Micro CT and Micro MR imaging of 3D architecture of animal skeleton

Quantitative assessment of three-dimensional (3D) trabecular structural characteristics may improve our ability to understand the pathophysiology of osteoporosis, to test the efficacy of pharmaceutical intervention, and to estimate bone biomechanical properties. Considerable progress has been made in advanced imaging techniques for noninvasive and/or nondestructive assessment of 3D trabecular structure and connectivity. Micro computed tomography (microCT) has been used to measure 3D trabecular bone structure in rats, both in vivo and in vitro. It can directly quantify 3D trabecular bone structure such as trabecular volume, trabecular thickness, number, separation, structure model index, degree of anisotropy, and connectivity, in a model-independent manner. We have used microCT to study ovariectomy (OVX) induced osteopenia in rats and its treatment with agents such as estrogen, and sodium fluoride. We have demonstrated that 3D microCT can quantify mouse trabecular and cortical bone structure with an isotropic resolution of 9 microm(3). It is also useful for studying osteoporosis in mice and in phenotypes of transgenic mice or gene knockout mice. MicroCT can be used to quantify osteogenesis in mouse Ilizarov leg lengthening procedures, to quantify osteoconduction in a rat cranial defect model, and to quantify cortical bone porosity. Recently, microCT using high intensity and tight collimation synchrotron radiation to achieve spatial resolution of 1-2 microm has provided the capability to assess additional features such as resorption cavities. Unlike microCT, micro magnetic resonance imaging (IMRI) is nonionizing. Recently, the ability of microMRI to assess osteoporosis in animal models has been explored. Using a small, high-efficiency coil in a high-field imager, microMRI can give resolutions sufficient to discriminate individual trabeculae. We have shown that, with appropriate settings, it is possible to image trabecular bone in rats in vivo and in vitro. In our study of OVX rats, analysis of microMR images can demonstrate differences in rat trabecular bone that are not detected by DXA measurements. In a rabbit OA model, with the OA induced by meniscectomy or anterior cruciate ligament transection, MRI shows decreased cartilage thickness, subchondral osteosclerosis and osteophytes, while radiographs can only show subchondral osteosclerosis and osteophytes could not be found. Advanced imaging methods are able to measure 3D trabecular structure and connectivity in arbitrary orientations in a highly automated, objective, non-user-specific manner, allowing greater numbers of samples for unbiased comparisons between controls and the disordered or treated. They can be utilized on a large sample leading to fewer sampling errors. They are non-destructive allowing multiple tests such as biomechanical testing and chemical analysis on the same sample; and non-invasive permitting longitudinal studies and reducing the number of animals needed.     

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.     

A cellular solid model for modulus reduction due to resorption of trabeculae in bone

In osteoporotic trabecular bone, bone loss occurs by thinning and subsequent resorption of the trabeculae. In this study, we compare the effects of density reductions from uniform thinning of struts or from removal of struts in a random, open-cell, three-dimensional Voronoi structure. The results of this study, combined with those previous studies on other regular and random structures, suggest that the modulus and strength of trabecular bone are reduced more dramatically by density losses from resorption of trabeculae than by those from uniform thinning of trabeculae.     

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.     

Finite element analysis of ramming in Ovis canadensis

The energy produced during the ramming of bighorn sheep (Ovis canadensis) would be expected to result in undesirable stresses in their frontal skull, which in turn would cause brain injury; yet, this animal seems to suffer no ill effects. In general, horn is made of an α-keratin sheath covering a bone. Despite volumes of data on the ramming behavior of Ovis canadensis, the extent to which structural components of horn and horn-associated structure or tissue absorb the impact energy generated by the ramming event is still unknown. This study investigates the hypothesis that there is a mechanical relationship present among the ramming event, the structural constituents of the horn, and the horn-associated structure. The three-dimensional complex structure of the bighorn sheep horn was successfully constructed and modeled using a computed tomography (CT) scan and finite element (FE) method, respectively. Three different three-dimensional quasi-static models, including a horn model with trabecular bone, a horn model with compact bone that instead of trabecular bone, and a horn model with trabecular bone as well as frontal sinuses, were studied. FE simulations were used to compare distributions of principal stress in the horn and the frontal sinuses and the strain energy under quasi-static loading conditions. It was noticed that strain energy due to elastic deformation of the complex structure of horn modeled with trabecular bone and with trabecular bone and frontal sinus was different. In addition, trabecular bone in the horn distributes the stresses over a larger volume, suggesting a mechanical link between the structural constituents and the ramming event. This phenomenon was elucidated through the principal stress distribution in the structure. This study will help designers in choosing appropriate material combinations for the successful design of protective structures against a similar impact.     

Angular orientation of trabecular bone in the femoral head and its relationship to hip joint loads in leaping primates

The elastic properties and mechanical behavior of trabecular bone are largely determined by its three-dimensional (3D) fabric structure. Recent work demonstrating a correlation between the primary mechanical and material axes in trabecular bone specimens suggests that fabric orientation may be used to infer directional components of the material strength and, by extension, the hypothetical loading regime. Here we quantify the principal orientation of trabecular bone in the femoral head and relate these principal fabric directions to loading patterns during various locomotor behaviors. The proximal femora of a diverse sample of prosimians were scanned using a high-resolution X-ray computed tomography scanner with resolution of better than 50 mum. Spherical volumes of interest were defined within the femoral heads and the 3D fabric anisotropy was calculated using the mean intercept length and star volume distribution methods. In addition to differences in bone volume and anisotropy, significant differences were found in the spatial orientation of the principal trabecular axes depending on locomotor behavior. The principal orientations for leapers (Galago, Tarsius, Avahi) are relatively tightly clustered (alpha(95) confidence limit: 8.2; angular variance s: 18.2 degrees ) and oriented in a superoanterior direction, while those of nonleapers are more variable across a range of directions (alpha(95): 16.8; s: 42.0 degrees ). The mean principal directions are significantly different for leaping vs. nonleaping taxa. These results further suggest a relationship between bone microstructure in the hip joint and locomotor behavior and indicate a similarity of loading across leapers despite differences in kinematics and phylogeny.     

Mathematical modelling of trabecular bone structure: the evaluation of analytical and quantified surface to volume relationships in the femoral head and iliac crest

The three-dimensional architecture of trabecular bone has structural trends related to physical function as described by Wolff's law. Mathematical modelling provides a means of analysing these structures through the use of simplified representations. A single measure of mineralized bone volume per unit volume of structure (Vv) and the surface area of mineralized bone per unit volume of structure (Sv) does not identify a particular architecture in any detail; the way in which Sv changes in relation to Vv does provide this information as the structure remodels. A series of structures using the elements of plates and rods were created. The rates of change of Sv with respect to Vv for trabecular structures give insight into differences in such models. Structures in the femoral head and iliac crest were analysed by power curve regression. In the principal compressive region, just above the medial cortex, advanced osteoarthritis was associated with a preferential loss of rods from the normal trabecular structure, resulting in a more plate-like architecture. The iliac crest remodelling that takes place in the osteoporotic appears to be the result of a generalised bone loss with some of the thinner elements of the structure being removed completely, resulting in an increase in unit cell dimension. The consequence of changing unit cell size has a major impact on surface availability for osteoblastic and osteoclastic activity. The simple plate model as a basis for the stereological analysis of trabecular structures is therefore limited because of the mixed plate and rod nature of trabecular architecture.     

Mechanisms of reduced implant stability in osteoporotic bone

The determining factors for the fixation of uncemented screws in bone are the bone-implant interface and the peri-implant bone. The goal of this work was to explore the role of the peri-implant bone architecture on the mechanics of the bone-implant system. In particular, the specific aims of the study were to investigate: (i) the impact of the different architectural parameters, (ii) the effects of disorder, and (iii) the deformations in the peri-implant region. A three-dimensional beam lattice model to describe trabecular bone was developed. Various microstructural features of the lattice were varied in a systematic way. Implant pull-out tests were simulated, and the stiffness and strength of the bone-implant system were computed. The results indicated that the strongest decrease in pull-out strength was obtained by trabecular thinning, whereas pull-out stiffness was mostly affected by trabecular removal. These findings could be explained by investigating the peri-implant deformation field. For small implant displacements, a large amount of trabeculae in the peri-implant region were involved in the load transfer from implant to bone. Therefore, trabecular removal in this region had a strong negative effect on pull-out stiffness. Conversely, at higher displacements, deformations mainly localized in the trabeculae in contact with the implant; hence, thinning those trabeculae produced the strongest decrease in the strength of the system. Although idealized, the current approach is helpful for a mechanical understanding of the role played by peri-implant 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.     

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.     

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.     

Static and dynamic finite element analyses of an idealized structural model of vertebral trabecular bone.

An idealized three-dimensional finite element model of a rodlike trabecular bone structure was developed to study its static and dynamic responses under compressive loading, considering the effects of bone marrow and apparent density. Static analysis of the model predicted hydraulic stiffening of trabecular bone due to the presence of bone marrow. The predicted power equation relating trabecular bone apparent elastic modulus to its apparent density was in good agreement with those of the reported experimental investigations. The ratio of the maximum stress in the trabecular bone tissue to its apparent stress had a high value, decreasing with increasing bone apparent density. Frequency analyses of the model predicted higher natural frequencies for the bone without marrow than those for the bone with marrow. Adding a mass relatively large compared to that of bone rendered a single-degree-of-freedom response. In this case, the resonant frequency was higher for the bone with marrow than that for the bone without marrow. The predicted vibrational measurement of apparent modulus was in good agreement with that of the static measurement, suggesting vibrational testing as a method for nondestructive measurement of trabecular bone elastic moduli.     

Trabecular bone structure and strength - remodelling and repair

The strength of the spinal trabecular bone declines by a factor of 4-5 from the age of 20 to 80 years. At the same time, the volumetric (apparent) density declines by a factor of only 2. This discrepancy can be explained by the known power relationship between density and strength; this power relationship is based on the fact that trabecular bone is a porous material. To date, it has not been possible to determine or quantify the influence other factors may have in determining the strength of a loadbearing trabecular network. However, it is known that with age: 1) There is a loss of connectivity through osteoclastic perforations of horizontal struts. 2) There is an increase in anisotropy - again due to loss of horizontal struts, and perhaps also due to micro-modelling drift or to thickening of some vertical trabeculae. 3) The changes in the network can lead to the slenderness ratio between vertical and horizontal struts reaching a certain magnitude and thereby inducing buckling under compression. 4) Microdamage and microfractures will occur - mainly in these very loaded vertical struts. The microfractures will be repaired by microcallus formation, and these calluses will later be removed by the remodelling process. 5) Bone material quality will slightly change, leading to a decrease in collagen content and a relative increase in the degree of mineralisation. But, it is not known how these factors will influence the power relationship between density and strength. Nor is it known how different treatment regimens will affect the 'natural' power relationship: will the same curve be followed, but in the opposite direction? Or will the curve be less or more steep? Will the gain in bone strength be larger if treatment is started early - on the steep part of the curve? Furthermore, as trabecular bone can never be isolated in vivo, other factors need to be investigated: The interplay between the cortical shell and the trabecular network; transmission of load; the interplay between soft tissues (cartilage, connective tissue, muscle) and bone; the shock absorbing capacity of the discs; and the hydraulic effect of the bone marrow. In order to answer these questions, more in vitro and in vivo studies on human bone in relation to aging, to immobilisation, to exercise and in relation to different treatment regimens are needed.     

Tensile trabeculae--myth or reality?

Understanding of the functional role of the trabecular bone is very important for the analysis and computer-aided simulations of bone remodelling processes. The aspired wide clinical applications remain a remote future despite a great number of developed up-to-date approaches and theories and collected data on both material properties of the trabecular bone and its reaction to various stimuli. It is widely accepted that the mechanical loading plays the major role for the structure of the cancellous bone. The in vivo loading conditions of the cancellous bone are not known. Hence, for the computer-aided analysis and modelling of the trabecular bone specimens, simplified loading conditions are used. Also for the analysis of the cancellous bone as a part of a whole bone simplified loading conditions are assumed based on previous research without questioning its accuracy or relevance to the real in vivo conditions. In particular, the bending loading of the bone, which originates from the well-known observations made more than a century ago that have evolved in the trajectorial theory or "tensile trabeculae tradition", is often assumed to reflect the physiological loading conditions of bones. Some studies show that the bending or tensile-compressive orthogonal loading conditions for the cancellous bone may lead to plausible results. However, some other research works suggest that the presence of the tensile trabecular structures (particularly in the proximal femur) is doubtful and the bending loading conditions in bone should be treated with caution. Moreover, the loading conditions with compensated (or minimised) bending also produce results that correlate with the material distribution in the bone. The purpose of this review is to analyse some of the data and ideas available in the literature and to discuss the question of the major factors that define the shape and structure of the trabecular bone during the process of functional adaptation.     

Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models

A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional adaptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcomputed tomography (microCT), and was uniaxially compressed. As a result, the apparent stiffness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investigation of the adaptive bone remodeling phenomenon.     

Changes in the Fabric and Compliance Tensors of Cancellous Bone due to Trabecular Surface Remodeling,Predicted by a Digital Image-based Model

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.     

Testing two predictions for fracture load using computer models of trabecular bone

Aging induces several types of architectural changes in trabecular bone including thinning, increased levels of anisotropy, and perforation. It has been determined, on the basis of analysis of mathematical models, that reduction in fracture load caused by perforation is significantly higher than those due to equivalent levels of thinning or anisotropy. The analysis has also provided an expression which relates the fractional reduction of strength tau to the fraction of elements nu that have been removed from a network. Further, it was proposed that the ratio Gamma of the elastic constant of a sample and its linear response at resonance can be used as a surrogate for tau. Experimental validation of these predictions requires following architectural changes in a given sample of trabecular bone; techniques to study such changes using microcomputed tomography are only beginning to be available. In the present study, we use anatomically accurate computer models constructed from digitized images of bone samples for the purpose. Images of healthy bone are subjected to successive levels of synthetic degradation via surface erosion. Computer models constructed from these images are used to calculate their fracture load and other mechanical properties. Results from these computations are shown to be consistent with predictions derived from the analysis of mathematical models. Although the form of tau(nu) is known, parameters in the expression are expected to be sample-specific, and hence nu is not a reliable predictor of strength. We provide an example to demonstrate this. In contrast, analysis of model networks shows that the linear part of tau(Gamma) depends only on the structure of trabecular bone. Computations on models constructed from samples of iliac crest trabecular bone are shown to be in agreement with this assertion. Since Gamma can be computed from a vibrational assessment of bone, we argue that the latter can be used to introduce new surrogates for bone strength and hence diagnostic tools for osteoporosis.     

Engineering of bone tissue with porcine bone marrow stem cells in three-dimensional trabecular metal: in vitro and in vivo studies

The aim of this study was to investigate capability of cell attachment and ectopic bone formation in pigs after either ex vivo transplantation and expansion of bone marrow stem cells (BMSc) into three-dimensional porous tantalum, or porous tantalum supplemented with BMSc. After 24 hours incubation, cells adhering to the porous tantalum discs were quantified by means of scintillation counting of 3H-thymidine-labeled cells. After 7 days of incubation, the cell-loaded porous tantalum discs were harvested for histological analysis or implanted in the infrasternal muscle; an empty disc and disc implanted immediately after cell loading served as controls. All implants were taken out after 8 weeks of implantation and histological examination was performed. The results of in vitro cell attachment to the porous tantalum discs were not improved significantly with gelatin, collagen or fibronectin coatings. Histological analysis of cell loaded discs in vitro demonstrated viable BMSc within the 3-D tantalum structure. In vivo bone induction was demonstrated when the porous tantalum discs were cultured with BMSc. Our findings indicated that porous tantalum was suitable for cell attachment, and ectopic bone formation in pigs was achieved by means of BMSc cultured with porous tantalum. The present study suggests that cell-mediated hard bone tissue repair technology makes it possible to prefabricate autologous BMSc into three-dimensional trabecular metal in order to engineer bone tissue.     

Numerical modeling of bone tissue adaptation—A hierarchical approach for bone apparent density and trabecular structure

In this work, a three-dimensional model for bone remodeling is presented, taking into account the hierarchical structure of bone. The process of bone tissue adaptation is mathematically described with respect to functional demands, both mechanical and biological, to obtain the bone apparent density distribution (at the macroscale) and the trabecular structure (at the microscale). At global scale bone is assumed as a continuum material characterized by equivalent (homogenized) mechanical properties. At local scale a periodic cellular material model approaches bone trabecular anisotropy as well as bone surface area density. For each scale there is a material distribution problem governed by density-based design variables which at the global level can be identified with bone relative density. In order to show the potential of the model, a three-dimensional example of the proximal femur illustrates the distribution of bone apparent density as well as microstructural designs characterizing both anisotropy and bone surface area density. The bone apparent density numerical results show a good agreement with Dual-energy X-ray Absorptiometry (DXA) exams. The material symmetry distributions obtained are comparable to real bone microstructures depending on the local stress field. Furthermore, the compact bone porosity is modeled giving a transversal isotropic behavior close to the experimental data. Since, some computed microstructures have no permeability one concludes that bone tissue arrangement is not a simple stiffness maximization issue but biological factors also play an important role.