Mechanical properties of cancellous bone in the human mandibular condyle are anisotropic

The objective of the present study was (1) to test the hypothesis that the elastic and failure properties of the cancellous bone of the mandibular condyle depend on the loading direction, and (2) to relate these properties to bone density parameters. Uniaxial compression tests were performed on cylindrical specimens (n=47) obtained from the condyles of 24 embalmed cadavers. Two loading directions were examined, i.e., a direction coinciding with the predominant orientation of the plate-like trabeculae (axial loading) and a direction perpendicular to the plate-like trabeculae (transverse loading). Archimedes' principle was applied to determine bone density parameters. The cancellous bone was in axial loading 3.4 times stiffer and 2.8 times stronger upon failure than in transverse loading. High coefficients of correlation were found among the various mechanical properties and between them and the apparent density and volume fraction. The anisotropic mechanical properties can possibly be considered as a mechanical adaptation to the loading of the condyle in vivo.     

Cellulose orientation at the surface of the Arabidopsis seedling. Implications for the biomechanics in plant development

In diffuse growing cells the orientation of cellulose fibrils determines mechanical anisotropy in the cell wall and hence also the direction of plant and organ growth. This paper reports on the mean or net orientation of cellulose fibrils in the outer epidermal wall of the whole Arabidopsis plant. This outer epidermal wall is considered as the growth-limiting boundary between plant and environment. In the root a net transverse orientation of the cellulose fibrils occurs in the elongation zone, while net random and longitudinal orientations are found in subsequent older parts of the differentiation zone. The position and the size of the transverse zone is related with root growth rate. In the shoot the net orientation of cellulose fibrils is transverse in the elongating apical part of the hypocotyl, and longitudinal in the fully elongated basal part. Leaf primordia and very young leaves have a transverse orientation. Throughout further development the leaf epidermis builds a very complex pattern of cells with a random orientation and cells with a transverse or a longitudinal orientation of the cellulose fibrils. The patterns of net cellulose orientation correlate well with the cylindrical growth of roots and shoots and with the typical planar growth of the leaf blade. On both the shoot and the root surface very specific patterns of cellulose orientation occur at sites of specific cell differentiation: trichome-socket cells complexes on the shoot and root hairs on the root.     

Type and orientation of yielded trabeculae during overloading of trabecular bone along orthogonal directions

Trabecular architecture plays a major role in bone mechanics. Osteoporosis leads to a transition from a plate-like to a more rod-like trabecular morphology, which may contribute to fracture risk beyond that predicted by changes in density. In this study, microstructural finite element analysis results were analyzed using individual trabeculae segmentation (ITS) to identify the type and orientation of trabeculae where tissue yielded during compressive overloads in two orthogonal directions. For both apparent loading conditions, most of the yielded tissue was found in longitudinally oriented plates. However, the primary loading mode of yielded trabeculae was axial compression with superposed bending for on-axis loading in contrast to bending for transverse loading. For either loading direction, most plate-like trabeculae yielded in the same loading mode, regardless of their orientation. In contrast, rods oriented parallel to the loading axis yielded in compression, while rods oblique or perpendicular to the loading axis yielded in combined bending and tension. The predominance of tissue yielding in plates during both on-axis and transverse overloading explains why on-axis overloading is detrimental to the off-axis mechanical properties. At the same time, a large fraction of the tissue in rod-like trabeculae parallel to the loading direction yielded in both on-axis and transverse loading. Hence, rods may be more likely to be damaged and potentially resorbed by damage mediated remodeling.     

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

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

The micromechanics versus the macromechanics of cortical bone--a comprehensive presentation

Secondary cortical bone is a complicated patchwork of structures which can be viewed as a hierarchy of four different orders. As far as the biomechanical properties of cortical bone are concerned, the lamellae is the most important of the four. The relative distribution of longitudinal lamellae (whose fiber bundles and crystallites have a longitudinal course and withstand loading by tension) with respect to transverse lamellae (whose fiber bundles and crystallites have a transverse course and withstand loading by compression) governs the mechanical properties of bone at macroscopic level both in normal and pathological conditions.     

Cortical bone failure mechanisms during screw pullout

An experimental and computational study of screw pullout from cortical bone has been conducted. A novel modification of standard pullout tests providing real time image capture of damage mechanisms during screw pullout was developed. Pullout forces, measured using the novel test rig, have been validated against standard pullout tests. Pullout tests were conducted, considering osteon alignment, to investigate the effect of osteons aligned parallel to the axis of the orthopaedic screw (longitudinal pullout) as well as the effect of osteons aligned perpendicular to the axis of the screw (transverse pullout). Distinctive alternate failure mechanisms, for longitudinally and transversely orientated cortical bone during screw pullout, were uncovered. Vertical crack propagation, parallel to the axis of the screw, was observed for a longitudinal pullout. Horizontal crack propagation, perpendicular to the axis of the screw, was observed for a transverse pullout. Finite element simulation of screw pullout, incorporating material damage and crack propagation, was also performed. Simulations revealed that a homogenous material model for cortical bone predicts vertical crack propagation patterns for both longitudinal and transverse screw pullout. A bi-layered composite model representing cortical bone microstructure was developed. A unique set of material and damage properties was used for both transverse and longitudinal pullout simulations, with only layer orientations being changed. Simulations predicted: (i) higher pullout forces for transverse pullout; (ii) horizontal crack paths perpendicular to screw axis for transverse pullout, whereas vertical crack paths were computed for longitudinal pullout. Computed results agreed closely with experimental observations in terms of pullout force and crack propagation.     

Anisotropy of age-related toughness loss in human cortical bone: a finite element study

A mechanistic understanding of the role of bone quality on fracture processes is essential for determining the underlying causes of age-related changes in the mechanical response of the human bone. In this study, a previously developed cohesive finite element model was used to investigate the effects of age-related changes and the orientation of crack growth on the toughening behavior of human cortical bone. The change in the anisotropy of toughening mechanisms with age was also studied. Finite element method (FEM) simulations showed that the initiation toughness decreased by 3% and 8%/decade for transverse and longitudinal crack growth, respectively. In contrast, fracture resistance curve slope for transverse and longitudinal crack growth decreased by 2% and 3%/decade, respectively. Initiation fracture toughness values were higher for the transverse than for the longitudinal for a given age. On the other hand, propagation fracture toughness values were higher for longitudinal than for transverse crack growth for a given age. With respect to age, the toughness ratio for crack initiation decreased by 6%/decade, but that for propagation showed almost no change (less than 1%). In light of these findings, an analytical model evaluating the crack arresting feature of cement lines, is proposed to explain the factors that determine crack penetration into osteons or its deflection by cement lines.     

Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.     

Bone creep-fatigue damage accumulation

Creep and fatigue tests were performed on human femoral cortical bone and the results were compared to a cumulative damage model for bone fracture. Fatigue tests in tension, compression, and reversed loading with a tensile mean stress were conducted at 2 Hz and 0.02 Hz. Load frequency had a strong influence on the number of cycles to failure but did not influence the total time to failure. Bone displayed poor creep-fracture properties in both tension and compression. The fracture surfaces of the tensile creep specimens are distinctly different than those of the compressive specimens. The results suggest that tensile cyclic loading creates primarily time-dependent damage and compressive cyclic loading creates primarily cycle-dependent damage. However, data for load histories involving both tensile and compressive loading indicate lower time to failure than predicted by a simple summation of time-dependent and cycle-dependent damage.     

Biaxial failure behavior of bovine tibial trabecular bone

Multiaxial failure properties of trabecular bone are important for modeling of whole bone fracture and can provide insight into structure-function relationships. There is currently no consensus on the most appropriate form of multiaxial yield criterion for trabecular bone. Using experimentally validated, high-resolution, non-linear finite element models, biaxial plain strain boundary conditions were applied to seven bovine tibial specimens. The dependence of multiaxial yield properties on volume fraction was investigated to quantify the interspecimen heterogeneity in yield stresses and strains. Two specimens were further analyzed to determine the yield properties for a wide range of biaxial strain loading conditions. The locations and quantities of tissue level yielding were compared for on-axis, transverse, and biaxial apparent level yielding to elucidate the micromechanical failure mechanisms. As reported for uniaxial loading of trabecular bone, the yield strains in multiaxial loading did not depend on volume fraction, whereas the yield stresses did. Micromechanical analysis indicated that the failure mechanisms in the on-axis and transverse loading directions were mostly independent. Consistent with this, the biaxial yield properties were best described by independent curves for on-axis and transverse loading. These findings establish that the multiaxial failure of trabecular bone is predominantly governed by the strain along the loading direction, requiring separate analytical expressions for each orthotropic axis to capture the apparent level yield behavior.     

Age-related properties at the microscale affect crack propagation in cortical bone

The increased risk for fracture with age is associated not only with reduced bone mass but also with impaired bone quality. At the microscale, bone quality is related to porosity, microstructural organization, accumulated microdamage and intrinsic material properties. However, the link between these characteristics and fracture behavior is still missing. Bone tissue has a complex structure and as age-related compositional and structural changes occur at all hierarchical length scales it is difficult to experimentally identify and discriminate the effect of each mechanism. The aim of this study was therefore to use computational models to analyze how microscale characteristics in terms of porosity, intrinsic toughness properties and microstructural organization affect the mechanical behavior of cortical bone. Tensile tests were simulated using realistic microstructural geometries based on microscopy images of human cortical bone. Crack propagation was modelled using the extended finite element method where cement lines surrounding osteons were modelled with an interface damage law to capture crack deflections along osteon boundaries. Both increased porosity and impaired material integrity resulted in straighter crack paths with cracks penetrating osteons, similar to what is seen experimentally for old cortical bone. However, only the latter predicted a more brittle failure behavior. Furthermore, the local porosity influenced the crack path more than the macroscopic porosity. In conclusion, age-related changes in cortical bone affect the crack path and the mechanical response. However, increased porosity alone was not driving damage in old bone, but instead impaired tissue integrity was required to capture brittle failure in aging bone.     

Strain rate does not affect cortical microtubule orientation in the isolated epidermis of sunflower hypocotyls

A hypothesis exists that external and internal factors affect the orientation of cortical microtubules in as much as these lead to changes in cell elongation rate. Factors that stimulate elongation are proposed to lead to transverse microtubule orientation, whereas factors that inhibit elongation lead to longitudinal orientation. The elongation rate is equal to the rate of longitudinal irreversible strain in cell walls. Incubated epidermis peeled from sunflower hypocotyls does not extend unless it is stretched by loading and the pH of the incubation medium is appropriately low. Thus, peels provide a convenient model to investigate the relationship between longitudinal strain rate and cortical microtubule orientation. In the present study, it was found that peeling affects microtubule orientation. Peels were incubated for several hours in Murashige & Skoog medium (both unbuffered and buffered) to attain a steady state of microtubule orientation before loading. The effects of loading and pH on strain rate and orientation of microtubules under the outer epidermal walls were examined in three portions of peels positioned with respect to the cotyledonary node. Appropriate loading caused longitudinal strain of peels at pH 4.5 but not at pH 6.5. However, no clear effect of strain rate on microtubule orientation in the peels was observed. Independent of applied load and pH of the incubation medium, the microtubule orientation remained unchanged, i.e. orientation was mainly oblique. Our results show that strain rate does not affect cortical microtubule orientation in isolated epidermis of the sunflower hypocotyl model system, although orientation could be changed by white light.     

Damage in trabecular bone at small strains

Evidence that damage decreases bone quality, increases fracture susceptibility, and serves as a remodeling stimulus motivates further study of what loading magnitudes induce damage in trabecular bone. In particular, whether damage occurs at the smaller strains characteristic of habitual, as opposed to traumatic, loading is not known. The overall goal of this study was to characterize damage accumulation in trabecular bone at small strains (0.20 - 0.45% strain). A continuum damage mechanics approach was taken whereby damage was quantified by changes in modulus and residual strain. Human vertebral specimens (n = 7) were tested in compression using a multi-cycle load - unload protocol in which the maximum applied strain for each cycle, epsilonmax, was increased incrementally from epsilonmax = 0.20% on the first loading cycle to epsilonmax = 0.45% on the last cycle. Modulus and residual strain were measured for each cycle. Both changes in modulus and residual strains commenced at small strains, beginning as early as 0.24 and 0.20% strain, respectively. Strong correlations between changes in modulus and residual strains were observed (r = 0.51 - 0.98). Fully nonlinear, high-resolution finite element analyses indicated that even at small apparent strains, tissue-level strains were sufficiently high to cause local yielding. These results demonstrate that damage in trabecular bone occurs at apparent strains less than half the apparent compressive yield strain reported previously for human vertebral trabecular bone. Further, these findings imply that, as a consequence of the highly porous trabecular structure, tissue yielding can initiate at very low apparent strains and that this local failure has detectable and negative consequences on the apparent mechanical properties of trabecular bone.     

Shear strength and toughness of trabecular bone are more sensitive to density than damage

Microdamage occurs in trabecular bone under normal loading, which impairs the mechanical properties. Architectural degradation associated with osteoporosis increases damage susceptibility, resulting in a cumulative negative effect on the mechanical properties. Treatments for osteoporosis could be targeted toward increased bone mineral density, improved architecture, or repair and prevention of microdamage. Delineating the relative roles of damage and architectural degradation on trabecular bone strength will provide insight into the most beneficial targets. In this study, damage was induced in bovine trabecular bone samples by axial compression, and the effects on the mechanical properties in shear were assessed. The damaged shear modulus, shear yield stress, ultimate shear stress, and energy to failure all depended on induced damage and decreased as the architecture became more rod-like. The changes in ultimate shear strength and toughness were proportional to the decrease in shear modulus, consistent with an effective decrease in the cross-section of trabeculae based on cellular solid analysis. For typical ranges of bone volume fraction in human bone, the strength and toughness were much more sensitive to decreased volume fraction than to induced mechanical damage. While ultimately repairing or avoiding damage to the bone structure and increasing bone density both improve mechanical properties, increasing bone density is the more important contributor to bone strength.     

Computational biomechanics of articular cartilage of human knee joint: Effect of osteochondral defects

Articular cartilage and its supporting bone functional conditions are tightly coupled as injuries of either adversely affects joint mechanical environment. The objective of this study was set to quantitatively investigate the extent of alterations in the mechanical environment of cartilage and knee joint in presence of commonly observed osteochondral defects. An existing validated finite element model of a knee joint was used to construct a refined model of the tibial lateral compartment including proximal tibial bony structures. The response was computed under compression forces up to 2000 N while simulating localized bone damage, cartilage–bone horizontal split, bone overgrowth and absence of deep vertical collagen fibrils.Localized tibial bone damage increased overall joint compliance and substantially altered pattern and magnitude of contact pressures and cartilage strains in both tibia and femur. These alterations were further exacerbated when bone damage was combined with base cartilage split and absence of deep vertical collagen fibrils. Local bone boss markedly changed contact pressures and strain patterns in neighbouring cartilage. Bone bruise/fracture and overgrowth adversely perturbed the homeostatic balance in the mechanical environment of articulate cartilage surrounding and opposing the lesion as well as the joint compliance. As such, they potentially contribute to the initiation and development of post-traumatic osteoarthritis.     

Multi-axial mechanical properties of human trabecular bone

In the context of osteoporosis, evaluation of bone fracture risk and improved design of epiphyseal bone implants rely on accurate knowledge of the mechanical properties of trabecular bone. A multi-axial loading chamber was designed, built and applied to explore the compressive multi-axial yield and strength properties of human trabecular bone from different anatomical locations. A thorough experimental protocol was elaborated for extraction of cylindrical bone samples, assessment of their morphology by micro-computed tomography and application of different mechanical tests: torsion, uni-axial traction, uni-axial compression and multi-axial compression. A total of 128 bone samples were processed through the protocol and subjected to one of the mechanical tests up to yield and failure. The elastic data were analyzed using a tensorial fabric–elasticity relationship, while the yield and strength data were analyzed with fabric-based, conewise generalized Hill criteria. For each loading mode and more importantly for the combined results, strong relationships were demonstrated between volume fraction, fabric and the elastic, yield and strength properties of human trabecular bone. Despite the reviewed limitations, the obtained results will help improve the simulation of the damage behavior of human bones and bone-implant systems using the finite element method.     

Interaction of auxin, light, and mechanical stress in orienting microtubules in relation to tropic curvature in the epidermis of maize coleoptiles

Summary Changes in the orientation of cortical microtubules (longitudinal vs. transverse with respect to the long cell axis) at the outer epidermal wall of maize coleoptile segments were induced by auxin, red or blue light, and mechanical stresses (cell extension or compression produced by bending). Immunofluorescent techniques were used for the quantitative determination of frequency distributions of microtubule orientation. Detailed kinetic studies showed that microtubule reorientations are temporally correlated with the simultaneously measured changes in growth rate elicited by auxin, red light, or blue light. Growth inhibition induced by depletion of endogenous auxin produces a longitudinal microtubule pattern that can be changed into a transverse pattern in a dose-dependent manner by applying exogenous auxin. A mid-point pattern with equal frequencies of longitudinal and transverse microtubules was adjusted at 2 mol/1 auxin. Bending stress applied under these conditions adjusts permanent, maximally longitudinal and transverse microtubule orientations at the compressed and extended segment sides, respectively, quantitatively mimicking the responses to differential flank growth during phototropic and gravitropic curvature. During tropic curvature the changes in microtubule pattern reflect the distribution of growth rather than the distribution of auxin. The microtubule pattern responds to auxin-dependent growth changes and mechanical stress in a synergistic manner, confirming the functional equivalence of these factors in affecting microtubule orientation. Similar results were obtained when segment growth was altered by blue or red light instead of auxin in the presence or absence of mechanical stress. It is concluded from these results that growth changes, elicited by auxin, light, etc., and mechanical stress affect microtubule orientation through a common signal perception and transduction chain.Abbreviations IAA indole-3-acetic acid (auxin) - MT cortical microtubule     

Elastic properties of woven bone: effect of mineral content and collagen fibrils orientation

Woven bone is a type of tissue that forms mainly during fracture healing or fetal bone development. Its microstructure can be modeled as a composite with a matrix of mineral (hydroxyapatite) and inclusions of collagen fibrils with a more or less random orientation. In the present study, its elastic properties were estimated as a function of composition (degree of mineralization) and fibril orientation. A self-consistent homogenization scheme considering randomness of inclusions’ orientation was used for this purpose. Lacuno-canalicular porosity in the form of periodically distributed void inclusions was also considered. Assuming collagen fibrils to be uniformly oriented in all directions led to an isotropic tissue with a Young’s modulus \(E = 1.90\) GPa, which is of the same order of magnitude as that of woven bone in fracture calluses. By contrast, assuming fibrils to have a preferential orientation resulted in a Young’s modulus in the preferential direction of 9–16 GPa depending on the mineral content of the tissue. These results are consistent with experimental evidence for woven bone in foetuses, where collagen fibrils are aligned to a certain extent.     

Experimental and probabilistic analysis of distal femoral periprosthetic fracture: a comparison of locking plate and intramedullary nail fixation. Part A: experimental investigation

The following is a two-part study. Part A evaluates biomechanically intramedullary (IM) nails vs. locking plates for fixation of femoral fractures in osteoporotic bone. Part B of this study introduces a deterministic finite element model of each construct type and investigates the probability of periprosthetic fracture of the locking plate compared with the retrograde IM nail using Monte Carlo simulation. For Part A, an extra-articular, metaphyseal wedge fracture pattern was created in 11 osteoporotic fourth-generation composite femurs. Fixation was performed with a locking plate or a retrograde IM nail. Axial, torsion and bending cyclic loading to simulate post-operative damage accumulation were performed followed by ramped load to failure. Locking plates proved to be more stable (using stiffness as the determining factor) in osteoporotic bone as observed under low load cycle conditions. However, some of these advantages were offset by a greater incidence of sudden periprosthetic fracture observed under ramped loading conditions. Cadaveric, osteoporotic femurs included as a case study also exhibited periprosthetic fracture, but failure was accompanied by catastrophic comminution of the cortex. Periprosthetic failure at the implant end including bone comminution is difficult to salvage with revision fixation. The weakened trabecular matrix and thinned cortex of osteoporotic bone may increase the incidence of periprosthetic fracture. It is, therefore, essential for the surgeon to consider all possible loading scenarios when recommending an ideal implant for the osteoporotic patient.     

Post-yield nanomechanics of human cortical bone in compression using synchrotron X-ray scattering techniques

The ultrastructural response to applied loads governs the post-yield deformation and failure behavior of bone, and is correlated with bone fragility fractures. Combining a novel progressive loading protocol and synchrotron X-ray scattering techniques, this study investigated the correlation of the local deformation (i.e., internal strains of the mineral and collagen phases) with the bulk mechanical behavior of bone. The results indicated that the internal strains of the longitudinally oriented collagen fibrils and mineral crystals increased almost linearly with respect to the macroscopic strain prior to yielding, but markedly decreased first and then gradually leveled off after yielding. Similar changes were also observed in the applied stress before and after yielding of bone. However, the collagen to mineral strain ratio remained nearly constant throughout the loading process. In addition, the internal strains of longitudinal mineral and collagen phases did not exhibit a linear relationship with either the modulus loss or the plastic deformation of bulk bone tissue. Finally, the time-dependent response of local deformation in the mineral phase was observed after yielding. Based on the results, we speculate that the mineral crystals and collagen fibrils aligned with the loading axis only partially explain the post-yield deformation, suggesting that shear deformation involving obliquely oriented crystals and fibrils (off axis) is dominant mechanism of yielding for human cortical bone in compression.