Comparative morphological examination of vertebral bodies of teleost fish using high-resolution micro-CT scans

Vertebral bodies of teleost fish are formed by the sclerotomal bone covering the chordacentrum. The internal part of the sclerotomal bone is composed of an amphicoelous hourglass shaped autocentrum, which is common in most fish species. In contrast, the external shape of the sclerotomal bone varies extensively among species. There are multiple hypotheses regarding the composition and formation of the external structure. However, as they are based on studies of few extant or extinct species, their applicability to other species remains to be clarified. To understand the morphology, formation, and composition of vertebral bodies in teleosts, we performed a comparative analysis using micro-CT scans of 32 species from 10 orders of Teleostei and investigated the detailed morphology of the sclerotomal bone, especially its plate-like ridge and trabeculae. We discovered two structural characteristics that are shared among most of the examined species. One was the sheet-like trabeculae that extend radially from the center of the vertebral body with a constant thickness. The other was the presence of hollow spaces on the internal parts of the lateral ridge and trabeculae. The combination of different arrangements of sheet-like trabeculae and internal hollow spaces formed different shapes of the lateral structure of the vertebral body. The properties of these two characteristics suggest that the external part of the sclerotomal bone grows outward by deposition at the bone tip, and that, concurrently, bone absorption occurs in the internal part of the sclerotomal bone. The vertebral arches were also formed by the sheet-like trabeculae, indicating that both, the vertebral body and the arches, are formed by the same component. The micro-CT scanning data were uploaded to a public database so they can be used for future studies on fish vertebrae.     

The susceptibility of the femoral neck to fracture: an assessment incorporating the effects of age-remodeling and stress reduction

Age-related bone remodeling may cause fragility of the femoral neck, thereby increasing fracture risk in elderly populations. We investigated the effects of age-remodeling and stress-reduction on the femoral neck region using the Finite Strip Method (FSM). We verified the possibility that the femoral neck is likely to undergo fracture through two mechanisms: yielding and local buckling. We hypothesized that the femoral necks of young subjects are more prone to fracture by yielding, whereas those of elderly subjects are more susceptible to fracture initiated by local buckling. The slices from the CT-scans of 15 subjects corresponding to the lowest area moment of inertia were segregated into cortex and trabeculae. Geometric and material properties for each strip were obtained from the CT-scans. The FSM, proposed here as an approximation to the better-known Finite Element Method (FEM), was implemented on a model comprising both cortex and trabeculae. Finite strip (FS) analyses were performed on models that incorporated the effects of age-related bone remodeling, as well as a reduction in physiological stress on the bone (as a result of weight loss). Comparisons were made with similar FS analyses performed on only the cortical shell, in order to ascertain the contributions of the trabeculae to femoral neck strength. We observed that the femoral necks of simulated young subjects manifested a marked predisposition to undergo yielding, whereas the femoral neck models of simulated elderly subjects were more prone to buckling before yielding. The trabecular degradation and cortical thinning involved in aging render the femoral neck more susceptible to failure by buckling.     

Biomechanical properties across trabeculae from the proximal femur of normal and ovariectomised sheep

The elastic behaviour of trabecular bone is a function not only of bone volume and architecture, but also of tissue material properties. Variation in tissue modulus can have a substantial effect on the biomechanical properties of trabecular bone. However, the nature of tissue property variation within a single trabecula is poorly understood. This study uses nanoindentation to determine the mechanical properties of bone tissue in individual trabeculae. Using an ovariectomised ovine model, the modulus and hardness distribution across trabeculae were measured. In both normal and ovariectomised bone, the modulus and hardness were found to increase towards the core of the trabeculae. Across the width of the trabeculae, the modulus was significantly less in the ovariectomised bone than in the control bone. However, in contrast to this hardness was found not to differ significantly between the two groups. This study provides valuable information on the variation of mechanical material properties in healthy and diseased trabecular bone tissue. The results of the current study will be useful in finite element modelling where more accurate values of trabecular bone modulus will enable the prediction of the macroscale behaviour of trabecular bone.     

Age-related changes in human trabecular bone: Relationship between microstructural stress and strain and damage morphology

Accumulation of microdamage in aging and disease can cause skeletal fragility and is one of several factors contributing to osteoporotic fractures. To better understand the role of microdamage in fragility fracture, the mechanisms of bone failure must be elucidated on a tissue-level scale where interactions between bone matrix properties, the local biomechanical environment, and bone architecture are concurrently examined for their contributions to microdamage formation. A technique combining histological damage assessment of individual trabeculae with linear finite element solutions of trabecular von Mises and principal stress and strain was used to compare the damage initiation threshold between pre-menopausal (32-37 years, n=3 donors) and post-menopausal (71-80 years, n=3 donors) femoral cadaveric bone. Strong associations between damage morphology and stress and strain parameters were observed in both groups, and an age-related decrease in undamaged trabecular von Mises stress was detected. In trabeculae from younger donors, the 95% CI for von Mises stress on undamaged regions ranged from 50.7-67.9MPa, whereas in trabeculae from older donors, stresses were significantly lower (38.7-50.2, p<0.01). Local microarchitectural analysis indicated that thinner, rod-like trabeculae oriented along the loading axis are more susceptible to severe microdamage formation in older individuals, while only rod-like architecture was associated with severe damage in younger individuals. This study therefore provides insight into how damage initiation and morphology relate to local trabecular microstructure and the associated stresses and strains under loading. Furthermore, by comparison of samples from pre- and post-menopausal women, the results suggest that trabeculae from younger individuals can sustain higher stresses prior to microdamage initiation.     

Mineral heterogeneity affects predictions of intratrabecular stress and strain

Knowledge of the influence of mineral variations (i.e., mineral heterogeneity) on biomechanical bone behavior at the trabecular level is limited. The aim of this study is to investigate how this material property affects the intratrabecular distributions of stress and strain in human adult trabecular bone. Two different sets of finite element (FE) models of trabecular samples were constructed; tissue stiffness was either scaled to the local degree of mineralization of bone as measured with microCT (heterogeneous) or tissue stiffness was assumed to be homogeneous. The influence of intratrabecular mineral heterogeneity was analyzed by comparing both models. Interesting effects were seen regarding intratrabecular stress and strain distributions. In the homogeneous model, the highest stresses were found at the surface with a significant decrease towards the core. Higher superficial stresses could indicate a higher predicted fracture risk in the trabeculae. In the heterogeneous model this pattern was different. A significant increase in stress with increasing distance from the trabecular surface was found followed by a significant decrease towards the core. This suggests trabecular bending during a compression. In both models a decrease in strain values from surface to core was predicted, which is consistent with trabecular bending. When mineral heterogeneity was taken into account, the predicted intratrabecular patterns of stress and strain are more consistent with the expected biomechanical behavior as based on mineral variations in trabeculae. Our findings indicate that mineral heterogeneity should not be neglected when performing biomechanical studies on topics such as the (long-term or dose dependent) effects of antiresorptive treatments.     

Evolution of grasping among anthropoids

The prevailing hypothesis about grasping in primates stipulates an evolution from power towards precision grips in hominids. The evolution of grasping is far more complex, as shown by analysis of new morphometric and behavioural data. The latter concern the modes of food grasping in 11 species (one platyrrhine, nine catarrhines and humans). We show that precision grip and thumb-lateral behaviours are linked to carpus and thumb length, whereas power grasping is linked to second and third digit length. No phylogenetic signal was found in the behavioural characters when using squared-change parsimony and phylogenetic eigenvector regression, but such a signal was found in morphometric characters. Our findings shed new light on previously proposed models of the evolution of grasping. Inference models suggest that Australopithecus, Oreopithecus and Proconsul used a precision grip.     

Trabecular bone adaptation with an orthotropic material model.

Most bone adaptation algorithms, that attempt to explain the connection between bone morphology and loads, assume that bone is effectively isotropic. An isotropic material model can explain the bone density distribution, but not the structure and pattern of trabecular bone, which clearly has a mechanical significance. In this paper, an orthotropic material model is utilized to predict the proximal femur trabecular structure. Two hypotheses are combined to determine the local orientation and material properties of each element in the model. First, it is suggested that trabecular directions, which correspond to the orthotropic material axes, are determined locally by the maximal principal stress directions due to the multiple load cases (MLC) the femur is subject to. The second hypothesis is that material properties in each material direction can be determined using directional stimuli, thus extending existing adaptation algorithms to include directionality. An algorithm is utilized, where each iteration comprises of two stages. First, material axes are rotated to the direction of the largest principal stress that occurs from a multiple load scheme applied to the proximal femur. Next, material properties are modified in each material direction, according to a directional stimulus. Results show that local material directions correspond with known trabecular patterns, reproducing all main groups of trabeculae very well. The local directional stiffnesses, degree of anisotropy and density distribution are shown to conform to real femur morphology.     

Determination of dynamically adapting anisotropic material properties of bone under cyclic loading

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 Danilov (1971) 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.     

Stress-concentrating effect of resorption lacunae in trabecular bone

Analyses of the distributions of stress and strain within individual bone trabeculae have not yet been reported. In this study, four trabeculae were imaged and finite elements models were generated in an attempt to quantify the variability of stress/strain in real trabeculae. In three of these trabeculae, cavities were identified with depths comparable to values reported for resorption lacunae ( approximately 50 microm)-although we cannot be certain, it is most probable that they are indeed resorption lacunae. A tensile load was applied to each trabeculum to simulate physiological loading and to ensure that bending was minimized. The force carried by each trabecula was calculated from this value using the average cross sectional area of each trabecula. The analyses predict that very high stresses (>100 MPa) existed within bone trabecular tissue. Stress and strain distributions were highly heterogeneous in all cases, more so in trabeculae with the presumptive resorption lacunae where at least 30% of the tissue had a strain greater than 4000 micoepsilon in all cases. Stresses were elevated at the pit of the lacunae, and peak stress concentrations were located in the longitudinal direction ahead of the lacunae. Given these high strains, we suggest that microdamage is inevitable around resorption lacunae in trabecular bone, and may cause the bone multicellular unit to proceed to resorb a packet of bone in the trabeculum rather than just resorb whatever localized area was initially targeted.     

Effect of trabecular curvature on the stiffness of trabecular bone

Simplified structural models of trabecular bone have been used to model various forms of trabecular variability. The structural effects of variability of direction, length and thickness of the trabeculae have been studied using 'lattice-type' finite element models. However, many of the trabeculae are not perfectly straight, and have a small degree of curvature. The objective of this study is to quantify the influence of small curvatures of the trabeculae on the effective modulus of trabecular bone, in the principal material direction. An analytical analysis of the effect of curvature on a single trabecula is performed, utilizing the concept of cellular-solid models. Closed-form expressions are derived for the effect of curvature on the flexibility in the principal material direction. For comparison, expressions are derived for the flexibility of a straight oblique element, representing angular variability. A quantitative comparison is presented, which is dependent on the thickness of the trabeculae. It was found that small curvatures have a large effect on the stiffness of the trabecular structure. This effect is largest for thin trabeculae, and decreases for thick trabeculae. The stiffness of the trabecular structure can be reduced by a factor of up to four for thin trabeculae and up to two for thick trabeculae, even for small curvatures. The flexibility of curved elements is found to be larger than the flexibility of oblique elements with similar eccentricities. Thus it seems that curvature might play a role in determining the effective modulus of trabecular bone.     

Ontogeny and phylogeny of the pelvis in Gorilla, Pongo, Pan, Australopithecus and Homo

To examine the evolutionary differences between hominoid locomotor systems, a number of observations concerning the growth of the pelvis among the great apes as compared to modern and fossil hominids are reported. We are interested in the size and shape of the coxal bones at different developmental stages across species that may elucidate the relationship between ontogeny and phylogeny (i.e., heterochrony) in the hominoid pelvis. Our hypotheses are: (1) do rates of absolute growth differ?, (2) do rates of relative growth differ?, and (3) does heterochrony explain these differences? Bivariate and multivariate analyses of pelvic dimensions demonstrate both the diversity of species-specific ontogenetic patterns among hominoids, and an unequivocal separation of hominids and the great apes. Heterochrony alone fails to account for the ontogenetic differences between hominids and the great apes. Compared to recent Homo,Australopithecus can be described as 'hyper-human' from the relative size of the ischium, and short but broad ilium. Australopithecus afarensis differs from Australopithecus africanus by its relatively long pubis. In multivariate analyses of ilium shape, the most complete coxal bone attributed to Homo erectus, KNM-ER 3228, falls within the range of juvenile and adult Australopithecus, whereas Broken Hill falls within the range of modern Homo, suggesting that the modern human ilium shape arose rather recently. Among the great apes, patterns of pelvic ontogeny do not exclusively separate the African apes from Pongo.     

The effects of plaque morphology and material properties on peak cap stress in human coronary arteries

Heart attacks are often caused by rupture of caps of atherosclerotic plaques in coronary arteries. Cap rupture occurs when cap stress exceeds cap strength. We investigated the effects of plaque morphology and material properties on cap stress. Histological data from 77 coronary lesions were obtained and segmented. In these patient-specific cross sections, peak cap stresses were computed by using finite element analyses. The finite element analyses were 2D, assumed isotropic material behavior, and ignored residual stresses. To represent the wide spread in material properties, we applied soft and stiff material models for the intima. Measures of geometric plaque features for all lesions were determined and their relations to peak cap stress were examined using regression analyses. Patient-specific geometrical plaque features greatly influence peak cap stresses. Especially, local irregularities in lumen and necrotic core shape as well as a thin intima layer near the shoulder of the plaque induce local stress maxima. For stiff models, cap stress increased with decreasing cap thickness and increasing lumen radius (R = 0.79). For soft models, this relationship changed: increasing lumen radius and increasing lumen curvature were associated with increased cap stress (R = 0.66). The results of this study imply that not only accurate assessment of plaque geometry, but also of intima properties is essential for cap stress analyses in atherosclerotic plaques in human coronary arteries.     

Vertical stratification of oribatid (Acari: Oribatida) communities in relation to their morphological and life-history traits and tree structures in a subtropical forest in Japan

To clarify the effect of tree structure on the diversity of oribatid mites (Acari: Oribatida), we collected a total of 16,325 oribatids in 181 morphospecies from the leaves, branches, and trunk bark of trees and from the forest-floor soil and litter in a subtropical forest, Okinawa, Japan, and tested three predictions: (1) moisture stress in arboreal habitats would lead to larger body size (not supported); (2) morphological traits related to gripping a surface (number and size of claws) would be more developed in arboreal species (supported); and (3) advantages in colonization (no cost for searching mates and doubled population growth) would favor parthenogenesis in the arboreal oribatid communities (not supported). We observed vertical stratification among the five habitats in terms of mite density, species diversity, and species composition, but found no difference in the body length of oribatid species between the arboreal and forest-floor habitats. However, (homo-)tridactylous species predominated in the arboreal habitat, suggesting that this claw morphology facilitates adherence to and movement on arboreal substrates. Sexual species were common in the arboreal oribatid communities, whereas about half of the dominant species collected from the forest floor were likely to be parthenogenetic. It is unclear how these different reproductive systems may be advantageous for oribatid mites in arboreal and forest-floor habitats. Nevertheless, the structural complexity provided by trees appears to enhance and maintain the diversity of oribatid communities through vertical stratification in this subtropical forest.     

Postcranial morphology and the locomotor habits of living and extinct carnivorans

Members of the order Carnivora display a broad range of locomotor habits, including cursorial, scansorial, arboreal, semiaquatic, aquatic, and semifossorial species from multiple families. Ecomorphological analyses from osteological measurements have been used successfully in prior studies of carnivorans and rodents to accurately infer the locomotor habits of extinct species. This study uses 20 postcranial measurements that have been shown to be effective indicators of locomotor habits in rodents and incorporates an extensive sample of over 300 individuals from more than 100 living carnivoran species. We performed statistical analyses, including analysis of variance (ANOVA) and stepwise discriminant function analysis, using a set of 16 functional indices (ratios). Our ANOVA results reveal consistent differences in postcranial skeletal morphology among locomotor groups. Cursorial species display distal elongation of the limbs, gracile limb elements, and relatively narrow humeral and femoral epicondyles. Aquatic and semiaquatic species display relatively robust, shortened femora and elongate metatarsals. Semifossorial species display relatively short, robust limbs with enlarged muscular attachment sites and elongate claws. Both semiaquatic and semifossorial species have relatively elongate olecranon process of the ulna and enlarged humeral and femoral epicondyles. Terrestrial, scansorial, and arboreal species are characterized by having primarily intermediate features, but arboreal species do show relatively elongate manual digits. Morphological indices effectively discriminate locomotor groups, with cursorial and arboreal species more accurately classified than terrestrial, scansorial, or semiaquatic species. Both within and between families, species with similar locomotor habits converge toward similar postcranial morphology despite their independent evolutionary histories. The discriminant analysis worked particularly well to correctly classify members of the Canidae, but not as well for members of the Mustelidae or Ursidae. Results are used to infer the locomotor habits of extinct carnivorans, including members of several extinct families, and also 12 species from the Pleistocene of Rancho La Brea. J. Morphol., 2013. © 2012 Wiley Periodicals, Inc.     

Morphological and numerical studies of the stress compatibility of patella implants]

Failure of total knee arthroplasty is relatively often caused by problems of the patellofemoral replacement. The purpose of this study was to analyze the distribution of stresses within an anatomical patella and the changes in stress distribution after patellar resurfacing with a Miller-Galante I patellar implant using two- and three dimensional finite element models (FEM). To assess validity, FEM results were compared with morphological findings from contact radiographs and densitographs. Internal orientation of bone trabeculae is in good agreement with the orientation of theoretically calculated principal stresses. Almost unchanged principal tensile stresses after implantation, together with the lack of extreme stress peaks within the cancellous bone ensure stress compatibility of the implant. In the case of a firmly seated implant with good bone ingrowth, increased von Mises stresses are found near the fixation peg/plate junction. Their relevance for improved bone ingrowth near this part of the interface is emphasized. At the same time, material failure at the peg/plate junction can be better understood. An analysis of the early postoperative period assuming nonlinear interface conditions failed to demonstrate an uniform distribution of normal and tangential interface forces.     

Free body analysis,beam mechanics,and finite element modeling of the mandible of Alligator mississippiensis

The mechanical behavior of mammalian mandibles is well‐studied, but a comprehensive biomechanical analysis (incorporating detailed muscle architecture, accurate material properties, and three‐dimensional mechanical behavior) of an extant archosaur mandible has never been carried out. This makes it unclear how closely models of extant and extinct archosaur mandibles reflect reality and prevents comparisons of structure–function relationships in mammalian and archosaur mandibles. We tested hypotheses regarding the mechanical behavior of the mandible of Alligator mississippiensis by analyzing reaction forces and bending, shear, and torsional stress regimes in six models of varying complexity. Models included free body analysis using basic lever arm mechanics, 2D and 3D beam models, and three high‐resolution finite element models of the Alligator mandible, incorporating, respectively, isotropic bone without sutures, anisotropic bone with sutures, and anisotropic bone with sutures and contact between the mandible and the pterygoid flange. Compared with the beam models, the Alligator finite element models exhibited less spatial variability in dorsoventral bending and sagittal shear stress, as well as lower peak values for these stresses, suggesting that Alligator mandibular morphology is in part designed to reduce these stresses during biting. However, the Alligator models exhibited greater variability in the distribution of mediolateral and torsional stresses than the beam models. Incorporating anisotropic bone material properties and sutures into the model reduced dorsoventral and torsional stresses within the mandible, but led to elevated mediolateral stresses. These mediolateral stresses were mitigated by the addition of a pterygoid‐mandibular contact, suggesting important contributions from, and trade‐offs between, material properties and external constraints in Alligator mandible design. Our results suggest that beam modeling does not accurately represent the mechanical behavior of the Alligator mandible, including important performance metrics such as magnitude and orientation of reaction forces, and mediolateral bending and torsional stress distributions. J.Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

The effects of modeling simplifications on craniofacial finite element models: the alveoli (tooth sockets) and periodontal ligaments

Several finite element models of a primate cranium were used to investigate the biomechanical effects of the tooth sockets and the material behavior of the periodontal ligament (PDL) on stress and strain patterns associated with feeding. For examining the effect of tooth sockets, the unloaded sockets were modeled as devoid of teeth and PDL, filled with teeth and PDLs, or simply filled with cortical bone. The third premolar on the left side of the cranium was loaded and the PDL was treated as an isotropic, linear elastic material using published values for Young's modulus and Poisson's ratio. The remaining models, along with one of the socket models, were used to determine the effect of the PDL's material behavior on stress and strain distributions under static premolar biting and dynamic tooth loading conditions. Two models (one static and the other dynamic) treated the PDL as cortical bone. The other two models treated it as a ligament with isotropic, linear elastic material properties. Two models treated the PDL as a ligament with hyperelastic properties, and the other two as a ligament with viscoelastic properties. Both behaviors were defined using published stress-strain data obtained from in vitro experiments on porcine ligament specimens. Von Mises stress and strain contour plots indicate that the effects of the sockets and PDL material behavior are local. Results from this study suggest that modeling the sockets and the PDL in finite element analyses of skulls is project dependent and can be ignored if values of stress and strain within the alveolar region are not required.     

Middle Miocene dispersals of apes

The earliest record of fossil apes outside Africa is in the latest early Miocene of Turkey and eastern Europe. There were at least 2, and perhaps 4, species of ape, which were found associated with subtropical mixed environments of forest and more open woodland. Postcranial morphology is similar to that of early Miocene primates and indicates mainly generalized arboreal quadrupedal behaviours similar to those of less specialized New World monkeys such as Cebus. Robust jaws and thick enamelled teeth indicate a hard fruit diet. The 2 best known species of fossil ape are known from the site of Pa?alar in Turkey. They have almost identical molar and jaw morphology. Molar morphology is also similar to that of specimens from Germany and Slovakia, but there are significant differences in the anterior teeth of the 2 Pa?alar species. The more common species, Griphopithecus alpani, shares mainly primitive characters with early and middle Miocene apes in Africa, and it is most similar phenetically to Equatorius africanus from Maboko Island and Kipsaramon. The second species is assigned to a new species of Kenyapithecus, an African genus from Fort Ternan in Kenya, on the basis of a number of shared derived characters of the anterior dentition, and it is considered likely that there is a phylogenetic link between them. The African sites all date from the middle Miocene, similar in age to the Turkish and European ones, and the earliest emigration of apes from Africa coincides with the closure of the Tethys Sea preceding the Langhian transgression. Environments indicated for the African sites are mixtures of seasonal woodlands with some forest vegetation. The postcrania of both African taxa again indicate generalized arboreal adaptation but lacking specialized arboreal function. This middle Miocene radiation of both African and non-African apes was preceded by a radiation of arboreal catarrhine primates in the early Miocene, among which were the earliest apes. The earliest Miocene apes in the genus Proconsul and Rangwapithecus were arboreal, and because of their association with the fruits of evergreen rain forest plants at Mfwangano Island, it would appear that they were forest adapted, i.e. were living in multi-storied evergreen forest. The same or similar species of the same genera from Rusinga Island, together with other genera such as Nyanzapithecus and the small ape Limnopithecus, were associated with plants and animals indicating seasonal woodland environments, probably with gallery forest forming corridors alongside rivers. While the stem ancestors of the Hominoidea were almost certainly forest adapted, the evidence of environments associated with apes in the later part of the early Miocene and the middle Miocene of East Africa indicates more seasonal woodlands, similar to those reconstructed for the middle Miocene of Pa?alar in Turkey. This environmental shift was probably a requisite for the successful emigration of apes out of Africa and made possible later movement between the continents for much of the middle Miocene, including possible re-entry of at least one ape lineage back into Africa.     

A two-layer elasto-visco-plastic rheological model for the material parameter identification of bone tissue

The ability to measure bone tissue material properties plays a major role in diagnosis of diseases and material modeling. Bone’s response to loading is complex and shows a viscous contribution to stiffness, yield and failure. It is also ductile and damaging and exhibits plastic hardening until failure. When performing mechanical tests on bone tissue, these constitutive effects are difficult to quantify, as only their combination is visible in resulting stress–strain data. In this study, a methodology for the identification of stiffness, damping, yield stress and hardening coefficients of bone from a single cyclic tensile test is proposed. The method is based on a two-layer elasto-visco-plastic rheological model that is capable of reproducing the specimens’ pre- and postyield response. The model’s structure enables for capturing the viscously induced increase in stiffness, yield, and ultimate stress and for a direct computation of the loss tangent. Material parameters are obtained in an inverse approach by optimizing the model response to fit the experimental data. The proposed approach is demonstrated by identifying material properties of individual bone trabeculae that were tested under wet conditions. The mechanical tests were conducted according to an already published methodology for tensile experiments on single trabeculae. As a result, long-term and instantaneous Young’s moduli were obtained, which were on average 3.64 GPa and 5.61 GPa, respectively. The found yield stress of 16.89 MPa was lower than previous studies suggest, while the loss tangent of 0.04 is in good agreement. In general, the two-layer model was able to reproduce the cyclic mechanical test data of single trabeculae with an root-mean-square error of 2.91 ± 1.77 MPa. The results show that inverse rheological modeling can be of great advantage when multiple constitutive contributions shall be quantified based on a single mechanical measurement.

     

Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error ～0.5 mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.