Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions

Quantitative Load Dependency Analysis of Local Trabecular Bone Microstructure to Understand the Spatial Characteristics in the Synthetic Proximal Femur

Analysis of the dependency of the trabecular structure on loading conditions is essential for understanding and predicting bone structure formation. Although previous studies have investigated the relationship between loads and structural adaptations, there is a need for an in-depth analysis of this relationship based on the bone region and load specifics. In this study, the load dependency of the trabecular bone microstructure for twelve regions of interest (ROIs) in the synthetic proximal femur was quantitatively analyzed to understand the spatial characteristics under seven different loading conditions. To investigate the load dependency, a quantitative measure, called the load dependency score (LDS), was established based on the statistics of the strain energy density (SED) distribution. The results showed that for the global model and epiphysis ROIs, bone microstructures relied on the multiple-loading condition, whereas the structures in the metaphysis depended on single or double loads. These results demonstrate that a given ROI is predominantly dependent on a particular loading condition. The results confirm that the dependency analysis of the load effects for ROIs should be performed both qualitatively and quantitatively.

Effect of reconstruction parameters on cone beam CT trabecular bone microstructure quantification in sheep

Background

Cone Beam Computed Tomography (CBCT) is a reliable radiographic modality to assess trabecular bone microarchitecture. The aim of this study was to determine the effect of CBCT image reconstruction parameters, namely, the threshold value and reconstruction voxel size, on trabecular bone microstructure assessment.

Methods

Five sectioned maxilla of adult Dorper male sheep were scanned using a CBCT system with a resolution of 76 μm³ (Kodak 9000). The CBCT images were reconstructed using different reconstruction parameters and analysed. The effect of reconstruction voxel size (76, 100 and 200 μm³) and threshold values (±15% from the global threshold value) on trabecular bone microstructure measurement was assessed using image analysis software (CT analyser version 1.15).

Results

There was no significant difference in trabecular bone microstructure measurement between the reconstruction voxel sizes, but a significant difference (Tb.N = 0.03, Tb.Sp = 0.04, Tb.Th = 0.01, BV/TV = 0.00) was apparent when the global threshold value was decreased by 15%.

Conclusions

Trabecular bone microstructure measurements are not compromised by changing the CBCT reconstruction voxel size. However, measurements can be affected when applying a threshold value of less than 15% of the recommended global value.

Cancellous bone and theropod dinosaur locomotion. Part I-an examination of cancellous bone architecture in the hindlimb bones of theropods

This paper is the first of a three-part series that investigates the architecture of cancellous ('spongy') bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and has previously been used to infer locomotor biomechanics in extinct tetrapod vertebrates, especially primates. Despite great promise, cancellous bone architecture has remained little utilized for investigating locomotion in many other extinct vertebrate groups, such as dinosaurs. Documentation and quantification of architectural patterns across a whole bone, and across multiple bones, can provide much information on cancellous bone architectural patterns and variation across species. Additionally, this also lends itself to analysis of the musculoskeletal biomechanical factors involved in a direct, mechanistic fashion. On this premise, computed tomographic and image analysis techniques were used to describe and analyse the three-dimensional architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs for the first time. A comprehensive survey across many extant and extinct species is produced, identifying several patterns of similarity and contrast between groups. For instance, more stemward non-avian theropods (e.g. ceratosaurs and tyrannosaurids) exhibit cancellous bone architectures more comparable to that present in humans, whereas species more closely related to birds (e.g. paravians) exhibit architectural patterns bearing greater similarity to those of extant birds. Many of the observed patterns may be linked to particular aspects of locomotor biomechanics, such as the degree of hip or knee flexion during stance and gait. A further important observation is the abundance of markedly oblique trabeculae in the diaphyses of the femur and tibia of birds, which in large species produces spiralling patterns along the endosteal surface. Not only do these observations provide new insight into theropod anatomy and behaviour, they also provide the foundation for mechanistic testing of locomotor hypotheses via musculoskeletal biomechanical modelling.

3D bioprinting of tissues and organs for regenerative medicine

3D bioprinting is a pioneering technology that enables fabrication of biomimetic, multiscale, multi-cellular tissues with highly complex tissue microenvironment, intricate cytoarchitecture, structure-function hierarchy, and tissue-specific compositional and mechanical heterogeneity. Given the huge demand for organ transplantation, coupled with limited organ donors, bioprinting is a potential technology that could solve this crisis of organ shortage by fabrication of fully-functional whole organs. Though organ bioprinting is a far-fetched goal, there has been a considerable and commendable progress in the field of bioprinting that could be used as transplantable tissues in regenerative medicine. This paper presents a first-time review of 3D bioprinting in regenerative medicine, where the current status and contemporary issues of 3D bioprinting pertaining to the eleven organ systems of the human body including skeletal, muscular, nervous, lymphatic, endocrine, reproductive, integumentary, respiratory, digestive, urinary, and circulatory systems were critically reviewed. The implications of 3D bioprinting in drug discovery, development, and delivery systems are also briefly discussed, in terms of in vitro drug testing models, and personalized medicine. While there is a substantial progress in the field of bioprinting in the recent past, there is still a long way to go to fully realize the translational potential of this technology. Computational studies for study of tissue growth or tissue fusion post-printing, improving the scalability of this technology to fabricate human-scale tissues, development of hybrid systems with integration of different bioprinting modalities, formulation of new bioinks with tuneable mechanical and rheological properties, mechanobiological studies on cell-bioink interaction, 4D bioprinting with smart (stimuli-responsive) hydrogels, and addressing the ethical, social, and regulatory issues concerning bioprinting are potential futuristic focus areas that would aid in successful clinical translation of this technology.

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus [Formula: see text] on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of [Formula: see text], were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and [Formula: see text]140 KPa and (2) [Formula: see text], 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35[Formula: see text], 0.235[Formula: see text] and 0.6[Formula: see text]) than for FA attachment (0.0952[Formula: see text], 0.0472[Formula: see text] and 0.05[Formula: see text]). For increasing [Formula: see text], the largest maximum principal strain was 4.4[Formula: see text], 5[Formula: see text], 5.3[Formula: see text] and 5.3[Formula: see text] in the membrane, 9.5[Formula: see text], 1.1[Formula: see text], 1.2[Formula: see text] and 1.2[Formula: see text] in the cytosol, and 4.5[Formula: see text], 5.3[Formula: see text], 5.7[Formula: see text] and 5.7[Formula: see text] in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.

Mimetization of the elastic properties of cancellous bone via a parameterized cellular material

Bone tissue mechanical properties and trabecular microarchitecture are the main factors that determine the biomechanical properties of cancellous bone. Artificial cancellous microstructures, typically described by a reduced number of geometrical parameters, can be designed to obtain a mechanical behavior mimicking that of natural bone. In this work, we assess the ability of the parameterized microstructure introduced by Kowalczyk (Comput Methods Biomech Biomed Eng 9:135-147, 2006. doi: 10.1080/10255840600751473 ) to mimic the elastic response of cancellous bone. Artificial microstructures are compared with actual bone samples in terms of elasticity matrices and their symmetry classes. The capability of the parameterized microstructure to combine the dominant isotropic, hexagonal, tetragonal and orthorhombic symmetry classes in the proportions present in the cancellous bone is shown. Based on this finding, two optimization approaches are devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of a target natural bone specimen: a Sequential Quadratic Programming algorithm that minimizes the norm of the difference between the elasticity matrices, and a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions. The pattern search approach is found to produce the best results. The performance of the method is demonstrated via analyses for 146 bone samples.

A novel approach for extracting viscoelastic parameters of living cells through combination of inverse finite element simulation and Atomic Force Microscopy

Dynamic mechanical behaviour of living cells has been described by viscoelasticity. However, quantitation of the viscoelastic parameters for living cells is far from sophisticated. In this paper, combining inverse finite element (FE) simulation with Atomic Force Microscope characterization, we attempt to develop a new method to evaluate and acquire trustworthy viscoelastic index of living cells. First, influence of the experiment parameters on stress relaxation process is assessed using FE simulation. As suggested by the simulations, cell height has negligible impact on shape of the force-time curve, i.e. the characteristic relaxation time; and the effect originates from substrate can be totally eliminated when stiff substrate (Young's modulus larger than 3 GPa) is used. Then, so as to develop an effective optimization strategy for the inverse FE simulation, the parameters sensitivity evaluation is performed for Young's modulus, Poisson's ratio, and characteristic relaxation time. With the experiment data obtained through typical stress relaxation measurement, viscoelastic parameters are extracted through the inverse FE simulation by comparing the simulation results and experimental measurements. Finally, reliability of the acquired mechanical parameters is verified with different load experiments performed on the same cell.

A review of trabecular bone functional adaptation: what have we learned from trabecular analyses in extant hominoids and what can we apply to fossils?

Many of the unresolved debates in palaeoanthropology regarding evolution of particular locomotor or manipulative behaviours are founded in differing opinions about the functional significance of the preserved external fossil morphology. However, the plasticity of internal bone morphology, and particularly trabecular bone, allowing it to respond to mechanical loading during life means that it can reveal greater insight into how a bone or joint was used during an individual's lifetime. Analyses of trabecular bone have been commonplace for several decades in a human clinical context. In contrast, the study of trabecular bone as a method for reconstructing joint position, joint loading and ultimately behaviour in extant and fossil non-human primates is comparatively new. Since the initial 2D studies in the late 1970s and 3D analyses in the 1990 s, the utility of trabecular bone to reconstruct behaviour in primates has grown to incorporate experimental studies, expanded taxonomic samples and skeletal elements, and improved methodologies. However, this work, in conjunction with research on humans and non-primate mammals, has also revealed the substantial complexity inherent in making functional inferences from variation in trabecular architecture. This review addresses the current understanding of trabecular bone functional adaptation, how it has been applied to hominoids, as well as other primates and, ultimately, how this can be used to better interpret fossil hominoid and hominin morphology. Because the fossil record constrains us to interpreting function largely from bony morphology alone, and typically from isolated bones, analyses of trabecular structure, ideally in conjunction with that of cortical structure and external morphology, can offer the best resource for reconstructing behaviour in the past.

The use of micro-CT to study bone architecture dynamics noninvasively

High-resolution micro-CT has become a standard tool in the evaluation of bone architecture. It has recently progressed from an invasive tool for bone specimens into an in vivo tool for small animals. The combination of novel sophisticated evaluation methods, such as registration (matching) of sequential scans and computer simulation models will further evolve in vivo micro-CT into an optimal tool for small animal phenotyping and contemporary approaches for drug discovery relating to the skeleton.:

The effects of misalignment during in vivo loading of bone: techniques to detect the proximity of objects in three-dimensional models

Theories of mechanical adaptation of bone suggest that mechanical loading causes bone formation at discrete locations within bone microstructure experiencing the greatest mechanical stress/strain. Experimental testing of such theories requires in vivo loading experiments and high-resolution finite element models to determine the distribution of mechanical stresses. Finite element models of in vivo loading experiments typically assume idealized boundary conditions with applied load perfectly oriented on the bone, however small misalignments in load orientation during an in vivo experiment are unavoidable, and potentially confound the ability of finite element models to predict locations of bone formation at the scale of micrometers. Here we demonstrate two different three-dimensional spatial correlation methods to determine the effects of misalignment in load orientation on the locations of high mechanical stress/strain in the rodent tail loading model. We find that, in cancellous bone, the locations of tissue with high stress are maintained under reasonable misalignments in load orientation (p<0.01). In cortical bone, however, angular misalignments in the dorsal direction can alter the locations of high mechanical stress, but the locations of tissue with high stress are maintained under other misalignments (p<0.01). We conclude that, when using finite element models of the rodent tail loading model, small misalignments in loading orientation do not affect the predicted locations of high mechanical stress within cancellous bone.

The application of digital volume correlation (DVC) to study the microstructural behaviour of trabecular bone during compression

Digital Volume Correlation (DVC) has been emerged recently as an innovative approach to full volume (i.e. internal) displacement and strain field measurement in materials and structures, particularly in conjunction with high resolution X-ray computed tomography (CT). As a relatively novel technique certain aspects of precision, accuracy and the breadth of application are yet to be fully established. This study has applied DVC to volume images of porcine trabecular bone assessing the effect of noise and sub-volume size on strain measurement. Strain resolutions ranging between 70 and 800με were obtained for the optimum sub-volume size of 64 voxels with a 50% overlap for metrological studies conducted. These values allowed the mechanical behaviour of porcine trabecular bone during compression to be investigated. During compression a crushed layer formed adjacent to the boundary plate which increased in thickness as the specimen was further deformed. The structure of the crushed layer was altered to such an extent that it confounded the correlation method. While investigating this factor, it was found that for reliable strain calculations a correlation coefficient of 0.90 or above was required between the sub-volumes in the reference and the deformed volumes. Good agreements between the results and published bone strain failures were obtained. Using the full field strain measurements, Poisson's ratio was identified for each compression step using a dedicated inverse method called the virtual fields method (VFM). It was found that for a given region outside of the crushed zone the Poisson ratio decreased from 0.32 to 0.21 between the first and the final compression steps, which was hypothesised to be due to the bone geometry and its resulting deformation behaviour. This study demonstrates that volumetric strain measurement can be obtained successfully using DVC, making it a useful tool for quantitatively investigating the micro-mechanical behaviour of macroscale bone specimens.

Validation of finite element models for strain analysis of implant-supported prostheses using digital image correlation

OBJECTIVES

A validated numerical model for stress/strain predictions is essential in understanding the biomechanical behavior of implant-supported dental prostheses. The digital image correlation (DIC) method for full-field strain measurement was compared with finite element analysis (FEA) in assessing bone strain induced by implants.

METHODS

An epoxy resin model simulating the lower arch was made for the experimental test with acrylic resin replicas of the first premolar and second molar and threaded implants replacing the second premolar and first molar. Splinted (G1/G3) and non-splinted (G2/G4) metal-ceramic screw-retained crowns were fabricated and loaded with (G1/G2) or without (G3/G4) the second molar that provided proximal contact. A single-camera, two-dimensional DIC system was used to record deformation of the resin model surface under a load of 250N. Three-dimensional finite element (FE) models were constructed for the physical models using computer-aided design (CAD) software. Surface strains were used for comparison between the two methods, while internal strains at the implant/resin block interface were calculated using FEA.

RESULTS

Both methods found similar strain distributions over the simulant bone block surface, which indicated possible benefits of having splinted crowns and proximal contact in reducing bone strains. Internal strains predicted by FEA at the implant-resin interface were 8 times higher than those on the surface of the model, and they confirmed the results deduced from the surface strains. FEA gave higher strain values than experiments, probably due to incorrect material properties being used.

SIGNIFICANCE

DIC is a useful tool for validating FE models used for the biomechanical analysis of dental prosthesis.

Design and optimization of the oriented groove on the hip implant surface to promote bone microstructure integrity

We proposed a novel surface modification for an artificial hip joint stem from the viewpoint of maintenance and establishment of appropriate bone function and microstructure, represented by the preferred alignment of biological apatite (BAp) and collagen (Col). Oriented grooves were introduced into the proximal medial region of the femoral stem to control the principal stress applied to the bone inside the grooves, which is a dominant factor contributing to the promotion of Col/BAp alignment. The groove angle and the stem material were optimized based on the stress inside the grooves through a finite element analysis (FEA). Only the groove oriented proximally by 60° from the normal direction of the stem surface generated the healthy maximum principal stress distribution. The magnitude of the maximum principal stress inside the groove decreased with increasing the stem Young's modulus, while the direction of the stress did not largely changed. An in vivo implantation experiment showed that this groove was effective in inducing the new bone with preferential Col/BAp alignment along the groove depth direction which corresponded to the direction of maximum principal stress inside the groove. The anisotropic principal stress distribution and the oriented microstructure inside the groove are similar to those found in the femoral trabeculae; therefore, the creation of the oriented groove is a potent surface modification for optimizing implant design for a long-term fixation.

Computationally-optimized bone mechanical modeling from high-resolution structural images

Image-based mechanical modeling of the complex micro-structure of human bone has shown promise as a non-invasive method for characterizing bone strength and fracture risk in vivo. In particular, elastic moduli obtained from image-derived micro-finite element (μFE) simulations have been shown to correlate well with results obtained by mechanical testing of cadaveric bone. However, most existing large-scale finite-element simulation programs require significant computing resources, which hamper their use in common laboratory and clinical environments. In this work, we theoretically derive and computationally evaluate the resources needed to perform such simulations (in terms of computer memory and computation time), which are dependent on the number of finite elements in the image-derived bone model. A detailed description of our approach is provided, which is specifically optimized for μFE modeling of the complex three-dimensional architecture of trabecular bone. Our implementation includes domain decomposition for parallel computing, a novel stopping criterion, and a system for speeding up convergence by pre-iterating on coarser grids. The performance of the system is demonstrated on a dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM. Models of distal tibia derived from 3D in-vivo MR images in a patient comprising 200,000 elements required less than 30 seconds to converge (and 40 MB RAM). To illustrate the system's potential for large-scale μFE simulations, axial stiffness was estimated from high-resolution micro-CT images of a voxel array of 90 million elements comprising the human proximal femur in seven hours CPU time. In conclusion, the system described should enable image-based finite-element bone simulations in practical computation times on high-end desktop computers with applications to laboratory studies and clinical imaging.

Nonunion of capital femoral physeal fracture with a large metaphyseal fragment

This report presents a case demonstrating the nonunion of a capital femoral physeal fracture with a large metaphyseal fragment in a 10-year-old boy. To our knowledge, there is no previously reported case of this type of nonunion. The treatment of this nonunion presented a potential risk of premature physeal closure and avascular necrosis of the femoral head, so internal fixation using cannulated screws and percutaneously drilling with a Kirschner wire to the metaphyseal fragment was used and was effective in bone union without these complications.

Parameter study for the finite element modelling of long bones with computed-tomography-imaging-based stiffness distribution

Four radii of different horses were tested in three-point bending and in pure torsion. Detailed finite element (FE) models of these long bones were established by means of computed-tomography (CT) images and tests simulated for both load cases. For the allocation of the local isotropic material stiffness, individual exponential functions were applied whose factor and exponent were determined solely by fitting them to the measured torsional stiffness and bending stiffness of the entire bones. These stiffness functions referring directly to the CT number and having exponents between 1.5 and 2 were in good agreement with Young's moduli subsequently measured from small samples cut from the investigated bones. Based on a model with local orthotropic material definition, an additional parameter study was conducted to verify the sensitivities of the FE analysis results on single variations in the orthotropic elastic constants. This study revealed that the bending test simulations could be enhanced by substantial reduction in Young's moduli in the directions perpendicular to the bone axis; thus, orthotropic material definition is preferable for the FE analysis of long bones.

Finite element analysis performed on radius and tibia HR-pQCT images and fragility fractures at all sites in postmenopausal women

Assessment of bone strength at the radius by micro-finite element analysis (muFEA) has already been associated with wrist fractures. In this study, the analysis has been extended to the distal tibia, and to a larger group of subjects to examine the association with several types of fragility fractures. We have compared muFEA based on in vivo HR-pQCT measurements of BMD and microarchitecture at the radius and tibia, in a case-control study involving 101 women with prevalent fragility fracture and 101 age-matched controls, from the OFELY cohort. Areal BMD was measured by DXA at the radius and the hip. All parameters were analyzed in a principal component (PC) analysis (PCA), and associations between PCs and fractures were computed as odds ratios (OR [95% CI]) per SD change. Radius (tibia) PCA revealed three independent components explaining 76% (77%) of the total variability of bone characteristics. The first PC describing bone strength and quantity, explained 50% (46%) of variance with an OR=1.84 [1.27-2.67] (2.92 [1.73-4.93]). The second PC including trabecular microarchitecture, explained 16% (10%) of variance, with OR=1.29 [0.90-1.87] (1.11 [0.82-1.52]). The third PC related to load distribution explained 10% (20%) of variance, with OR=1.54 [1.06-2.24] (1.32 [0.89-1.96]). Moreover, at the radius, vertebral fractures were associated with trabecular microarchitecture PC with OR=1.86 [1.14-3.03], whereas nonvertebral fractures were associated with bone strength and quantity PC with OR=2.03 [1.36-3.02]. At the tibia, both vertebral (OR=2.92 [1.61-5.28]) and nonvertebral fracture (2.64 [1.63-4.27]) were associated to bone strength and quantity PC. In conclusion, muFEA parameters at the radius and tibia were associated with all types of fragility fractures. We have also shown that muFEA parameters obtained with distal tibia data were associated with prevalent fractures with a similar magnitude that with parameters obtained at the radius.

Compressive axial mechanical properties of rat bone as functions of bone volume fraction, apparent density and micro-ct based mineral density

Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure-function properties of the skeleton. With recent advances in computing power of personal computers, virtual alternatives to mechanical testing are gaining acceptance and use. We have previously introduced such a technique called structural rigidity analysis to assess mechanical strength of skeletal tissue with defects. The application of this technique is predicated upon the use of relationships defining the strength of bone as a function of its density for a given loading mode. We are to apply this technique in rat models to assess their compressive skeletal response subjected to a host of biological and pharmaceutical stimulations. Therefore, the aim of this study is to derive a relationship expressing axial compressive mechanical properties of rat cortical and cancellous bone as a function of equivalent bone mineral density, bone volume fraction or apparent density over a range of normal and pathologic bones. We used bones from normal, ovariectomized and partially nephrectomized animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial compression to failure. We obtained univariate relationships describing 71-78% of the mechanical properties of rat cortical and cancellous bone based on equivalent mineral density, bone volume fraction or apparent density over a wide range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity analysis introduced by the authors to provide a non-invasive method to assess the compressive strength of bones affected by pathology and/or treatment options.

In vitro bone growth responds to local mechanical strain in three-dimensional polymer scaffolds

Mechanical stimulation plays a key role in healing and remodelling of bone tissue in vivo, and is used in bone tissue regeneration strategies in vitro. Although macroscopic compression of three-dimensional (3-D) seeded constructs can increase bone formation, it is not yet reported how this response is related to differences in local mechanical strains inside the scaffolds. In this study, we experimentally test the hypothesis that differences in local average of heterogeneous strains in a polymer scaffold will correlate with induced differences in the local biological response. Twenty-four poly(L-lactic acid) porous scaffolds seeded with rat bone cells were cultured first for 2 and 3 weeks under static conditions, respectively. Then for 1 week, half of the scaffolds were cyclically compressed (1.5%, 1 Hz), 1 h daily, with continuous perfusion (0.1 ml/min). The remaining half was kept under static conditions. The pore-surface strains in the scaffolds at the start of culture were calculated with micro-finite element modelling based on micro-Computed Tomography (microCT) images. The locations of mineralized nodules were determined from microCT images and coupled to the calculated strains. Detectable mineralized nodules (>10(3) microm3) were only present in the loaded samples. Averages of absolute principal strains at the start of culture were significantly higher at nodule sites than at sites without a nodule. The results support the hypothesis that regenerating bone tissue in a 3-D porous scaffold responds to local mechanical strain. The methodology presented in this study can contribute design optimisation of tissue regeneration strategies relying on mechanical stimulation.

Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law

Ever since Julius Wolff proposed the law of bone transformation in the 19th century, it has been widely known that the trabecular structure of cancellous bone adapts functionally to the loading environment. To understand the mechanism of Wolff's law, a three-dimensional (3D) computer simulation of trabecular structural changes due to surface remodeling was performed for a human proximal femur. A large-scale voxel finite element model was constructed to simulate the structural changes of individual trabeculae over the entire cancellous region. As a simple remodeling model that considers bone cellular activities regulated by the local mechanical environment, nonuniformity of local stress was assumed to drive the trabecular surface remodeling to seek a uniform stress state. Simulation results demonstrated that cell-scale ( approximately 10microm) remodeling in response to mechanical stimulation created complex 3D trabecular structures of the entire bone-scale ( approximately 10cm), as illustrated in the reference of Wolff. The bone remodeling reproduced the characteristic anisotropic structure in the coronal cross section and the isotropic structures in other cross sections. The principal values and axes of a structure characterized by fabric ellipsoids corresponded to those of the apparent stress of the structure. The proposed large-scale computer simulation indicates that in a complex mechanical environment of a hierarchical bone structure of over 10(4) length scale (from approximately 10microm to approximately 10cm), a simple remodeling at the cellular/trabecular levels creates a highly complex and functional trabecular structure, as characterized by bone density and orientation.

Elastic strains in antler trabecular bone determined by synchrotron X-ray diffraction

The microstructure and associated mechanical properties of antler trabecular bone have been studied using a variety of techniques. The local trabeculae properties, as well as the three-dimensional architecture were characterized using nanoindentation and X-ray microtomography, respectively. An elastic modulus of 10.9+/-1.1 GPa is reported for dry bone, compared with 5.4+/-0.9 GPa for fully hydrated bone. Trabeculae thickness and separation were found to be comparable to those of bovine trabecular bone. Uniaxial compression conducted in situ during X-ray microtomography showed that antler can undergo significant architectural rearrangement, dominated by trabeculae bending and buckling, due to its low mineral content. High-energy synchrotron X-ray diffraction was used to measure elastic strains in the apatite crystals of the trabeculae, also under in situ uniaxial compression. During elastic loading, strain was found to be accommodated largely by trabeculae aligned parallel to the loading direction. Prior to the macroscopic yield point, internal strains increased as trabeculae deformed by bending, and load was also found to be redistributed to trabeculae aligned non-parallel to the loading direction. Significant bending of trabecular walls resulted in tensile strains developing in trabeculae aligned along the loading direction.

A numerical model of heterogeneous surface strains in polymer scaffolds

In vitro bone tissue growth inside porous scaffolds can be enhanced by macroscopic cyclic compression of the construct, but the heterogeneous strain generated inside the construct must be investigated to determine appropriate levels of compression. For this purpose a linear micro-finite element (muFE) technique based on micro-computed tomography (muCT) was verified for the calculation of local displacements inside polymer scaffolds, from which local strains may be estimated. Local displacements in the axial direction at the surface of microstructures inside the scaffold in 60 locations were calculated with the muFE model, based on compression simulation of a muCT reconstruction of the scaffold. These displacements were compared with accurately measured displacements in the axial direction in the same polymer scaffold at the same 60 locations, using a micro-compression chamber and muCT reconstructions of the scaffold under two fixed levels of compression (5% and 0%). The correlation between the calculated and the measured displacements, after correction for the dependence of the axial displacement on the axial position, was r=0.786 (r2=0.617). From this we conclude that the linear muFE model is suitable to estimate local surface strains inside polymer scaffolds for tissue engineering applications. This technique can not only be used to determine appropriate parameters such as the level of macroscopic compression in experimental design, but also to investigate the cellular response to local surface strains generated inside three-dimensional scaffolds.

Finite element analysis based on in vivo HR-pQCT images of the distal radius is associated with wrist fracture in postmenopausal women

BMD, bone microarchitecture, and bone mechanical properties assessed in vivo by finite element analysis were associated with wrist fracture in postmenopausal women.

INTRODUCTION

Many fractures occur in individuals with normal BMD. Assessment of bone mechanical properties by finite element analysis (FEA) may improve identification of those at high risk for fracture.

MATERIALS AND METHODS

We used HR-pQCT to assess volumetric bone density, microarchitecture, and microFE-derived bone mechanical properties at the radius in 33 postmenopausal women with a prior history of fragility wrist fracture and 33 age-matched controls from the OFELY cohort. Radius areal BMD (aBMD) was also measured by DXA. Associations between density, microarchitecture, mechanical parameters and fracture status were evaluated by univariate logistic regression analysis and expressed as ORs (with 95% CIs) per SD change. We also conducted a principal components (PCs) analysis (PCA) to reduce the number of parameters and study their association (OR) with wrist fracture.

RESULTS

Areal and volumetric densities, cortical thickness, trabecular number, and mechanical parameters such as estimated failure load, stiffness, and the proportion of load carried by the trabecular bone at the distal and proximal sites were associated with wrist fracture (p < 0.05). The PCA revealed five independent components that jointly explained 86.2% of the total variability of bone characteristics. The first PC included FE-estimated failure load, areal and volumetric BMD, and cortical thickness, explaining 51% of the variance with an OR for wrist fracture = 2.49 (95% CI, 1.32-4.72). Remaining PCs did not include any density parameters. The second PC included trabecular architecture, explaining 12% of the variance, with an OR = 1.82 (95% CI, 0.94-3.52). The third PC included the proportion of the load carried by cortical versus trabecular bone, assessed by FEA, explaining 9% of the variance, and had an OR = 1.61 (95% CI, 0.94-2.77). Thus, the proportion of load carried by cortical versus trabecular bone seems to be associated with wrist fracture independently of BMD and microarchitecture (included in the first and second PC, respectively).

CONCLUSIONS

These results suggest that bone mechanical properties assessed by microFE may provide information about skeletal fragility and fracture risk not assessed by BMD or architecture measurements alone and are therefore likely to enhance the prediction of wrist fracture risk.

Stress distribution in maxillary alveolar ridge according to finite element analysis using micro-CT

The purpose of the present study was to evaluate stress distribution by finite element analysis in an accurate model simulating trabecular bone using micro-CT. Dentulous and edentulous maxillary jaws of Japanese adult cadavers were used (5 sides each; total, 10 sides). Imaging was performed using a micro-CT, followed by reconstruction with 3-D images. Finite element analysis models were developed using the maxilla with average bone morphometry. A load corresponding to occlusal force was applied in different loading conditions, followed by evaluation of stress distribution. In dentulous maxillas, a load was applied in the dental axis direction to the first molar crown (LD). In edentulous maxillas, a load was applied directly to a circular area 4mm in diameter (LER0) to a cylinder 4mm in diameter and 10mm in height (LER10) corresponding to the first molar area. Stress was concentrated in cortical bone around the first molar, trabecular bone and cortical bone at the maxillary sinus base in LD, cortical bone of the alveolar ridge in LER0, and trabecular bone around the cylinder and cortical bone at the maxillary sinus base in LER10. LER0 showed a stress distribution markedly different from that in LD. Compared with LER0, LER10 showed a stress distribution close to that in LD. A model simulating trabecular bone allows a more accurate evaluation of stress distribution.

The Influence of Mineralization on Intratrabecular Stress and Strain Distribution in Developing Trabecular Bone

The load-transfer pathway in trabecular bone is largely determined by its architecture. However, the influence of variations in mineralization is not known. The goal of this study was to examine the influence of inhomogeneously distributed degrees of mineralization (DMB) on intratrabecular stresses and strains. Cubic mandibular condylar bone specimens from fetal and newborn pigs were used. Finite element models were constructed, in which the element tissue moduli were scaled to the local DMB. Disregarding the observed distribution of mineralization was associated with an overestimation of average equivalent strain and underestimation of von Mises equivalent stress. From the surface of trabecular elements towards their core the strain decreased irrespective of tissue stiffness distribution. This indicates that the trabecular elements were bent during the compression experiment. Inhomogeneously distributed tissue stiffness resulted in a low stress at the surface that increased towards the core. In contrast, disregarding this tissue stiffness distribution resulted in high stress at the surface which decreased towards the core. It was concluded that the increased DMB, together with concurring alterations in architecture, during development leads to a structure which is able to resist increasing loads without an increase in average deformation, which may lead to damage.

Loading conditions and bone formation in the GH region of the shoulder

The present study investigates how loading of the shoulder effect the formation of the trabeculae in the subarticular region of the gleno-humeral joint. Bone morphology was determined from scapular cadaveric specimens and finite element (FE) analysis was employed to analyse principal stress trajectories. Boundary conditions corresponded to five functional activities were considered. The results show deviations of the computed trajectories from actual trabecular lines obtained from the bone specimens ranged on average from 10% to 17%. Each activity produced different regional deviation corresponding to the specific loading condition. This study concludes that certain loading conditions are more significant in explaining the formation of the trabecular architecture. The results also suggest that due to the extra sensitivity of the front and the rear aspects of the "lateral region" to the loading conditions, these regions may be more indicative in reflecting shoulder injuries.

Postcranial skeletal pneumaticity: a case study in the use of quantitative microCT to assess vertebral structure in birds

Limb elements in birds have been characterized as exhibiting a reduction in trabecular bone, thinner cortices and decreased bending strength when pneumatized, yet it is unclear if these characteristics generalize to the axial skeleton. Thin section techniques, the traditional gold standard for bone structure studies, have most commonly been applied to the study of avian bone. This destructive technique, however, makes it subsequently impossible to use the same samples in experimental testing systems that allow researchers to correlate structure with the mechanical properties of the bone. Micro-computed tomography (microCT), a non-destructive X-ray imaging technique, can be used to assess the effect of pneumatization on vertebral cortical and trabecular bone through virtual extraction and structural quantification of each tissue type. We conducted a preliminary investigation of the application of microCT methods to the study of cortical and trabecular bone structure in a small sample of pneumatic and apneumatic thoracic vertebrae. The sample consisted of two similar-sized anatids, Aix sponsa (n = 7) and Oxyura jamaicensis (n = 5). Volumes of interest were created that contoured (outlined) the boundaries of the ventral cortical bone shell, the trabecular compartment and the whole centrum (cortical bone + trabecular bone), and allowed independent structural analysis of each volume of interest. Results indicated that bone volume fraction of the whole centrum was significantly higher in the apneumatic O. jamaicensis than in the pneumatized A. sponsa (A. sponsa = 36%, O. jamaicensis = 48%, P < 0.05). In contrast, trabecular bone volume fraction was similar between the two species. The ventral cortical bone shell was approximately 23% thinner (P < 0.05) in A. sponsa (0.133 mm) compared with apneumatic O. jamaicensis (0.172 mm). This case study demonstrates that microCT is a powerful non-destructive imaging technique that may be applied to the three-dimensional study of avian bone. The preliminary results suggest that pneumatic and apneumatic vertebrae of comparably sized avian species differ in relative bone volume, with the largest difference apparent at the level of the cortex, and not within trabecular bone. The presence of relatively thin cortices in pneumatic vertebrae is consistent with previous studies contrasting diaphyseal cortical bone between pneumatic and apneumatic long bones. Methodological issues related to this and any comparative microCT study of bone structure are discussed.

A method for patient-specific evaluation of vertebral cancellous bone strength: in vitro validation

BACKGROUND

In the context of osteoporosis, important determinants of the fracture risk are the apparent strength and stiffness of cancellous bone, as well as its brittleness and energy absorption capacity. Standard medical imaging, however, cannot measure these mechanical properties directly. Consequently, an estimation of the risk for fracture is made by correlating relative density or mineral density at a skeletal site with statistics of fracture occurrence, which provides limited and partial indications on fracture risks. A better method for evaluating the patient-specific mechanical properties of cancellous bone is therefore required.

METHODS

In order to asses the mechanical properties of vertebral cancellous bone, we developed a finite element parametric model of lattice trabecular architecture that, in the future, will be suitable for use with bone imaging modalities. The model inputs are apparent morphological parameters (trabecular thickness and trabecular separation) and the bone mineral density. We conducted uniaxial compression tests on 36 canine vertebral cancellous bone specimens (C7 and L1) to validate model predictions of strength and stiffness in vitro.

FINDINGS

Predictions of strength and stiffness matched the experimental results within relative absolute errors of 17.7% and 12.8%, respectively (average of differences between model-predicted and measured values, divided by the average of measured values). We also employed the model for evaluation of strength and stiffness of human L1 and L5 vertebrae and found mean strength of 1.67 MPa (confidence interval 0.42 MPa) and mean elastic modulus of 190 MPa (confidence interval 50 MPa), which are well within the range of previously reported apparent strength and stiffness properties.

INTERPRETATION

The present model can be used to improve medical imaging-based evaluation of the spine in osteoporotic individuals by providing more specific information on the individual bone's susceptibility to fracture once clinical bone scans will be able to provide more reliable measures of trabecular thickness and separation.

Variations in mineralization affect the stress and strain distributions in cortical and trabecular bone

The mechanical properties of bone depend largely on its degree and distribution of mineralization. The present study analyzes the effect of an inhomogeneous distribution of mineralization on the stress and strain distributions in the human mandibular condyle during static clenching. A condyle was scanned with a micro-CT scanner to create a finite element model. For every voxel the degree of mineralization (DMB) was determined from the micro-CT scan. The Young's moduli of the elements were calculated from the DMB using constant, linear, and cubic relations, respectively. Stresses, strains, and displacements in cortical and trabecular bone, as well as the condylar deformation (extension along the antero-posterion axis) and compliance were compared. Over 90% of the bone mineral was located in the cortical bone. The DMB showed large variations in both cortical bone (mean: 884, SD: 111 mg/cm(3)) and trabecular bone (mean: 738, SD: 101 mg/cm(3)). Variations of the stresses and the strains were small in cortical bone, but large in trabecular bone. In the cortical bone an inhomogeneous mineral distribution increased the stresses and the strains. In the trabecular bone, however, it decreased the stresses and increased the strains. Furthermore, the condylar compliance remained relatively constant, but the condylar deformation doubled. It was concluded that neglect of the inhomogeneity of the mineral distribution results in a large underestimation of the stresses and strains of possibly more than 50%. The stiffness of trabecular bone strongly influences the condylar deformation. Vice versa, the condylar deformation largely determines the magnitude of the strains in the trabecular bone.

Effects of Thresholding Techniques on μCT-Based Finite Element Models of Trabecular Bone

Microimaging based finite element analysis is widely used to predict the mechanical properties of trabecular bone. The choice of thresholding technique, a necessary step in converting grayscale images to finite element models, can significantly influence the predicted bone volume fraction and mechanical properties. Therefore, we investigated the effects of thresholding techniques on microcomputed tomography (micro-CT) based finite element models of trabecular bone. Three types of thresholding techniques were applied to 16-bit micro-CT images of trabecular bone to create three different models per specimen. Bone volume fractions and apparent moduli were predicted and compared to experimental results. In addition, trabecular tissue mechanical parameters and morphological parameters were compared among different models. Our findings suggest that predictions of apparent mechanical properties and structural properties agree well with experimental measurements regardless of the choice of thresholding methods or the format of micro-CT images.

Trabecular bone ontogeny in the human proximal femur

Ontogenetic changes in the human femur associated with the acquisition of bipedal locomotion, especially the development of the bicondylar angle, have been well documented. The purpose of this study is to quantify changes in the three-dimensional structure of trabecular bone in the human proximal femur in relation to changing functional and external loading patterns with age. High-resolution X-ray computed tomography scan data were collected for 15 juvenile femoral specimens ranging in age from prenatal to approximately nine years of age. Serial slices were collected for the entire proximal femur of each individual with voxel resolutions ranging from 0.017 to 0.046 mm depending on the size of the specimen. Spherical volumes of interest were defined within the proximal femur, and the bone volume fraction, trabecular thickness, trabecular number, and fabric anisotropy were calculated in three dimensions. Bone volume fraction, trabecular number, and degree of anisotropy decrease between the age of 6 months and 12 months, with the lowest values for these parameters occurring in individuals near 12 months of age. By age 2-3 years, the bone volume, thickness, and degree of anisotropy increase slightly, and regions in the femoral neck become more anisotropic corresponding to the thickening of the inferior cortical bone of the neck. These results suggest that trabecular structure in the proximal femur reflects the shift in external loading patterns associated with the initiation of unassisted walking in infants.

Three-dimensional bone microstructures of the mandibular angle using micro-CT and finite element analysis: relationship between partially impacted mandibular third molars and angle fractures

The mandibular angle is one of the areas of the mandible that are prone to bone fractures, and the presence of an impacted third molar has been found to be associated with increased risk of angle fractures. The factors involved in bone fractures are the amount and direction of load, and the biomechanical and anatomical properties of bone. In the present study, micro-focused X-ray computed tomography was performed to observe and analyze the three-dimensional (3D) bone microstructure of the mandibular angle, and finite element analysis was conducted to examine the relationship between angle fractures and the presence or absence of mandibular third molars. 3D bone microstructure showed no marked difference between mandibles with and without third molars. Finite element analysis showed that, in the mandible with a third molar, stress was concentrated around the root apex of the third molar, and was transmitted in a direction matching the clinical findings of angle fractures. The results obtained in this study suggest that the presence of an impacted third molar changes the concentration and transmission of stress in the mandible, thus increasing the risk of an angle fracture.

Trabecular architecture can remain intact for both disuse and overload enhanced resorption characteristics

The paradigm that bone metabolic processes are controlled by osteocyte signals have been the subject of investigation in many recent studies. One hypothesis is that osteoblast formation is enhanced by these signals, and that osteoclast resorption is enhanced by the lack of them. Reduced, or absent, osteocyte signaling can be an effect of reduced mechanical loading (disuse) or of defects in the canalicular network, due to microcracks. This would mean that bone is resorbed precisely there where it is mostly needed. In our study, we addressed this apparent contradiction. The purpose was to investigate how alternative strain-based local stimuli for osteoclasts to resorb bone would affect remodeling and adaptation of the trabecular architecture. For this purpose, a computer-simulation model was used, which couples morphological and mechanical effects of local bone metabolism to changes in trabecular architecture and density at large. Six resorption characteristics were studied in the model: (I) resorption occurs spatially random, (II) resorption is enhanced or (III) strongly enhanced where there is disuse, (IV) resorption is enhanced or (V) strongly enhanced where there are high strains, i.e. overload, and (VI) resorption is enhanced where there is disuse and where there are high strains. Results showed that the rates of structural adaptation to alternative loading were higher for disuse-controlled resorption than for overload-controlled resorption. Architecture and mass remained stable for all cases except (V) in which the structure deteriorated as in osteoporotic bone. We conclude that, given the potential of osteoblasts to form bone in highly strained areas, based on signals from osteocytes, osteoclast resorption can normally be compensated for.

Comparison of micro-level and continuum-level voxel models of the proximal femur

Continuum-level finite element (FE) models became standard computational tools for the evaluation of bone mechanical behavior from in vivo computed tomography scans. Such scans do not account for the anisotropy of the bone. Instead, local mechanical properties in the continuum-level FE models are assumed isotropic and are derived from bone density, using statistical relationships. Micro-FE models, on the other hand, incorporate the anisotropic structure in detail. This study aimed to quantify the effects of assumed isotropy, by comparing continuum-level voxel models of a healthy and a severely osteoporotic proximal femur with recently analyzed micro-FE models of the same bones. The micro-model element size was coarsened to generate continuum FE models with two different element sizes (0.64 and 3.04 mm) and two different density-modulus relationships found in the literature for wet and ash density. All FE models were subjected to the same boundary conditions that simulated a fall to the side, and the stress and strain distributions, model stiffness and yield load were compared. The results indicated that the stress and strain distributions could be reproduced well with the continuum models. The smallest differences between the continuum-level model and micro-level model predictions of the stiffness and yield load were obtained with the coarsest element size. Better results were obtained for both continuum-element sizes when isotropic moduli were based on ash density rather than wet density.

The Effect of the Loading Condition Corresponding to Functional Shoulder Activities on Trabecular Architecture of Glenoid

There is little information on bone morphology as it relates to shoulder activities. This study investigated how loads corresponding to functional shoulder activities affect the trabecular architecture of the glenoid. Two different protocols were used. Protocol 1 investigated the material and morphological characteristics of the glenoid by analyzing digitized trabecular bone images obtained from 12 cadaver scapula specimens. Protocol 2 used a finite element analysis (FEA) to compute the principal stress trajectories acting within the glenoid. The principal stresses were derived for five loading conditions, which represent typical functional shoulder activities. The study showed that shoulder activity involved in carrying a light load makes the greatest contribution to the trabecular architecture compared with other shoulder activities considered in this study (p<0.05). With all of the activities considered in this study, the lateral region, particularly in the anterior and posterior portions, showed greater deviation and greater sensitivity to variation under loading conditions than did the other regions (p<0.05). These results suggest that owing to the extra sensitivity of the anterior and posterior parts of the lateral region, these regions may be more informative in the analysis of the trabecular architecture following shoulder musculoskeletal injuries. These results may provide essential design information for shoulder prostheses and contribute to an understanding of morphological changes resulting from injury.

The application of topology optimization on the quantitative description of the external shape of bone structure

The aim of this paper was to introduce the idea of topology optimization in engineering to the simulation of bone morphology. The external shape of bone structure was predicted with the quantitative bone functional adaptation theory. The high-order nonlinear equation of bone remodeling proposed by Zhu et al. (J. Biomech. 35(7)(2002)951) combining with the finite element method was adopted to a rectangular design domain, which occupies a larger space than the external shape of bone structure. It was at this point we imported the idea of topology optimization in engineering. The proximal femur was used here as an example, whose external shape and internal density distribution were simultaneously simulated quantitatively to validate that the external shape of bone structure could be successfully predicted in this way. Then the growth of vertebral body from young to old was simulated numerically in its coronal section to discuss the significance of the prediction of external shape. The study in this paper provides computational basis for further studies on osteophyte formation, osteoporosis, osteoarthritis, bone growth and even bone evolution, etc.

How to select the elastic modulus for cancellous bone in patient-specific continuum models of the spine

Patient-specific finite element (FE) modelling is a promising technology that is expected to support clinical assessment of the spine in the near future. To allow rapid, robust and economic patient-specific modelling of the whole spine or of large spine segments, it is practicable to consider vertebral cancellous bone in the spine as a continuum material, but the elastic modulus of that continuum material must reflect the quality of the individual vertebral bone. A numerical parametric model of lattice trabecular architecture has been developed for determining the apparent elastic modulus of cancellous bone Ecb in vertebrae. The model inputs were apparent morphological parameters (trabecular thickness TbTh and trabecular separation TbSp) and the bone mineral density (BMD), which can all be measured in vivo, using the spatial resolution of current clinical quantitative computed tomography (QCT) commercial whole-body scanners. The model predicted that Ecb values between 30 and 110 MPa represent normal morphology and BMD of human spinal cancellous bone. The present Ecb to TbTh, TbSp and BMD relationships pave the way for automatic generation of patient-specific continuum FE spine models that consider the individual's osteoporotic or other degenerative condition of cancellous bone.

Single-trabecula building block for large-scale finite element models of cancellous bone

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) 'building-block' of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of approximately 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of approximately 30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.