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

Associations between longitudinal fluoride intakes from birth to age 23 and multi-row detector computed tomography bone densitometry outcomes at age 23

OBJECTIVES

To assess the relationships between longitudinal fluoride intakes and bone densitometry outcomes in young adults.

METHODS

Data were analyzed from the Iowa Fluoride Study and Iowa Bone Development Study, which followed 1,882 infants from birth in 1992. Daily fluoride intakes were assessed using detailed questionnaires sent every 1.5-6 months, and multi-row detector computed tomography (MDCT) scans of distal tibia were obtained from 330 participants aged 23 years. Sex-specific bivariate and multivariable associations with MDCT outcomes were examined using linear regression. Because of the multiple statistical analyses being conducted, p-values < 0.01 were considered statistically significant.

RESULTS

In fully adjusted analyses, no statistically significant (p < 0.01) or suggestive (0.01 < p < 0.05) associations were found between period-specific or cumulative fluoride intake and bone measures for either sex, although there were suggestive positive relationships in unadjusted analyses.

CONCLUSIONS

Longitudinal fluoride intakes had little association with bone measures at age 23. As there were no adverse effects from fluoride intake on bone health in young adults, results support the continued use of fluorides, particularly community water fluoridation is the most cost-effective method of dental caries prevention.

Deep learning-based harmonization of trabecular bone microstructures between high- and low-resolution CT imaging

BACKGROUND

Osteoporosis is a bone disease related to increased bone loss and fracture-risk. The variability in bone strength is partially explained by bone mineral density (BMD), and the remainder is contributed by bone microstructure. Recently, clinical CT has emerged as a viable option for in vivo bone microstructural imaging. Wide variations in spatial-resolution and other imaging features among different CT scanners add inconsistency to derived bone microstructural metrics, urging the need for harmonization of image data from different scanners.

PURPOSE

This paper presents a new deep learning (DL) method for the harmonization of bone microstructural images derived from low- and high-resolution CT scanners and evaluates the method's performance at the levels of image data as well as derived microstructural metrics.

METHODS

We generalized a three-dimensional (3D) version of GAN-CIRCLE that applies two generative adversarial networks (GANs) constrained by the identical, residual, and cycle learning ensemble (CIRCLE). Two GAN modules simultaneously learn to map low-resolution CT (LRCT) to high-resolution CT (HRCT) and vice versa. Twenty volunteers were recruited. LRCT and HRCT scans of the distal tibia of their left legs were acquired. Five-hundred pairs of LRCT and HRCT image blocks of64 × 64 × 64 $64 \times 64 \times 64 $ voxels were sampled for each of the twelve volunteers and used for training in supervised as well as unsupervised setups. LRCT and HRCT images of the remaining eight volunteers were used for evaluation. LRCT blocks were sampled at 32 voxel intervals in each coordinate direction and predicted HRCT blocks were stitched to generate a predicted HRCT image.

RESULTS

Mean ± standard deviation of structural similarity (SSIM) values between predicted and true HRCT using both 3DGAN-CIRCLE-based supervised (0.84 ± 0.03) and unsupervised (0.83 ± 0.04) methods were significantly (p < 0.001) higher than the mean SSIM value between LRCT and true HRCT (0.75 ± 0.03). All Tb measures derived from predicted HRCT by the supervised 3DGAN-CIRCLE showed higher agreement (CCC  ∈ $ \in $ [0.956 0.991]) with the reference values from true HRCT as compared to LRCT-derived values (CCC  ∈ $ \in $ [0.732 0.989]). For all Tb measures, except Tb plate-width (CCC = 0.866), the unsupervised 3DGAN-CIRCLE showed high agreement (CCC  ∈ $ \in $ [0.920 0.964]) with the true HRCT-derived reference measures. Moreover, Bland-Altman plots showed that supervised 3DGAN-CIRCLE predicted HRCT reduces bias and variability in residual values of different Tb measures as compared to LRCT and unsupervised 3DGAN-CIRCLE predicted HRCT. The supervised 3DGAN-CIRCLE method produced significantly improved performance (p < 0.001) for all Tb measures as compared to the two DL-based supervised methods available in the literature.

CONCLUSIONS

3DGAN-CIRCLE, trained in either unsupervised or supervised fashion, generates HRCT images with high structural similarity to the reference true HRCT images. The supervised 3DGAN-CIRCLE improves agreements of computed Tb microstructural measures with their reference values and outperforms the unsupervised 3DGAN-CIRCLE. 3DGAN-CIRCLE offers a viable DL solution to retrospectively improve image resolution, which may aid in data harmonization in multi-site longitudinal studies where scanner mismatch is unavoidable.

A graph model to describe the network connectivity of trabecular plates and rods

Introduction: The trabecular network is perceived as a collection of interconnected plate- (P) and rod-like (R) elements. Previous research has highlighted how these elements and their connectivity influence the mechanical properties of bone, yet further work is required to elucidate better the deeply interconnected nature of the trabecular network with distinct element formations conducting forces per their mechanical boundary conditions. Within this network, forces act through elements: a rod or plate with force applied to one end will transmit this force to a component connected to the other end, defining the boundary conditions for the loading of each element. To that end, this study has two aims: First, to investigate the connectivity of individually segmented elements of trabecular bone with respect to their local boundary conditions as defined by the surrounding trabecular network and linking them directly to the bone's overall mechanical response during loading using a mathematical graph model of the plate and rod (PR) Network. Second, we use this model to quantify side artifacts, a known artifact when testing an excised specimen of trabecular bone, where vertical trabeculae lose their load-bearing capacity due to a loss of connectivity, ultimately resulting in a change of the trabecular network topology. Resuts: Connected elements derived from our model predicted apparent elastic modulus by fitting a linear regression (R 2 = 0.81). In comparison, prediction using conventional bone volume fraction results in a lower accuracy (R 2 = 0.72), demonstrating the ability of the PR Network to estimate compressive elastic modulus independent of specimen size or loading boundary condition. Discussion: PR Network models are a novel approach to describing connectivity within the trabecular network and incorporating mechanical boundary conditions within the morphological analysis, thus enabling the study of intrinsic material properties of trabecular bone. Ultimately, PR Network models may be an early predictor or provide further insights into osteo-degenerative diseases.

Tensile Stress-Activated and Exosome-Transferred YAP/TAZ-Notch Circuit Specifies Type H Endothelial Cell for Segmental Bone Regeneration

The Ilizarov technique has been continuously innovated to utilize tensile stress (TS) for inducing a bone development-like regenerative process, aiming to achieve skeletal elongation and reconstruction. However, it remains uncertain whether this distraction osteogenesis (DO) process induced by TS involves the pivotal coupling of angiogenesis and osteogenesis mediated by type H endothelial cells (THECs). In this study, it is demonstrated that the Ilizarov technique induces the formation of a metaphysis-like architecture composed of THECs, leading to segmental bone regeneration during the DO process. Mechanistically, cell-matrix interactions-mediated activation of yes-associated protein (YAP)/transcriptional co-activator with PDZ-binding motif (TAZ) transcriptionally upregulates the expression of Notch1 and Delta-like ligand 4, which act as direct positive regulators of THECs phenotype, in bone marrow endothelial cells (BMECs) upon TS stimulation. Simultaneously, the Notch intracellular domain enhances YAP/TAZ activity by transcriptionally upregulating YAP expression and stabilizing TAZ protein, thus establishing the YAP/TAZ-Notch circuit. Additionally, TS-stimulated BMECs secrete exosomes enriched with vital molecules in this positive feedback pathway, which can be utilized to promote segmental bone defect healing, mimicking the therapeutic effects of Ilizarov technique. The findings advance the understanding of TS-induced segmental bone regeneration and establish the foundation for innovative biological therapeutic strategies aimed at activating THECs.

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.

A robust approach to 3D neuron shape representation for quantification and classification

We consider the problem of finding an accurate representation of neuron shapes, extracting sub-cellular features, and classifying neurons based on neuron shapes. In neuroscience research, the skeleton representation is often used as a compact and abstract representation of neuron shapes. However, existing methods are limited to getting and analyzing "curve" skeletons which can only be applied for tubular shapes. This paper presents a 3D neuron morphology analysis method for more general and complex neuron shapes. First, we introduce the concept of skeleton mesh to represent general neuron shapes and propose a novel method for computing mesh representations from 3D surface point clouds. A skeleton graph is then obtained from skeleton mesh and is used to extract sub-cellular features. Finally, an unsupervised learning method is used to embed the skeleton graph for neuron classification. Extensive experiment results are provided and demonstrate the robustness of our method to analyze neuron morphology.

3D Neuron Morphology Analysis

We consider the problem of finding an accurate representation of neuron shapes, extracting sub-cellular features, and classifying neurons based on neuron shapes. In neuroscience research, the skeleton representation is often used as a compact and abstract representation of neuron shapes. However, existing methods are limited to getting and analyzing"curve"skeletons which can only be applied for tubular shapes. This paper presents a 3D neuron morphology analysis method for more general and complex neuron shapes. First, we introduce the concept of skeleton mesh to represent general neuron shapes and propose a novel method for computing mesh representations from 3D surface point clouds. A skeleton graph is then obtained from skeleton mesh and is used to extract sub-cellular features. Finally, an unsupervised learning method is used to embed the skeleton graph for neuron classification. Extensive experiment results are provided and demonstrate the robustness of our method to analyze neuron morphology.

Continuum finite element analysis generalizesin vivotrabecular bone microstructural strength measures between two CT scanners with different image resolution

Fragility of trabecular bone (Tb) microstructure is increased in osteoporosis, which is associated with rapid bone loss and enhanced fracture-risk. Accurate assessment of Tb strength usingin vivoimaging available in clinical settings will be significant for management of osteoporosis and understanding its pathogenesis. Emerging CT technology, featured with high image resolution, fast scan-speed, and wide clinical access, is a promising alternative forin vivoTb imaging. However, variation in image resolution among different CT scanners pose a major hurdle in CT-based bone studies. This paper presents nonlinear continuum finite element (FE) methods for computation of Tb strength fromin vivoCT imaging and evaluates their generalizability between two scanners with different image resolution. Continuum FE-based measures of Tb strength under different loading conditions were found to be highly reproducible (ICC ≥ 0.93) using ankle images of twenty healthy volunteers acquired on low- and high-resolution CT scanners 44.6 ± 2.7 days apart. FE stress propagation was mostly confined to Tb micro-network (2.3 ± 1.7 MPa) with nominal leakages over the marrow space (0.4 ± 0.5 MPa) complying with the fundamental principle of mechanics atin vivoimaging. In summary, nonlinear continuum FE-based Tb strength measures are reproducible among different CT scanners and suitable for multi-site longitudinal human studies.

A morphological, topological and mechanical investigation of gyroid, spinodoid and dual-lattice algorithms as structural models of trabecular bone

In this study, we evaluate the performance of three algorithms as computational models of trabecular bone architecture, through systematic evaluation of morphometric, topological, and mechanical properties. Here, we consider the widely-used gyroid lattice structure, the recently-developed spinodoid structure and a structure similar to Voronoi lattices introduced here as the dual-lattice. While all computational models were calibrated to recreate the trabecular tissue volume (e.g. BV/TV), it was found that both the gyroid- and spinodoid-based structures showed substantial differences in many other morphometric and topological parameters and, in turn, showed lower effective mechanical properties compared to trabecular bone. The newly-developed dual-lattice structures better captured both morphometric parameters and mechanical properties, despite certain differences being evident their topological configuration compared to trabecular bone. Still, these computational algorithms provide useful platforms to investigate trabecular bone mechanics and for designing biomimetic structures, which could be produced through additive manufacturing for applications that include bone substitutes, scaffolds and porous implants. Furthermore, the software for the creation of the structures has been added to the open source toolbox GIBBON and is therefore freely available to the community.

Analyzing fibrous tissue pattern in fibrous dysplasia bone images using deep R-CNN networks for segmentation

Predictive health monitoring systems help to detect human health threats in the early stage. Evolving deep learning techniques in medical image analysis results in efficient feedback in quick time. Fibrous dysplasia (FD) is a genetic disorder, triggered by the mutation in Guanine Nucleotide binding protein with alpha stimulatory activities in the human bone genesis. It slowly occupies the bone marrow and converts the bone cell into fibrous tissues. It weakens the bone structure and leads to permanent disability. This paper proposes the study of FD bone image analyzing techniques with deep networks. Also, the linear regression model is annotated for predicting the bone abnormality levels with observed coefficients. Modern image processing begins with various image filters. It describes the edges, shades, texture values of the receptive field. Different types of segmentation and edge detection mechanisms are applied to locate the tumor, lesion, and fibrous tissues in the bone image. Extract the fibrous region in the bone image using the region-based convolutional neural network algorithm. The segmented results are compared with their accuracy metrics. The segmentation loss is reduced by each iteration. The overall loss is 0.24% and the accuracy is 99%, segmenting the masked region produces 98% of accuracy, and building the bounding boxes is 99% of accuracy.

Effects of fluoride intake on cortical and trabecular bone microstructure at early adulthood using multi-row detector computed tomography (MDCT)

PURPOSE

The aim of this study was to examine the effects of period-specific and cumulative fluoride (F) intake on bone at the levels of cortical and trabecular bone microstructural outcomes at early adulthood using emerging multi-row detector computed tomography (MDCT)-based novel techniques.

METHODS

Ultra-high resolution MDCT distal tibia scans were collected at age 19 visits under the Iowa Bone Development Study (IBDS), and cortical and trabecular bone microstructural outcomes were computed at the distal tibia using previously validated methods. CT scans of a tissue characterization phantom were used to calibrate CT numbers (Hounsfield units) into bone mineral density (mg/cc). Period-specific and cumulative F intakes from birth up to the age of 19 years were assessed for IBDS participants through questionnaire, and their relationships with MDCT-derived bone microstructural outcomes were examined using bivariable and multivariable analyses, adjusting for height, weight, maturity offset (years since age of peak height velocity (PHV)), physical activity (questionnaire for adolescents (PAQ-A)), healthy eating index version 2010 (HEI-2010) scores, and calcium and protein intakes.

RESULTS

MDCT distal tibia scans were acquired for 324 participants from among the total of 329 participants at age 19 visits. No motion artifacts were observed in any MDCT scans, and all images were successfully processed to measure cortical and trabecular bone microstructural outcomes. At early adulthood, males were observed to have stronger trabecular bone microstructural features, as well as thicker cortical bone (p < 0.01), as compared to age-similar females; however, females were found to have less cortical bone porosity as compared to males. Among participants with available F intake estimates (75 to 91% of the 324 with MDCT scans, depending on the period-specific F intake measure), no statistically significant associations were detected between any period-specific or cumulative F intake and bone microstructural outcomes of the tibia at the p < 0.01 level. Only for females, statistically suggestive associations (p < 0.05) were found between recent F intake (from 14 to 19 years) and trabecular mean plate width and trabecular thickness at the tibia. Those associations became somewhat weaker, but still statistically suggestive, for trabecular thickness in fully adjusted analysis with height, weight, PHV, calcium and protein intake, and HEI-2010 and PAQ-A scores as covariates.

CONCLUSION

The findings show that the effects of lifelong or period-specific F intake from combined sources for adolescents typical to the United States Midwest region are not strongly associated with bone microstructural outcomes at age 19 years. These findings are generally consistent with previously reported results of IBDS analyses, which further confirms that effects of lifelong or period-specific F intake on skeletons in early adulthood are absent or weak, even at the levels of cortical and trabecular bone microstructural details.

Quantitative CT-Based Methods for Bone Microstructural Measures and Their Relationships With Vertebral Fractures in a Pilot Study on Smokers

Osteoporosis causes fragile bone, and bone microstructural quality is a critical determinant of bone strength and fracture risk. This study pursues technical validation of novel CT-based methods for assessment of peripheral bone microstructure together with a human pilot study examining relationships between bone microstructure and vertebral fractures in smokers. To examine the accuracy and reproducibility of the methods, repeat ultra-high-resolution (UHR) CT and micro-CT scans of cadaveric ankle specimens were acquired. Thirty smokers from the University of Iowa COPDGene cohort were recruited at their 5-year follow-up visits. Chest CT scans, collected under the parent study, were used to assess vertebral fractures. UHR CT scans of distal tibia were acquired for this pilot study to obtain peripheral cortical and trabecular bone (Cb and Tb) measures. UHR CT-derived Tb measures, including volumetric bone mineral density (BMD), network area, transverse trabecular density, and mean plate width, showed high correlation (r > 0.901) with their micro-CT-derived values over small regions of interest (ROIs). Both Cb and Tb measures showed high reproducibility-intra-class correlation (ICC) was greater than 0.99 for all Tb measures except erosion index and greater than 0.97 for all Cb measures. Female sex was associated with lower transverse Tb density (p < 0.1), higher Tb spacing (p < 0.05), and lower cortical thickness (p < 0.001). Participants with vertebral fractures had significantly degenerated values (p < 0.05) for all Tb measures except thickness. There were no statistically significant differences for Cb measures between non-fracture and fracture groups. Vertebral fracture-group differences of Tb measures remained significant after adjustment with chronic obstructive pulmonary disease (COPD) status. Although current smokers at baseline had more fractures-81.8% versus 63.2% for former smokers-the difference was not statistically significant. This pilot cross-sectional human study demonstrates CT-based peripheral bone microstructural differences among smokers with and without vertebral fractures. © 2021 The Authors. JBMR Plus published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

A comparative study of trabecular bone micro-structural measurements using different CT modalities

Osteoporosis, characterized by reduced bone mineral density and micro-architectural degeneration, significantly enhances fracture-risk. There are several viable methods for trabecular bone micro-imaging, which widely vary in terms of technology, reconstruction principle, spatial resolution, and acquisition time. We have performed an excised cadaveric bone specimen study to evaluate different computed tomography (CT)-imaging modalities for trabecular bone micro-structural analysis. Excised cadaveric bone specimens from the distal radius were scanned using micro-CT and fourin vivoCT imaging modalities: high-resolution peripheral quantitative computed tomography (HR-pQCT), dental cone beam CT (CBCT), whole-body multi-row detector CT (MDCT), and extremity CBCT. A new algorithm was developed to optimize soft thresholding parameters for individualin vivoCT modalities for computing quantitative bone volume fraction maps. Finally, agreement of trabecular bone micro-structural measures, derived from differentin vivoCT imaging, with reference measures from micro-CT imaging was examined. Observed values of most trabecular measures, including trabecular bone volume, network area, transverse and plate-rod micro-structure, thickness, and spacing, forin vivoCT modalities were higher than their micro-CT-based reference values. In general, HR-pQCT-based trabecular bone measures were closer to their reference values as compared to otherin vivoCT modalities. Despite large differences in observed values of measures among modalities, high linear correlation (rε [0.94 0.99]) was found between micro-CT andin vivoCT-derived measures of trabecular bone volume, transverse and plate micro-structural volume, and network area. All HR-pQCT-derived trabecular measures, except the erosion index, showed high correlation (rε [0.91 0.99]). The plate-width measure showed a higher correlation (rε [0.72 0.91]) amongin vivoand micro-CT modalities than its counterpart binary plate-rod characterization-based measure erosion index (rε [0.65 0.81]). Although a strong correlation was observed between micro-structural measures fromin vivoand micro-CT imaging, large shifts in their values forin vivomodalities warrant proper scanner calibration prior to adopting in multi-site and longitudinal studies.

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.

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]).

CT-Based Characterization of Transverse and Longitudinal Trabeculae and Its Applications

Osteoporosis is a common age-related disease characterized by reduced bone mineral density (BMD), micro-structural deterioration, and enhanced fracture-risk. Although, BMD is clinically used to define osteoporosis, there are compelling evidences that bone micro-structural properties are strong determinants of bone strength and fracture-risk. Reliable measures of effective trabecular bone (Tb) micro-structural features are of paramount clinical significance. Tb consists of transverse and longitudinal micro-structures, and there is a hypothesis that transverse trabeculae improve bone strength by arresting buckling of longitudinal trabeculae. In this paper, we present an emerging clinical CT-based new method for characterizing transverse and longitudinal trabeculae, validate the method, and examine its application in human studies. Specifically, we examine repeat CT scan reproducibility, and evaluate the relationships of these measures with gender and body size using human CT data from the Iowa Bone Development Study (IBDS) (n = 99; 49 female). Based on a cadaveric ankle study (n = 12), both transverse and longitudinal Tb measures are found reproducible (ICC > 0.94). It was observed in the IBDS human data that males have significantly higher trabecular bone measures than females for both inner (p < 0.05) and outer (p < 0.01) regions of interest (ROIs). For weight, Spearman correlations ranged 0.43-0.48 for inner ROI measures and 0.50-0.52 for outer ROI measures for females versus 0.30-0.34 and 0.23-0.25 for males. Correlation with height was lower (0.36-0.39), but still mostly significant for females. No association of trabecular measures with height was found for males.

Development of a simple numerical model for trabecular bone structures

PURPOSE

Advances in additive manufacturing processes are enabling the fabrication of surrogate bone structures for applications including use in high-resolution anthropomorphic phantoms. In this research, a simple numerical model is proposed that enables the generation of microarchitecture with similar statistical distribution to trabecular bone.

METHODS

A human humerus, radius, ulna, and several vertebrae were scanned on the Imaging and Medical beamline at the Australian Synchrotron and the proposed numerical model was developed through the definition of two complex functions that encode the trabecular thickness and position-dependant spacing to generate volumetric surrogate trabecular structures. The structures reproduced those observed at 19 separate axial locations through the experimental bone volumes. The applicability of the model when incorporating a two-material approximation to absorption- and phase-contrast CT was also investigated through simulation.

RESULTS

The synthetic structures, when compared with the real trabecular microarchitecture, yielded an average mean thickness error of 2 μm, and a mean difference in standard deviation of 33 μm for the humerus, 24 μm for the ulna and radius, and 15 μm for the vertebrae. Simulated absorption- and propagation-based phase contrast CT projection data were generated and reconstructed using the derived mathematical simplifications from the two-material approximation, and the phase-contrast effects were successfully demonstrated.

CONCLUSIONS

The presented model reproduced trabecular distributions that could be used to generate phantoms for quality assurance and validation processes. The implication of utilizing a two-material approximation results in simplification of the additive manufacturing process and the generation of synthetic data that could be used for training of machine learning applications.

Fuzzy Object Skeletonization: Theory, Algorithms, and Applications

Skeletonization offers a compact representation of an object while preserving important topological and geometrical features. Literature on skeletonization of binary objects is quite mature. However, challenges involved with skeletonization of fuzzy objects are mostly unanswered. This paper presents a new theory and algorithm of skeletonization for fuzzy objects, evaluates its performance, and demonstrates its applications. A formulation of fuzzy grassfire propagation is introduced; its relationships with fuzzy distance functions, level sets, and geodesics are discussed; and several new theoretical results are presented in the continuous space. A notion of collision-impact of fire-fronts at skeletal points is introduced, and its role in filtering noisy skeletal points is demonstrated. A fuzzy object skeletonization algorithm is developed using new notions of surface- and curve-skeletal voxels, digital collision-impact, filtering of noisy skeletal voxels, and continuity of skeletal surfaces. A skeletal noise pruning algorithm is presented using branch-level significance. Accuracy and robustness of the new algorithm are examined on computer-generated phantoms and micro- and conventional CT imaging of trabecular bone specimens. An application of fuzzy object skeletonization to compute structure-width at a low image resolution is demonstrated, and its ability to predict bone strength is examined. Finally, the performance of the new fuzzy object skeletonization algorithm is compared with two binary object skeletonization methods.

3-T MR Imaging of Proximal Femur Microarchitecture in Subjects with and without Fragility Fracture and Nonosteoporotic Proximal Femur Bone Mineral Density

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.

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.

Multiscale Opening of Conjoined Fuzzy Objects: Theory and Applications

Theoretical properties of a multi-scale opening (MSO) algorithm for two conjoined fuzzy objects are established, and its extension to separating two conjoined fuzzy objects with different intensity properties is introduced. Also, its applications to artery/vein (A/V) 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 (FDT), 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 data sets 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, twenty-five to thirty-five user-specified seeds/separators are needed for each CTA data through a custom designed graphical interface requiring an average of thirty minutes to complete carotid vascular segmentation in a patient's CTA data set.

Trabecular bone characterization on the continuum of plates and rods using in vivo MR imaging and volumetric topological analysis

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.

Characterization of trabecular bone plate-rod microarchitecture using multirow detector CT and the tensor scale: Algorithms, validation, and applications to pilot human studies

PURPOSE

Osteoporosis is a common bone disease associated with increased risk of low-trauma fractures leading to substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density (BMD); however, increasing evidence suggests that trabecular bone (TB) microarchitectural quality is an important determinant of bone strength and fracture risk. A tensor scale based algorithm for in vivo characterization of TB plate-rod microarchitecture at the distal tibia using multirow detector CT (MD-CT) imaging is presented and its performance and applications are examined.

METHODS

The tensor scale characterizes individual TB on the continuum between a perfect plate and a perfect rod and computes their orientation using optimal ellipsoidal representation of local structures. The accuracy of the method was evaluated using computer-generated phantom images at a resolution and signal-to-noise ratio achievable in vivo. The robustness of the method was examined in terms of stability across a wide range of voxel sizes, repeat scan reproducibility, and correlation between TB measures derived by imaging human ankle specimens under ex vivo and in vivo conditions. Finally, the application of the method was evaluated in pilot human studies involving healthy young-adult volunteers (age: 19 to 21 yr; 51 females and 46 males) and patients treated with selective serotonin reuptake inhibitors (SSRIs) (age: 19 to 21 yr; six males and six females).

RESULTS

An error of (3.2% ± 2.0%) (mean ± SD), computed as deviation from known measures of TB plate-width, was observed for computer-generated phantoms. An intraclass correlation coefficient of 0.95 was observed for tensor scale TB measures in repeat MD-CT scans where the measures were averaged over a small volume of interest of 1.05 mm diameter with limited smoothing effects. The method was found to be highly stable at different voxel sizes with an error of (2.29% ± 1.56%) at an in vivo voxel size as compared to the original ex vivo voxel size. Tensor scale measures derived from imaging under in vivo and ex vivo conditions with significantly different modulation transfer function, i.e., difference in "true resolution," showed strong linear correlation (r = 0.92). The study of healthy volunteers shows that, after adjustment for height and weight, males have a 14% higher mean TB plate-width as compared to females (p < 0.05). SSRI-treated patients have 12.5% lower mean TB plate-width (p = 0.052) as compared to age-similar and sex-, height-, and weight-matched healthy controls. In contrast, the observed group difference in dual-energy x-ray absorptiometry (DXA)-derived hip BMD was 10.5% between males and females and only 5.04% between healthy controls and patients on SSRIs.

CONCLUSIONS

Tensor scale analysis of MD-CT images yields accurate and reproducible characterization of TB plate-rod microarchitecture that may be more sensitive than DXA-derived BMD to sex differences and to the skeletal changes associated with medical conditions or their treatments.

Automated cortical bone segmentation for multirow-detector CT imaging with validation and application to human studies

PURPOSE

Cortical bone supports and protects human skeletal functions and plays an important role in determining bone strength and fracture risk. Cortical bone segmentation at a peripheral site using multirow-detector CT (MD-CT) imaging is useful for in vivo assessment of bone strength and fracture risk. Major challenges for the task emerge from limited spatial resolution, low signal-to-noise ratio, presence of cortical pores, and structural complexity over the transition between trabecular and cortical bones. An automated algorithm for cortical bone segmentation at the distal tibia from in vivo MD-CT imaging is presented and its performance and application are examined.

METHODS

The algorithm is completed in two major steps-(1) bone filling, alignment, and region-of-interest computation and (2) segmentation of cortical bone. After the first step, the following sequence of tasks is performed to accomplish cortical bone segmentation-(1) detection of marrow space and possible pores, (2) computation of cortical bone thickness, detection of recession points, and confirmation and filling of true pores, and (3) detection of endosteal boundary and delineation of cortical bone. Effective generalizations of several digital topologic and geometric techniques are introduced and a fully automated algorithm is presented for cortical bone segmentation.

RESULTS

An accuracy of 95.1% in terms of volume of agreement with manual outlining of cortical bone was observed in human MD-CT scans, while an accuracy of 88.5% was achieved when compared with manual outlining on postregistered high resolution micro-CT imaging. An intraclass correlation coefficient of 0.98 was obtained in cadaveric repeat scans. A pilot study was conducted to describe gender differences in cortical bone properties. This study involved 51 female and 46 male participants (age: 19-20 yr) from the Iowa Bone Development Study. Results from this pilot study suggest that, on average after adjustment for height and weight differences, males have thicker cortex (mean difference 0.33 mm and effect size 0.92 at the anterior region) with lower bone mineral density (mean difference -28.73 mg/cm(3) and effect size 1.35 at the posterior region) as compared to females.

CONCLUSIONS

The algorithm presented is suitable for fully automated segmentation of cortical bone in MD-CT imaging of the distal tibia with high accuracy and reproducibility. Analysis of data from a pilot study demonstrated that the cortical bone indices allow quantification of gender differences in cortical bone from MD-CT imaging. Application to larger population groups, including those with compromised bone, is needed.

Bone architecture adaptations after spinal cord injury: impact of long-term vibration of a constrained lower limb

SUMMARY

This study examined the effect of a controlled dose of vibration upon bone density and architecture in people with spinal cord injury (who eventually develop severe osteoporosis). Very sensitive computed tomography (CT) imaging revealed no effect of vibration after 12 months, but other doses of vibration may still be useful to test.

INTRODUCTION

The purposes of this report were to determine the effect of a controlled dose of vibratory mechanical input upon individual trabecular bone regions in people with chronic spinal cord injury (SCI) and to examine the longitudinal bone architecture changes in both the acute and chronic state of SCI.

METHODS

Participants with SCI received unilateral vibration of the constrained lower limb segment while sitting in a wheelchair (0.6g, 30 Hz, 20 min, three times weekly). The opposite limb served as a control. Bone mineral density (BMD) and trabecular micro-architecture were measured with high-resolution multi-detector CT. For comparison, one participant was studied from the acute (0.14 year) to the chronic state (2.7 years).

RESULTS

Twelve months of vibration training did not yield adaptations of BMD or trabecular micro-architecture for the distal tibia or the distal femur. BMD and trabecular network length continued to decline at several distal femur sub-regions, contrary to previous reports suggesting a "steady state" of bone in chronic SCI. In the participant followed from acute to chronic SCI, BMD and architecture decline varied systematically across different anatomical segments of the tibia and femur.

CONCLUSIONS

This study supports that vibration training, using this study's dose parameters, is not an effective anti-osteoporosis intervention for people with chronic SCI. Using a high-spatial-resolution CT methodology and segmental analysis, we illustrate novel longitudinal changes in bone that occur after spinal cord injury.

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.

A Robust and Efficient Curve Skeletonization Algorithm for Tree-Like Objects Using Minimum Cost Paths

Conventional curve skeletonization algorithms using the principle of Blum's transform, often, produce unwanted spurious branches due to boundary irregularities, digital effects, and other artifacts. This paper presents a new robust and efficient curve skeletonization algorithm for three-dimensional (3-D) elongated fuzzy objects using a minimum cost path approach, which avoids spurious branches without requiring post-pruning. Starting from a root voxel, the method iteratively expands the skeleton by adding new branches in each iteration that connects the farthest quench voxel to the current skeleton using a minimum cost path. The path-cost function is formulated using a novel measure of local significance factor defined by the fuzzy distance transform field, which forces the path to stick to the centerline of an object. The algorithm terminates when dilated skeletal branches fill the entire object volume or the current farthest quench voxel fails to generate a meaningful skeletal branch. Accuracy of the algorithm has been evaluated using computer-generated phantoms with known skeletons. Performance of the method in terms of false and missing skeletal branches, as defined by human experts, has been examined using in vivo CT imaging of human intrathoracic airways. Results from both experiments have established the superiority of the new method as compared to the existing methods in terms of accuracy as well as robustness in detecting true and false skeletal branches. The new algorithm makes a significant reduction in computation complexity by enabling detection of multiple new skeletal branches in one iteration. Specifically, this algorithm reduces the number of iterations from the number of terminal tree branches to the worst case performance of tree depth. In fact, experimental results suggest that, on an average, the order of computation complexity is reduced to the logarithm of the number of terminal branches of a tree-like object.

A robust algorithm for thickness computation at low resolution and its application to in vivo trabecular bone CT imaging

Adult bone diseases, especially osteoporosis, lead to increased risk of fracture which in turn is associated with substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density; however, increasing evidence suggests that the microarchitectural quality of trabecular bone (TB) is an important determinant of bone strength and fracture risk. Accurate measures of TB thickness and marrow spacing is of significant interest for early diagnosis of osteoporosis or treatment effects. Here, we present a new robust algorithm for computing TB thickness and marrow spacing at a low resolution achievable in vivo. The method uses a star-line tracing technique that effectively deals with partial voluming effects of in vivo imaging with voxel size comparable to TB thickness. Also, the method avoids the problem of digitization associated with conventional algorithms based on sampling distance transform along skeletons. Accuracy of the method was examined using computer-generated phantom images, while the robustness of the method was evaluated on human ankle specimens in terms of stability across a wide range of voxel sizes, repeat scan reproducibility under in vivo conditions, and correlation between thickness values computed at ex vivo and in vivo imaging resolutions. Also, the sensitivity of the method was examined by evaluating its ability to predict the bone strength of cadaveric specimens. Finally, the method was evaluated in a human study involving 40 healthy young-adult volunteers (age: 19-21 years; 20 males and 20 females) and ten athletes (age: 19-21 years; six males and four females). Across a wide range of voxel sizes, the new method is significantly more accurate and robust as compared to conventional methods. Both TB thickness and marrow spacing measures computed using the new method demonstrated strong associations (R2 ∈ [0.83, 0.87]) with bone strength. Also, the TB thickness and marrow spacing measures allowed discrimination between male and female volunteers (p ∈ [0.01, 0.04]) as well as between athletes and nonathletes (p ∈ [0.005, 0.03]).

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.

The Ellipsoid Factor for Quantification of Rods, Plates, and Intermediate Forms in 3D Geometries

The ellipsoid factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid that fits inside the structure and that contains the point of interest, and ranges from -1 for strongly oblate (discus-shaped) ellipsoids, to +1 for strongly prolate (javelin-shaped) ellipsoids. For an ellipsoid with axes a ≤ b ≤ c, EF = a/b - b/c. Here, EF is demonstrated in a Java plugin, "Ellipsoid Factor" for ImageJ, distributed in the BoneJ plugin collection. Ellipsoid Factor utilizes an ellipsoid optimization algorithm, which assumes that maximal ellipsoids are centered on the medial axis, then dilates, rotates, and translates slightly each ellipsoid until it cannot increase in volume any further. EF successfully identifies rods, plates, and intermediate structures within trabecular bone, and summarizes the distribution of geometries with an overall EF mean and SD, EF histogram, and Flinn diagram displaying a/b versus b/c. EF is released to the community for testing, use, and improvement.

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.

Structural analysis of cortical porosity applied to HR-pQCT data

PURPOSE

The investigation of cortical porosity is an important aspect of understanding biological, pathoetiological, and biomechanical processes occurring within the skeleton. With the emergence of HR-pQCT as a noninvasive tool suitable for clinical use, cortical porosity at appendicular sites can be directly visualized in vivo. The aim of this study was to introduce a novel topological analysis of the cortical pore network for HR-pQCT data and determine the influence of resolution on measures of cortical pore network microstructure and topology.

METHODS

Cadaveric radii were scanned using HR-pQCT at two different voxel sizes (41 and 82 μm) and also using μCT at a voxel size of 18 μm. HR-pQCT and μCT image sets were spatially coregistered. Segmentation and quantification of cortical porosity (Ct.Po) and mean pore diameter (Ct.Po.Dm) were achieved using an established extended cortical analysis technique. Topological classification of individual pores was performed using topology-preserving skeletonization and multicolor dilation algorithms. Based on the pore skeleton topological classification, the following parameters were quantified: total number of planar surface-skeleton canals (N.Slabs), tubular curve-skeleton canals (N.Tubes), and junction elements (N.Junctions), mean slab volume (Slab.Vol), mean tube volume (Tube.Vol), mean slab orientation (Slab.θ), mean tube orientation (Tube.θ), N.Slabs/N.Tubes, and integral (total) slab volume/integral tube volume (iSlab.Vol/iTube.Vol). An in vivo reproducibility study was also conducted to assess short-term precision of the topology parameters. Precision error was characterized using root mean square coefficient of variation (RMSCV%).

RESULTS

Correlations to μCT values for Ct.Po were significant for both the 41 and 82 μm HR-pQCT data (41: r(2) = 0.82, p < 0.001, 82: r(2) = 0.75, p < 0.001). For Ct.Po.Dm, only the 41 μm data were significantly predictive of μCT values (r(2) = 0.72, p < 0.01) Data at both HR-pQCT voxel sizes were strongly predictive of the μCT values for N.Slabs (41: r(2) = 0.93, p < 0.001; 82: r(2) = 0.84, p < 0.001), N.Tubes (41: r(2) = 0.94, p < 0.001; 82: r(2) = 0.84, p < 0.001), and N.Junctions (41: r(2) = 0.93, p < 0.001; 82: r(2) = 0.78, p < 0.001), though proportional bias was evident in these correlations. Weak correlations were seen for iSlab.Vol/iTube.Vol at both voxel sizes (41: r(2) = 0.52, p < 0.01; 82: r(2) = 0.39, p < 0.05). Slab.Vol was significantly correlated to μCT data at 41 μm (r(2) = 0.60, p < 0.01) but not at 82 μm, while Tube.Vol was significantly correlated at both voxel sizes (41: r(2) = 0.79, p < 0.001; 82: r(2) = 0.68, p < 0.01). In vivo precision error for these parameters ranged from 2.31 to 9.68 RMSCV%.

CONCLUSIONS

Strong correlations between μCT- and HR-pQCT-derived measurements were found, particularly in HR-pQCT images obtained at 41 μm. These data are in agreement with our previous study investigating the effect of voxel size on standard HR-pQCT metrics of trabecular and cortical microstructure, and extend our previous findings to include topological descriptors of the cortical pore network.

A New Approach of Arc Skeletonization for Tree-Like Objects Using Minimum Cost Path

Traditional arc skeletonization algorithms using the principle of Blum's transform, often, produce unwanted spurious branches due to boundary irregularities and digital effects on objects and other artifacts. This paper presents a new robust approach of extracting arc skeletons for three-dimensional (3-D) elongated fuzzy objects, which avoids spurious branches without requiring post-pruning. Starting from a root voxel, the method iteratively expands the skeleton by adding a new branch in each iteration that connects the farthest voxel to the current skeleton using a minimum-cost geodesic path. The path-cost function is formulated using a novel measure of local significance factor defined by fuzzy distance transform field, which forces the path to stick to the centerline of the object. The algorithm terminates when dilated skeletal branches fill the entire object volume or the current farthest voxel fails to generate a meaningful branch. Accuracy of the algorithm has been evaluated using computer-generated blurred and noisy phantoms with known skeletons. Performance of the method in terms of false and missing skeletal branches, as defined by human expert, has been examined using in vivo CT imaging of human intrathoracic airways. Experimental results from both experiments have established the superiority of the new method as compared to a widely used conventional method in terms of accuracy of medialness as well as robustness of true and false skeletal branches.

High bone density masks architectural deficiencies in an individual with spinal cord injury

Context Spinal cord injury (SCI) causes a decline of bone mineral density (BMD) in the paralyzed extremities via the gradual degradation and resorption of trabecular elements. Clinical tools that report BMD may not offer insight into trabecular architecture flaws that could affect bone's ability to withstand loading. We present a case of a woman with a 30-year history of SCI and abnormally high distal femur BMD. Findings Peripheral quantitative-computed tomography-based BMD for this subject was ∼20% higher than previously published non-SCI values. Computed tomography (CT) revealed evidence of sclerotic bone deposition in the trabecular envelope, most likely due to glucocorticoid-induced osteonecrosis. Volumetric topologic analysis of trabecular architecture indicated that the majority of the bone mineral was organized into thick, plate-like structures rather than a multi-branched trabecular network. Visual analysis of the CT stack confirmed that the sclerotic bone regions were continuous with the cortex at only a handful of points. Conclusions Conventional clinical BMD analysis could have led to erroneous assumptions about this subject's bone quality. CT-based analysis revealed that this subject's high BMD masked underlying architectural flaws. For patients who received prolonged glucocorticoid therapy, excessively high BMD should be viewed with caution. The ability of this subject's bone to resist fracture is, in our view, extremely suspect. A better understanding of the mechanical competency of this very dense, but architecturally flawed bone would be desirable before this subject engaged in activities that load the limbs.

Bone metabolism in obese rats programmed by early weaning

OBJECTIVE

Obesity and osteoporosis seem to have a common pathogenesis, especially because bone and adipose tissue have common origins. Since early weaning (EW) decreases adipogenesis and osteogenesis in neonate, further programming for obesity and hyperleptinemia, we hypothesized that these changes in adipogenesis could affect bone metabolism.

MATERIALS/METHODS

Lactating rats were separated into 3 groups: control - dams whose pups ate milk throughout lactation; mechanical EW (MEW) - dams were involved with a bandage interrupting suckling in the last 3days of lactation; pharmacological EW (PEW) - dams were bromocriptine-treated (0.5mg/twice a day via intraperitoneal injection) 3days before weaning. The adult offspring was subjected to dual-energy X-ray absorptiometry and bone tissue was also evaluated by computed tomography, microcomputed tomography and biomechanical tests, beyond serum analyses.

RESULTS

MEW and PEW presented higher total bone mineral density (BMD), total bone mineral content, spine BMD and bone area in postnatal day 150 (PN150). In PN180, both groups also presented increase of these parameters and higher femur BMD and fourth lumbar vertebra (LV4) BMD, femoral head radiodensity and LV4 vertebral body radiodensity, trabecular number, stiffness and break load; lower trabecular separation, maximal deformation and break deformation, and also hyperleptinemia and higher visceral fat mass and 25-hydroxivitamin D, whereas parathyroid hormone was unchanged. Serum C-terminal cross-linked telopeptide of type I collagen was lower for both groups.

CONCLUSIONS

Since both models program for obesity and increased bone mass, and leptin increases plasma vitamin D levels, probably leptin is the link between obesity and higher bone mass.

A NEW ALGORITHM FOR TRABECULAR BONE THICKNESS COMPUTATION AT LOW RESOLUTION ACHIEVED UNDER IN VIVO CONDITION

Adult bone diseases, especially osteoporosis, lead to increased risk of fracture associated with substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density (BMD); however, increasing evidence suggests that the micro-architectural quality of trabecular bone (TB) is an important determinant of bone strength and fracture risk. Accurate measurement of trabecular thickness and marrow spacing is of significant interest for early diagnosis of osteoporosis or treatment effects. Here, we present a new robust algorithm for computing TB thickness and marrow spacing at a low resolution achievable in vivo. The method uses a star-line tracing technique that effectively deals with partial voluming effects of in vivo imaging where voxel size is comparable to TB thickness. Experimental results on cadaveric ankle specimens have demonstrated the algorithm's robustness (ICC>0.98) under repeat scans of multi-row detector computed tomography (MD-CT) imaging. It has been observed in experimental results that TB thickness and marrow spacing measures as computed by the new algorithm have strong association (R² ∈{0.85, 0.87}) with TB's experimental mechanical strength measures.

Application of fuzzy skeletonization ot quantitatively assess trabecular bone micro-architecture

Adult bone diseases, especially osteoporosis, lead to increased risk of fracture associated with substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density; however, increasing evidence suggests that the micro-architectural quality of trabecular bone (TB) is an important determinant of bone strength and fracture risk. Skeletonization plays an important role providing a compact representation of TB network that allows computation of several quantitative parameters relating to TB micro-architecture. Literature of three-dimensional skeletonization is quite matured for binary digital objects. However, the challenges of skeletonization for fuzzy objects are mostly unanswered. Here, an algorithm for fuzzy skeletonization is presented using fuzzy grassfire propagation and a branch-level noise pruning strategy and, finally, its application to TB micro-architectural assessment is investigated. Specifically, the fuzzy skeletonization algorithm is applied to compute TB plateness, plate/rod ratio, thickness, and spacing. Finally, the effectiveness of these measures to predict experimental bone strength is investigated on twelve cadaveric specimens and the results are encouraging with the R(2) value of linear correlation with bone strength being as high as 0.93, 0.88, 0.85 and 0.86, respectively.

Mechanical competence of bone: a new parameter to grade trabecular bone fragility from tortuosity and elasticity

With the elderly population increase, osteoporosis and its consequences have become not just a health issue but also a serious economic burden. The trabecular bone structure plays a very important role for the bone quality and mechanical competence of the scaffold. Currently, it is claimed that the trabecular microarchitecture understanding can improve the fracture risk prediction above 65%. Several parameters seem to be correlated providing structural details of the trabecular bone network. However, the tortuosity of the trabeculae has not yet been systematically taken into account and its contribution has not been fully investigated and understood. In this paper, we discuss the relationship between the trabecular tortuosity, connectivity, volume fraction, and elasticity, and provide a unified parameter to estimate the mechanical competence of the structure. It is shown that the trabecular network tortuosity presents high linear correlation with the other parameters and that the trabeculae tend to get aligned in the direction where the structure is mostly submitted to stress, corresponding to higher stiffness orientation. This new parameter will help to integrate the relevant information of bone microarchitecture quality and assess more directly the real trabecular fragility in osteoporotic patients.

Tensor scale: An analytic approach with efficient computation and applications

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as "tensor scale" using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert's structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.

High dose compressive loads attenuate bone mineral loss in humans with spinal cord injury

People with spinal cord injury (SCI) lose bone and muscle integrity after their injury. Early doses of stress, applied through electrically induced muscle contractions, preserved bone density at high-risk sites. Appropriately prescribed stress early after the injury may be an important consideration to prevent bone loss after SCI.

INTRODUCTION

Skeletal muscle force can deliver high compressive loads to bones of people with spinal cord injury (SCI). The effective osteogenic dose of load for the distal femur, a chief site of fracture, is unknown. The purpose of this study is to compare three doses of bone compressive loads at the distal femur in individuals with complete SCI who receive a novel stand training intervention.

METHODS

Seven participants performed unilateral quadriceps stimulation in supported stance [150% body weight (BW) compressive load-"High Dose" while opposite leg received 40% BW-"Low Dose"]. Five participants stood passively without applying quadriceps electrical stimulation to either leg (40% BW load-"Low Dose"). Fifteen participants performed no standing (0% BW load-"Untrained") and 14 individuals without SCI provided normative data. Participants underwent bone mineral density (BMD) assessment between one and six times over a 3-year training protocol.

RESULTS

BMD for the High Dose group significantly exceeded BMD for both the Low Dose and the Untrained groups (p < 0.05). No significant difference existed between the Low Dose and Untrained groups (p > 0.05), indicating that BMD for participants performing passive stance did not differ from individuals who performed no standing. High-resolution CT imaging of one High Dose participant revealed 86% higher BMD and 67% higher trabecular width in the High Dose limb.

CONCLUSION

Over 3 years of training, 150% BW compressive load in upright stance significantly attenuated BMD decline when compared to passive standing or to no standing. High-resolution CT indicated that trabecular architecture was preserved by the 150% BW dose of load.

The effect of voxel size on high-resolution peripheral computed tomography measurements of trabecular and cortical bone microstructure

PURPOSE

Accurate quantification of bone microstructure plays a significant role in understanding bone mechanics and response to disease or treatment. High-resolution peripheral quantitative computed tomography (HR-pQCT) allows for the quantification of trabecular and cortical structure in vivo, with the capability of generating images at multiple voxel sizes (41, 82, and 123 μm). The aim of this study was to characterize the effect of voxel size on structural measures of trabecular and cortical bone and to determine accuracy in reference to micro-CT ([micro sign]CT), the gold standard for bone microstructure quantification.

METHODS

Seventeen radii from human cadaver specimens were imaged at each HR-pQCT voxel size and subsequently imaged using [micro sign]CT. Bone density and microstructural assessment was performed in both the trabecular and cortical compartments, including cortical porosity quantification. Two distinct analysis techniques were applied to the 41 μm HR-pQCT data: the standard clinical indirect analysis and a direct analysis requiring no density or structural model assumptions. Analysis parameters were adjusted to enable segmentation and structure extraction at each voxel size.

RESULTS

For trabecular microstructural measures, the 41 μm HR-pQCT data displayed the strongest correlations and smallest errors compared to [micro sign]CT data. The direct analysis technique applied to the 41 μm data yielded an additional improvement in accuracy, especially for measures of trabecular thickness. The 123 μm data performed poorly, with all microstructural measures either having moderate or nonsignificant correlations with [micro sign]CT data. Trabecular densitometric measures showed strong correlations to [micro sign]CT data across all voxel sizes. Cortical thickness was strongly correlated with [micro sign]CT values across all HR-pQCT voxel sizes. The accuracy of cortical porosity parameters was highly dependent on voxel size; again, the 41 μm data was most strongly correlated. Measures of cortical density and pore diameter at all HR-pQCT voxel sizes had either weak or nonsignificant correlations.

CONCLUSIONS

This study demonstrates the effect of voxel size on the accuracy of HR-pQCT measurements of trabecular and cortical microstructure and presents parameters for HR-pQCT analysis at nonstandard resolutions. For all parameters measured, correlations were strongest at 41 μm. Weak correlations for porosity measures indicate that a better understanding of pore structure and resolution dependence is needed.

New laboratory tools in the assessment of bone quality

Bone quality is a complex set of intricated and interdependent factors that influence bone strength. A number of methods have emerged to measure bone quality, taking into account the organic or the mineral phase of the bone matrix, in the laboratory. Bone quality is a complex set of different factors that are interdependent. The bone matrix organization can be described at five different levels of anatomical organization: nature (organic and mineral), texture (woven or lamellar), structure (osteons in the cortices and arch-like packets in trabecular bone), microarchitecture, and macroarchitecture. Any change in one of these levels can alter bone quality. An altered bone remodeling can affect bone quality by influencing one or more of these factors. We have reviewed here the main methods that can be used in the laboratory to explore bone quality on bone samples. Bone remodeling can be evaluated by histomorphometry; microarchitecture is explored in 2D on histological sections and in 3D by microCT or synchrotron. Microradiography and scanning electron microscopy in the backscattered electron mode can measure the mineral distribution; Raman and Fourier-transformed infra-red spectroscopy and imaging can simultaneously explore the organic and mineral phase of the matrix on multispectral images; scanning acoustic microscopy and nanoindentation provide biomechanical information on individual trabeculae. Finally, some histological methods (polarization, surface staining, fluorescence, osteocyte staining) may also be of interest in the understanding of quality as a component of bone fragility. A growing number of laboratory techniques are now available. Some of them have been described many years ago and can find a new youth; others having benefited from improvements in physical and computer techniques are now available.