Topological analysis of trabecular bone MR images

Six-minute, in vivo MRI quantification of proximal femur trabecular bone 3D microstructure

BACKGROUND

Assessment of proximal femur trabecular bone microstructure in vivo by magnetic resonance imaging has recently been validated for acquiring information independent of bone mineral density in osteoporotic patients. However, the requisite signal-to-noise ratio (SNR) and resolution for interrogation of the trabecular microstructure at this anatomical location prolongs the scan duration and renders the imaging protocol clinically infeasible. Parallel imaging and compressed sensing (PICS) techniques can reduce the scan duration of the imaging protocol without substantially compromising image quality. The present work investigates the limits of acceleration for a commonly used PICS technique, ℓ1-ESPIRiT, for the purpose of quantifying measures of trabecular bone microarchitecture. Based on a desired error tolerance, a six-minute, prospectively accelerated variant of the imaging protocol was developed and assessed for intersession reproducibility and agreement with the longer reference scan.

PURPOSE

To investigate the limits of acceleration for MRI-based trabecular bone quantification by parallel imaging and compressed sensing reconstruction, and to develop a prototypical imaging protocol for assessing the proximal femur microstructure in a clinically practical scan time.

METHODS

Healthy participants (n = 11) were scanned by a 3D balanced steady-state free precession (bSSFP) sequence satisfying the Nyquist criterion with a scan duration of about 18 min. The raw data were retrospectively undersampled and reconstructed to mimic various acceleration factors ranging from 2 to 6. Trabecular volumes-of-interest in four major femoral regions (greater trochanter, intertrochanteric region, femoral neck, and femoral head) were analyzed and six relevant measures of trabecular bone microarchitecture (bone volume fraction, surface-to-curve ratio, erosion index, elastic modulus, trabecular thickness, plates-to-rods ratio) were obtained for images of all accelerations. To assess agreement, median percent error and intraclass correlation coefficients (ICCs) were computed using the fully-sampled data as reference. Based on this analysis, a prospectively 3-fold accelerated sequence with a duration of about 6 min was developed and the analysis was repeated.

RESULTS

A prospective acceleration factor of 3 demonstrated comparable performance in reproducibility and absolute agreement to the fully-sampled scan. The median CoV over all image-derived metrics was generally <6 % and ICCs >0.70. Also, measurements from prospectively 3-fold accelerated scans demonstrated in general median percent errors of <7 % and ICCs >0.70.

CONCLUSION

The present work proposes a method to make in vivo quantitative assessment of proximal femur trabecular microstructure with a clinically practical scan duration of about 6 min.

MRI-Based Quantitative Osteoporosis Imaging at the Spine and Femur

Osteoporosis is a systemic skeletal disease with a high prevalence worldwide, characterized by low bone mass and microarchitectural deterioration, predisposing an individual to fragility fractures. Dual-energy X-ray absorptiometry (DXA) has been the clinical reference standard for diagnosing osteoporosis and for assessing fracture risk for decades. However, other imaging modalities are of increasing importance to investigate the etiology, treatment, and fracture risk. The purpose of this work is to review the available literature on quantitative magnetic resonance imaging (MRI) methods and related findings in osteoporosis at the spine and proximal femur as the clinically most important fracture sites. Trabecular bone microstructure analysis at the proximal femur based on high-resolution MRI allows for a better prediction of osteoporotic fracture risk than DXA-based bone mineral density (BMD) alone. In the 1990s, T₂ * mapping was shown to correlate with the density and orientation of the trabecular bone. Recently, quantitative susceptibility mapping (QSM), which overcomes some of the limitations of T₂ * mapping, has been applied for trabecular bone quantifications at the spine, whereas ultrashort echo time (UTE) imaging provides valuable surrogate markers of cortical bone quantity and quality. Magnetic resonance spectroscopy (MRS) and chemical shift encoding-based water-fat MRI (CSE-MRI) enable the quantitative assessment of the nonmineralized bone compartment through extraction of the bone marrow fat fraction (BMFF). Furthermore, CSE-MRI allows for the differentiation of osteoporotic vs. pathologic fractures, which is of high clinical relevance. Lastly, advanced postprocessing and image analysis tools, particularly considering statistical parametric mapping and region-specific BMFF distributions, have high potential to further improve MRI-based fracture risk assessments at the spine and hip. LEVEL OF EVIDENCE: 5 TECHNICAL EFFICACY STAGE: 2.

A novel mechanical parameter to quantify the microarchitecture effect on apparent modulus of trabecular bone: A computational analysis of ineffective bone mass

BACKGROUND

One of the characteristics of osteoporotic bone is the deterioration of trabecular microarchitecture. Previous studies have shown microarchitecture alone can vary the apparent modulus of trabecular bone significantly independent of bone volume fraction (BV/TV) from morphological and topological perspectives. However, modulus is a mechanical quantity and there is a lack of mechanical explanatory parameters. This study aims to propose a novel mechanical parameter to quantify the microarchitecture effect on the apparent modulus of trabecular bone.

MATERIALS AND METHODS

Fourteen human female cadaveric vertebrae were scanned with a dual-energy X-ray (DXA) equipment followed by a micro-CT (μCT) system at 18 μm isotropic resolution. Four trabecular bone specimens (3.46 × 3.46 × 3.46 mm) were obtained from each vertebral body and converted to voxel-based micro finite element (μFE) models. The apparent modulus (E) of the μFE model was computed using a linear micro finite element analysis (μFEA). The normalized apparent modulus (E*) was computed as E divided by BV/TV. The relationship between E and BV/TV was analyzed by linear, power-law and exponential regressions. Linear regression was performed between E* and BV/TV. Ineffective bone mass (InBM) was defined as the bone mass with a negligible contribution to the load-resistance and represented by elements with von Mises stress less than a certain stress threshold. InBM was quantified as the low von Mises stress ratio (LS_VMR), which is the ratio of the number of InBM elements to the total number of elements in the μFE model. An incremental search technique with coarse and fine search intervals of 10 and 1 MPa, respectively, was adopted to determine the stress threshold for calculating LS_VMR of the μFE model. Correlation between E* and LS_VMR was analyzed using linear and power-law models for each stress threshold. The threshold producing the highest coefficient of determination (R²) in the correlation between E* and LS_VMR was taken as the optimal stress threshold for calculating LS_VMR. Linear regression was performed between E and LS_VMR. Multiple linear regression of E against both BV/TV and LS_VMR was further analyzed.

RESULTS

E significantly (p < .001) correlates to BV/TV whereas E* has no significant (p = .75) correlation with BV/TV. Incremental search suggests 59 MPa to be the optimal stress threshold for calculating LS_VMR. BV/TV alone can explain 59% of the variation in E using power-law regression model (E = 2254.64BV/TV^1.04, R² = 0.59, p < .001). LS_VMR alone can explain 48% of the variation in E using linear regression model (E = 1696.4-1647.1LS_VMR, R² = 0.48, p < .001). With these two predictors taken into consideration, 95% of the variation in E can be explained in a multiple linear regression model (E = 1364.89 + 2184.37BV/TV - 1605.38LS_VMR, adjusted R² = 0.95, p < .001).

CONCLUSION

LS_VMR can be adopted as the mechanical parameter to quantify the microarchitecture effect on the apparent modulus of trabecular bone.

Deep Learning Based High-Resolution Reconstruction of Trabecular Bone Microstructures from Low-Resolution CT Scans using GAN-CIRCLE

Osteoporosis is a common age-related disease characterized by reduced bone density and increased fracture-risk. Microstructural quality of trabecular bone (Tb), commonly found at axial skeletal sites and at the end of long bones, is an important determinant of bone-strength and fracture-risk. High-resolution emerging CT scanners enable in vivo measurement of Tb microstructures at peripheral sites. However, resolution-dependence of microstructural measures and wide resolution-discrepancies among various CT scanners together with rapid upgrades in technology warrant data harmonization in CT-based cross-sectional and longitudinal bone studies. This paper presents a deep learning-based method for high-resolution reconstruction of Tb microstructures from low-resolution CT scans using GAN-CIRCLE. A network was developed and evaluated using post-registered ankle CT scans of nineteen volunteers on both low- and high-resolution CT scanners. 9,000 matching pairs of low- and high-resolution patches of size 64×64 were randomly harvested from ten volunteers for training and validation. Another 5,000 matching pairs of patches from nine other volunteers were used for evaluation. Quantitative comparison shows that predicted high-resolution scans have significantly improved structural similarity index (p < 0.01) with true high-resolution scans as compared to the same metric for low-resolution data. Different Tb microstructural measures such as thickness, spacing, and network area density are also computed from low- and predicted high-resolution images, and compared with the values derived from true high-resolution scans. Thickness and network area measures from predicted images showed higher agreement with true high-resolution CT (CCC = [0.95, 0.91]) derived values than the same measures from low-resolution images (CCC = [0.72, 0.88]).

A Comparison of Peripheral Imaging Technologies for Bone and Muscle Quantification: A Review of Segmentation Techniques

Musculoskeletal science has developed many overlapping branches, necessitating specialists from 1 area of focus to often require the expertise in others. In terms of imaging, this means obtaining a comprehensive illustration of bone, muscle, and fat tissues. There is currently a lack of a reliable resource for end users to learn about these tissues' imaging and quantification techniques together. An improved understanding of these tissues has been an important progression toward better prediction of disease outcomes and better elucidation of their interaction with frailty, aging, and metabolic disorders. Over the last decade, there have been major advances into the image acquisition and segmentation of bone, muscle, and fat features using computed tomography (CT), magnetic resonance imaging (MRI), and peripheral modules of these systems. Dedicated peripheral quantitative musculoskeletal imaging systems have paved the way for mobile research units, lower cost clinical research facilities, and improved resolution per unit cost paid. The purpose of this review was to detail the segmentation techniques available for each of these peripheral CT and MRI modalities and to describe advances in segmentation methods as applied to study longitudinal changes and treatment-related dynamics. Although the peripheral CT units described herein have established feasible standardized protocols that users have adopted globally, there remain challenges in standardizing MRI protocols for bone and muscle imaging.

Segmentation of the Proximal Femur from MR Images using Deep Convolutional Neural Networks

Magnetic resonance imaging (MRI) has been proposed as a complimentary method to measure bone quality and assess fracture risk. However, manual segmentation of MR images of bone is time-consuming, limiting the use of MRI measurements in the clinical practice. The purpose of this paper is to present an automatic proximal femur segmentation method that is based on deep convolutional neural networks (CNNs). This study had institutional review board approval and written informed consent was obtained from all subjects. A dataset of volumetric structural MR images of the proximal femur from 86 subjects were manually-segmented by an expert. We performed experiments by training two different CNN architectures with multiple number of initial feature maps, layers and dilation rates, and tested their segmentation performance against the gold standard of manual segmentations using four-fold cross-validation. Automatic segmentation of the proximal femur using CNNs achieved a high dice similarity score of 0.95 ± 0.02 with precision = 0.95 ± 0.02, and recall = 0.95 ± 0.03. The high segmentation accuracy provided by CNNs has the potential to help bring the use of structural MRI measurements of bone quality into clinical practice for management of osteoporosis.

Subchondral bone microarchitecture analysis in the proximal tibia at 7-T MRI

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.

Relationship between subchondral bone microstructure and articular cartilage in the osteoarthritic knee using 3T MRI

BACKGROUND

The importance of subchondral bone in the pathogenesis of osteoarthritis (OA) has drawn interest.

PURPOSE

To investigate subregional trabecular bone microstructural features and to determine the relationship between cartilage and trabecular bone in the osteoarthritic human knee.

STUDY TYPE

Prospective study.

SUBJECTS

In all, 92 knees were enrolled and divided into three groups: without OA, mild OA, and severe OA.

SEQUENCE

A sagittal 3D balanced fast field echo (3D B-FFE) sequence and FatSat 3D fast field echo (3D-FFE) sequence at 3T MRI.

ASSESSMENT

The trabecular bone in 12 sites of the knee joint was evaluated using digital topological analysis, and the cartilage thickness in four sites was calculated.

STATISTICAL TEST

Trabecular bone and cartilage parameters between groups were compared using analysis of variance (ANOVA) with Bonferroni adjustment, and their correlations were analyzed using Pearson's correlation coefficient.

RESULTS

Within both femoral condyles, the trabecular bone structure deteriorated in mild OA, showing a lower bone volume fraction (BVF) (0.15 to 0.12, P < 0.05), higher erosion index (EI) (2.25 to 2.28, P < 0.01), and a lower plate-to-rod ratio (SCR) (6.22 to 5.96, P < 0.05). Within medial and lateral tibia, deterioration in the trabecular bone was also observed, demonstrating a lower BVF (0.15 to 0.12 P < 0.05) and a higher EI (2.25 to 2.61, P < 0.05). Cartilage attrition mainly occurred in the medial joint. Extensive correlations were found between the medial cartilage thickness and subregional trabecular parameters. There was mainly a positive correlation with both femoral BVFs (r > 0.3, P < 0.05), and a negative correlation with the tibia SCR (r < -0.2, P < 0.05).

DATA CONCLUSION

In the early stage of OA, trabecular bone osteoporotic changes were observed in both femoral condyles and the tibia. Based on a strong correlation with the medial cartilage thickness, the trabecular structural topological analysis may be useful for elucidating OA onset and progression.

LEVEL OF EVIDENCE

2 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2018.

Quantitative evaluation of subchondral bone microarchitecture in knee osteoarthritis using 3T MRI

Background

Osteoarthritis (OA) is now increasingly recognized as being related to the whole joint instead of the cartilage alone. In particular, the importance of subchondral bone in OA pathogenesis has drawn a lot of interest. The aim of this study is to investigate subchondral bone microstructural features in two femoral condyles of human knee osteoarthritis.

Methods

Eighty subjects were enrolled in our study and divided into three groups: without OA (group 0), mild OA (group 1), and severe OA (group 2). Sagittal 3D Balanced Fast Field Echo (3D–FFE) images were obtained by 3T MRI to quantify trabecular bone structure, and sagittal FatSat 3D Fast Field Echo (3D–FFE) images were acquired to assess cartilage thickness. Trabecular bone parameters, including bone volume fraction (BVF), erosion index (EI) and the trabecular plate-to-rod ratio (SCR), and trabecular thickness were evaluated using digital topological analysis. Subchondral bone and cartilage parameters between different groups and different locations were compared, and their correlations were analyzed.

Results

Within two femoral condyles, subchondral bone structure was deteriorated in mild OA, showing a lower BVF (−0.011 to −0.014 P < 0.001), a higher EI (0.346 to 0.310 P < 0.001), a lower SCR (−0.581 to −0.542 P < 0.001)) and lower trabecular thickness (−6.588 to −4.759 P < 0.05). In severe OA, BVF was further decreased, but EI, SCR and trabecular thickness showed no significant difference than mild OA(P > 0.05). Moreover, there was a lower BVF, SCR and higher EI in the medial femoral condyle in each group. Interestingly, cartilage attrition mainly occurred in the medial femoral condyle. Medial cartilage thickness was not only positively correlated with the ipsilateral femoral BVF (r = 0.321 P = 0.004) but also with the opposite femoral BVF (r = 0.270 P = 0.015).

Conclusions

Our results indicated that deterioration in the trabecular bone structure in both femoral condyles could more sensitively reveal early OA, and BVF could be a better biomarker to evaluate OA severity.

Quantitative imaging of peripheral trabecular bone microarchitecture using MDCT

PURPOSE

Osteoporosis associated with reduced bone mineral density (BMD) and microarchitectural changes puts patients at an elevated risk of fracture. Modern multidetector row CT (MDCT) technology, producing high spatial resolution at increasingly lower dose radiation, is emerging as a viable modality for trabecular bone (Tb) imaging. Wide variation in CT scanners raises concerns of data uniformity in multisite and longitudinal studies. A comprehensive cadaveric study was performed to evaluate MDCT-derived Tb microarchitectural measures. A human pilot study was performed comparing continuity of Tb measures estimated from two MDCT scanners with significantly different image resolution features.

METHOD

Micro-CT imaging of cadaveric ankle specimens (n=25) was used to examine the validity of MDCT-derived Tb microarchitectural measures. Repeat scan reproducibility of MDCT-based Tb measures and their ability to predict mechanical properties were examined. To assess multiscanner data continuity of Tb measures, the distal tibias of 20 volunteers (age:26.2±4.5Y,10F) were scanned using the Siemens SOMATOM Definition Flash and the higher resolution Siemens SOMATOM Force scanners with an average 45-day time gap between scans. The correlation of Tb measures derived from the two scanners over 30% and 60% peel regions at the 4% to 8% of distal tibia was analyzed.

RESULTS

MDCT-based Tb measures characterizing bone network area density, plate-rod microarchitecture, and transverse trabeculae showed good correlations (r∈0.85,0.92) with the gold standard micro-CT-derived values of matching Tb measures. However, other MDCT-derived Tb measures characterizing trabecular thickness and separation, erosion index, and structure model index produced weak correlation (r<0.8) with their micro-CT-derived values. Most MDCT Tb measures were found repeatable (ICC∈0.94,0.98). The Tb plate-width measure showed a strong correlation (r = 0.89) with experimental yield stress, while the transverse trabecular measure produced the highest correlation (r = 0.81) with Young's modulus. The data continuity experiment showed that, despite significant differences in image resolution between two scanners (10% MTF along xy-plane and z-direction - Flash: 16.2 and 17.9 lp/cm; Force: 24.8 and 21.0 lp/cm), most Tb measures had high Pearson correlations (r > 0.95) between values estimated from the two scanners. Relatively lower correlation coefficients were observed for the bone network area density (r = 0.91) and Tb separation (r = 0.93) measures.

CONCLUSION

Most MDCT-derived Tb microarchitectural measures are reproducible and their values derived from two scanners strongly correlate with each other as well as with bone strength. This study has highlighted those MDCT-derived measures which show the greatest promise for characterization of bone network area density, plate-rod and transverse trabecular distributions with a good correlation (r ≥ 0.85) compared with their micro-CT-derived values. At the same time, other measures representing trabecular thickness and separation, erosion index, and structure model index produced weak correlations (r < 0.8) with their micro-CT-derived values, failing to accurately portray the projected trabecular microarchitectural features. Strong correlations of Tb measures estimated from two scanners suggest that image data from different scanners can be used successfully in multisite and longitudinal studies with linear calibration required for some measures. In summary, modern MDCT scanners are suitable for effective quantitative imaging of peripheral Tb microarchitecture if care is taken to focus on appropriate quantitative metrics.

Digital Topology and Geometry in Medical Imaging: A Survey

Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.

In Vivo Precision of Digital Topological Skeletonization Based Individual Trabecula Segmentation (ITS) Analysis of Trabecular Microstructure at the Distal Radius and Tibia by HR-pQCT

Trabecular plate and rod microstructure plays a dominant role in the apparent mechanical properties of trabecular bone. With high-resolution computed tomography (CT) images, digital topological analysis (DTA) including skeletonization and topological classification was applied to transform the trabecular three-dimensional (3D) network into surface and curve skeletons. Using the DTA-based topological analysis and a new reconstruction/recovery scheme, individual trabecula segmentation (ITS) was developed to segment individual trabecular plates and rods and quantify the trabecular plate- and rod-related morphological parameters. High-resolution peripheral quantitative computed tomography (HR-pQCT) is an emerging in vivo imaging technique to visualize 3D bone microstructure. Based on HR-pQCT images, ITS was applied to various HR-pQCT datasets to examine trabecular plate- and rod-related microstructure and has demonstrated great potential in cross-sectional and longitudinal clinical applications. However, the reproducibility of ITS has not been fully determined. The aim of the current study is to quantify the precision errors of ITS plate-rod microstructural parameters. In addition, we utilized three different frequently used contour techniques to separate trabecular and cortical bone and to evaluate their effect on ITS measurements. Overall, good reproducibility was found for the standard HR-pQCT parameters with precision errors for volumetric BMD and bone size between 0.2%-2.0%, and trabecular bone microstructure between 4.9%-6.7% at the radius and tibia. High reproducibility was also achieved for ITS measurements using all three different contour techniques. For example, using automatic contour technology, low precision errors were found for plate and rod trabecular number (pTb.N, rTb.N, 0.9% and 3.6%), plate and rod trabecular thickness (pTb.Th, rTb.Th, 0.6% and 1.7%), plate trabecular surface (pTb.S, 3.4%), rod trabecular length (rTb.ℓ, 0.8%), and plate-plate junction density (P-P Junc.D, 2.3%) at the tibia. The precision errors at the radius were similar to those at the tibia. In addition, precision errors were affected by the contour technique. At the tibia, precision error by the manual contour method was significantly different from automatic and standard contour methods for pTb.N, rTb.N and rTb.Th. Precision error using the manual contour method was also significantly different from the standard contour method for rod trabecular number (rTb.N), rod trabecular thickness (rTb.Th), rod-rod and plate-rod junction densities (R-R Junc.D and P-R Junc.D) at the tibia. At the radius, the precision error was similar between the three different contour methods. Image quality was also found to significantly affect the ITS reproducibility. We concluded that ITS parameters are highly reproducible, giving assurance that future cross-sectional and longitudinal clinical HR-pQCT studies are feasible in the context of limited sample sizes.

In vivo measurement reproducibility of femoral neck microarchitectural parameters derived from 3T MR images

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.

Topology preserving thinning of cell complexes

A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is a very active research area. It plays a central role in reducing the amount of information to be processed during image analysis and visualization, computer-aided diagnosis, or by pattern recognition algorithms. This paper introduces a novel topology preserving thinning algorithm, which removes simple cells-a generalization of simple points-of a given cell complex. The test for simple cells is based on acyclicity tables automatically produced in advance with homology computations. Using acyclicity tables render the implementation of thinning algorithms straightforward. Moreover, the fact that tables are automatically filled for all possible configurations allows to rigorously prove the generality of the algorithm and to obtain fool-proof implementations. The novel approach enables, for the first time, according to our knowledge, to thin a general unstructured simplicial complex. Acyclicity tables for cubical and simplicial complexes and an open source implementation of the thinning algorithm are provided as an additional material to allow their immediate use in the vast number of applications arising in medical imaging and beyond.

Cylinders or walls? A new computational model to estimate the MR transverse relaxation rate dependence on trabecular bone architecture

OBJECTIVE

Bone density is distributed in a complex network of interconnecting trabecular plates and rods that are interspersed with bone marrow. A computational model to assess the dependence of the relaxation rate on the geometry of bone can consider the distribution of bone material in the form of two components: cylinders and open walls (walls with gaps). We investigate whether the experimentally known dependence of the transverse relaxation rate on the trabecular bone structure can be usefully interpreted in terms of these two components.

MATERIALS AND METHODS

We established a computer model based on an elementary computational cell. The model includes a variable number of open walls and infinitely long cylinders as well as multiple geometric parameters. The transverse relaxation rate is computed as a function of these parameters. Within the model, increasing the trabecular spacing with a fixed trabecular radius is equivalent to thinning the trabeculae while maintaining constant spacing.

RESULTS

Increasing the number of cylinder and wall gap elements beyond their nearest neighbors does not change the transverse relaxation rate. Although the absolute contribution to the relaxation due to open walls is on average more important than that due to cylinders, the latter drops off rapidly. The change on transverse relaxation rate is larger for changing cylinder geometry than for changing wall geometry, as it can be seen from the effect on the relaxation rate when trabecular spacing is varied, compared to varying the size of wall gaps.

CONCLUSION

Our results provide strong evidence that trabecular thinning, which is associated with increasing age, decreases the relaxation rates. The effect of thinning plates and rods on the transverse relaxation can be understood in terms of simple cylinders and open walls. A reduction in the relaxation rate can be seen as an indication of thinning cylinders, corresponding to reduced bone stability and ultimately, osteoporosis.

Evaluation of trabecular microarchitecture in nonosteoporotic postmenopausal women with and without fracture

This study compared microscopic magnetic resonance imaging (µMRI) parameters of trabecular microarchitecture between postmenopausal women with and without fracture who have normal or osteopenic bone mineral density (BMD) on dual-energy X-ray absorptiometry (DXA). It included 36 postmenopausal white women 50 years of age and older with normal or osteopenic BMD (T-scores better than -2.5 at the lumbar spine, proximal femur, and one-third radius on DXA). Eighteen women had a history of low-energy fracture, whereas 18 women had no history of fracture and served as an age, race, and ultradistal radius BMD-matched control group. A three-dimensional fast large-angle spin-echo (FLASE) sequence with 137 µm × 137 µm × 400 µm resolution was performed through the nondominant wrist of all 36 women using the same 1.5T scanner. The high-resolution images were used to measure trabecular bone volume fraction, trabecular thickness, surface-to-curve ratio, and erosion index. Wilcoxon signed-rank tests were used to compare differences in BMD and µMRI parameters between postmenopausal women with and without fracture. Post-menopausal women with fracture had significantly lower (p < 0.05) trabecular bone volume fraction and surface-to-curve ratio and significantly higher (p < 0.05) erosion index than postmenopausal women without fracture. There was no significant difference between postmenopausal women with and without fracture in trabecular thickness (p = 0.80) and BMD of the spine (p = 0.21), proximal femur (p = 0.19), one-third radius (p = 0.47), and ultradistal radius (p = 0.90). Postmenopausal women with normal or osteopenic BMD who had a history of low-energy fracture had significantly different (p < 0.05) µMRI parameters than an age, race, and ultradistal radius BMD-matched control group of postmenopausal women with no history of fracture. Our study suggests that µMRI can be used to identify individuals without a DXA-based diagnosis of osteoporosis who have impaired trabecular microarchitecture and thus a heretofore-unappreciated elevated fracture risk.

Generation of an atlas of the proximal femur and its application to trabecular bone analysis

Automatic placement of anatomically corresponding volumes of interest and comparison of parameters against a standard of reference are essential components in studies of trabecular bone. Only recently, in vivo MR images of the proximal femur, an important fracture site, could be acquired with high-spatial resolution. The purpose of this MRI trabecular bone study was two-fold: (1) to generate an atlas of the proximal femur to automatically place anatomically corresponding volumes of interest in a population study and (2) to demonstrate how mean models of geodesic topological analysis parameters can be generated to be used as potential standard of reference. Ten females were used to generate the atlas and geodesic topological analysis models, and 10 females were used to demonstrate the atlas-based trabecular bone analysis. All alignments were based on three-dimensional (3D) multiresolution affine transformations followed by 3D multiresolution free-form deformations. Mean distances less than 1 mm between aligned femora, and sharp edges in the atlas and in fused gray-level images of registered femora indicated that the anatomical variability was well accommodated and explained by the free-form deformations.

On the significance of motion degradation in high-resolution 3D μMRI of trabecular bone

RATIONALE AND OBJECTIVES

Subtle subject movement during high-resolution three-dimensional micro-magnetic resonance imaging of trabecular bone (TB) causes blurring, thereby rendering the data unreliable for quantitative analysis. In this work, the effects of translational and rotational motion displacements were evaluated qualitatively and quantitatively.

MATERIALS AND METHODS

In experiment 1, motion was induced by applying various simulated and previously observed in vivo trajectories as phase shifts to k-space or rotation angles to k-space segments of a virtually motion-free data set. In experiment 2, images that were visually free of motion artifacts from two groups of 10 healthy individuals, differing in age, were selected to probe the effects of motion on TB parameters. In both experiments, images were rated for motion severity, and the scores were compared to a focus criterion, the normalized gradient squared.

RESULTS

Strong correlations were observed between the motion quality scores and the corresponding normalized gradient squared values (R(2) = 0.52-0.64, P < .01). The results from experiment 1 demonstrated consistently lower image quality and alterations in structural parameters of 9% to 45% with increased amplitude of displacements. In experiment 2, the significant differences in structural parameter group means of the motion-free images were lost upon motion degradation. Autofocusing, a postprocessing correction method, partially recovered the sharpness of the original motion-free images in 13 of 20 subjects.

CONCLUSIONS

Quantitative TB structural measures are highly sensitive to subtle motion-induced degradation, which adversely affects precision and statistical power. The results underscore the influence of subject movement in high-resolution three-dimensional micro-magnetic resonance imaging and its correction for TB structure analysis.

Performance of μMRI-Based virtual bone biopsy for structural and mechanical analysis at the distal tibia at 7T field strength

PURPOSE

To assess the performance of a 3D fast spin echo (FSE) pulse sequence utilizing out-of-slab cancellation through phase alternation and micro-magnetic resonance imaging (μMRI)-based virtual bone biopsy processing methods to probe the serial reproducibility and sensitivity of structural and mechanical parameters of the distal tibia at 7.0T.

MATERIALS AND METHODS

The distal tibia of five healthy subjects was imaged at three timepoints with a 3D FSE sequence at 137 × 137 × 410 μm(3) voxel size. Follow-up images were retrospectively 3D registered to baseline images. Coefficients of variation (CV) and intraclass correlation coefficients (ICCs) for measures of scale and topology of the whole tibial trabecular bone (TB) cross-section as well as finite-element-derived Young's and shear moduli of central cuboidal TB subvolumes (8 × 8 × 5 mm(3) ) were evaluated as measures of reproducibility and reliability. Four additional cubic TB subregions (anterior, medial, lateral, and posterior) of similar dimensions were extracted and analyzed to determine associations between whole cross-section and subregional structural parameters.

RESULTS

The mean signal-to-noise ratio (SNR) over the 15 image acquisitions was 27.5 ± 2.1. Retrospective registration yielded an average common analysis volume of 67% across the three exams per subject. Reproducibility (mean CV = 3.6%; range, 1.5%-5%) and reliability (ICCs, 0.95-0.99) of all parameters permitted parameter-based discrimination of the five subjects in spite of the narrow age range (26-36 years) covered. Parameters characterizing topology were better able to distinguish two individuals who demonstrated similar values for scalar measurements (≈ 34% difference, P < 0.001). Whole-section axial stiffness encompassing the cortex was superior at distinguishing two individuals relative to its central subregional TB counterpart (≈ 8% difference; P < 0.05). Interregion comparisons showed that although all parameters were correlated (mean R(2) = 0.78; range 0.57-0.99), the strongest associations observed were those for the erosion index (mean R(2) = 0.95, P ≤ 0.01).

CONCLUSION

The reproducibility and structural and mechanical parameter-based discriminative ability achieved in five healthy subjects suggests that 7T-derived μMRI of TB can be applied towards serial patient studies of osteoporosis and may enable earlier detection of disease or treatment-based effects.

Volumetric topological analysis: a novel approach for trabecular bone classification on the continuum between plates and rods

Trabecular bone (TB) is a complex quasi-random network of interconnected plates and rods. TB constantly remodels to adapt to the stresses to which it is subjected (Wolff's Law). In osteoporosis, this dynamic equilibrium between bone formation and resorption is perturbed, leading to bone loss and structural deterioration. Both bone loss and structural deterioration increase fracture risk. Bone's mechanical behavior can only be partially explained by variations in bone mineral density, which led to the notion of bone structural quality. Previously, we developed digital topological analysis (DTA) which classifies plates, rods, profiles, edges, and junctions in a TB skeletal representation. Although the method has become quite popular, a major limitation of DTA is that it provides only hard classifications of different topological entities, failing to distinguish between narrow and wide plates. Here, we present a new method called volumetric topological analysis (VTA) for regional quantification of TB topology. At each TB location, the method uniquely classifies its topology on the continuum between perfect plates and perfect rods, facilitating early detections of TB alterations from plates to rods according to the known etiology of osteoporotic bone loss. Several new ideas, including manifold distance transform, manifold scale, and feature propagation have been introduced here and combined with existing DTA and distance transform methods, leading to the new VTA technology. This method has been applied to multidetector computed tomography (CT) and micro-computed tomography ( μCT) images of four cadaveric distal tibia and five distal radius specimens. Both intra- and inter-modality reproducibility of the method has been examined using repeat CT and μCT scans of distal tibia specimens. Also, the method's ability to predict experimental biomechanical properties of TB via CT imaging under in vivo conditions has been quantitatively examined and the results found are very encouraging.

Structural and mechanical parameters of trabecular bone estimated from in vivo high-resolution magnetic resonance images at 3 tesla field strength

PURPOSE

To evaluate the performance of a new 3 Tesla (T) high-resolution trabecular bone (TB) imaging technique at two resolution regimens in terms of serial reproducibility and sensitivity.

MATERIALS AND METHODS

The left distal tibial metaphysis of seven healthy volunteers was imaged at three time-points using a FLASE (fast large-angle spin-echo) pulse sequence at 137 x 137 x 410 mum(3) and (160 mum)(3) voxel sizes. Image artifacts, motion degradation, and serial image volume misalignments were controlled to maximize reproducibility of image-derived measures of scale, topology, orientation in terms of structural anisotropy, and finite-element derived Young's and shear moduli. Coefficients of variation (CV) and intraclass correlation coefficients (ICC) for structural and mechanical parameters were evaluated as measures of reproducibility and reliability. The ability of structural and mechanical parameters to distinguish between subjects was tested by analysis of variance.

RESULTS

Reproducibility was generally higher in the anisotropic data (CVs 1-5% versus 1-9% for isotropic images). Anisotropic voxel size yielded greater measurement reliability (ICCs 0.75-0.99, mean = 0.92 versus 0.62-0.99, mean = 0.86) and better discrimination of the seven subjects (75% versus 50% of the possible comparisons were significantly different [P < 0.05]) except for measures of structural anisotropy and topology. Isotropic resolution improved detection of structural orientation and permitted visualization of small perforations in longitudinal trabecular plates not detected at anisotropic resolution.

CONCLUSION

Improved image acquisition and processing techniques enhance reproducibility of structural and mechanical parameters derived from high-resolution MRI of metaphyseal bone in the distal tibia.

High-resolution imaging techniques for the assessment of osteoporosis

The importance of assessing the bone's microarchitectural make-up in addition to its mineral density in the context of osteoporosis has been emphasized in several publications. The high spatial resolution required to resolve the bone's microstructure in a clinically feasible scan time is challenging. At present, the best suited modalities meeting these requirements in vivo are high-resolution peripheral quantitative imaging (HR-pQCT) and magnetic resonance imaging (MRI). Whereas HR-pQCT is limited to peripheral skeleton regions like the wrist and ankle, MRI can also image other sites like the proximal femur but usually with lower spatial resolution. In addition, multidetector computed tomography has been used for high-resolution imaging of trabecular bone structure; however, the radiation dose is a limiting factor. This article provides an overview of the different modalities, technical requirements, and recent developments in this emerging field. Details regarding imaging protocols as well as image postprocessing methods for bone structure quantification are discussed.

Mechanical implications of estrogen supplementation in early postmenopausal women

Whereas the structural implications of drug intervention are well established, there are few data on the possible mechanical consequences of treatment. In this work we examined the changes in elastic and shear moduli (EM and SM) in a region of trabecular bone in the distal radius and distal tibia of early postmenopausal women on the basis of MRI-based micro-finite-element (microFE) analysis. Whole-section axial stiffness (AS) encompassing both trabecular and cortical compartments was evaluated as well. The study was conducted on previously acquired high-resolution images at the two anatomic sites. Images were processed to yield a 3D voxel array of bone-volume fraction (BVF), which was converted to a microFE model of hexahedral elements in which tissue modulus was set proportional to voxel BVF. The study comprised 65 early postmenopausal women (age range 45 to 55 years), of whom 32 had chosen estrogen supplementation (estradiol group); the remainder had not (control group). Subjects had been scanned at baseline and 12 and 24 months thereafter. At the distal tibia, EM and SM were reduced by 2.9% to 5.5% in the control group (p < .05 to <.005), but there was no change in the estradiol subjects. AS decreased 3.9% (4.0%) in controls (p < .005) and increased by 5.8% (6.2%) in estradiol group subjects (p < .05) at 12 (24) months. At the distal radius, EM and SM changes from baseline were not significant, but at both time points AS was increased in estradiol group subjects and decreased in controls (p < .005 to <.05), albeit by a smaller margin than at the tibia. EM and SM were strongly correlated with BV/TV (r(2) = 0.44 to 0.92) as well as with topologic parameters expressing the ratio of plates to rods (r(2) = 0.45 to 0.82), jointly explaining up to 96% of the variation in the mechanical parameters. Finally, baseline AS was strongly correlated between the two anatomic sites (r(2) = 0.58), suggesting that intersubject variations in the bone's mechanical competence follows similar mechanisms. In conclusion, the results demonstrate that micro-MRI-based microFE models are suited for the study of the mechanical implications of antiresorptive treatment. The data further highlight the anabolic effect of short-term estrogen supplementation.

Microcomputed tomography and microfinite element modeling for evaluating polymer scaffolds architecture and their mechanical properties

Detailed knowledge of the porous architecture of synthetic scaffolds for tissue engineering, their mechanical properties, and their interrelationship was obtained in a nondestructive manner. Image analysis of microcomputed tomography (microCT) sections of different scaffolds was done. The three-dimensional (3D) reconstruction of the scaffold allows one to quantify scaffold porosity, including pore size, pore distribution, and struts' thickness. The porous morphology and porosity as calculated from microCT by image analysis agrees with that obtained experimentally by scanning electron microscopy and physically measured porosity, respectively. Furthermore, the mechanical properties of the scaffold were evaluated by making use of finite element modeling (FEM) in which the compression stress-strain test is simulated on the 3D structure reconstructed from the microCT sections. Elastic modulus as calculated from FEM is in agreement with those obtained from the stress-strain experimental test. The method was applied on qualitatively different porous structures (interconnected channels and spheres) with different chemical compositions (that lead to different elastic modulus of the base material) suitable for tissue regeneration. The elastic properties of the constructs are explained on the basis of the FEM model that supports the main mechanical conclusion of the experimental results: the elastic modulus does not depend on the geometric characteristics of the pore (pore size, interconnection throat size) but only on the total porosity of the scaffold.

Trabecular bone analysis in CT and X-ray images of the proximal femur for the assessment of local bone quality

Currently, conventional X-ray and CT images as well as invasive methods performed during the surgical intervention are used to judge the local quality of a fractured proximal femur. However, these approaches are either dependent on the surgeon's experience or cannot assist diagnostic and planning tasks preoperatively. Therefore, in this work a method for the individual analysis of local bone quality in the proximal femur based on model-based analysis of CT- and X-ray images of femur specimen will be proposed. A combined representation of shape and spatial intensity distribution of an object and different statistical approaches for dimensionality reduction are used to create a statistical appearance model in order to assess the local bone quality in CT and X-ray images. The developed algorithms are tested and evaluated on 28 femur specimen. It will be shown that the tools and algorithms presented herein are highly adequate to automatically and objectively predict bone mineral density values as well as a biomechanical parameter of the bone that can be measured intraoperatively.

Evaluation of correction methods for coil-induced intensity inhomogeneities and their influence on trabecular bone structure parameters from MR images

Magnetic resonance (MR) imaging-based quantitative trabecular bone structure analysis has gained increasing interest in osteoporotic fracture risk assessment and treatment evaluation related to osteoporosis. In vivo MR images of anatomic regions such as the proximal femur and distal tibia are generally acquired with a surface coil in order to obtain sufficient sensitivity and resolution for quantification of the trabeculae. However, these coils introduce intensity inhomogeneities which affect the trabecular bone structure analysis. This work evaluates the applicability of a fully automatic coil correction by nonparametric nonuniform intensity normalization (N3) in the analysis of trabecular bone parameters. The ability to correct for coil-induced intensity inhomogeneity was evaluated ex vivo on proximal femur specimens scanned with both a surface coil and a volume coil, which allowed for a direct evaluation of the performance of the coil correction methods without any major confounding factors. In addition, trabecular bone parameter values were correlated with values from high-resolution peripheral computed tomography (HR-pQCT) scans, and the reproducibility of trabecular bone parameters was evaluated in an in vivo study of repeat hip MR scans. The trabecular bone parameters determined from MR surface coil scans processed with the N3 coil correction method showed significant correlation (p < 0.05) with corresponding values from homogeneous intensity data in the ex vivo study. This can be compared to the correlation without coil correction (p < 0.5), and coil correction using low-pass filtering (LPF) (p < 0.53). The in vivo interscan variability was reduced from 8.9% to 12.8% using LPF-based to 3.6%-8.4% (CV) using N3 coil correction; hence the results showed that N3 is advantageous to LPF-based coil correction. No significant differences in correlation to HR-pQCT data were found for the coil correction methods. The significant correlations with volume coil data and high reproducibility of the N3 processed data imply that N3 coil correction preserve image information while accurately correcting for coil-induced intensity inhomogeneities, which makes it suitable for quantitative analysis of trabecular bone structure from MR images acquired with surface coils.

Geodesic topological analysis of trabecular bone microarchitecture from high-spatial resolution magnetic resonance images

In vivo assessment of trabecular bone microarchitecture could improve the prediction of fracture risk and the efficacy of osteoporosis treatment and prevention. Geodesic topological analysis (GTA) is introduced as a novel technique to quantify the trabecular bone microarchitecture from high-spatial resolution magnetic resonance (MR) images. Trabecular bone parameters that quantify the scale, topology, and anisotropy of the trabecular bone network in terms of its junctions are the result of GTA. The reproducibility of GTA was tested with in vivo images of human distal tibiae and radii (n = 6) at 1.5 Tesla; and its ability to discriminate between subjects with and without vertebral fracture was assessed with ex vivo images of human calcanei at 1.5 and 3.0 Tesla (n = 30). GTA parameters yielded an average reproducibility of 4.8%, and their individual areas under the curve (AUC) of the receiver operating characteristic curve analysis for fracture discrimination performed better at 3.0 than at 1.5 Tesla reaching values of up to 0.78 (p < 0.001). Logistic regression analysis demonstrated that fracture discrimination was improved by combining GTA parameters, and that GTA combined with bone mineral density (BMD) allow for better discrimination than BMD alone (AUC = 0.95; p < 0.001). Results indicate that GTA can substantially contribute in studies of osteoporosis involving imaging of the trabecular bone microarchitecture.

Implications of resolution and noise for in vivo micro-MRI of trabecular bone

Osteoporotic bone loss is accompanied by impaired structural integrity of the trabecular network, leading to a decrease in the overall mechanical properties of the bone. The development of the "virtual bone biopsy" (VBB), a method combining magnetic resonance microimaging (microMRI) and digital image processing techniques, has previously been shown to quantify topology and scale of human trabecular bone noninvasively. The aim of this work was to determine the extent to which structural parameters derived from images acquired in the limited spatial resolution regime of in vivo imaging are sensitive to resolution and noise and further, whether under these conditions, a small amount of bone loss and its associated structural manifestations can be detected. Toward these goals 3D models of trabecular bone representing multiple anatomic locations were generated on the basis of microCT images of human cadaveric bone cores. These images were binarized and the resulting data arrays representing pure bone (proton density=0) and pure marrow (proton density=255) subjected to simulated MR imaging by Cartesian sampling of k space, yielding, after 3D Fourier reconstruction, voxel sizes currently achievable in vivo. Subsequently, realistic levels of Gaussian noise were superimposed on the complex data and magnitude images were computed. The resulting images were subsequently VBB processed for a range of signal-to-noise ratio (SNR) values and image voxel sizes. For comparison of the predicted behavior to in vivo data, images from a recent patient study were evaluated as well. Systematic changes of the derived structural parameters changing progressively with decreasing SNR were noted, and it is shown that the errors are correctable using simple linear transformations, thereby allowing the data to be normalized. The predicted dependence of the structural parameters on SNR also closely parallel those observed in vivo. Finally, in order to assess the sensitivity of the VBB processing algorithms to detect bone loss during disease progression or regression in response to treatment, the high-resolution specimen data were subjected to 5% bone loss either by homogeneous or heterogeneous erosion and microMR images simulated at in vivo resolution and SNR. At typical in vivo SNR (SNR=12) and effective image resolution (160 microm isotropic and 137 x 137 X 410 microm3), VBB algorithms were able to detect the structural implications of a 5% loss in bone volume fraction with high statistical significance.

Retrospective 3D registration of trabecular bone MR images for longitudinal studies

PURPOSE

To evaluate an automatic 3D registration algorithm for serial high-resolution images of trabecular bone (TB) in studies designed to evaluate the response of the trabecular architecture to intervention or disease progression.

MATERIALS AND METHODS

An efficient algorithm for registering high-resolution 3D images of TB is presented. The procedure identifies the six parameters of rigid displacement between two scans performed at different timepoints. By assuming a relatively small through-plane rotation, considerable time is saved by combining the results of a collection of regional 2D registrations throughout the TB region of interest (ROI). The algorithm was applied to 26 pairs of MR images acquired 6 months apart. Reproducibility of local TB structural parameters (plate, rod, and junction density) computed in manually selected regions were compared between baseline and registered follow-up images.

RESULTS

All 26 registrations were completed successfully in less than 30 seconds per image pair. The resampled follow-up images agreed with baseline to around one pixel throughout the volume at 137 x 137 x 410 microm(3) image resolution. Structural parameters in each region correlated well from baseline to follow-up with intraclass correlation coefficients ranging between 85%-97% for TB plate density. Interregional variations in the parameters were large as compared with intraregion reproducibility.

CONCLUSION

The proposed algorithm was successful in automatically registering baseline and follow-up TB images in a translational study, and may be useful in regional analyses in longitudinal MR studies of TB architecture.

In vivo microMRI-based finite element and morphological analyses of tibial trabecular bone in eugonadal and hypogonadal men before and after testosterone treatment

Osteoporosis is a major public health problem in men. Hypogonadal men have decreased BMD and deteriorated trabecular bone architecture compared with eugonadal men. Testosterone treatment improves their BMD and trabecular structure. We tested the hypothesis that testosterone replacement in hypogonadal men would also improve their bone's mechanical properties. Ten untreated severely hypogonadal and 10 eugonadal men were selected. The hypogonadal men were treated with a testosterone gel for 24 mo to maintain their serum testosterone concentrations within the normal range. Each subject was assessed before and after 6, 12, and 24 mo of testosterone treatment by microMRI of the distal tibia. A subvolume of each microMR image was converted to a microfinite element (microFE) model, and six analyses were performed, representing three compression and three shear tests. The anisotropic stiffness tensor was calculated, from which the orthotropic elastic material constants were derived. Changes in microarchitecture were also quantified using newly developed individual trabeculae segmentation (ITS)-based and standard morphological analyses. The accuracy of these techniques was examined with simulated microMR images. Significant differences in four estimated anisotropic elastic material constants and most morphological parameters were detected between the eugonadal and hypogonadal men. No significant change in estimated elastic moduli and morphological parameters was detected in the eugonadal group over 24 mo. After 24 mo of treatment, significant increases in estimated elastic moduli E(22) (9.0%), E(33) (5.1%), G(23) (7.2%), and G(12) (9.4%) of hypogonadal men were detected. These increases were accompanied by significant increases in trabecular plate thickness. These results suggest that 24 mo of testosterone treatment of hypogonadal men improves estimated elastic moduli of tibial trabecular bone by increased trabecular plate thickness.

In vivo magnetic resonance detects rapid remodeling changes in the topology of the trabecular bone network after menopause and the protective effect of estradiol

INTRODUCTION

Estrogen depletion after menopause is accompanied by bone loss and architectural deterioration of trabecular bone. The hypothesis underlying this work is that the microMRI-based virtual bone biopsy can capture the temporal changes of scale and topology of the trabecular network and that estrogen supplementation preserves the integrity of the trabecular network.

MATERIALS AND METHODS

Subjects studied were early postmenopausal women, 45-55 yr of age (N = 65), of whom 32 were on estrogen (estradiol group), and the remainder were not (control group). Early menopause was defined by amenorrhea for 6-24 mo and elevated serum follicle-stimulating hormone (FSH) concentration. The subjects were evaluated with three imaging modalities at baseline and 12 and 24 mo to determine the temporal changes in trabecular and cortical architecture and density. microMRI of the distal radius and tibia was performed at 137 x 137 x 410-microm(3) voxel size. The resulting bone volume fraction maps were Fourier interpolated to a final voxel size of 45.7 x 45.7 x 136.7 microm(3), binarized, skeletonized, and subjected to 3D digital topological analysis (DTA). Skeletonization converts trabecular rods to curves and plates to surfaces. Parameters quantifying scale included BV/TV, whereas DTA parameters included the volume densities of curves (C) and surface (S)-type voxels, as well as composite parameters: the surface/curve ratio (S/C), and erosion index (EI, ratio of the sum of parameters expected to increase with osteoclastic resorption divided by the sum of those expected to decrease). For comparison, pQCT of the same peripheral locations was conducted, and trabecular density and cortical structural parameters were measured. Areal BMD of the lumbar vertebrae and hip was also measured.

RESULTS

Substantial changes in trabecular architecture of the distal tibia, in particular as they relate to topology of the network, were detected after 12 mo in the control group. S/C decreased 5.6% (p < 0.0005), and EI increased 7.1% (p < 0.0005). Most curve- and profile-type voxels (representative of trabecular struts), increased significantly (p < 0.001). Curve and profile edges resulting from disconnection of rod-like trabeculae increased by 9.8% and 5.1% (p = 0.0001 and <0.001, respectively). Similarly, DXA BMD in the spine and hip decreased 2.6% and 1.3% (p < 0.0001 and <0.005, respectively), and pQCT cortical area decreased 3.6% (p = 0.0001). However, neither trabecular density nor BV/TV changed. Furthermore, none of the parameters measured in the estradiol group were significantly different after 12 mo. Substantial differences in the mean changes from baseline between the estradiol treatment and control groups, in particular after 24 mo, were observed, with relative group differences as large as 13% (S/C, p = 0.005), and the relative changes in the two groups had the opposite sign for most parameters. The observed temporal alterations in architecture are consistent with remodeling changes that involve gradual conversion of plate-like to rod-like trabecular bone along with disconnection of trabecular elements, even in the absence of a net loss of trabecular bone. The high-resolution 3D rendered images provide direct evidence of the above remodeling changes in individual subjects. The radius structural data indicated similar trends but offered no definitive conclusions.

CONCLUSIONS

The short-term temporal changes in trabecular architecture after menopause, and the protective effects of estradiol ensuring maintenance of a more plate-like TB architecture, reported here, have not previously been observed in vivo. This work suggests that MRI-based in vivo micromorphometry of trabecular bone has promise as a tool for monitoring osteoporosis treatment.

Adaptations in trabecular bone microarchitecture in Olympic athletes determined by 7T MRI

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.

Trabecular structure quantified with the MRI-based virtual bone biopsy in postmenopausal women contributes to vertebral deformity burden independent of areal vertebral BMD

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.

Noninvasive assessments of bone strength

PURPOSE OF REVIEW

Description of new noninvasive technologies or modifications of existing technologies with which individual components of bone strength and bone strength as a whole can be quantified.

RECENT FINDINGS

Although bone mineral density has served as an able surrogate for bone strength, it is clear that aspects of bone strength are either not captured or are not discernible within the measurement of bone density. New, noninvasive technologies have been developed to quantify aspects of bone strength such as biomechanical parameters based on geometry and scale and topological parameters of microarchitecture. Finite element modeling utilizes sophisticated mathematical approaches to predict the strength of the whole bone. At present, most of these technologies remain beyond the reach of clinicians, with the exception of hip structural or strength analysis.

SUMMARY

Hip strength or structural analysis is widely available because of its incorporation with dual energy X-ray absorptiometry and has been extensively used in clinical research. None of these new approaches has been shown to be superior to the measurement of bone density in the prediction of fracture risk. This fact does not diminish their potential to enhance the understanding of the pathophysiology of fracture and the mechanisms of therapeutic efficacy.

Clinical software for the assessment of trabecular bone disease in distal radius based on a magnetic resonance structural analysis

As Bone Mineral Density has been demonstrated to be insufficient to elaborate a correct diagnosis of bone diseases such as osteoporosis, a new software tool called EsTra has been developed in order to estimate the most significant structural parameters of trabecular bone microarchitecture. In EsTra, different techniques as automated segmentation, snakes, filtering, skeletonization, voxel classification and three-dimensional reconstruction are applied to Magnetic Resonance images of distal radius and ulna. A microarchitectural study is also carried out from three different viewpoints involving morphological, topological and fractal analysis. Results can be exported to a database to help the research of the disease and a clinical report is elaborated containing the most significant parameters obtained from the analysis.

Image metric-based correction (autofocusing) of motion artifacts in high-resolution trabecular bone imaging

PURPOSE

To evaluate the performance of the autofocusing (AF) motion correction technique in high-resolution trabecular bone imaging where image signal-to noise ratio (SNR) is limited.

MATERIALS AND METHODS

Raw data from 26 clinical three-dimensional (3D) wrist exams were motion corrected using AF for both in-plane rotation and translation. Changes in image metrics (a measurement of image sharpness) and structural parameters subsequently computed, were used to gauge the performance of the AF algorithm, and comparisons were made with translation-only navigator-corrected results.

RESULTS

On average, AF generated images with higher image sharpness compared to the navigator echo technique. The average normalized gradient squared (NGS) metric improved by 0.40%, 0.73%, and 0.84%, respectively, following translation-only navigator, translation-only AF and combined rotation/translation AF. For all structural parameters, the rotation/translation AF resulted in an approximately two-fold greater change compared to the navigator technique.

CONCLUSION

The data provide evidence that errors from subtle translational and rotational motion in the structural parameters in high-resolution trabecular bone images are alleviated by AF and that the resulting improvements are superior to translation-only 2D navigator correction.

Fuzzy logic structure analysis of trabecular bone of the calcaneus to estimate proximal femur fracture load and discriminate subjects with and without vertebral fractures using high-resolution magnetic resonance imaging at 1.5 T and 3 T

Newly developed fuzzy logic-derived structural parameters were used to characterize trabecular bone architecture in high-resolution magnetic resonance imaging (HR-MRI) of human cadaver calcaneus specimens. These parameters were compared to standard histomorphological structural measures and analyzed concerning performance in discriminating vertebral fracture status and estimating proximal femur fracture load. Sets of 60 sagittal 1.5 T and 3.0 T HR-MRI images of the calcaneus were obtained in 39 cadavers using a fast gradient recalled echo sequence. Structural parameters equivalent to bone histomorphometry and fuzzy logic-derived parameters were calculated using two chosen regions of interest. Calcaneal, spine, and hip bone mineral density (BMD) measurements were also obtained. Fracture status of the thoracic and lumbar spine was assessed on lateral radiographs. Finally, mechanical strength testing of the proximal femur was performed. Diagnostic performance in discriminating vertebral fracture status and estimating femoral fracture load was calculated using regression analyses, two-tailed t-tests of significance, and receiver operating characteristic (ROC) analyses. Significant correlations were obtained at both field strengths between all structural and fuzzy logic parameters (r up to 0.92). Correlations between histomorphological or fuzzy logic parameters and calcaneal BMD were mostly significant (r up to 0.78). ROC analyses demonstrated that standard structural parameters were able to differentiate persons with and without vertebral fractures (area under the curve [A(Z)] up to 0.73). However, none of the parameters obtained in the 1.5-T images and none of the fuzzy logic parameters discriminated persons with and without vertebral fractures. Significant correlations were found between fuzzy or structural parameters and femoral fracture load. Using multiple regression analysis, none of the structural or fuzzy parameters were found to add discriminative value to BMD alone. In summary significant correlations were obtained at both field strengths between all structural and fuzzy logic parameters. However, fuzzy logic-based calcaneal parameters were not well suited for vertebral fracture discrimination. Although significant correlations were found between fuzzy or structural parameters and femoral fracture load, multiple regression analysis showed limited improvement for estimating femoral failure load in addition to femoral BMD alone. Local femoral measurements are still needed to estimate femoral bone strength. Overall, parameters obtained at 3.0 T performed better than those at 1.5 T.

Structural and functional assessment of trabecular and cortical bone by micro magnetic resonance imaging

Osteoporosis is a multifactorial disorder of bone mineral homeostasis affecting the elderly. It is a major public health issue with significant socioeconomic consequences. Recent findings suggest that bone loss-the key manifestation of the disease-is accompanied by architectural deterioration, both affecting the bone's mechanical competence and susceptibility to fracture. This article reviews the potential of quantitative micro MRI (mu-MRI), including a discussion of the technical requirements for image acquisition, processing, and analysis for assessing the architectural implications of osteoporosis and as a means to monitor the response to treatment. With current technology, the resolution achievable in clinically acceptable scan times and necessary signal-to-noise ratio (SNR) is comparable to trabecular thickness. This limited spatial resolution regime demands processing and analysis algorithms designed to operate under such limiting conditions. It is shown that three different classes of structural parameters can be distinguished, characterizing scale, topology, and orientation. There is considerable evidence that osteoporotic bone loss affects all three classes but that topological changes, resulting from conversion of trabecular plates to rods, with the latter's eventual disconnection, are particularly prominent. Clinical applications discussed can be divided into those dealing with assessment of osteoporotic fracture risk as opposed to the study of the effect of disease progression and regression in response to treatment. Current data suggest that noninvasive assessment of cortical and trabecular bone (TB) architecture by mu-MRI may provide new surrogate endpoints to assess the efficacy of intervention in osteoporosis treatment and prevention.

Noninvasive assessment of bone microarchitecture by MRI

In determining fracture risk, it has become apparent that bone mineral density accounts for only a portion of bone strength, with the remainder being determined by the material and structural properties of the bone tissue. Over the past 15 years, high-resolution MRI has provided a window into the structural nature of bone disease. Cross-sectional studies imaging the trabecular bone in patients with conditions ranging from postmenopausal osteoporosis to organ transplantation to renal osteodystrophy have all demonstrated a correlation of microarchitecture with fracture burden and have done so at a variety of anatomic sites. Recently, the utility of longitudinal studies for monitoring treatment in vivo has been demonstrated. This technique is noninvasive, involving no contrast or ionizing radiation, and provides useful clinical information independent of bone mineral density, thereby allowing for better classification of those at high risk for fracture.

Quantitative MRI for the assessment of bone structure and function

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.

Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone

The roles of microarchitecture and types of trabeculae in determining elastic modulus of trabecular bone have been studied in microCT images of 29 trabecular bone samples by comparing their Young's moduli calculated by finite element analysis (FEA) with different trabecular type-specific reconstructions. The results suggest that trabecular plates play an essential role in determining elastic properties of trabecular bone.

INTRODUCTION

Osteoporosis is an age-related disease characterized by low bone mass and architectural deterioration. Other than bone volume fraction (BV/TV), microarchitecture of bone is also believed to be important in governing mechanical properties of trabecular bone. We quantitatively examined the role of microarchitecture and relative contribution of trabecular types of individual trabecula in determining the elastic property of trabecular bone.

MATERIALS AND METHODS

Twenty-nine human cadaveric trabecular bone samples were scanned at 21-mum resolution using a microCT system. Digital topological analysis (DTA) consisting of skeletonization and classification was combined with a trabecular type-specific reconstruction technique to extract the skeleton and identify topological type of trabeculae of the original trabecular bone image. Four different microCT-based finite element (FE) models were constructed for each specimen: (1) original full voxel; (2) skeletal voxel; (3) rod-reconstructed, preserving rod volume and plate skeleton; and (4) plate-reconstructed, preserving plate volume and rod skeleton. For each model, the elastic moduli were calculated under compression along each of three image-coordinate axis directions. Plate and rod tissue fractions directly measured from DTA-based topological classification were correlated with the elastic moduli computed from full voxel model.

RESULTS

The elastic moduli of skeleton models were significantly correlated with those of full voxel models along all three coordinate axes (r(2) = 0.38 approximately 0.53). The rod-reconstructed model contained 21.3% of original bone mass and restored 1.5% of elastic moduli, whereas the plate-reconstructed model contained 90.3% of bone mass and restored 53.2% of elastic moduli. Plate tissue fraction showed a significantly positive correlation (r(2) = 0.49) with elastic modulus by a power law, whereas rod tissue fraction showed a significantly negative correlation (r(2) = 0.42).

CONCLUSIONS

These results quantitatively show that the microarchitecture alone affects elastic moduli of trabecular bone and trabecular plates make a far greater contribution than rods to the bone's elastic behavior.

Characterization of trabecular bone structure from high-resolution magnetic resonance images using fuzzy logic

The purpose of this work was to apply fuzzy logic image processing techniques to characterize the trabecular bone structure with high-resolution magnetic resonance images. Fifteen ex vivo high-resolution magnetic resonance images of specimens of human radii at 1.5 T and 12 in vivo high-resolution magnetic resonance images of the calcanei of peri- and postmenopausal women at 3 T were obtained. Soft segmentation using fuzzy clustering was applied to MR data to obtain fuzzy bone volume fraction maps, which were then analyzed with three-dimensional (3D) fuzzy geometrical parameters and measures of fuzziness. Geometrical parameters included fuzzy perimeter and fuzzy compactness, while measures of fuzziness included linear index of fuzziness, quadratic index of fuzziness, logarithmic fuzzy entropy, and exponential fuzzy entropy. Fuzzy parameters were validated at 1.5 T with 3D structural parameters computed from microcomputed tomography images, which allow the observation of true trabecular bone structure and with apparent MR structural indexes at 1.5 T and 3 T. The validation was statistically performed with the Pearson correlation coefficient as well as with the Bland-Altman method. Bone volume fraction correlation values (r) were up to .99 (P<.001) with good agreements based on Bland-Altman analysis showing that fuzzy clustering is a valid technique to quantify this parameter. Measures of fuzziness also showed consistent correlations to trabecular number parameters (r>.85; P<.001) and good agreements based on Bland-Altman analysis, suggesting that the level of fuzziness in high-resolution magnetic resonance images could be related to the trabecular bone structure.