurysms are presented. The new algorithm accounts for distinct intensity properties of individual conjoined objects by combining fuzzy distance transform, a morphologic feature, with fuzzy connectivity, a topologic feature. The algorithm iteratively opens the two conjoined objects starting at large scales and progressing toward finer scales. Results of application of the method in separating arteries and veins in a physical cast phantom of a pig lung are presented. Accuracy of the algorithm is quantitatively evaluated in terms of sensitivity and specificity on patients’ CTA datasets, and its performance is compared with existing methods. Reproducibility of the algorithm is examined in terms of volumetric agreement between two users’ carotid vessel segmentation results. Experimental results using this algorithm on patients’ CTA data demonstrate a high average accuracy of 96.3% with 95.1% sensitivity and 97.5% specificity and a high reproducibility of 94.2% average agreement between segmentation results from two mutually independent users. Approximately, 25–35 user-specified seeds/separators are needed for each CTA data through a custom-designed graphical interface requiring an average of 30 min to complete carotid vascular segmentation in a patient's CTA dataset. [ABSTRACT FROM PUBLISHER]

High-resolution magnetic resonance imaging (MRI) of trabecular bone combined with quantitative image analysis represents a powerful technique to gain insight into trabecular bone micro-architectural derangements in osteoporosis and osteoarthritis. The increased signal-to-noise ratio of ultra high-field MR (≥7 Tesla) permits images to be obtained with higher resolution and/or decreased scan time compared to scanning at 1.5/3T. In this small feasibility study, we show high measurement precision for subregional trabecular bone micro-architectural analysis performed on 7T knee MR images. The results provide further support for the use of trabecular bone measures as biomarkers in clinical studies of bone disorders. [ABSTRACT FROM AUTHOR]

Supraphysiological levels of glucocorticoids (GC) cause bone atrophy and growth retardation. In this study, we examine whether these adverse structural effects are reversible and whether treatment with bisphosphonate is protective by in vivo serial micro-magnetic resonance (µ-MR) imaging and spectroscopy. Rabbits ( n = 16) were divided into four groups, a control group ( n = 4) and three groups ( n = 4 each) receiving GC in the form of dexamethasone (0.45 mg/kg/day). In one of the GC groups dexamethasone exposure was discontinued after 2 weeks, the other two groups were maintained on dexamethasone, with one receiving risedronate (5 µg/kg twice per week) from the beginning of treatment, the other one receiving risedronate after 2 weeks. Animals were imaged at baseline and at 2, 4, and 8 weeks. Trabecular bone volume fraction (trabecular bone volume/tissue volume, TB/TV), trabecular bone thickness (Tb.Th), and topological structural parameters were measured in the distal femoral epiphysis, as was the epiphyseal growth plate (EGP), and marrow fat fraction, which was computed from the integrated proton spectra. Two weeks of dexamethasone exposure substantially reduced TB/TV, along with thinning of the epiphyseal growth plate and conversion of hematopoietic to adipocytic marrow. However, TB/TV recovered to normal levels within 2 weeks after cessation of GC exposure and remained constant throughout the remainder of the protocol. In contrast, neither EGP thickness nor marrow composition returned to control levels after cessation of GC exposure as rapidly as did TB/TV. Besides increased TB/TV, bisphosphonate treatment resulted in a more connected platelike network than observable at baseline, but GP atrophy and marrow conversion caused by GC exposure were not affected. The data lend support to a protective effect of risedronate on trabecular architecture during GC exposure. The improvement in trabecular network parameters beyond baseline values further suggest a therapeutic effect of risedronate. [ABSTRACT FROM AUTHOR]

Computerized segmentation of 3D tracheobronchial tree is a necessary first step for subsequent registration and analysis of pulmonary airway and vascular magnetic resonance (MR) images obtained by using hyperpolarized 3Helium gas and Gadolinium. The scientific and clinical implications of acquiring these data on the tracheobronchial tree (for studying ventilation, V) and on the coinciding pulmonary arterioles (for studying perfusion, Q), is the next frontier for static and dynamic pulmonary MRI. In this paper, we report an airway segmentation method from 3He MR images based on the scale-based fuzzy connectedness approach. Incorporated in this method are the pre-processing steps of inhomogeneity correction and intensity standardization. The basic sequential steps in the proposed airway segmentation method are: (1) image acquisition, (2) radio frequency field inhomogeneity correction, (3) standardization of MR image intensity scale, (4) seed specification, (5) scale-based fuzzy connected segmentation of airways, and (6) thresholding and binarization. The majority of these steps are automatically executed; others allow interaction through a graphical interface provided in the 3DVIEWNIX software system, in which the algorithms are implemented. The method achieves an overall precision of about 98% in terms of the extent of overlap in repeated segmentations. Its level of accuracy can be described by a true positive volume fraction of about 98% (considering manual delineation as the surrogate of true delineation), and a false negative and positive volume fraction of about 1%. The total operator and computational time required per study are on the average 2 and 20 min. [Copyright &y& Elsevier]

In many medical imaging applications, due to the limited field of view of imaging devices, acquired images often include only a part of a structure. In such situations, it is impossible to guarantee that the images will contain exactly the same physical extent of the structure at different scans, which leads to difficulties in registration and in many other tasks, such as the analysis of the morphology, architecture, and kinematics of the structures. To facilitate such analysis, we developed a general method, referred to as iso-shaping, that generates structures of the same shape from segmented image sequences. The basis for this method is to automatically find a set of key points, called shape centers, in the segmented partial anatomic structure such that these points are present in all images and that they represent the same physical location in the object, and then trim the structure using these points as reference. The application area considered here is the analysis of the morphology, architecture, and kinematics of the joints of the foot from magnetic resonance images acquired at different joint positions and load conditions. The accuracy of the method is analyzed by utilizing ten data sets for iso-shaping the tibia and the fibula via four evaluative experiments. The analysis indicates that iso-shaping produces results as predicted by the theoretical framework. [ABSTRACT FROM AUTHOR]

The mechanical competence of trabecular bone, the type of bone constituting the vertebrae and ends of the long bones, is largely determined by the bone's volume fraction and architectural make-up. Experimental and clinical evidence suggests that up to 50% of trabecular bone strength is determined by parameters characterizing the network's architecture. Although rarely clinically indicated because of its invasiveness, a bone biopsy can provide detailed insight into the bone's structural arrangement. Recent advances in magnetic resonance micro-imaging (μMRI), in conjunction with new image processing and feature extraction approaches, now allow detailed structural information to be obtained by what we refer to as "virtual bone biopsy" (VBB). Governed by signal-to-noise, the voxel size achievable in vivo is of the same order as trabecular thickness (100-150 μm). Therefore, methods had to be conceived to deal with the inherently fuzzy nature of the objects to be extracted. It is shówn that a cascade of image processing steps, starting with noise deconvolution of the images to yield bone volume fraction maps, followed by what we refer to as "subvoxel processing" for resolution enhancement, are essential for evaluating topology and scale of the trabecular network. Digital topological analysis of the binarized and skeletonized images can provide a detailed picture of network connectivity and the nature of the structural elements (plate and strut architecture). In addition to its complicated topological make-up, trabecular bone is highly anisotropic since bone adapts to the stresses to which it is subjected (Wolff's law). Therefore, evaluation of structural orientation or fabric is... [ABSTRACT FROM AUTHOR]

Presents information on a study which described a near-automatic process for separating vessels from background and other clutter as well as for separating arteries and veins in contrast-enhanced magnetic resonance angiographic image data. Methodology; Results and discussion; Conclusions.

Cancellous bone consists of a network of bony struts and plates that provide mechanical strength to much of the skeleton at minimum weight. It has been shown that loss in bone mass is accompanied by architectural changes that relate to both scale and topology of the network. In this paper, the concept of three-dimensional (3D) digital topology is presented for characterizing the local topology of each bone voxel after skeletonization of the binary bone images. This method allows us to identify each voxel as belonging to a surface, curve, or junction structure in the trabecular bone network. The method has been quantitatively validated on synthetic images demonstrating its relative immunity to partial volume blurring and noise. Parameters introduced to characterize network topology include surface-to-curve ratio and erosion index. Finally, the technique is shown to quantify the architecture of human trabecular bone in magnetic resonance micro-images acquired from cadavers and in vivo.© 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 81–90, 2000 [ABSTRACT FROM AUTHOR]