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Retrocalcaneal exostosis can be debilitating and in severe cases, surgical resection is indicated. Complications can arise from surgical resection of the exostosis and reattachment of the Achilles tendon, including irritation of the suture knot, recurrence of the bony prominence, and dehiscence. The use of a buried knot technique with functional lengthening of the Achilles tendon and gastroc-soleal muscle complex can minimize these complications. Complete detachment of the Achilles tendon allows for aggressive and thorough resection of the exostosis and functional lengthening with reattachment. The buried cruciate knot technique allows for firm reattachment with buried knots to prevent soft tissue irritation. A total of fourteen patients (14 limbs) underwent retrocalcaneal enthesophyte resection with functional Achilles tendon lengthening, (8/14) of which had difficultly wearing shoe gear, (10/14) had edema, and (2/14) had erythema preoperatively. Postoperatively, (11/14) of patients returned to full activities and sports, and (11/14) returned to normal shoe gear. Complications included (1/14) of patients with Achilles tendon avulsion and (3/14) of patients with surgical site dehiscence requiring revisional surgery. Overall, this technique helps prevent short-term complications and long-term recurrence due to the functional lengthening mitigating insertional forces on the Achilles tendon. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to discuss the mechanical function of subchondral bone cysts and its relationship with Wolff's law. Methods: One hundred forty symptomatic knees (120 patients) with osteoarthritis were subjected to MRI before high tibial osteotomy (HTO). Subchondral bone cysts (SBCs) were detected on 72 knees of these 140 knees. SBCs, bone marrow lesion (BML), and hip-knee-ankle (HKA) axis were measured by using validated methods. After HTO, the evolution of cysts was evaluated on MRI performed with a five year follow-up on the 72 knees with pre-operative cysts. Results: At baseline, 70 (97%) of these 72 knees had a BML surrounding the SBCs; the maximum cyst volume was 874 mm3 and the average cyst volume 9. 6 ± 4.1 mm3. In the subregions where cysts were present, adjacent cartilage was still present without full thickness defects. The mean pre-operative hip-knee-ankle angle was 7.3 ± 3 degrees (0° to 14°) of varus and differed significantly (p = 0.01) between the 68 knees without cysts (average 3 ± 2 degrees) and the 72 knees with cysts (average 9.2 ± 4 degrees). Five years after HTO, the number of cysts had decreased, the maximum cyst volume was 532 mm3, and the average cyst volume was 6.3 ± 2.8 mm3. Conclusion: Regression of subchondral bone cysts may be related to restoration of an appropriate load at the subchondral bone. With applying poroelasticity to bone mechaincs, this finding may suggest that SBCs and BMLs may be a physiological adaptation to mechanic overload. More basic research is needed to prove this matter. [ABSTRACT FROM AUTHOR]

BACKGROUND: It is well known that there is a relationship between bone strength and the forces that are daily applied to the bone. However, bone is a highly heterogeneous material and it is still not clear how mechanical variables regulate the distribution of bone mass in a femur. METHODS: We studied the role of four mechanical variables, i.e. principal tensile/compressive stress, von Mises stress, and strain energy density (SED), in the regulation of bone mineral density (BMD) distribution in the human femur. The actual BMD in a femur was extracted from quantitative computed tomography (QCT) and used as a reference for comparison. A finite element model of the femur was constructed from the same set of QCT scans and then used in iterative simulations of femur remodeling under stance and walking loading. The finite element model was initially assigned a homogeneous BMD distribution. During the remodeling, femur BMD was locally modified according to one of the four mechanical variables. The simulations were stopped when BMD change in two consecutive iterations was adequately small. The four simulated BMD patterns were then compared with the actual BMD. RESULTS: It was found that the BMD pattern regulated by SED had the best similarity with the actual BMD. The medullary canal was successfully reproduced by simulated remodeling, indicating that in addition to its biological functions, the medullary canal has important biomechanical functions. CONCLUSIONS: Both the actual and simulated BMD distributions showed that the proximal femur has much lower BMD than the femur shaft, which may explain why hip fractures most often occur at the proximal femur. [ABSTRACT FROM AUTHOR]

Summary: Horses are precocial animals and able to stand and walk within hours after birth. To cope with associated loading, intrauterine bone development has shown to be anticipative. This study provides further insight into the post‐natal development of structurally important features of trabecular and subchondral bone of the talus and sagittal ridge of the tibia of warm‐blooded horses. In all areas studied, the average bone volume fraction showed a gradual increase over time, which was the result of a significant increase in trabecular thickness, without significant changes in the degree of anisotropy. Similar to the mineralised part of the bone, collagen content, measured as average retardation using polarised light microscopy, increased significantly, but the degree of anisotropy of the collagen type I network did not. At birth, the subchondral bone layer had a more trabecular aspect, gradually changing to an even surface with only a few vascular canals at an age of 2 months. Presented results indicate the necessity for a stronger structure, but not for a different structural design after birth, providing further evidence for anticipatory bone development in the horse. More knowledge about the strategies used to cope with mechanical loading after birth might be helpful in understanding the developmental bone and joint diseases. [ABSTRACT FROM AUTHOR]

It was 140 years ago that George von Meyer presented his anatomical diagrams of human bones to a meeting in Zurich. There he was told by Prof. Karl Culmann that the trabecular lines shown within the diagram of the upper femur closely resembled those lines of force which Culmann had determined with Graphic Statics to be passing through a curved, loaded Fairbairn crane. This drew the attention of Julius Wolff, who used this as the basis for his 'Trajectorial theory' which was widely accepted and, to date, has been the underlying basis for all biomechanical investigations of this region. Following Wolff and Culmann, the upper femur is considered to be a curved structure and is investigated as such. Unfortunately, this concept is wrong. The upper femur is not curved but is angular. It is formed by the junction of two straight bones, the femoral neck and the femoral shaft, as may be simply seen as the neck/shaft angle constructed on the antero-posterior radiograph of any normal femur. The internal trabecular bone forms only part of the load bearing structure of the femoral neck. The configuration of this trabecular substance in this region suggests that it is related specifically to the force present during flexion and extension movements of the hip joint. This being so, combined with the delayed timing of the appearance of the trabecular columns, it must be questioned as to whether the remodelling of the upper femur is in response to one or to two distinct forces. [ABSTRACT FROM AUTHOR]

To understand Wolff's law, bone adaptation by remodeling at the cellular and tissue levels has been discussed extensively through experimental and simulation studies. For the clinical application of a bone remodeling simulation, it is significant to establish a macroscopic model that incorporates clarified microscopic mechanisms. In this study, we proposed novel macroscopic models based on the microscopic mechanism of osteocytic mechanosensing, in which the flow of fluid in the lacuno-canalicular porosity generated by fluid pressure gradients plays an important role, and theoretically evaluated the proposed models, taking biological rationales of bone adaptation into account. The proposed models were categorized into two groups according to whether the remodeling equilibrium state was defined globally or locally, i.e., the global or local uniformity models. Each remodeling stimulus in the proposed models was quantitatively evaluated through image-based finite element analyses of a swine cancellous bone, according to two introduced criteria associated with the trabecular volume and orientation at remodeling equilibrium based on biological rationales. The evaluation suggested that nonuniformity of the mean stress gradient in the local uniformity model, one of the proposed stimuli, has high validity. Furthermore, the adaptive potential of each stimulus was discussed based on spatial distribution of a remodeling stimulus on the trabecular surface. The theoretical consideration of a remodeling stimulus based on biological rationales of bone adaptation would contribute to the establishment of a clinically applicable and reliable simulation model of bone remodeling. [ABSTRACT FROM AUTHOR]

Bone, despite its relatively inert appearance, is a tissue that is capable of adapting to its environment. Wolff’s law, first described in the 19th century, describes the ability of bone to change structure depending on the mechanical forces applied to it. The mechanostat model extended this principle and suggested that the amount of strain a bone detects depends on bone strength and the amount of muscle force applied to the bone. Experimental studies have found that low-magnitude, high-frequency mechanical loading is considered to be the most effective at increasing bone formation. The osteocyte is considered to be the master regulator of the bone response to mechanical loading. Deformation of bone matrix by mechanical loading is thought to result in interstitial fluid flow within the lacunar–canalicular system, which may activate osteocyte mechanosensors, leading to changes in osteocyte gene expression and ultimately increased bone formation and decreased bone resorption. However, repetitive strain applied to bone can result in microcracks, which may propagate and coalesce, and if not repaired predispose to catastrophic fracture. Osteocytes are a key component in this process, whereby apoptotic osteocytes in an area of microdamage promote targeted remodeling of the damaged bone. If fractures do occur, fracture repair can be divided into 2 types: primary and secondary healing. Secondary fracture repair is the most common and is a multistage process consisting of hematoma formation and acute inflammation, callus formation, and finally remodeling, whereby bone may return to its original form. [ABSTRACT FROM AUTHOR]

Trabecular bone is an intricate 3D network of struts and plates. Although the structure-function relations in trabecular bone have been studied since the time of Julius Wolff, controversy still exists regarding the architectural parameters responsible for its stability and resilience. We present a parameter that measures the angle between two connected trabeculae – the Inter-Trabecular Angle (ITA). We studied the ITA values derived from μCT scans of different regions of the proximal femora of 5 individuals of different age and sex. We show that the ITA angle distribution of nodes with 3 connecting trabeculae has a mean close to 120°, nodes with 4 connecting trabeculae has a mean close to 109° and nodes of higher connectivity have mean ITA values around 100°. This tendency to spread the ITAs around geometrically symmetrical motifs is highly conserved. The implication is that the ITAs are optimized such that the smallest amount of material spans the maximal 3D volume, and possibly by so doing trabecular bone might be better adapted to multidirectional loading. We also draw a parallel between trabecular bone and tensegrity structures – where lightweight, resilient and stable tetrahedron-based shapes contribute to strain redistribution amongst all the elements and to collective impact dampening. Statement of Significance The Inter-Trabecular Angle (ITA) is a new topological parameter of trabecular bone. The ITA characterizes the way trabeculae connect with each other at nodes, regardless of their thickness and shape. The mean ITA value of nodes with 3 trabeculae is close to 120°, of nodes with 4 trabeculae is just below 109°, and the mean ITA of nodes with 5 and more trabeculae is around 100°. Thus the connections of trabeculae trend towards adopting symmetrical shapes. This implies that trabeculae can maximally span 3D space using the minimal amount of material. We draw a parallel between this motif and the concept of tensegrity – an engineering premise to which many living creatures conform at multiple levels of organization. [ABSTRACT FROM AUTHOR]

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 1990s, 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. [ABSTRACT FROM AUTHOR]

The upper femur has long held a fascination for both clinicians and bioengineers as it contains two trabecular columns obviously related to its function. In this respect two theories as to the formation of these columns have developed, both associated with Wolff: the Trajectorial Theory, which relates mainly to the passage of forces through the cancellous bone of the upper femur, and Wolff's Law of bone formation, which describes the bone's reaction to these forces and relates to bone in general. The two concepts nevertheless are often used synonymously. The Trajectorial Theory propounds that these cancellous structures in the femoral neck are due to both tension and compression forces, while modern day concepts of Wolff's Law only acknowledge the action of compression forces: and herein lies the paradox. The Trajectorial Theory and Wolff's Law, when applied to the upper femur, are mutually exclusive. The evidence, anatomical and physiological, indicates that bone forms within the femoral neck solely under the influence of compression forces. This would indicate that the Trajectorial Theory is not appropriate for this region. An alternative conceptual way of looking at this region is presented which eliminates this theory and resolves the paradox. [ABSTRACT FROM AUTHOR]

Abstract: In this study, we investigated the scaling relations between trabecular bone volume fraction (BV / TV) and parameters of the trabecular microstructure at different skeletal sites. Cylindrical bone samples with a diameter of 8mm were harvested from different skeletal sites of 154 human donors in vitro: 87 from the distal radius, 59/69 from the thoracic/lumbar spine, 51 from the femoral neck, and 83 from the greater trochanter. μCT images were obtained with an isotropic spatial resolution of 26μm. BV / TV and trabecular microstructure parameters (TbN, TbTh, TbSp, scaling indices (< > and σ of α and αz ), and Minkowski Functionals (Surface, Curvature, Euler)) were computed for each sample. The regression coefficient β was determined for each skeletal site as the slope of a linear fit in the double-logarithmic representations of the correlations of BV / TV versus the respective microstructure parameter. Statistically significant correlation coefficients ranging from r =0.36 to r =0.97 were observed for BV / TV versus microstructure parameters, except for Curvature and Euler. The regression coefficients β were 0.19 to 0.23 (TbN), 0.21 to 0.30 (TbTh), −0.28 to −0.24 (TbSp), 0.58 to 0.71 (Surface) and 0.12 to 0.16 (<α>), 0.07 to 0.11 (<αz >), −0.44 to −0.30 (σ(α)), and −0.39 to −0.14 (σ(αz )) at the different skeletal sites. The 95% confidence intervals of β overlapped for almost all microstructure parameters at the different skeletal sites. The scaling relations were independent of vertebral fracture status and similar for subjects aged 60–69, 70–79, and >79years. In conclusion, the bone volume fraction–microstructure scaling relations showed a rather universal character. [Copyright &y& Elsevier]

Abstract: For over a century, the arched trabecular patterns of the human proximal femur have been considered to resemble tension and compression stress trajectories produced by stereotypical bending loads. This reflects conventional modeling of the human femoral neck–head region as a short cantilevered beam. Although this conception is the foundation of many biomechanical, clinical, paleontological, and comparative morphological studies of trabecular bone in various species, attempts have not been made to contrast these data to a bone that could be considered a ‘control’ for simple/stereotypical bending. We quantified trabecular architectural characteristics in sheep and deer calcanei as a first step in potentially establishing them as ‘controls’ in this context because they have arched trabecular patterns that resemble tension/compression stress trajectories, and have been shown by strain gauge measurements to be relatively simply loaded in bending. Using micro-computed tomography, calcanei from adult domesticated sheep and wild deer were analyzed where in the dorsal ‘compression’ and plantar ‘tension’ trabecular tracts they begin to separate and bending is less complex (mid-shaft), and where trabeculae extensively interconnect and loading is more complex (distal shaft). Of the eight trabecular architectural characteristics evaluated, only one (trabecular number, Tb.N) showed a probable mechanically relevant dorsal/plantar difference. However, this was paradoxically opposite in the sheep calcanei. Aside from Tb.N, the architectural characteristics showed little, if any, evidence of habitual bending. The non-uniformity of the stresses between the trabecular tracts in these bones might be reduced by load-sharing functions of their robust cortices and the nearby ligament and tendon, which might account for the similar morphologies between the tracts. These findings may help to explain why in many cases regional trabecular architectural variations seem to lack sufficient sensitivity and specificity for interpreting habitual bending in other bone regions. This cautions against simple interpretations of trabecular bone adaptation in the anthropoid femoral neck. [Copyright &y& Elsevier]

Background: Talpids include forms with different degree of fossoriality, with major specializations in the humerus in the case of the fully fossorial moles. We studied the humeral microanatomy of eleven extant and eight extinct talpid taxa of different lifestyles and of two non-fossorial outgroups and examined the effects of size and phylogeny. We tested the hypothesis that bone microanatomy is different in highly derived humeri of fossorial taxa than in terrestrial and semi-aquatic ones, likely due to special mechanical strains to which they are exposed to during digging. This study is the first comprehensive examination of histological parameters in an ecologically diverse and small-sized mammalian clade. Results: No pattern of global bone compactness was found in the humeri of talpids that could be related to biomechanical specialization, phylogeny or size. The transition zone from the medullary cavity to the cortical compacta was larger and the ellipse ratio smaller in fossorial talpids than in non-fossorial talpids. No differences were detected between the two distantly related fossorial clades, Talpini and Scalopini. Conclusions: At this small size, the overall morphology of the humerus plays a predominant role in absorbing the load, and microanatomical features such as an increase in bone compactness are less important, perhaps due to insufficient gravitational effects. The ellipse ratio of bone compactness shows relatively high intraspecific variation, and therefore predictions from this ratio based on single specimens are invalid. [ABSTRACT FROM AUTHOR]

In this study, a computational model of bone remodelling problem as proposed by Weinans et al. (1992) is described and solved by other temporal integration techniques different from the Euler scheme. This model considers three types of numerical integration schemes of the evolution of the material density during the remodelling: Euler, Heun and Runge–Kutta methods. Also the strain and the density field are obtained inside each element, at Gauss points or at the nodes of the mesh. A square plate with 1.00 m of side subjected to non-uniform pressure is simulated with two meshes of quadrilateral element with size and  m. Two increments time size: and days are used. The results show that Euler, Heun and Runge–Kutta's methods correctly approached the problem of bone remodelling and that there were no appreciable differences in the patterns obtained by the mesh and time step used. In contrast, using an element-based approach and node-based approach, substantial differences were produced in bone remodelling density pattern. ‘Chess board’ type discontinuities were found in the element approach near the applied pressure area, as were well-defined columns away from this. The node-based approach showed continuity in density distribution. These patterns were well represented by the methods for resolving the density equation. This study concluded that any method of time integration could be used for these meshes and time steps size. [ABSTRACT FROM AUTHOR]

Abstract: This study tested the hypothesis that talar trabecular microarchitecture reflects the loading patterns in the primate ankle joint, to determine whether talar trabecular morphology might be useful for inferring locomotor behavior in fossil hominins. Trabecular microarchitecture was quantified in the anteromedial, anterolateral, posteromedial, and posterolateral quadrants of the talar body in humans and non-human primates using micro-computed tomography. Trabecular bone parameters, including bone volume fraction, trabecular number and thickness, and degree of anisotropy differed between primates, but not in a manner entirely consistent with hypotheses derived from locomotor kinematics. Humans have highly organized trabecular struts across the entirety of the talus, consistent with the compressive loads incurred during bipedal walking. Chimpanzees possess a high bone volume fraction, consisting of plate-like trabecular struts. Orangutan tali are filled with a high number of thin, connected trabeculae, particularly in the anterior portion of the talus. Gorillas and baboons have strikingly similar internal architecture of the talus. Intraspecific analyses revealed no regional differences in trabecular architecture unique to bipedal humans. Of the 22 statistically significant regional differences in the human talus, all can also be found in other primates. Trabecular thickness, number, spacing, and connectivity density had the same regional relationship in the talus of humans, chimpanzees, gorillas, and baboons, suggesting a deeply conserved architecture in the primate talus. Australopithecus tali are human-like in most respects, differing most notably in having more oriented struts in the posteromedial quadrant of the body compared with the posterolateral quadrant. Though this result could mean that australopiths loaded their ankles in a unique manner during bipedal gait, the regional variation in degree of anisotropy was similar in humans, chimpanzees, and gorillas. These results collectively suggest that the microarchitecture of the talus does not simply reflect the loading environment, limiting its utility in reconstructing locomotion in fossil primates. [Copyright &y& Elsevier]

Abstract: Most work done on bone simulation has modeled the tissue as inhomogeneous and isotropic even though it is a recognized anisotropic material. Some recent investigations have included orthotropic behavior in bone finite elements (FE) models; however the problem regarding the orientation of these properties along the irregular bone anatomy remains. In this work, a procedure to orientate orthotropic properties in a proximal femur FE model using the directions of the principal stresses produced by a physiological load scheme was developed. Two heterogeneous material models, one isotropic and one orthotropic, were employed to test their influence on the mechanical behavior of the bone model. In the developed orthotropic material, the mechanical properties are aligned with the highest principal stress produced from the successive application of a multi load scenario corresponding to 10%, 30% and 45% of the gait cycle. A solid match between anatomical structures in the proximal femur and the corresponding directions of the main principal stress of the elements of the model suggests that the developed methodology works accurately. The differences found in the stress distributions were small (maximum 7.6%); nevertheless the changes in the strain distributions were important (maximum 27%) and located in areas of clinical relevance. [Copyright &y& Elsevier]

Abstract: This study tests Wolff''s law of trabecular bone adaptation by examining if induced changes in joint loading orientation cause corresponding adjustments in trabecular orientation. Two groups of sheep were exercised at a trot, 15min/day for 34days on an inclined (7°) or level (0°) treadmills. Incline trotting caused the sheep to extend their tarsal joints by 3–4.5° during peak loading (P<0.01) but has no effect on carpal joint angle (P=0.984). Additionally, tarsal joint angle in the incline group sheep were maintained more extended throughout the day using elevated platform shoes on their forelimbs. A third “sedentary group” group did not run but wore platform shoes throughout the day. As predicted by Wolff''s law, trabecular orientation in the distal tibia (tarsal joint) were more obtuse by 2.7 to 4.3° in the incline group compared to the level group; trabecular orientation was not significantly different in the sedentary and level groups. In addition, trabecular orientations in the distal radius (carpal joint) of the sedentary, level and incline groups did not differ between groups, and were aligned almost parallel to the radius long axis, corresponding to the almost straight carpal joint angle at peak loading. Measurements of other trabecular bone parameters revealed additional responses to loading, including significantly higher bone volume fraction (BV/TV), Trabecular number (Tb.N) and trabecular thickness (Tb.Th), lower trabecular spacing (Tb.Sp), and less rod-shaped trabeculae (higher structure model index, SMI) in the exercised than sedentary sheep. Overall, these results demonstrate that trabecular bone dynamically adjusts and realigns itself in very precise relation to changes in peak loading direction, indicating that Wolff''s law is not only accurate but also highly sensitive. [Copyright &y& Elsevier]

Abstract: The law of bone remodeling, commonly referred to as Wolff''s Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. The goal of the current study was to utilize an advanced structural optimization algorithm, called design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff''s hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The result is a “fully stressed” structure with minimized compliance and increased stiffness. The large-scale computational simulation utilized a 175μm mesh resolution and the routine daily loading activities of walking and stair climbing. The resulting anisotropic trabecular architecture was compared to both Wolff''s trajectory hypothesis and natural femur samples from literature using a variety of visualization techniques, including radiography and computed tomography (CT). The results qualitatively revealed several anisotropic trabecular regions, that were comparable to the natural human femurs. Quantitatively, the various regional bone volume fractions from the computational results were consistent with quantitative CT analyses. The global strain energy proceeded to become more uniform during optimization; implying increased mechanical efficiency was achieved. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as the Wolff hypothesized. [Copyright &y& Elsevier]

Abstract: Because bone tissue adapts to loading conditions, finite element simulations of remodelling bone require a precise prediction of dynamically changing anisotropic elastic parameters. We present a phenomenological theory that refers to the tissue in terms of the tendency of the structure to align with principal stress directions. We describe the material parameters of remodelling bone. This work follows findings by the same research group and independently by in the field of plasticity, where the dependencies of the components of the stiffness tensor in terms of time are based on Hill’s anisotropy. We modify such an approach in this novel theory that addresses bone tissue that can regenerate. The computational assumption of the theory is that bone trabeculae have the tendency to orient along one of the principal stress directions but during remodelling the principal stresses change continuously and the resulting orientation of the trabeculae can differ from the principal stress direction at any given time. The novelty of this work consists in the limited number of parameters needed to compute the twenty-one anisotropic material parameters at any given location in the bone tissue. In addition to the theory, we present here two cases of simplified geometry, loading and boundary conditions to show the effect of (1) time on the material properties; and (2) change of loading conditions on the anisotropic parameters. The long term goal is to experimentally verify that the predictions generated by theory provide a reliable simulation of cancellous bone properties. [ABSTRACT FROM AUTHOR]

Background: Scoliosis with vertebral wedging is thought to be caused by asymmetric growth (Hueter-Volkmann law), but vertebral diaphyseal remodeling (Wolff's law) may also contribute to the deformity. We investigated whether vertebral wedging in scoliosis might involve both mechanisms. Methods: An external fixator was used to impose a 30° scoliosis and compression of 0.1 or 0.2 MPa to the tails of 10 5-week-old and 20 14-week-old Sprague-Dawley rats for 6 weeks. The rats were divided into three groups of 10 animals each: Group 1: 5-week-old animals with 0.1 MPa compression; Group 2: 14-week-old animals with 0.1 MPa compression; Group 3: 14-week-old animals with 0.2 MPa compression. Vertebral wedging and diaphyseal curvature were measured from micro CT scans performed at weeks 1, 3, and 6. Wedging due to asymmetrical growth and remodeling was calculated from a Calcein label administered at week 3 and a Xylenol label at week 6. Results: The growth rate of the loaded vertebrae as a per cent of control vertebrae was 60% in Group 1, 40% in Group 2, and 30% in Group 3. The growth rate of control vertebrae in 14-week-old animals was 16% that of 5-week-old animals. The animals in all 3 groups developed a scoliosis with vertebral wedging that averaged 18.7° in Group 1, 8.2° in Group 2, and 10.1° in Group 3. Asymmetric growth was much greater in Group 1 (5-week-old) animals. The ossified epiphyses became wedged and diaphyseal remodeling occurred in all groups. Conclusions: The major contribution to the vertebral wedging was asymmetric growth in the 5-week-old animals and diaphyseal remodeling in the 14-week-old animals. The results support the concept that if appropriate loads can be applied to human vertebrae through minimally invasive techniques, scoliosis and vertebral wedging can be corrected without a spinal fusion in both adolescents and adults. [ABSTRACT FROM AUTHOR]

Abstract: 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 (∼10μm) remodeling in response to mechanical stimulation created complex 3D trabecular structures of the entire bone-scale (∼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 104 length scale (from ∼10μm to ∼10cm), a simple remodeling at the cellular/trabecular levels creates a highly complex and functional trabecular structure, as characterized by bone density and orientation. [Copyright &y& Elsevier]

Abstract: In the field of bone adaptation, it is believed that the morphology of bone is affected by its mechanical loads, and bone has self-optimizing capability; this phenomenon is well known as Wolff''s law of the transformation of bone. In this paper, we simulated trabecular bone adaptation in the human proximal femur using topology optimization and quantitatively investigated the validity of Wolff''s law. Topology optimization iteratively distributes material in a design domain producing optimal layout or configuration, and it has been widely and successfully used in many engineering fields. We used a two-dimensional micro-FE model with 50μm pixel resolution to represent the full trabecular architecture in the proximal femur, and performed topology optimization to study the trabecular morphological changes under three loading cases in daily activities. The simulation results were compared to the actual trabecular architecture in previous experimental studies. We discovered that there are strong similarities in trabecular patterns between the computational results and observed data in the literature. The results showed that the strain energy distribution of the trabecular architecture became more uniform during the optimization; from the viewpoint of structural topology optimization, this bone morphology may be considered as an optimal structure. We also showed that the non-orthogonal intersections were constructed to support daily activity loadings in the sense of optimization, as opposed to Wolff''s drawing. [Copyright &y& Elsevier]

The topology optimization of geometrical nonlinear and linear elastic continuum structures is investigated by the bionics method based on Wolff s Law in biomechanics. In the present approach, the design variable is called as fabric tensor, which is introduced to express both of geometry of the microstructure and the elasticity properties of a material point in the design domain. Simultaneously, the interval of reference strain for the structure is adopted and is applied to renew the fabric tensor of a point together with Wolff s Law. The mesh-dependence of optimal topology of a structure and the influences of the interval of reference strain on the optimal topology are investigated. By numerical examples, several conclusions are drawn as follows: Firstly, the optimal topology of a structure is not dependent on the mesh-refine. Secondly, the optimal topology of a structure with geometric nonlinearity obviously depends on the specified interval of reference strain. Thirdly, if the length of the interval of reference strain equals to zero and the loading conditions are specified displacements on structure, then changing the superimum of the interval and the given displacements proportionally, the optimal topology and the amount of material of the final structure are approximately identical. [ABSTRACT FROM AUTHOR]

The article reports on probing the genetics of fracture resistance. It is noted that fracture resistance is a complex trait caused by bone volume, internal architecture, shape, and material performance of the calcified tissue itself. This can also be influenced by various genetic and environmental processes. A Quantitative Trait Loci (QTL) analyses was used in illustrating the importance of considering genes in context.

Wolff's law in biomechanics states that bone microstructure and local stiffness tend to align with the stress principal directions to adapt to their mechanical environments. In this paper, a new method for topology optimization of continuum structure based on Wolff's law is presented. The major idea of the present approach is to consider the structure to be optimized as a piece of bone that obeys Wolff's law and the process of finding the optimum topology of a structure is equivalent to the bone remodeling process. A second rank positive and definite fabric tensor, which is viewed as the design variable in design domain, is introduced to express the porosity and anisotropy properties of material points. The update rule of the design variables is established as: during the iteration process of the optimization of a structure, at any material point, the eigenvectors of the stress tensor in the present step are those of the fabric tensor in the next step based on Wolff's law; the increments of the eigenvalues of the fabric tensor depend on the principal strains and an interval of reference strain, which is corresponding to the dead zone in bone mechanics. The process is called anisotropic growth if the eigenpairs of the fabric tensors need to be updated. Otherwise, the process is called as isotropic growth if all the fabric tensors are proportional to the second rank identity tensor in the simulation. Numerical examples show that the present method is appropriate to solve large-scale problems, such as 3D structures and the geometrical nonlinear structures. As an application in biomechanics, it is extended to predict the mass distribution of the proximal femur and the results are the same as those obtained by using the other models. [ABSTRACT FROM AUTHOR]

Abstract: 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°) 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 ∼70°), 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. [Copyright &y& Elsevier]

Stress shielding is a biomechanical phenomenon causing adaptive changes in bone strength and stiffness around metallic implants, which potentially lead to implant loosening. Accordingly, there is a need for standard, objective engineering measures of the ‘stress shielding’ performances of an implant that can be employed in the process of computer-aided implant design. To provide and test such measures, we developed hierarchical computational models of adaptation of the trabecular microarchitecture at different sites in the proximal femur, in response to insertion of orthopaedic screws and in response to hypothetical reductions in hip joint and gluteal muscle forces. By identifying similar bone adaptation outcomes from the two scenarios, we were able to quantify the stress shielding caused by screws in terms of analogous hypothetical reductions in hip joint and gluteal muscle forces. Specifically, we developed planar lattice models of trabecular microstructures at five regions of interest (ROI) in the proximal femur. The homeostatic and abnormal loading conditions for the lattices were determined from a finite element model of the femur at the continuum scale and fed to an iterative algorithm simulating the adaptation of each lattice to these loads. When screws were inserted to the femur model, maximal simulated bone loss (17% decrease in apparent density, 10% decrease in thickness of trabeculae) was at the greater trochanter and this effect was equivalent to the effect of 50% reduction in gluteal force and normal hip joint force. We conclude that stress shielding performances can be quantified for different screw designs using model-predicted hypothetical musculoskeletal load fractions that would cause a similar pattern and extent of bone loss to that caused by the implants. [ABSTRACT FROM AUTHOR]

Wolff's law of trajectorial orientation proposes that trabecular struts align with the orientation of dominant compressive loads within a joint. Although widely considered in skeletal biology, Wolff's law has never been experimentally tested while controlling for ontogenetic stage, activity level, and species differences, all factors that may affect trabecular bone growth. Here we report an experimental test of Wolff's law using a within-species design in age-matched subjects experiencing physiologically normal levels of bone strain. Two age-matched groups of juvenile guinea fowl Numida meleagris ran on a treadmill set at either 0° (Level group) or 20° (Incline group), for 10 min per day over a 45-day treatment period. Birds running on the 20° inclined treadmill used more-flexed knees than those in the Level group at midstance (the point of peak ground reaction force). This difference in joint posture enabled us to test the sensitivity of trabecular alignment to altered load orientation in the knee. Using a new radon transform-based method for measuring trabecular orientation, our analysis shows that the fine trabecular bone in the distal femur has a high degree of correspondence between changes in joint angle and trabecular orientation. The sensitivity of this response supports the prediction that trabecular bone adapts dynamically to the orientation of peak compressive forces. [ABSTRACT FROM AUTHOR]

The human fossil record is one of the most complete for any mammal. A basal ancestral species, Australopithecus afarensis, exhibits a well-preserved postcranium that permits reconstruction of important events in the evolution of our locomotor skeleton. When compared to those of living apes and humans, it provides insights into the origin and design of the modern human frame. Evolutionary aspects of the human hip and thigh are reviewed, including the unusual corticotrabecular structure of the human proximal femur, and our markedly elongated lower limb. It is postulated that the latter may be more related to birthing capacity than to locomotion. [Copyright &y& Elsevier]

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°, 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. [Copyright &y& Elsevier]