Dynamic simulation of three dimensional architectural and mechanical alterations in human trabecular bone during menopause

The Duration of Hardware Retention After Radiologic Union of Surgically Treated Femoral Neck Fractures in Children May Predict the Aggravation or Occurrence of Avascular Necrosis of the Femoral Head or Neck After Hardware Removal

BACKGROUND

The incidence of aggravation or occurrence of avascular necrosis (AVN) following hardware removal in surgically treated pediatric femoral neck fractures who achieved radiologic consolidation is unknown. This study aimed to investigate the risk factors for this complication.

METHODS

Seventy-one pediatric (mean age: 9.8±3.9 y) were retrospectively analyzed. Risk factors (age, sex, laterality, severity of initial displacement, type of fracture, time from trauma to reduction, reduction and fixation method, quality of reduction, time required to achieve radiologic union, duration of hardware retention, presence of AVN before hardware removal and follow-up time) were recorded. The severity of AVN was assessed based on radiographs with Ratliff's classification.

RESULTS

Following hardware removal, the aggravation/occurrence of AVN was detected in 11 hips (15.5%). Among the 5 hips (7%) with aggravation of AVN, 1 (1.4%) with type II AVN and 3 (4.2%) with type III AVN exhibited aggravation of type I AVN, while the remaining hip (1.4%; type I) showed enlargement of the involved AVN area. Six hips (8.5%) developed AVN following hardware removal: 2 (2.8%) were classified as type I and 4 (5.6%) as type III. Receiver operating characteristic curve analysis indicated that hardware retention >7 months after union is associated with a decreased rate of aggravation or occurrence of AVN of the femoral neck or head following hardware removal.

CONCLUSIONS

The incidence of aggravation or occurrence of AVN following hardware removal in surgically treated pediatric femoral neck fractures is 15.5%; hardware retention >7 months after radiologic union may reduce the risk of aggravation or occurrence of AVN of the femoral neck or head postimplant removal.

LEVEL OF EVIDENCE

Level III.

Equivalent loads from the life-cycle of acetabular cages in relation to bone-graft transformation

BACKGROUND AND OBJECTIVES

Bone grafts placed behind acetabular cages change their structure in response to mechanical stimuli. The full consideration of lifestyle loads is extremely resource-intensive, so a method using substitutive loads was proposed to reduce the calculation cost. The aim of the study is to present and prove this method.

METHODS

By means of mechanical equations and using the force vectors from the literature which have the same initial point and their relative frequency, while applying a linear model, the average strain energy density distribution for all load cases can be calculated, compiling a matrix from the external loads. From the elements of this matrix, three substitutive load vectors can be calculated, which can be proven to produce the same strain energy density distribution by averaging their effects. The feasibility of using this to model the transformation of bone grafts placed behind acetabular cages is demonstrated with a finite element model, along with a reference calculation.

RESULTS

The substitutive load vectors could be calculated in closed form and the simulations showed that they produced a similar density distribution to the reference model with a numerical calculation error range. Accordingly, the density distribution calculated from bone graft transformation is almost the same.

CONCLUSIONS

In addition to the aforementioned linearity and the same initial point limitations, the applied method is able to produce the substitutive load vectors with which the calculation of the strain energy density distribution and the bone graft's new density distributions can be carried out faster.

Biomechanical properties and clinical significance of cancellous bone in proximal femur: A review

Trabecular bone plays an important role in the load-bearing capacity of the femur. Understanding the structural characteristics, biomechanics, and mechanical conduction of the trabecular bone is of great value in studying the mechanism of fractures and formulating surgical plans. The past decade has witnessed unprecedented progress in imaging, biomechanics and finite element analysis techniques, translating into a better understanding of trabecular bone. This article reviews the research progress achieved over the years regarding femoral trabecular bone, especially on factors influencing the strength of the proximal femoral cancellous bone and cancellous bone microfractures and provides a comprehensive overview of the latest findings on proximal femoral trabecular bone and their clinical significance.

The effect of denosumab and alendronate on trabecular plate and rod microstructure at the distal tibia and radius: A post-hoc HR-pQCT study

BACKGROUND

Age-related trabecular microstructural deterioration and conversion from plate-like trabeculae to rod-like trabeculae occur because of unbalanced rapid remodeling. As denosumab achieves greater remodeling suppression and lower cortical porosity than alendronate, we hypothesized that denosumab might also preserve trabecular plate microstructure, bone stiffness and strength more effectively than alendronate.

METHODS

In this post hoc analysis of a phase 2 study, postmenopausal women randomized to placebo (P, n = 74), denosumab (D, n = 72), or alendronate (A, n = 68). HR-pQCT scans of the distal radius and tibia were performed at baseline and Month-12 (M12). Trabecular compartment was subjected to Individual Trabecula Segmentation while finite element analysis was performed to estimate stiffness and strength. Percent change from baseline at M12 of each parameter was compared between patient groups.

RESULTS

At the distal tibia, in the placebo group, plate surface area (pTb.S, -1.3%) decreased while rod bone volume fraction (rBV/TV, +4.5%) and number (rTb.N, +2.1%) increased. These changes were prevented by denosumab but persisted despite alendronate therapy (pTb.S: -1.7%; rBV/TV: +6.9%; rTb.N: +3.0%). Both treatments improved whole bone stiffness (D: +3.1%; A: +1.8%) and failure load (D: +3.0%; A: +2.2%); improvements using denosumab was significant compared to placebo (stiffness: p = 0.004; failure load: p = 0.003). At the distal radius, denosumab increased total trabecular bone volume fraction (BV/TV, +3.4%) and whole bone failure load (+4.0%), significantly different from placebo (BV/TV: p = 0.044; failure load: p = 0.046). Significantly different effects of either drug on plate and rod microstructure were not detected.

CONCLUSIONS

Denosumab preserved trabecular plate microstructure. Alendronate did not. However, estimated strength did not differ between denosumab and alendronate treated groups.

Trabecular bone porosity and pore size distribution in osteoporotic patients - A low field nuclear magnetic resonance and microcomputed tomography investigation

The study of bone morphology is of great importance as bone morphology is influenced by factors such as age and underlying comorbidities and is associated with bone mechanical properties and fracture risk. Standard diagnostic techniques used in bone disease, such as Dual-Energy X-ray absorptiometry and ultrasonography do not provide qualitative and quantitative morphological information. In recent years, techniques such as High Resolution Computed Tomography (HR-CT), micro- CT, Magnetic Resonance Imaging (MRI), and Low Field Nuclear Magnetic Resonance (LF-NMR) have been developed for the study of bone structure and porosity. Data obtained from these techniques have been used to construct models to predict bone mechanical properties thanks to finite element analysis. Cortical porosity has been extensively studied and successfully correlated with disease progression and mechanical properties. Trabecular porosity and pore size distribution, however, have increasingly been taken into consideration to obtain a comprehensive analysis of bone pathology and mechanic. Therefore, we have decided to evaluate the ability of micro- CT (chosen for its high spatial resolving power) and LF-NMR (chosen to analyze the behavior of water molecules within trabecular bone pores) to characterize the morphology of trabecular bone in osteoporosis. Trabecular bone samples from human femoral heads collected during hip replacement surgery were from osteoporosis (test group) and osteoarthritis (control group) patients. Our data show that both micro- CT and LF-NMR can detect qualitative changes in trabecular bone (i.e., transition from plate-like to rod-like morphology). Micro- CT failed to detect significant differences in trabecular bone morphology parameters between osteoporotic and osteoarthritic specimens, with the exception of Trabecular Number and Connectivity Density, which are markers of osteoporosis progression. In contrast, LF-NMR was able to detect significant differences in porosity and pore size of trabecular bone from osteoporotic versus osteoarthritic (control) samples. However, only the combination of these two techniques allowed the detection of structural morphometric changes (increase in the larger pore fraction and enlargement of the larger pores) in the trabecular bone of osteoporotic specimens compared to osteoarthritic ones. In conclusion, the combined use of LF-NMR and micro- CT provides a valuable tool for characterizing the morphology of trabecular bone and may offer the possibility for a new approach to the study and modeling of bone mechanics in the context of aging and disease.

Microstructure Determines Apparent-Level Mechanics Despite Tissue-Level Anisotropy and Heterogeneity of Individual Plates and Rods in Normal Human Trabecular Bone

Trabecular plates and rods determine apparent elastic modulus and yield strength of trabecular bone, serving as important indicators of bone's mechanical integrity in health and disease. Although trabecular bone's apparent-level mechanical properties have been widely reported, tissue mechanical properties of individual trabeculae have not been fully characterized. We systematically measured tissue mineral density (TMD)-dependent elastic modulus of individual trabeculae using microindentation and characterized its anisotropy as a function of trabecular type (plate or rod), trabecular orientation in the global coordinate (longitudinal, oblique, or transverse along the anatomic loading axis), and indentation direction along the local trabecular coordinate (axial or lateral). Human trabecular bone samples were scanned by micro-computed tomography for TMD and microstructural measurements. Individual trabecula segmentation was used to decompose trabecular network into individual trabeculae, where trabecular type and orientation were determined. We performed precise, selective indentation of trabeculae in each category using a custom-built, microscope-coupled microindentation device. Co-localization of TMD at each indentation site was performed to obtain TMD-to-modulus correlations. We found significantly higher TMD and tissue modulus in trabecular plates than rods. Regardless of trabecular type and orientation, axial tissue modulus was consistently higher than lateral tissue modulus, with ratios ranging from 1.13 to 1.41. Correlations between TMD and tissue modulus measured from axial and lateral indentations were strong but distinct: axial correlation predicted higher tissue modulus than lateral correlation at the same TMD level. To assess the contribution of experimentally measured anisotropic tissue properties of individual trabeculae to apparent-level mechanics, we constructed non-linear micro-finite element models using a new set of trabecular bone samples and compared model predictions to mechanical testing measurements. Heterogeneous anisotropic models accurately predicted apparent elastic modulus but were no better than a simple homogeneous isotropic model. Variances in tissue-level properties may therefore contribute nominally to apparent-level mechanics in normal human trabecular bone. © 2021 American Society for Bone and Mineral Research (ASBMR).

Peak trabecular bone microstructure predicts rate of estrogen-deficiency-induced bone loss in rats

Postmenopausal osteoporosis affects a large number of women worldwide. Reduced estrogen levels during menopause lead to accelerated bone remodeling, resulting in low bone mass and increased fracture risk. Both peak bone mass and the rate of bone loss are important predictors of postmenopausal osteoporosis risk. However, whether peak bone mass and/or bone microstructure directly influence the rate of bone loss following menopause remains unclear. Our study aimed to establish the relationship between peak bone mass/microstructure and the rate of bone loss in response to estrogen deficiency following ovariectomy (OVX) surgery in rats of homogeneous background by tracking the skeletal changes using in vivo micro-computed tomography (μCT) and three-dimensional (3D) image registrations. Linear regression analyses demonstrated that the peak bone microstructure, but not peak bone mass, was highly predictive of the rate of OVX-induced bone loss. In particular, the baseline trabecular thickness was found to have the highest correlation with the degree of OVX-induced bone loss and trabecular stiffness reduction. Given the same bone mass, the rats with thicker baseline trabeculae had a lower rate of trabecular microstructure and stiffness deterioration after OVX. Moreover, further evaluation to track the changes within each individual trabecula via our novel individual trabecular dynamics (ITD) analysis suggested that a trabecular network with thicker trabeculae is less likely to disconnect or perforate in response to estrogen deficiency, resulting a lower degree of bone loss. Taken together, these findings indicate that the rate of estrogen-deficiency-induced bone loss could be predicted by peak bone microstructure, most notably the trabecular thickness. Given the same bone mass, a trabecular bone phenotype with thin trabeculae may be a risk factor toward accelerated postmenopausal bone loss.

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.

Dimorphism in axial and appendicular dimensions, cortical and trabecular microstructure and matrix mineral density in Chinese and Caucasian women

INTRODUCTION

Appendicular fractures are less common in Chinese than Caucasian women. Bone mineral density (BMD) is lower, not higher than in Caucasians because Chinese have smaller appendicular dimensions than Caucasians. However, smaller bones may offset the liability to fracture by being assembled with a more robust microstructure. We hypothesized that Chinese assemble an appendicular skeleton with a thicker, less porous and more mineralized cortex that is less deteriorated in advanced age than in Caucasians.

METHODS

We compared anthropometry in 477 Chinese and 278 Caucasian women and compared bone microstructure using high-resolution peripheral quantitative computed tomography in another cohort of 186 Chinese and 381 Caucasian women aged 18 to 86 years, all living in Melbourne, Australia. Trabecular plate (p) and rod (r) bone volume/total volume (BV/TV) were quantified using individual trabecula segmentation (ITS). Bone strength was estimated using micro-finite element analysis (μFEA).

RESULTS

Premenopausal Chinese were shorter than Caucasian women, mainly due to shorter leg length. Distal radial total cross sectional area (CSA) was 14.8% smaller (p < 0.001). After adjusting for age and total CSA, Chinese had similar cortical and medullary areas but 0.30 SD lower cortical porosity and 0.27 SD higher matrix mineral density (both p < 0.05). Trabecular plate-to-rod ratio was 0.55 SD higher due to a 0.41 SD higher pBV/TV and 0.36 SD lower rBV/TV (p ranging 0.001 to 0.023). Chinese also had 0.36 SD greater whole bone stiffness and 0.36 SD greater failure load than Caucasians (both p < 0.05). After adjusting for age and total CSA, postmenopausal Chinese had 3.3% smaller cortical area, medullary area was 2.1% larger, cortical porosity was no lower, matrix mineral density and pBV/TV were no higher compared with Caucasians at the distal radius. Whole bone stiffness was 0.39 SD lower and failure load was 0.40 SD lower in Chinese (both p < 0.05).

CONCLUSION

Chinese build a more robust skeleton than Caucasians during growth, an advantage not observed in advanced age due to greater bone loss or race-specific secular trends in bone morphology.

Structural Adaptations in the Rat Tibia Bone Induced by Pregnancy and Lactation Confer Protective Effects Against Future Estrogen Deficiency

The female skeleton undergoes substantial structural changes during the course of reproduction. Although bone mineral density recovers postweaning, reproduction may induce permanent alterations in maternal bone microarchitecture. However, epidemiological studies suggest that a history of pregnancy and/or lactation does not increase the risk of postmenopausal osteoporosis or fracture and may even have a protective effect. Our study aimed to explain this paradox by using a rat model, combined with in vivo micro-computed tomography (μCT) imaging and bone histomorphometry, to track the changes in bone structure and cellular activities in response to estrogen deficiency following ovariectomy (OVX) in rats with and without a reproductive history. Our results demonstrated that a history of reproduction results in an altered skeletal response to estrogen-deficiency-induced bone loss later in life. Prior to OVX, rats with a reproductive history had lower trabecular bone mass, altered trabecular microarchitecture, and more robust cortical structure at the proximal tibia when compared to virgins. After OVX, these rats underwent a lower rate of trabecular bone loss than virgins, with minimal structural deterioration. As a result, by 12 weeks post-OVX, rats with a reproductive history had similar trabecular bone mass, elevated trabecular thickness, and increased robustness of cortical bone when compared to virgins, resulting in greater bone stiffness. Further evaluation suggested that reproductive-history-induced differences in post-OVX trabecular bone loss were likely due to differences in baseline trabecular microarchitecture, particularly trabecular thickness. Rats with a reproductive history had a larger population of thick trabeculae, which may be protective against post-OVX trabecular connectivity deterioration and bone loss. Taken together, these findings indicate that reproduction-associated changes in bone microarchitecture appear to reduce the rate of bone loss induced by estrogen deficiency later in life, and thereby exert a long-term protective effect on bone strength. © 2018 American Society for Bone and Mineral Research.

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

A bone loading estimation algorithm was previously developed that provides in vivo loading conditions required for in vivo bone remodelling simulations. The algorithm derives a bone's loading history from its microstructure as assessed by high-resolution (HR) computed tomography (CT). This reverse engineering approach showed accurate and realistic results based on micro-CT and HR-peripheral quantitative CT images. However, its voxel size dependency, reproducibility and sensitivity still need to be investigated, which is the purpose of this study. Voxel size dependency was tested on cadaveric distal radii with micro-CT images scanned at 25 µm and downscaled to 50, 61, 75, 82, 100, 125 and 150 µm. Reproducibility was calculated with repeated in vitro as well as in vivo HR-pQCT measurements at 82 µm. Sensitivity was defined using HR-pQCT images from women with fracture versus non-fracture, and low versus high bone volume fraction, expecting similar and different loading histories, respectively. Our results indicate that the algorithm is voxel size independent within an average (maximum) error of 8.2% (32.9%) at 61 µm, but that the dependency increases considerably at voxel sizes bigger than 82 µm. In vitro and in vivo reproducibility are up to 4.5% and 10.2%, respectively, which is comparable to other in vitro studies and slightly higher than in other in vivo studies. Subjects with different bone volume fraction were clearly distinguished but not subjects with and without fracture. This is in agreement with bone adapting to customary loading but not to fall loads. We conclude that the in vivo bone loading estimation algorithm provides reproducible, sensitive and fairly voxel size independent results at up to 82 µm, but that smaller voxel sizes would be advantageous.

Estimation of Local Bone Loads for the Volume of Interest

Computational bone remodeling simulations have recently received significant attention with the aid of state-of-the-art high-resolution imaging modalities. They have been performed using localized finite element (FE) models rather than full FE models due to the excessive computational costs of full FE models. However, these localized bone remodeling simulations remain to be investigated in more depth. In particular, applying simplified loading conditions (e.g., uniform and unidirectional loads) to localized FE models have a severe limitation in a reliable subject-specific assessment. In order to effectively determine the physiological local bone loads for the volume of interest (VOI), this paper proposes a novel method of estimating the local loads when the global musculoskeletal loads are given. The proposed method is verified for the three VOI in a proximal femur in terms of force equilibrium, displacement field, and strain energy density (SED) distribution. The effect of the global load deviation on the local load estimation is also investigated by perturbing a hip joint contact force (HCF) in the femoral head. Deviation in force magnitude exhibits the greatest absolute changes in a SED distribution due to its own greatest deviation, whereas angular deviation perpendicular to a HCF provides the greatest relative change. With further in vivo force measurements and high-resolution clinical imaging modalities, the proposed method will contribute to the development of reliable patient-specific localized FE models, which can provide enhanced computational efficiency for iterative computing processes such as bone remodeling simulations.

Are the High Hip Fracture Rates Among Norwegian Women Explained by Impaired Bone Material Properties?

Hip fracture rates in Norway rank among the highest in the world, more than double that of Spanish women. Previous studies were unable to demonstrate significant differences between the two populations with respect to bone mass or calcium metabolism. In order to test whether the difference in fracture propensity between both populations could be explained by differences in bone material quality we assessed bone material strength using microindentation in 42 Norwegian and 46 Spanish women with normal BMD values, without clinical or morphometric vertebral fractures, no clinical or laboratory signs of secondary osteoporosis, and without use of drugs with known influence on bone metabolism. Bone material properties were assessed by microindentation of the thick cortex of the mid tibia following local anesthesia of the area using the Osteoprobe device (Active Life Scientific, Santa Barbara, CA, USA). Indentation distance was standardized against a calibration phantom of methylmethacrylate and results, as percentage of this reference value, expressed as bone material strength index units (BMSi). We found that the bone material properties reflected in the BMSi value of Norwegian women was significantly inferior when compared to Spanish women (77 ± 7.1 versus 80.7 ± 7.8, p < 0.001). Total hip BMD was significantly higher in Norwegian women (1.218 g/cm(2) versus 0.938 g/cm(2) , p < 0.001) but regression analysis revealed that indentation values did not vary with BMD r(2)  = 0.03 or age r(2)  = 0.04. In conclusion Norwegian women show impaired bone material properties, higher bone mass, and were taller than Spanish women. The increased height will increase the impact on bone after falls, and impaired bone material properties may further enhance the risk fracture after such falls. These ethnic differences in bone material properties may partly explain the higher propensity for fracture in Norwegian women.

From histology to micro-CT: Measuring and modeling resorption cavities and their relation to bone competence

The process of bone remodelling plays an essential role in the emergence and maintenance of bone geometry and its internal structure. Osteoclasts are one of the three main bone cell types that play a crucial role in the bone remodelling cycle. At the microstructural level, osteoclasts create bone deficits by eroding resorption cavities. Understanding how these cavities impair the mechanical quality of the bone is not only relevant in quantifying the impact of resorption cavities in healthy bone and normal aging, but maybe even more so in quantifying their role in metabolic bone diseases. Metabolic bone diseases and their treatment are both known to affect the bone remodelling cycle; hence, the bone mechanical competence can and will be affected. However, the current knowledge of the precise dimensions of these cavities and their effect on bone competence is rather limited. This is not surprising considering the difficulties in deriving three-dimensional (3D) properties from two-dimensional (2D) histological sections. The measurement difficulties are reflected in the evaluation of how resorption cavities affect bone competence. Although detailed 3D models are generally being used to quantify the mechanical impact of the cavities, the representation of the cavities themselves has basically been limited to simplified shapes and averaged cavity properties. Qualitatively, these models indicate that cavity size and location are important, and that the effect of cavities is larger than can be expected from simple bone loss. In summary, the dimensions of osteoclast resorption cavities were until recently estimated from 2D measures; hence, a careful interpretation of resorption cavity dimensions is necessary. More effort needs to go into correctly quantifying resorption cavities using modern 3D imaging techniques like micro-computed tomography (micro-CT) and synchrotron radiation CT. Osteoclast resorption cavities affect bone competence. The structure-function relationships have been analysed using computational models that, on one hand, provide rather detailed information on trabecular bone structure, but on the other incorporate rather crude assumptions on cavity dimensions. The use of high-resolution representations and parametric descriptions could be potential routes to improve the quantitative fidelity of these models.

Dependence of mechanical properties of trabecular bone on plate-rod microstructure determined by individual trabecula segmentation (ITS)

Individual trabecula segmentation (ITS) technique can decompose the trabecular bone network into individual trabecular plates and rods and is capable of quantifying the plate/rod-related microstructural characteristics of trabecular bone. This novel technique has been shown to be able to provide in-depth insights into micromechanics and failure mechanisms of human trabecular bone, as well as to distinguish the fracture status independent of area bone mineral density in clinical applications. However, the plate/rod microstructural parameters from ITS have never been correlated to experimentally determined mechanical properties of human trabecular bone. In this study, on-axis cylindrical trabecular bone samples from human proximal tibia (n=22), vertebral body (n=10), and proximal femur (n=21) were harvested, prepared, scanned using micro computed-tomography (µCT), analyzed with ITS and mechanically tested. Regression analyses showed that the plate bone volume fraction (pBV/TV) and axial bone volume fraction (aBV/TV) calculated by ITS analysis correlated the best with elastic modulus (R(2)=0.96-0.97) and yield strength (R(2)=0.95-0.96). Trabecular plate-related microstructural parameters correlated highly with elastic modulus and yield strength, while most rod-related parameters were found inversely and only moderately correlated with the mechanical properties. In addition, ITS analysis also identified that trabecular bone at human femoral neck had the highest trabecular plate-related parameters while the other sites were similar with each other in terms of plate-rod microstructure.

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.

The effect of resorption cavities on bone stiffness is site dependent

Resorption cavities formed during the bone remodelling cycle change the structure and thus the mechanical properties of trabecular bone. We tested the hypotheses that bone stiffness loss due to resorption cavities depends on anatomical location, and that for identical eroded bone volumes, cavities would cause more stiffness loss than homogeneous erosion. For this purpose, we used beam-shell finite element models. This new approach was validated against voxel-based FE models. We found an excellent agreement for the elastic stiffness behaviour of individual trabeculae in axial compression (R(2) = 1.00) and in bending (R(2)>0.98), as well as for entire trabecular bone samples to which resorption cavities were digitally added (R(2) = 0.96, RMSE = 5.2%). After validation, this new method was used to model discrete cavities, with dimensions taken from a statistical distribution, on a dataset of 120 trabecular bone samples from three anatomical sites (4th lumbar vertebra, femoral head, iliac crest). Resorption cavities led to significant reductions in bone stiffness. The largest stiffness loss was found for samples from the 4th lumbar vertebra, the lowest for femoral head samples. For all anatomical sites, resorption cavities caused significantly more stiffness loss than homogeneous erosion did. This novel technique can be used further to evaluate the impact of resorption cavities, which are known to change in several metabolic bone diseases and due to treatment, on bone competence.

Morphology analysis of vertebral trabecular bone under dynamic loading based on multi-scale theory

Trabecular bone has a complicated porous microstructure and consists of interconnected plates and rods known as trabeculae. The microarchitecture of the trabeculae contributes to load distribution capacity and, particularly, the optimal bone strength. Many previous studies have shown that morphological parameters are used to characterize the microarchitecture of trabecular bone, but little is known about the mechanical role of trabecular morphology in the context of load-bearing behavior. Therefore, this study proposes a new segmentation method for examining the morphology of trabecular structure foci of load-bearing capability. A micro-finite element model of trabecular bone was obtained from the fourth lumbar vertebra on the basis of a three-dimensionally reconstructed micro-computed tomography (CT) image. We used an asymptotic homogenization method to determine microscopic stress by applying three unidirectional compressive loads in the vertical, anteroposterior, and right-left axes of two trabecular bone volumes. We then classified the complicated trabecular microstructure into three segments: primary and secondary trabeculae and trabeculae of no contribution. Next, a dynamic analysis was conducted by applying a force impulse load. The result indicated that 1/3 of the trabecular volume functions as primary trabecula. The morphology of the trabecular network could be visualized successfully highlighting the percolation of the stress wave in the primary trabecular segment. Further, we found that the role of the plate-like structures was that of a hub in the trabecular network system.

Analysis of microstructural and mechanical alterations of trabecular bone in a simulated three-dimensional remodeling process

Bone remodeling is a complex dynamic process, which modulates both bone mass and bone microstructure. In addition to bone mass, bone microstructure is an important contributor to bone quality in osteoporosis and fragility fractures. However, the quantitative knowledge of evolution of three-dimensional (3D) trabecular microstructure in adaptation to the external forces is currently limited. In this study, a new 3D simulation method of remodeling of human trabecular bone was developed to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to different external loading conditions. The morphological features of trabecular plate and rod, such as thickness and number density in different orientations were monitored during the remodeling process using a novel imaging analysis technique, namely Individual Trabecula Segmentation (ITS). We showed that the volume fraction and microstructures of trabecular bone including, trabecular type and orientation, were determined by the applied mechanical load. Particularly, the morphological parameters of trabecular plates were more sensitive to the applied load, indicating that they played the major role in the mechanical properties of the trabecular bone. Reducing the applied load caused severe microstructural deteriorations of trabecular bone, such as trabecular plate perforation, rod breakage, and a conversion from plates to rods.

Individual trabecula segmentation (ITS)-based morphological analysis of microscale images of human tibial trabecular bone at limited spatial resolution

Individual trabecula segmentation (ITS), a rigorous model-independent 3D morphological analysis, has been developed to assess trabecular plate and rod microstructure separately based on micro-computed tomographic (µCT) images. We examined the influence of the limited spatial resolution, noise, and artifact of high-resolution peripheral quantitative CT (HR-pQCT) on ITS measurements of human tibial trabecular bone. In comparison with measurements from "gold standard" µCT images (25 µm), decreased spatial resolution (40, 60, and 80 µm) of µCT had minimal influence on the correlations of the scale of trabecular plates (ie, plate bone volume fraction, thickness, and surface area) and the orientation (ie, axial bone volume fraction) and structural type (ie, plate tissue fraction) of the trabecular network. ITS measurements of HR-pQCT images correlated significantly with those of µCT images at a similar voxel size (80 µm, r = 0.71-0.94); correlations were stronger for plate-related parameters, suggesting that measurements of trabecular rods are more subject to noise and artifact associated with HR-pQCT imaging technology. In comparison with measurements of "gold standard" µCT images, the percent absolute errors of HR-pQCT measurements such as axial and plate bone volume fraction, plate number and tissue fraction, and plate and rod thickness (3.5% to 10.3%) were comparable with those of bone volume fraction (9.3%). For both HR-pQCT and µCT images, measurements of the scale and junction densities of trabecular plates and orientation and structural type were strong and positive indicators of the elastic modulus of trabecular bone (r = 0.59-0.95). We conclude that ITS measurements of HR-pQCT images are highly reflective of trabecular bone microarchitecture from a biomechanical perspective.

A sclerostin-based theory for strain-induced bone formation

Bone formation responds to mechanical loading, which is believed to be mediated by osteocytes. Previous theories assumed that loading stimulates osteocytes to secrete signals that stimulate bone formation. In computer simulations this 'stimulatory' theory successfully produced load-aligned trabecular structures. In recent years, however, it was discovered that osteocytes inhibit bone formation via the protein sclerostin. To reconcile this with strain-induced bone formation, one must assume that sclerostin secretion decreases with mechanical loading. This leads to a new 'inhibitory' theory in which loading inhibits osteocytes from inhibiting bone formation. Here we used computer simulations to show that a sclerostin-based model is able to produce a load-aligned trabecular architecture. An important difference appeared when we compared the response of the stimulatory and inhibitory models to loss of osteocytes, and found that the inhibitory pathway prevents the loss of trabeculae that is seen with the stimulatory model. Further, we demonstrated with combined stimulatory/inhibitory models that the two pathways can work side-by-side to achieve a load-adapted bone architecture.

Type and orientation of yielded trabeculae during overloading of trabecular bone along orthogonal directions

Trabecular architecture plays a major role in bone mechanics. Osteoporosis leads to a transition from a plate-like to a more rod-like trabecular morphology, which may contribute to fracture risk beyond that predicted by changes in density. In this study, microstructural finite element analysis results were analyzed using individual trabeculae segmentation (ITS) to identify the type and orientation of trabeculae where tissue yielded during compressive overloads in two orthogonal directions. For both apparent loading conditions, most of the yielded tissue was found in longitudinally oriented plates. However, the primary loading mode of yielded trabeculae was axial compression with superposed bending for on-axis loading in contrast to bending for transverse loading. For either loading direction, most plate-like trabeculae yielded in the same loading mode, regardless of their orientation. In contrast, rods oriented parallel to the loading axis yielded in compression, while rods oblique or perpendicular to the loading axis yielded in combined bending and tension. The predominance of tissue yielding in plates during both on-axis and transverse overloading explains why on-axis overloading is detrimental to the off-axis mechanical properties. At the same time, a large fraction of the tissue in rod-like trabeculae parallel to the loading direction yielded in both on-axis and transverse loading. Hence, rods may be more likely to be damaged and potentially resorbed by damage mediated remodeling.

Effects of trabecular type and orientation on microdamage susceptibility in trabecular bone

Trabecular architecture becomes more rod-like and anisotropic in osteoporotic and aging trabecular bone. In order to address the effects of trabecular type and orientation on trabecular bone damage mechanics, microstructural finite element modeling was used to identify the yielded tissue in ten bovine tibial trabecular bone samples compressed to 1.2% on-axis apparent strain. The yielded tissue was mapped onto individual trabeculae identified by an Individual Trabeculae Segmentation (ITS) technique, and the distribution of the predicted yielding among trabecular types and orientations was compared to the experimentally measured microdamage. Although most of the predicted yielded tissue was found in longitudinal plates (73+/-11%), the measured microcrack density was positively correlated with the proportion of the yielded tissue in longitudinal rods (R(2)=0.52, p=0.02), but not in rods of other directions or plates. The overall fraction of rods and the fractions of rods along the longitudinal and transverse axes were also correlated with the measured microcrack density. In contrast, diffuse damage area did not correlate with any of these quantities. These results agree with the findings that both in vitro and in vivo microcrack densities are correlated with Structure Model Index (SMI), and are also consistent with decreased energy to failure in more rod-like trabecular bone. Together the results suggest that bending or buckling deformations of rod-like trabeculae may make trabecular structures more susceptible to microdamage formation. Moreover, while simple strain-based tissue yield criteria may account for macroscopic yielding, they may not be suitable for identifying damage.