Trabecular bone adaptation with an orthotropic material model

Adaptive bone remodeling using orthotropic Cosserat elasticity

The mechanical properties of bone are essential for supporting movement and protecting vital organs. Computational modeling is a key method for studying these properties. While some models address the anisotropic adaptive remodeling of bone, they often rely on classical elasticity theory, which inadequately describes materials with complex microstructures like bone. This study introduces a novel approach by incorporating the Cosserat elasticity theory into the adaptive remodeling framework, overcoming the limitations of classical elasticity. By modeling a proximal femur bone segment as an orthotropic material, we explore how Cosserat elasticity influences bone mechanics. The study also considers the adaptive behavior of the Cosserat parameters in relation to the stiffness modulus, Poisson's ratio, and the internal length scale. Our results indicate that Cosserat elasticity predicts bone behavior with a maximum displacement deviation of 36.33%, showing lower displacements compared to classical elasticity models, particularly at higher internal length scales. Furthermore, the Cosserat model shows a similar but lower average density distribution in the proximal femur, aligning well with existing literature, and more noticeable in localized stress areas. The study extends its analysis to a finite element model of a proximal femur specimen and concludes that the application of the Cosserat theory of elasticity in the context of adaptive bone remodeling yields more accurate results compared to classical elasticity. These findings suggest that the Cosserat theory offers a more realistic approach to bone modeling, particularly for materials where deformation is significantly influenced by microstructure. This advancement has important implications for biomechanics and materials science.

Bone remodeling simulation using spatial influence function in macroscopic cube case

Bone has the capability to adapt its density in response to mechanical stimuli through a process known as bone remodeling, which has been simulated in silico using various algorithms in several studies, with Strain Energy Density (SED) being a commonly used driving parameter. A spatial influence function has been introduced in addition to the remodeling algorithm, which accounts for the influence of neighboring regions on local mechanical stimuli, thereby reducing artificial mesh dependency and mimicking cellular communication in bone. However, no study has implemented the SED-driven algorithm with spatial influence function on a macroscopic 3D bone structure, and there is no physiological explanation on the value used in remodeling parameter. The goal of this study was to assess the effect of the spatial influence function's parameters on the resulting 3D simple cubic structure under compressive loading through a sensitivity analysis. The results demonstrated that the spatial influence function enabled the density distribution to propagate in directions not only aligned with external loads, thus simulating the work of cellular communication. This study also underscores the importance of selecting appropriate parameter values to accurately reflect physiological conditions in bone remodeling simulations, since different parameters influence not only bone mineral density but also the architecture of the resulting bone structure. This work represents a step forward in understanding the interplay between mechanical stimuli and bone remodeling in three dimensions, providing insights that could improve the accuracy of computational models in simulating physiology and pathophysiology.

Mechanobiochemical bone remodelling around an uncemented acetabular component: influence of bone orthotropy

Mechanical loosening of an implant is often caused by bone resorption, owing to stress/strain shielding. Adaptive bone remodelling elucidates the response of bone tissue to alterations in mechanical and biochemical environments. This study aims to propose a novel framework of bone remodelling based on the combined effects of bone orthotropy and mechanobiochemical stimulus. The proposed remodelling framework was employed in the finite element model of an implanted hemipelvis to predict evolutionary changes in bone density and associated orthotropic bone material properties. In order to account for variations in load transfer during common daily activities, several musculoskeletal loading conditions of hip joint corresponding to sitting down/up, stairs ascend/descend and normal walking were considered. The bone remodelling predictions were compared with those of isotropic strain energy density (SED)-based, isotropic mechanobiochemical and orthotropic strain-based bone remodelling formulations. Although similar trends of bone resorption were predicted by orthotropic mechanobiochemical (MBC) and orthotropic strain-based models across implanted acetabulum, more volume (10-20%) of bone elements was subjected to bone resorption for the orthotropic MBC model. Higher bone resorption (75-85%) was predicted by the orthotropic strain-based and orthotropic MBC models compared to the isotropic MBC and SED-based models. Higher bone apposition (35-160%) across the implanted acetabulum was predicted by the isotropic MBC model, compared to the SED-based model. The remodelling predictions indicated that a reduction in estrogen level might lead to an increase in bone resorption. The study highlighted the importance of including mechanobiochemical stimulus and bone anisotropy to predict bone remodelling adequately.

Mapping the Spatial Evolution of Proximal Femur Osteoporosis: A Retrospective Cross-Sectional Study Based on CT Scans

Purpose

The purpose of this study was to quantify the modifications occurring in osteoporosis at the level of the human proximal femur throughout the trabecular structure, along with the identification of certain anatomic regions preferentially affected by osteoporosis. Another goal was to map the evolution of the radiodensity of the trabecular bone as osteoporosis progresses to an advanced stage.

Methods

The study included CT scans (right femur) from 51 patients, out of which 40 had various degrees of osteoporosis, but no other local pathology. Ten regions of interest in two orthogonal slices have been identified and the differences in radiodensity as well as their evolution have been statistically analyzed in terms of relative and absolute changes.

Results

A detailed spatial map showing the evolution of osteoporosis was obtained. As osteoporosis evolved, the relative decrease in radiodensity was inversely correlated to the radiodensity of the healthy bone. In particular, the region covering the Ward triangle decreased the most, by an average 61-62% in osteopenia and 101-106% in advanced osteoporosis, while the principal compressive group was affected the least, showing a decrease by an average 14-15% in osteopenia and 29-32% in advanced osteoporosis. The absolute decrease in radiodensity was not correlated to the radiodensity of the healthy bone and was shifted to the inferior-posterior edge of the femur. Inside the femoral head, the upper region was affected the most in absolute terms, while the greater trochanter was less affected than the femoral neck. The maximum metaphyseal cortical bone density was unaffected by the progression of osteoporosis.

Conclusion

Significant differences were noticed in terms of the absolute and relative osteoporotic changes in radiodensity related to different anatomical regions of the human femoral bone. These differences become more pronounced as the disease progresses.

Bone remodelling in implanted proximal femur using topology optimization and parameterized cellular model

The clinical relevance of bone remodelling predictions calls for accurate finite element (FE) modelling of implant-bone structure and musculoskeletal loading conditions. However, simplifications in muscle loading, material properties, has often been used in FE simulations. Bone adaptation induces changes in bone apparent density and its microstructure. Multiscale simulations, involving optimization methods and biomimetic microstructural models, have proven to be promising for predicting changes in bone morphology. The objective of the study is to develop a novel computational framework to predict bone remodelling around an uncemented femoral implant, using multiscale topology optimization and a parameterized cellular model. The efficacy of the scheme was evaluated by comparing the remodelling predictions with those of isotropic strain energy density (SED) and orthotropy based formulations. The characteristic functional groups and low-density regions of Ward's triangle, predicted by the optimization scheme, were comparable to micro-CT images of the proximal femur. Although the optimization scheme predicted well comparable material distribution in the 2D femur models, the obscured material orientations in some planes of the 3D model indicate the need for a more robust modelling of the boundary conditions. Regression analysis revealed a higher correlation (0.6472) between the topology optimization and SED models than the orthotropic predictions (0.4219). Despite higher bone apposition of 10-20% around the distal tip of the implant, the bone density distributions were well comparable to clinical observations towards the proximal femur. The proposed computational scheme appears to be a viable method for including bone anisotropy in the remodelling formulation.

Modeling the musculoskeletal loading in bone remodeling at the hip of a child

BACKGROUND AND OBJECTIVES

The mechanical load associated with physical activity affects the bone adaptation process. The bone adaptationeffect varies with age, being more effective during childhood and adolescence, particularly during pre-pubertal years. Bone-strengthening physical activity is recommended for children and adolescents. The number of time periods (bouts) per day of vigorous physical activity seems to be more important than the total cumulative time for optimal bone strength. So, the aim of this study was to evaluate the effects of weight-bearing physical activity on bone mineral density (BMD) of the proximal femur through computational simulation considering the intensity, exposure time (bouts) and regionalization of the results.

METHODS

For this purpose, a finite element model of a 7 year-old child femur was developed based on computed tomography images. Musculoskeletal loads were obtained from experimental kinematic data of weight-bearing physical activity performed by children of the same age (standing, walking, running, jumping). The effects of physical activity on BMD of several regions of interest of the femur were analyzed using a bone remodeling model. A daily accumulation of 400 min of physical activity (200 min walking and 200 min standing) was considered as reference, against with which the effects of additional 10 min loading bouts were compared: 10 min bouts of vigorous intensity physical activity vs. 10 min bouts of light to moderate intensity physical activity.

RESULTS

The simulations revealed greater increases in BMD associated with higher intensity and longer duration of physical activity. The largest BMD increases occurs during the first 10 min bout compared to longer durations and in less mineralized central regions compared to regions far from the neutral axis of the bone.

CONCLUSION

Weight bearing physical activity is more effective in bone remodeling when the musculoskeletal loading is more intense and of short duration and, under these conditions, less mineralized regions are more positively impacted.

Orthotropic bone remodelling around uncemented femoral implant: a comparison with isotropic formulation

Peri-prosthetic bone adaptation has usually been predicted using subject-specific finite element analysis in combination with remodelling algorithms and assuming isotropic bone material property. The objective of the study is to develop an orthotropic bone remodelling algorithm for evaluation of peri-prosthetic bone adaptation in the uncemented implanted femur. The simulations considered loading conditions from a variety of daily activities. The orthotropic algorithm was tested on 2D and 3D models of the intact femur for verification of predicted results. The predicted orthotropic directionality, based on principal stress directions, was in agreement with the trabecular orientation in a micro-CT data of proximal femur. The validity of the proposed strain-based algorithm was assessed by comparing the predicted results of the orthotropic model with those of the strain-energy-density-based isotropic formulation. Despite agreement in cortical densities [Formula: see text], the isotropic remodelling algorithm tends to predict relatively higher values around the distal tip of the implant as compared to the orthotropic model. Both formulations predicted 4-8% bone resorption in the proximal femur. A linear regression analysis revealed a significant correlation [Formula: see text] between the stresses and strains on the cortex of the proximal femur, predicted by the isotropic and orthotropic formulations. Despite reasonable agreement in peri-prosthetic bone density distributions, the quantitative differences with isotropic model predictions highlight the combined influences of bone orthotropy and mechanical stimulus in the adaptation process.

Trabecular organization of the proximal femur in Paranthropus robustus: Implications for the assessment of its hip joint loading conditions

Reconstruction of the locomotor repertoire of the australopiths (Australopithecus and Paranthropus) has progressively integrated information from the mechanosensitive internal structure of the appendicular skeleton. Recent investigations showed that the arrangement of the trabecular network at the femoral head center is biomechanically compatible with the pattern of cortical bone distribution across the neck, both suggesting a full commitment to bipedalism in australopiths, but associated with a slightly altered gait kinematics compared to Homo involving more lateral deviation of the body center of mass over the stance limb. To provide a global picture in Paranthropus robustus of the trabecular architecture of the proximal femur across the head, neck and greater trochanter compartments, we applied techniques of virtual imaging to the variably preserved Early Pleistocene specimens SK 82, SK 97, SK 3121, SKW 19 and SWT1/LB-2 from the cave site of Swartkrans, South Africa. We also assessed the coherence between the structural signals from the center of the head and those from the trabecular network of the inferolateral portion of the head and the inferior margin of the neck, sampling the so-called vertical bundle, which in humans represents the principal compressive system of the joint. Our analyses show a functionally related trabecular organization in Pa. robustus that closely resembles the extant human condition, but which also includes some specificities in local textural arrangement. The network of the inferolateral portion of the head shows a humanlike degree of anisotropy and a bone volume fraction intermediate between the extant human and the African ape patterns. These results suggest slight differences in gait kinematics between Pa. robustus and extant humans. The neck portion of the vertical bundle revealed a less biomechanically sensitive signal. Future investigations on the australopith hip joint loading environment should more carefully investigate the trabecular structure of the trochanteric region and possible structural covariation between cortical bone distribution across the neck and site-specific trabecular properties of the arcuate bundle.

BONE ORTHOTROPIC REMODELING AS A THERMODYNAMICALLY-DRIVEN EVOLUTION

In this paper, we present and discuss a model of bone remodeling set up in the framework of the theory of generalized continuum mechanics which was first introduced by DiCarlo et al. [Sur le remodelage des tissus osseux anisotropes, Comptes Rendus Mécanique 334(11):651–661, 2006]. Bone is described as an orthotropic body experiencing remodeling as a rotation of its microstructure. Thus, the complete kinematic description of a material point is provided by its position in space and a rotation tensor describing the orientation of its microstructure. Material motion is driven by energetic considerations, namely by the application of the Clausius–Duhem inequality to the microstructured material. Within this framework of orthotropic remodeling, some key features of the remodeling equilibrium configurations are deduced in the case of homogeneous strain or stress loading conditions. First, it is shown that remodeling equilibrium configurations correspond to energy extrema. Second, stability of the remodeling equilibrium configurations is assessed in terms of the local convexity of the strain and complementary energy functionals hence recovering some classical energy theorems. Eventually, it is shown that the remodeling equilibrium configurations are not only highly dependent on the loading conditions, but also on the material properties.

Numerical Analysis of the Biomechanical Behavior for both Kinds of Dental Structures

The aim of the present study is to investigate the comparison between the biomechanical behavior of the dental prosthesis composed of three implants replacing successively the premolar and two molars and the dental bridge located between two implants. Both dental structures were subjected to the same masticatory loading (Corono-apical, Linguo-buccal and Disto- mesial). Three-dimensional finite element models of dental structures were developed to determine the stress distribution under simulated applied loads. In this study the biomechanical behavior of prosthetics dental crowns subjected to static loads in contact with the jawbone has been highlighted. Biomechanical simulations indicated that the equivalent stresses in the dental bridge are greater than that produced in the dental prosthesis. The dental bridge can be assimilated to a beam at the embedded ends, subjected to the bending.

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.

Cancellous bone and theropod dinosaur locomotion. Part II-a new approach to inferring posture and locomotor biomechanics in extinct tetrapod vertebrates

This paper is the second of a three-part series that investigates the architecture of cancellous 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 therefore has the potential to provide insight into locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part II, a new biomechanical modelling approach is outlined, one which mechanistically links cancellous bone architectural patterns with three-dimensional musculoskeletal and finite element modelling of the hindlimb. In particular, the architecture of cancellous bone is used to derive a single 'characteristic posture' for a given species-one in which bone continuum-level principal stresses best align with cancellous bone fabric-and thereby clarify hindlimb locomotor biomechanics. The quasi-static approach was validated for an extant theropod, the chicken, and is shown to provide a good estimate of limb posture at around mid-stance. It also provides reasonable predictions of bone loading mechanics, especially for the proximal hindlimb, and also provides a broadly accurate assessment of muscle recruitment insofar as limb stabilization is concerned. In addition to being useful for better understanding locomotor biomechanics in extant species, the approach hence provides a new avenue by which to analyse, test and refine palaeobiomechanical hypotheses, not just for extinct theropods, but potentially many other extinct tetrapod groups as well.

Validation of Material Algorithms for Femur Remodelling Using Medical Image Data

The aim of this study is the utilization of human medical CT images to quantitatively evaluate two sorts of "error-driven" material algorithms, that is, the isotropic and orthotropic algorithms, for bone remodelling. The bone remodelling simulations were implemented by a combination of the finite element (FE) method and the material algorithms, in which the bone material properties and element axes are determined by both loading amplitudes and daily cycles with different weight factor. The simulation results showed that both algorithms produced realistic distribution in bone amount, when compared with the standard from CT data. Moreover, the simulated L-T ratios (the ratio of longitude modulus to transverse modulus) by the orthotropic algorithm were close to the reported results. This study suggests a role for "error-driven" algorithm in bone material prediction in abnormal mechanical environment and holds promise for optimizing implant design as well as developing countermeasures against bone loss due to weightlessness. Furthermore, the quantified methods used in this study can enhance bone remodelling model by optimizing model parameters to gap the discrepancy between the simulation and real data.

The interplay of stiffness and force anisotropies drives embryo elongation

The morphogenesis of tissues, like the deformation of an object, results from the interplay between their material properties and the mechanical forces exerted on them. The importance of mechanical forces in influencing cell behaviour is widely recognized, whereas the importance of tissue material properties, in particular stiffness, has received much less attention. Using Caenorhabditis elegans as a model, we examine how both aspects contribute to embryonic elongation. Measuring the opening shape of the epidermal actin cortex after laser nano-ablation, we assess the spatiotemporal changes of actomyosin-dependent force and stiffness along the antero-posterior and dorso-ventral axis. Experimental data and analytical modelling show that myosin-II-dependent force anisotropy within the lateral epidermis, and stiffness anisotropy within the fiber-reinforced dorso-ventral epidermis are critical in driving embryonic elongation. Together, our results establish a quantitative link between cortical tension, material properties and morphogenesis of an entire embryo.

DOI:http://dx.doi.org/10.7554/eLife.23866.001

Animals come in all shapes and size, from ants to elephants. In all cases, the tissues and organs in the animal’s body acquire their shape as the animal develops. Cells in developing tissues squeeze themselves or push and pull on one another, and the resulting forces generate the final shape. This process is called morphogenesis and it is often studied in a worm called Caenorhabditis elegans. This worm’s simplicity makes it easy to work with in the laboratory. Yet processes that occur in C. elegans also take place in other animals, including humans, and so the discoveries made using this worm can have far-reaching implications.

As they develop, the embryos of C. elegans transform from a bean-shaped cluster of cells into the characteristic long shape of a worm, with the head at one end and the tail at the other. The force required to power this elongation is provided by the outer layer of cells of the embryo, known as the epidermis. In these cells, motor-like proteins called myosins pull against a mesh-like scaffold within the cell called the actin cytoskeleton; this pulling is thought to squeeze the embryo all around and cause it to grow longer.

Six strips of cells, running from the head to the tail, make up the epidermis of a C. elegans embryo. Myosin is mostly active in two strips of cells that run along the two sides of the embryo. In the strips above and below these strips (in other words, those on the upper and lower sides of the worm), the myosins are much less active. However, it is not fully understood how this distribution of myosin causes worms to elongate only along the head-to-tail axis.

Vuong-Brender et al. have now mapped the forces exerted in the cells of the worm’s epidermis. The experiments show that, in the strips of cells on the sides of the embryo, myosin’s activity causes the epidermis to constrict around the embryo, akin to a boa constrictor tightening around its prey. At the same time, the actin filaments in the other strips form rigid bundles oriented along the circumference that stiffen the cells in these strips. This prevents the constriction from causing the embryo to inflate at the top and bottom strips. As such, the only direction the embryo can expand is along the axis that runs from its head to its tail.

Together, these findings suggest that a combination of oriented force and stiffness ensure that the embryo only elongates along the head-to-tail axis. The next step is to understand how this orientation and the coordination between cells are controlled at the molecular level.

DOI:http://dx.doi.org/10.7554/eLife.23866.002

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone's material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur's volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.

Effects of Different Loading Patterns on the Trabecular Bone Morphology of the Proximal Femur Using Adaptive Bone Remodeling

In this study, the changes in the bone density of human femur model as a result of different loadings were investigated. The model initially consisted of a solid shell representing cortical bone encompassing a cubical network of interconnected rods representing trabecular bone. A computationally efficient program was developed that iteratively changed the structure of trabecular bone by keeping the local stress in the structure within a defined stress range. The stress was controlled by either enhancing existing beam elements or removing beams from the initial trabecular frame structure. Analyses were performed for two cases of homogenous isotropic and transversely isotropic beams. Trabecular bone structure was obtained for three load cases: walking, stair climbing and stumbling without falling. The results indicate that trabecular bone tissue material properties do not have a significant effect on the converged structure of trabecular bone. In addition, as the magnitude of the loads increase, the internal structure becomes denser in critical zones. Loading associated with the stumbling results in the highest density; whereas walking, considered as a routine daily activity, results in the least internal density in different regions. Furthermore, bone volume fraction at the critical regions of the converged structure is in good agreement with previously measured data obtained from combinations of dual X-ray absorptiometry (DXA) and computed tomography (CT). The results indicate that the converged bone architecture consisting of rods and plates are consistent with the natural bone morphology of the femur. The proposed model shows a promising means to understand the effects of different individual loading patterns on the bone density.

Quantification of trabecular spatial orientation from low-resolution images

No accepted methodology exists to assess trabecular bone orientation from clinical CT scans. The aim of this study was to test the hypothesis that the distribution of grey values in clinical CT images is related to the underlying trabecular architecture and that this distribution can be used to identify the principal directions and local anisotropy of trabecular bone. Fourteen trabecular bone samples were extracted from high-resolution (30 μm) micro-CT scans of seven human femoral heads. Trabecular orientations and local anisotropy were calculated using grey-level deviation (GLD), a novel method providing a measure of the three-dimensional distribution of image grey values. This was repeated for different image resolutions down to 300 μm and for volumes of interest (VOIs) ranging from 1 to 7 mm. Outcomes were compared with the principal mechanical directions and with mean intercept length (MIL) as calculated for the segmented 30-μm images. For the 30-μm images, GLD predicted the mechanical principal directions equally well as MIL. For the 300-μm images, which are resolutions that can be obtained in vivo using clinical CT, only a small increase (3°-6°) in the deviation from the mechanical orientations was found. VOIs of 5 mm resulted in a robust quantification of the orientation. We conclude that GLD can quantify structural bone parameters from low-resolution CT images.

Assessment of risk of femoral neck fracture with radiographic texture parameters: a retrospective study

PURPOSE

To investigate whether femoral neck fracture can be predicted retrospectively on the basis of clinical radiographs by using the combined analysis of bone geometry, textural analysis of trabecular bone, and bone mineral density (BMD).

MATERIALS AND METHODS

Formal ethics committee approval was obtained for the study, and all participants gave informed written consent. Pelvic radiographs and proximal femur BMD measurements were obtained in 53 women aged 79-82 years in 2006. By 2012, 10 of these patients had experienced a low-impact femoral neck fracture. A Laplacian-based semiautomatic custom algorithm was applied to the radiographs to calculate the texture parameters along the trabecular fibers in the lower neck area for all subjects. Intra- and interobserver reproducibility was calculated by using the root mean square average coefficient of variation to evaluate the robustness of the method.

RESULTS

The best predictors of hip fracture were entropy (P = .007; reproducibility coefficient of variation < 1%), the neck-shaft angle (NSA) (P = .017), and the BMD (P = .13). For prediction of fracture, the area under the receiver operating characteristic curve was 0.753 for entropy, 0.608 for femoral neck BMD, and 0.698 for NSA. The area increased to 0.816 when entropy and NSA were combined and to 0.902 when entropy, NSA, and BMD were combined.

CONCLUSION

Textural analysis of pelvic radiographs enables discrimination of patients at risk for femoral neck fracture, and our results show the potential of this conventional imaging method to yield better prediction than that achieved with dual-energy x-ray absorptiometry-based BMD. The combination of the entropy parameter with NSA and BMD can further enhance predictive accuracy.

Trabecular homogeneity index derived from plain radiograph to evaluate bone quality

Radiographic texture analysis has been developed lately to improve the assessment of bone architecture as a determinant of bone quality. We validate here an algorithm for the evaluation of trabecular homogeneity index (HI) in the proximal femur from hip radiographs, with a focus on the impact of the principal compressive system of the trabecular bone, and evaluate its correlation with femoral strength, bone mineral density (BMD), and volumetric trabecular structure parameters. A semiautomatic custom-made algorithm was applied to calculate the HI in the femoral neck and trochanteric areas from radiographs of 178 femoral bone specimens (mean age 79.3 ± 10.4 years). Corresponding neck region was selected in CT scans to calculate volumetric parameters of trabecular structure. The site-specific BMDs were assessed from dual-energy X-ray absorptiometry (DXA), and the femoral strength was experimentally tested in side-impact configuration. Regression analysis was performed between the HI and biomechanical femoral strength, BMD, and volumetric parameters. The correlation between HI and failure load was R(2)  = 0.50; this result was improved to R(2)  = 0.58 for cervical fractures alone. The discrimination of bones with high risk of fractures (load <3000 N) was similar for HI and BMD (AUC = 0.87). Regression analysis between the HIs versus site-specific BMDs yielded R(2)  = 0.66 in neck area, R(2)  = 0.60 in trochanteric area, and an overall of R(2)  = 0.66 for the total hip. Neck HI and BMD correlated significantly with volumetric structure parameters. We present here a method to assess HI that can explain 50% of an experimental failure load and determines bones with high fracture risk with similar accuracy as BMD. The HI also had good correlation with DXA and computed tomography-derived data.

Numerical simulation of dental bone remodeling induced by implant-supported fixed partial denture with or without cantilever extension

The current study aims to evaluate and compare the bony biomechanical response and possible long-term restorative consequences stemming from the use of two-unit fixed partial dentures (FPDs) with or without cantilever configuration. The numerical simulations of bone remodeling were performed using an adaptive strain energy density algorithm, which incorporates an overloading bone resorption process. A patient specific 3D finite element model of a maxillary bone with two absent central incisors was constructed on the basis of clinical computed tomography data. Two different implant-supported two-unit FPD models were developed. The simulated remodeling results were visualized by examining the variation of apparent bone density. Different bone responses under normal and overload conditions were compared quantitatively and qualitatively between the cantilever and non-cantilever models. The mechanical stress/strain distributions were also examined. Furthermore, the simulation results were compared with a similar clinical X-ray image of the implant site. This study revealed that bone resorption due to overloading was more severe in the cortical neck around the implant-supported cantilever FPD, as compared with the non-cantilever configuration, which is better for maintaining the overall health of bone tissue. It is expected that such simulation methodology can be helpful in improving longevity and reliability of future dental implants.

Some factors that affect the comparison between isotropic and orthotropic inhomogeneous finite element material models of femur

The objective of this study was to investigate whether there were significant differences between isotropic and orthotropic inhomogeneous material models of femur by taking into account the effects of some factors, such as comparative parameters, loading conditions and mesh refinement. Three femoral meshes of increasing refinement levels were assigned isotropic and orthotropic material properties. Then six different loading conditions were separately applied to each material model. Based on the analysis results of Von Mises stress and nodal displacement, eight regions of interest in femur were selected to compare the differences between isotropic and orthotropic material models. The results showed that marked differences for Von Mises stress (maximum 13.25%) and nodal displacement (maximum 15.04%) appeared in the regions where the maximum absolute Von Mises stress and the maximum absolute nodal displacement did not occur. It was observed that the comparison results were significantly different under different loading cases. The mesh refinement had a great influence on the comparison results, especially for the Von Mises stresses in the regions of the femoral neck. Therefore, it can be concluded that the differences between two material property assignments are significant, at least in some local regions.

The effects of the spatial influence function on orthotropic femur remodelling

The morphology and internal structure of bone are modulated by the mechanical stimulus. The osteocytes can sense the stimulus signals from the adjacent regions and respond to them through bone growth or bone absorption. This mechanism can be modelled as the spatial influence function (SIF) in bone adaptation algorithm. In this paper, the remodelling process was simulated in human femurs using an adaptation algorithm with and without SIF, and the trabecular bone was assumed to be orthotropic. A different influence radius and weighting factor were adopted to study the effects of the SIF on the bone density distribution and trabecular alignment. The results have shown that the mean density and L—T ratio (the ratio of longitudinal modulus to transverse modulus) had an excellent linear relationship with the weighting factor when the influence radius was small. The characteristics of density distribution and L—T ratio accorded with the actual observation or measurement when a small weighting factor was used. The large influence radius and weighting factor led to unrealistic results. In contrast, the SIF hardly affected the trabecular alignment, as the mean variation angles of principal axes were less than 1.0 degree for any influence radius and weighting factor

Inhomogeneity of tissue-level strain distributions in individual trabeculae: Mathematical model studies of normal and osteoporosis cases

Little is known about the distributions of mechanical strains and stresses in individual trabeculae of cancellous bone, despite evidence that tissue-level strains affect the metabolism of bone. Recently, micro-finite element (micro-FE) studies have provided the first insights into the mechanical conditions in trabeculae, and suggested that osteoporotic cancellous bone experience higher and substantially less-uniform strains with respect to healthy cancellous bone. We may therefore ask whether the inhomogeneity of bone tissue strains is predominantly a consequence of micro-architectural differences between trabeculae, or is it mostly caused by the curvatures of each individual trabecula. Accordingly, the objectives of the present study were to determine the contribution of the shape of a trabecula to the intra-trabecula strain inhomogeneity, and to determine potential differences in intra-trabecula strain inhomogeneities between normal and thinner, osteoporotic-like trabeculae. We employed our previously reported generic single-trabecula model, which is a mathematical representation of the shape of a trabecula based on statistical analyses of mammalian trabecular dimensions. The single-trabecula model was loaded axially and in bending, and strain distributions were calculated for individual trabeculae as well as for "populations" of trabeculae, formed by assigning different trabecular thickness values in the trabecular model, in order to represent the distributions of trabecular shapes in normal and osteoporotic bones. We found that when subjected to equivalent loads, thinner, osteoporotic-like individual trabeculae and populations of thin trabeculae developed substantially greater strain inhomogeneities compared with normal trabeculae. We conclude that the intra-trabecula strain inhomogeneities are likely to be an important factor contributing to the overall increased strain inhomogeneity in osteoporotic cancellous bone, as previously observed in micro-FE studies.

A topology optimization based model of bone adaptation

A novel topology optimization model based on homogenization methods was developed for predicting bone density distribution and anisotropy, assuming the bone structure to be a self-optimizing biological material which maximizes its own structural stiffness. The feasibility and efficiency of this method were tested on a 2D model for a proximal femur under single and multiple loading conditions. The main aim was to compute homogenized optimal designs using an optimal laminated microstructure. The computational results showed that high bone density levels are distributed along the diaphysis and form arching struts within the femoral head. The pattern of bone density distribution and the anisotropic bone behavior predicted by the model in the multiple load case were both in good agreement with the structural architecture and bone density distribution occurring in natural femora. This approach provides a novel means of understanding the remodeling processes involved in fracture repair and the treatment of bone diseases.

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.

Mathematical analysis of trabecular 'trajectories' in apparent trajectorial structures: the unfortunate historical emphasis on the human proximal femur

Wolff's "law" of the functional adaptation of bone is rooted in the trajectory hypothesis of cancellous bone architecture. Wolff often used the human proximal femur as an example of a trajectorial structure (i.e. arched trabecular patterns appear to be aligned along tension/compression stress trajectories). We examined two tenets of the trajectory hypothesis; namely, that the trabecular tracts from the tension- and compression-loaded sides of a bending environment will: (1) follow 'lines' (trajectories) of tension/compression stress that resemble an arch with its apex on a neutral axis, and (2) form orthogonal (90 degrees ) intersections. These predictions were analysed in proximal femora of chimpanzees and modern humans, and in calcanei of sheep and deer. Compared to complex loading of the human femoral neck, the chimpanzee femoral neck reputedly receives relatively simpler loading (i.e. temporally/spatially more consistent bending), and the artiodactyl calcaneus is even more simply loaded in bending. In order to directly consider Wolff's observations, measurements were also made on two-dimensional, cantilevered beams and curved beams, each with intersecting compression/tension stress trajectories. Results in the calcanei showed: (1) the same nonlinear equation best described the dorsal ("compression") and plantar ("tension") trabecular tracts, (2) these tracts could be exactly superimposed on the corresponding compression/tension stress trajectories of the cantilevered beams, and (3) trabecular tracts typically formed orthogonal intersections. In contrast, trabecular tracts in human and chimpanzee femoral necks were non-orthogonal (mean approximately 70 degrees ), with shapes differing from trabecular tracts in calcanei and stress trajectories in the beams. Although often being described by the same equations, the trajectories in the curved beams had lower r(2) values than calcaneal tracts. These results suggest that the trabecular patterns in the calcanei and stress trajectories in short beams are consistent with basic tenets of the trajectory hypothesis while those in human and chimpanzee femoral necks are not. Compared to calcanei, the more complexly loaded human and chimpanzee femoral necks probably receive more prevalent/predominant shear, which is best accommodated by non-orthogonal, asymmetric trabecular tracts. The asymmetrical trabecular patterns in the proximal femora may also reflect the different developmental 'fields' (trochanteric vs. neck/head) that formed these regions, of which there is no parallel in the calcanei.

Quantifying the Directional Parameter of Structural Anisotropy in Porous Media

A new method has been developed to define the directional parameter and characterize the structural anisotropy of a highly porous structure with extensive pore interconnectivity and surface area, such as scaffolds in tissue engineering. This new method called intercept segment deviation (ISD) was validated through the comparison of structural anisotropy from ISD measurements with mechanical anisotropy from finite-element stress analysis. This was carried out on a generated two-dimensional (2D) image of a two-phase material and a real three-dimensional (3D) image of a tissue scaffold. The performance of other methods for quantification of the directional parameter was also assessed. The results indicate that the structural anisotropy obtained from this new method conforms to the actual mechanical anisotropy and provides a better prediction of the material orientation than the other methods for the 2D and 3D images studied.

Elastic properties of external cortical bone in the craniofacial skeleton of the rhesus monkey

Knowledge of elastic properties and of their variation in the cortical bone of the craniofacial skeleton is indispensable for creating accurate finite-element models to explore the biomechanics and adaptation of the skull in primates. In this study, we measured elastic properties of the external cortex of the rhesus monkey craniofacial skeleton, using an ultrasonic technique. Twenty-eight cylindrical cortical specimens were removed from each of six craniofacial skeletons of adult Macaca mulatta. Thickness, density, and a set of longitudinal and transverse ultrasonic velocities were measured on each specimen to allow calculation of the elastic properties in three dimensions, according to equations derived from Newton's second law and Hooke's law. The axes of maximum stiffness were determined by fitting longitudinal velocities measured along the perimeter of each cortical specimen to a sinusoidal function. Results showed significant differences in elastic properties between different functional areas of the rhesus cranium, and that many sites have a consistent orientation of maximum stiffness among specimens. Overall, the cortical bones of the rhesus monkey skull can be modeled as orthotropic in many regions, and as transversely isotropic in some regions, e.g., the supraorbital region. There are differences from human crania, suggesting that structural differences in skeletal form relate to differences in cortical material properties across species. These differences also suggest that we require more comparative data on elastic properties in primate craniofacial skeletons to explore effectively the functional significance of these differences, especially when these differences are elucidated through modeling approaches, such as finite-element modeling.

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.

Comparison of the trabecular architecture and the isostatic stress flow in the human calcaneus

It is a common theory that the architecture of trabecular bone follows the principal stress trajectories, as suggested by Wolff's pioneering studies of the proximal femur. Since first published in the late 19th-century, this observation (popularized as "Wolff's law") has been supported by numerous studies, but nearly all of them have been focused on the femoral head and neck. In this study, the manifestation of Wolff's law in the human calcaneus has been analyzed. For this purpose, finite element (FE) analysis of the entire complex of the foot during standing was undertaken. Orientation of the principal stress flow through the calcaneus was compared with the trabecular alignment in a single cadaveric calcaneal specimen, by fitting second-order polynomials to real trabecular paths and FE-predicted isostatics and calculating their angle of inclination with the calcaneal cortex at their insertion points. Four dominant trabecular patterns were identified in the cadaveric sagittal section of the specimen of the calcaneus: one directed primarily in the dorsal-plantar direction, one aligned anteriorly-posteriorly, and two that are strongly oblique. Subsequent numerical simulations showed that the dorsal-plantar oriented and posterior oblique trabecular paths are aimed to support compressive stresses, while the antero-posteriorly directed and anterior oblique groups act to bear tension. Insertion angles of real trabecular paths into the calcaneal cortex were similar to those of the isostatics that were computed under musculoskeletal loading conditions of standing (maximum absolute local difference 13 degrees, maximum local error 60%). This suggests that the trabecular patterns of the calcaneus are mainly shaped by isostatics (static principal stress flow) that are characteristic of the standing posture. The present modeling approach can be utilized to explore effects of abnormal alterations in the isostatic flow on the microarchitecture of the calcaneal trabeculae, as well as for better understanding of the mechanisms of calcaneal fractures.

A density distribution algorithm for bone incorporating local orthotropy, modal analysis and theories of cellular solids

An algorithm for bone remodeling is presented which allows for both a redistribution of density and a continuous change of principal material directions for the orthotropic material properties of bone. It employs a modal analysis to add density for growth and a local effective strain based analysis to redistribute density. General re-distribution functions are presented. The model utilizes theories of cellular solids to relate density and strength. The code predicts the same general density distributions and local orthotropy as observed in reality.

Linear poroelastic cancellous bone anisotropy: trabecular solid elastic and fluid transport properties

The mechanical performance of cancellous bone is characterized using experiments which apply linear poroelasticity theory. It is hypothesized that the anisotropic organization of the solid and pore volumes of cancellous bone can be physically characterized separately (no deformable boundary interactive effects) within the same bone sample. Due to its spongy construction, the in vivo mechanical function of cancellous or trabecular bone is dependent upon fluid and solid materials which may interact in a hydraulic, convective fashion during functional loading. This project provides insight into the organization of the tissue, ie., the trabecular connectivity, by defining the separate nature of this biphasic performance. Previous fluid flow experiments [Kohles et al., 2001, Journal of Biomechanics, 34(11), pp. 1197-1202] describe the pore space via orthotropic permeability. Ultrasonic wave propagation through the trabecular network is used to describe the solid component via orthotropic elastic moduli and material stiffness coefficients. The linear poroelastic nature of the tissue is further described by relating transport (fluid flow) and elasticity (trabecular load transmission) during regression analysis. In addition, an empirical relationship between permeability and porosity is applied to the collected data. Mean parameters in the superior-inferior (SI) orientation of cubic samples (n=20) harvested from a single bovine distal femur were the largest (p<0.05) in comparison to medial-lateral (ML) and anterior-posterior (AP) orientations: Apparent elastic modulus (2,139 MPa), permeability (4.65x10(-10) m2), and material stiffness coefficient (13.6 GPa). A negative correlation between permeability as a predictor of structural elastic modulus supported a parametric relationship in the ML (R2=0.4793), AP (R2=0.3018), and SI (R2=0.6445) directions (p<0.05).