A New Computational Efficient Approach for Trabecular Bone Analysis using Beam Models Generated with Skeletonized Graph Technique

Micro-finite element (FE) analysis is a well established technique for the evaluation of the elastic properties of trabecular bone, but is limited in its application due to the large number of elements that it requires to represent the complex internal structure of the bone. In this paper, we present an alternative FE approach that makes use of a recently developed 3D-Line Skeleton Graph Analysis (LSGA) technique to represent the complex internal structure of trabecular bone as a network of simple straight beam elements in which the beams are assigned geometrical properties of the trabeculae that they represent. Since an enormous reduction of cputime can be obtained with this beam modeling approach, ranging from approximately 1,200 to 3,600 for the problems investigated here, we think that the FE modeling technique that we introduced could potentially constitute an interesting alternative for the evaluation of the elastic mechanical properties of trabecular bone.     

A new computational efficient approach for trabecular bone analysis using beam models generated with skeletonized graph technique

Micro-finite element (FE) analysis is a well established technique for the evaluation of the elastic properties of trabecular bone, but is limited in its application due to the large number of elements that it requires to represent the complex internal structure of the bone. In this paper, we present an alternative FE approach that makes use of a recently developed 3D-Line Skeleton Graph Analysis (LSGA) technique to represent the complex internal structure of trabecular bone as a network of simple straight beam elements in which the beams are assigned geometrical properties of the trabeculae that they represent. Since an enormous reduction of cputime can be obtained with this beam modeling approach, ranging from approximately 1,200 to 3,600 for the problems investigated here, we think that the FE modeling technique that we introduced could potentially constitute an interesting alternative for the evaluation of the elastic mechanical properties of trabecular bone.     

Simulation of vertebral trabecular bone loss using voxel finite element analysis

Trabecular bone loss in human vertebral bone is characterised by thinning and eventual perforation of the horizontal trabeculae. Concurrently, vertical trabeculae are completely lost with no histological evidence of significant thinning. Such bone loss results in deterioration in apparent modulus and strength of the trabecular core. In this study, a voxel-based finite element program was used to model bone loss in three specimens of human vertebral trabecular bone. Three sets of analyses were completed. In Set 1, strain adaptive resorption was modelled, whereby elements which were subject to the lowest mechanical stimulus (principal strain) were removed. In Set 2, both strain adaptive and microdamage mechanisms of bone resorption were included. Perforation of vertical trabeculae occurred due to microdamage resorption of elements with strains that exceeded a damage threshold. This resulted in collapse of the trabecular network under compression loading for two of the specimens tested. In Set 3, the damage threshold strain was gradually increased as bone loss progressed, resulting in reduced levels of microdamage resorption. This mechanism resulted in trabecular architectures in which vertical trabeculae had been perforated and which exhibited similar apparent modulus properties compared to experimental values reported in the literature. Our results indicate that strain adaptive remodelling alone does not explain the deterioration in mechanical properties that have been observed experimentally. Our results also support the hypothesis that horizontal trabeculae are lost principally by strain adaptive resorption, while vertical trabeculae may be lost due to perforation from microdamage resorption followed by rapid strain adaptive resorption of the remaining unloaded trabeculae.     

Hormone replacement therapy improves distal radius bone structure by endocortical mineral deposition

Hormone replacement therapy (HRT) produces a small increase in bone mineral density (BMD) when measured by dual energy X-ray absorptiometry (DXA). The corresponding decrease in fracture risk is more impressive, implying that other factors that contribute to bone strength are favourably modified by HRT. We investigated, using peripheral quantitated computed tomography (pQCT), the changes produced by HRT in both the distribution of mineral between cortical and trabecular bone and the changes produced by HRT in the apparent structure of trabecular bone, expressed as average hole area and apparent connectivity. Twenty-one postmenopausal women starting HRT and 32 control women were followed for 2 years, with distal radius pQCT measurements every 6 months. HRT prevented the loss of total bone mass seen in controls (p < 0.02). HRT also produced an apparent rapid loss of trabecular bone mass within the first 6 months of the study (p < 0.02), with an associated rapid loss in the apparent connectivity (p = 0.034). Average hole area also increased but not to a statistically significant extent. Exogenous estrogen apparently fills small marrow pores close to the endocortical surface, such that the pQCT-defined boundary between trabecular and cortical bone is shifted in favour of cortical bone. Trabecular bone structure indices are adversely affected, as the central, poorly interconnected trabecular bone with greater than average marrow spaces constitutes a greater fraction of the remaining trabecular bone. This study suggests that the improvements in fracture risk resulting from HRT are explained by a reversal of net endocortical resorption of bone.     

A quantitative method for the evaluation of three-dimensional structure of temporal bone pneumatization

Temporal bone pneumatization has been included in lists of characters used in phylogenetic analyses of human evolution. While studies suggest that the extent of pneumatization has decreased over the course of human evolution, little is known about the processes underlying these changes or their significance. In short, reasons for the observed reduction and the potential reorganization within pneumatized spaces are unknown. Technological limitations have limited previous analyses of pneumatization in extant and fossil species to qualitative observations of the extent of temporal bone pneumatization. In this paper, we introduce a novel application of quantitative methods developed for the study of trabecular bone to the analysis of pneumatized spaces of the temporal bone. This method utilizes high-resolution X-ray computed tomography (HRXCT) images and quantitative software to estimate three-dimensional parameters (bone volume fractions, anisotropy, and trabecular thickness) of bone structure within defined units of pneumatized spaces. We apply this approach in an analysis of temporal bones of diverse but related primate species, Gorilla gorilla, Pan troglodytes, Homo sapiens, and Papio hamadryas anubis, to illustrate the potential of these methods. In demonstrating the utility of these methods, we show that there are interspecific differences in the bone structure of pneumatized spaces, perhaps reflecting changes in the localized growth dynamics, location of muscle attachments, encephalization, or basicranial flexion.     

Trabecular Bone Structure Correlates with Hand Posture and Use in Hominoids

Bone is capable of adapting during life in response to stress. Therefore, variation in locomotor and manipulative behaviours across extant hominoids may be reflected in differences in trabecular bone structure. The hand is a promising region for trabecular analysis, as it is the direct contact between the individual and the environment and joint positions at peak loading vary amongst extant hominoids. Building upon traditional volume of interest-based analyses, we apply a whole-epiphysis analytical approach using high-resolution microtomographic scans of the hominoid third metacarpal to investigate whether trabecular structure reflects differences in hand posture and loading in knuckle-walking (Gorilla, Pan), suspensory (Pongo, Hylobates and Symphalangus) and manipulative (Homo) taxa. Additionally, a comparative phylogenetic method was used to analyse rates of evolutionary changes in trabecular parameters. Results demonstrate that trabecular bone volume distribution and regions of greatest stiffness (i.e., Young''s modulus) correspond with predicted loading of the hand in each behavioural category. In suspensory and manipulative taxa, regions of high bone volume and greatest stiffness are concentrated on the palmar or distopalmar regions of the metacarpal head, whereas knuckle-walking taxa show greater bone volume and stiffness throughout the head, and particularly in the dorsal region; patterns that correspond with the highest predicted joint reaction forces. Trabecular structure in knuckle-walking taxa is characterised by high bone volume fraction and a high degree of anisotropy in contrast to the suspensory brachiators. Humans, in which the hand is used primarily for manipulation, have a low bone volume fraction and a variable degree of anisotropy. Finally, when trabecular parameters are mapped onto a molecular-based phylogeny, we show that the rates of change in trabecular structure vary across the hominoid clade. Our results support a link between inferred behaviour and trabecular structure in extant hominoids that can be informative for reconstructing behaviour in fossil primates.     

A micro-computed tomography study of the trabecular bone structure in the femoral head

The goal of this study was to characterize the trabecular microarchitecture of the femoral head using micro-computed tomography (ICT). Femoral head specimens were obtained from subjects following total hip replacement. Cylindrical cores from the specimens were scanned to obtain 3-D images with an isotropic resolution of 26 Im. Bone structural parameters were evaluated on a per millimeter basis: relative bone volume (BV/TV), trabecular number (Tb.N), thickness (Tb.Th) and separation (Tb.Sp), structure model index (SMI), and connectivity (Conn.D). The ICT data show that the first two millimeters, starting at the joint surface, are characterized by more plate-like trabeculae, and are significantly denser than the underlying trabecular bone. Regional differences in the trabecular architecture reveal that the superior pole has significantly higher BV/TV, Tb.N and Tb.Th values, with lower Tb.Sp compared to the inferior and side poles. Because subchondral bone is essential in the load attenuation of joints, the difference in bone structure between the subchondral and trabecular bone might arise from the different functions each have within joint-forming bones. The denser trabecular structure of the superior pole as compared to the inferior pole can be interpreted as a functional adaptation to higher loading in this area.     

Predicting changes in mechanical properties of trabecular bone by adaptive remodeling

Because changes in the mechanical properties of bone are closely related to trabecular bone remodeling, methods that consider the temporal morphological changes induced by adaptive remodeling of trabecular bone are needed to estimate long-term fracture risk and bone quality in osteoporosis. We simulated bone remodeling using simplified and pig trabecular bone models and estimated the morphology of healthy and osteoporotic cases. We then displayed the fracture risk of the remodeled models based on a cumulative histogram from high stress. The histogram showed more elements had higher stresses in the osteoporosis model, indicating that the osteoporosis model had a greater risk.     

Patterns in ontogeny of human trabecular bone from SunWatch Village in the Prehistoric Ohio Valley: general features of microarchitectural change

Although adult skeletal morphological variation is best understood within the framework of age-related processes, relatively little research has been directed towards the structure of and variation in trabecular bone during ontogeny. We report here new quantitative and structural data on trabecular bone microarchitecture in the proximal tibia during growth and development, as demonstrated in a subadult archaeological skeletal sample from the Late Prehistoric Ohio Valley. These data characterize the temporal sequence and variation in trabecular bone structure and structural parameters during ontogeny as related to the acquisition of normal functional activities and changing body mass. The skeletal sample from the Fort Ancient Period site of SunWatch Village is composed of 33 subadult and three young adult proximal tibiae. Nondestructive microCT scanning of the proximal metaphyseal and epiphyseal tibia captures the microarchitectural trabecular structure, allowing quantitative structural analyses measuring bone volume fraction, degree of anisotropy, trabecular thickness, and trabecular number. The microCT resolution effects on structural parameters were analyzed. Bone volume fraction and degree of anisotropy are highest at birth, decreasing to low values at 1 year of age, and then gradually increasing to the adult range around 6-8 years of age. Trabecular number is highest at birth and lowest at skeletal maturity; trabecular thickness is lowest at birth and highest at skeletal maturity. The results of this study highlight the dynamic sequential relationships between growth/development, general functional activities, and trabecular distribution and architecture, providing a reference for comparative studies.     

骨小梁二维结构的自动分析

本文介绍一种以计算机图像处理为手段,对骨小梁的二维结构进行形态计量学分析的方法。该方法在二值图像上,用改进的HILDITCH算法细化二值图,计算分析骨小梁的结节、游离点。并用人工方法及计算机方法对骨小梁的结节、游离点作统计比较,结果显示两种方法呈正相关(r=0.95,p<0.01)。该方法具有自动、快速和准确性较高等优点。     

Assessing the accuracy of high-resolution X-ray computed tomography of primate trabecular bone by comparisons with histological sections

Different lines of evidence suggest that trabecular bone architecture contains a functional signal related to an organism's locomotor behavior. An understanding of the interspecific and intraspecific variation in extant nonhuman primate trabecular structure is needed to evaluate its usefulness as a tool to reconstruct the locomotor habits of extinct primates. High-resolution X-ray computed tomography (HRXCT) is a new imaging approach with a resolution in the tens of microns that allows nondestructive access to the internal structure of bony elements. Previous studies indicate that such resolution is necessary to accurately quantify structural parameters of trabecular bone. The primary goal of this study was to test the accuracy of HRXCT by comparing stereological measurements from HRXCT images and histological thin sections of cancellous bone taken from the proximal femur and humerus of baboons. To this end, 11 bone samples were scanned on an HRXCT scanner and then thin-sectioned to reveal the scanned plane. HRXCT images were thresholded using a modified half-maximum height protocol. The stereological measurements included bone volume fraction (BV/TV), trabecular number (Tb.N), bone surface to volume ratio (BS/BV), trabecular thickness (Tb.Th), and trabecular spacing (Tb.Sp). The measurement errors on the HRXCT images were 10.90% for BV/TV, 6.06% for Tb.N, 14.19% for BS/BV, 14.33% for Tb.Th, and 7.09% for Tb.Sp, but none of these measurements were significantly different from the histological standards (alpha = 0.05). A second goal of this study was to examine the influence of thresholding, a necessary step in any morphometric study using computed tomography, on the accuracy of the quantitative morphometry. Threshold values derived from a modified half-maximum height protocol showed that parameters derived from the region of interest (area in which stereological measurements were later taken) produced better reconstructions of the actual bone structure than threshold values derived from more inclusive areas of bone. We conclude that HRXCT can accurately reconstruct the complex architecture of trabecular bone, and that thresholding is a nontrivial step in trabecular bone studies, with even slight changes in the protocol greatly affecting the morphometric data. HRXCT represents a valuable analytical tool that should be of interest to a great many researchers in physical anthropology because it allows nondestructive access to internal morphology, thereby preserving valuable and limited skeletal collections.     

A global relationship between trabecular bone morphology and homogenized elastic properties.

An alternative concept of the relationship between morphological and elastic properties of trabecular bone is presented and applied to human tissue from several anatomical locations using a digital approach. The three-dimensional morphology of trabecular bone was assessed with a microcomputed tomography system and the method of directed secants as well as the star volume procedure were used to compute mean intercept length (MIL) and average bone length (ABL) of 4 mm cubic specimens. Assuming isotropic elastic properties for the trabecular tissue, the general elastic tensors of the bone specimens were determined using the homogenization method and the closest orthotropic tensors were calculated with an optimization algorithm. The assumption of orthotropy for trabecular bone was found to improve with specimen size and hold within 6.1 percent for a 4 mm cube size. A strong global relationship (r2 = 0.95) was obtained between fabric and the orthotropic elastic tensor with a minimal set of five constants. Mean intercept length and average bone length provided an equivalent power of prediction. These results support the hypothesis that the elastic properties of human trabecular bone from an arbitrary anatomical location can be estimated from an approximation of the anisotropic morphology and a prior knowledge of tissue properties.     

Doxycycline effects on mechanical and morphometrical properties of early- and late-stage osteoarthritic bone following anterior cruciate ligament injury.

As posttraumatic osteoarthritis (OA) progresses, the mechanical and morphometrical properties of the subchondral bone change and may be linked to damage of the articular cartilage. Potentially to slow that progression, doxycycline was administered orally twice daily (4 mg.kg(-1).day(-1)) in skeletally mature canines after anterior cruciate ligament transection (ACLX). To test if doxycycline significantly altered the structure and function of OA bone, we tested cancellous bone mechanical properties, measured bone mineral content, and analyzed bone structure by microcomputed tomography. Our investigation focused on subchondral trabecular bone changes in the medial femoral condyle at 36 and 72 wk after ACLX. Significant mechanical changes discovered at 36 wk post-ACLX were less obvious at 72 wk in both treated and ACLX groups. Doxycycline treatment conserved bone strain energy density at 72 wk. Doxycycline had little effect on the degradation of superficial osseous tissue at 36 wk post-ACLX; by 72 wk, doxycycline in an ACLX model limited subchondral bone loss within the first 3 mm of periarticular bone with established OA. Significant bone loss occurred in the deeper trabecular bone for all groups. Substantial architectural adaptation within deeper trabecular bone accompanied changes in mechanics in early and established OA.     

Finite element modeling of trabecular bone damage

This paper presents a finite element-based, computational model for analysis of structural damage to trabecular bone tissues. A modulus reduction method was formulated from elasto-plasticity theory, and was used to account for site-specific trabecular bone tissue damage. Trabecular bone tissue damage is illustrated using a large-scale, anatomically accurate, two-dimensional, microstructural finite element model of a human thoracic vertebral body. Four models with varying specifications for damage accumulation were subjected to compressive loading and unloading cycles. The numerical results and experimental validation demonstrated that the modulus reduction method reproduced the non-linear mechanical behaviour of vertebal trabecular bone. The iterative computational approach presented provides a methodology to study trabecular bone damage, and should provide researchers with a computational approach to study bone fracture and repair and to predict vertebral fragility.     

How morphology predicts mechanical properties of trabecular structures depends on intra-specimen trabecular thickness variations

Two observations underlie this work. First, that the architecture of trabecular bone can accurately predict the mechanical stiffness characteristics of bone specimens when considering the combination of volume fraction and fabric, which is a measure of architectural anisotropy. Second, that the same morphological measures could not accurately predict the mechanical properties of porous structures in general. We hypothesize that this discrepancy can be explained by the special nature of trabecular bone as a structure in remodeling equilibrium relative to the external loads. We tested this hypothesis using a generic model of trabecular bone. Five series of 153 different architectures were created with this model. Each architecture was subjected to morphological analysis, and four different fabric measures were calculated to evaluate their effectiveness in characterizing the architecture. Relationships were determined relating morphology to the elastic constants. The quality of these relationships was tested by correlating the predicted elastic constants with those determined from finite element analysis. We found that the four fabric measures used could estimate the mechanical properties almost equally well. So the suggestion that fabric measures based on trabecular bone volume better represent the architecture than mean intercept length could not be affirmed. We conclude that for structures with equally sized elliptical voids the mechanical properties can be predicted well only if trabecular thickness variations within each structure are limited. These structures closely resemble previously developed models of trabecular bone. Furthermore, they are stiff in the principal fabric direction, hence, according to Cowin (J. Biomech. Eng. (108) (1986) 83), they are in remodeling equilibrium. These structures are also stiff over a large range of loading orientations, hence, are relatively insensitive to deviations in direction of loading.     

Densitometric, morphometric and mechanical distributions in the human proximal femur

With the prevalent use of DXA-measured BMD to assess pathologic hip fractures and its recently reported lack of reliability to predict fracture or account for efficacy of anti-resorptive therapy, it is reasonable to assess whether variations in the primary and secondary tensile and compressive trabecular microstructure can account for variations in proximal femur strength in comparison to DXA-measured BMD. To that end, microstructural and densitometric measures of trabecular bone specimens, from discrete sites within the proximal femur, were correlated with their mechanical properties. We hypothesize that accounting for regional variations in trabecular microstructure will improve predictions of proximal femur strength and stiffness compared to bone density measured by DXA. Forty-seven samples (seven donors) from seven distinct sites of human proximal femur underwent DXA and muCT imaging and mechanical testing. The results revealed significant variations in BMC, morphometric indices and mechanical properties within the proximal femur. This work has demonstrated that the mechanical performance of each sub-region is highly dependent on the corresponding trabecular microstructure. BMD measured by DXA at standard regions of interest cannot resolve the variations in trabecular density and microstructure that govern the mechanical behavior of the proximal femur. This work suggests that a quantitative Singh index that uses high resolution QCT to monitor the trabecular microstructure at specific sub-regions of the proximal femur may allow better predictions of hip fracture risk in individual patients and an improved assessment of changing bone structure in response to pharmacological interventions.     

Gender specific LRP5 influences on trabecular bone structure and strength

A mutation in LRP5 (low-density lipoprotein receptor-related protein 5) has been shown to increase bone mass and density in humans and animals. Transgenic mice expressing the LRP5 mutation (G171V) demonstrate an increase in bone mass as compared to non-transgenic (NTG) littermates. This study evaluated LRP5 gene and gender-related influences on the structural and biomechanical strength properties of trabecular and cortical bone in femurs and vertebrae (L5) of 17-week-old mice. Micro-computed tomography was used to evaluate the trabecular bone structure of distal femurs and vertebrae ex vivo. Mechanical testing of the trabecular bone in the distal femur was done to determine biomechanical strength. Differences due to genotype and gender were tested using two-way ANOVA at a significance level of p<0.05. Trabecular bone structural parameters (BV/TV, trabecular thickness, number, etc.) at the distal femur, femoral neck, and vertebral body sites were greater in the transgenic as compared to the NTG mice. In addition, vertebral cortical thickness and trabecular strength parameters (ultimate and yield loads, stiffness, ultimate and yield stresses) in the distal femur were greater in the transgenic mice as compared to NTG. The increasing trends of cortical thickness were also noted in the transgenic mice as compared to NTG. Within LRP5 (G171V) mutant mice, there were significant gender-related differences in some of the trabecular bone structural parameters at all the sites (distal femur, femoral neck, and vertebral body). However, unlike trabecular structural parameters, the gender-specific differences were not found in the trabecular strength of LRP5 transgenic mice. In summary, these findings suggest that the LRP5 (G171V) mutation results in greater trabecular bone structure and strength at both the distal femurs and vertebral bodies as compared to NTG. In addition, only the trabecular structure parameters were affected by gender within the LRP5 (G171V) mutation.     

Multiscale modeling of bone tissue with surface and permeability control

Natural biological materials usually present a hierarchical arrangement with various structural levels. The biomechanical behavior of the complex hierarchical structure of bone is investigated with models that address the various levels corresponding to different scales. Models that simulate the bone remodeling process concurrently at different scales are in development. We present a multiscale model for bone tissue adaptation that considers the two top levels, whole bone and trabecular architecture. The bone density distribution is calculated at the macroscale (whole bone) level, and the trabecular structure at the microscale level takes into account its mechanical properties as well as surface density and permeability. The bone remodeling process is thus formulated as a material distribution problem at both scales. At the local level, the biologically driven information of surface density and permeability characterizes the trabecular structure. The model is tested by a three-dimensional simulation of bone tissue adaptation for the human femur. The density distribution of the model shows good agreement with the actual bone density distribution. Permeability at the microstructural level assures interconnectivity of pores, which mimics the interconnectivity of trabecular bone essential for vascularization and transport of nutrients. The importance of this multiscale model relays on the flexibility to control the morphometric parameters that characterize the trabecular structure. Therefore, the presented model can be a valuable tool to define bone quality, to assist with diagnosis of osteoporosis, and to support the development of bone substitutes.     

Magnetic resonance microscopy for the quantitative analysis of trabecular bone architecture

A major concern for long-term spaceflight is the effect of microgravity on bone structure and mass as a loss of cortical and trabecular bone volume and density, both of which can lead to decreased bone strength and an increased risk of bone fracture. Detailed analysis of the three-dimensional structure of trabecular bone, and its relation to bone strength has become feasible only recently using high-resolution 3D imaging techniques. In particular, magnetic resonance microscopy (MRM) has proved to be particularly useful for the ex vivo evaluation of the complex architecture of trabecular bone. In this study, we describe the use of two different MRM-based methods for the quantitative evaluation of the three-dimensional structure of trabecular bone explants and for the prediction of their biomechanical properties. The in vivo application of such methods is also discussed.     

Trabecular eccentricity and bone adaptation

It is well established that bones functionally adapt by mechanisms that control tissue density, whole bone geometry, and trabecular orientation. In this study, we propose the existence of another such powerful mechanism, namely, trabecular eccentricity, i.e. non-central placement of trabecular bone within a cortical envelope. In the human femoral neck, trabecular eccentricity results in a thicker cortical shell on the inferior than superior aspect. In an overall context of expanding understanding of bone adaptation, the goal of this study was to demonstrate the biomechanical significance of, and provide a mechanistic explanation for, the relationship between trabecular eccentricity and stresses in the human femoral neck. Using composite beam theory, we showed that the biomechanical effects of eccentricity during a habitual loading situation were to increase the stress at the superior aspect of the neck and decrease the stress at the inferior aspect, resulting in an overall protective effect. Further, increasing eccentricity had a stress-reducing effect equivalent to that of increasing cortical thickness or increasing trabecular modulus. We conclude that an asymmetric placement of trabecular bone within a cortical bone envelope represents yet another mechanism by which whole bones can adapt to mechanical demands.