A morphological model of vertebral trabecular bone

In their micro-structures, typical natural cellular materials such as vertebral trabecular bone have a network of doubly tapered struts, thickening near the strut joints. However, past analytical models for vertebral trabecular bone do not take account of the effect of strut taper on the mechanical properties.This paper presents an analytical cell model comprised of doubly tapered struts to predict the global mechanical properties of vertebral trabecular bone. The predicted results for male, female, and both sexes fit the experimental data well. By considering several strut taper geometries, it is shown that the horizontal Young's modulus and the horizontal uniaxial collapse stress are, in some cases, approximately 1.8- and 2.2-fold higher, respectively, than those of the uniform strut model. This finding illustrates the importance of increased trabecular thickening near the strut joints (i) for improving the accuracy of calculating the mechanical properties and (ii) for the effective treatment of aged bone using drug therapy. It also highlights the need to combine trabecular architecture measurements with information about the morphology near the strut joints.     

Simulation of vertebral trabecular bone loss using voxel finite element analysis

Trabecular bone loss in human vertebral bone is characterised by thinning and eventual perforation of the horizontal trabeculae. Concurrently, vertical trabeculae are completely lost with no histological evidence of significant thinning. Such bone loss results in deterioration in apparent modulus and strength of the trabecular core. In this study, a voxel-based finite element program was used to model bone loss in three specimens of human vertebral trabecular bone. Three sets of analyses were completed. In Set 1, strain adaptive resorption was modelled, whereby elements which were subject to the lowest mechanical stimulus (principal strain) were removed. In Set 2, both strain adaptive and microdamage mechanisms of bone resorption were included. Perforation of vertical trabeculae occurred due to microdamage resorption of elements with strains that exceeded a damage threshold. This resulted in collapse of the trabecular network under compression loading for two of the specimens tested. In Set 3, the damage threshold strain was gradually increased as bone loss progressed, resulting in reduced levels of microdamage resorption. This mechanism resulted in trabecular architectures in which vertical trabeculae had been perforated and which exhibited similar apparent modulus properties compared to experimental values reported in the literature. Our results indicate that strain adaptive remodelling alone does not explain the deterioration in mechanical properties that have been observed experimentally. Our results also support the hypothesis that horizontal trabeculae are lost principally by strain adaptive resorption, while vertical trabeculae may be lost due to perforation from microdamage resorption followed by rapid strain adaptive resorption of the remaining unloaded trabeculae.     

A cellular solid model for modulus reduction due to resorption of trabeculae in bone

In osteoporotic trabecular bone, bone loss occurs by thinning and subsequent resorption of the trabeculae. In this study, we compare the effects of density reductions from uniform thinning of struts or from removal of struts in a random, open-cell, three-dimensional Voronoi structure. The results of this study, combined with those previous studies on other regular and random structures, suggest that the modulus and strength of trabecular bone are reduced more dramatically by density losses from resorption of trabeculae than by those from uniform thinning of trabeculae.     

Peak power and body mass as predictors of tibial bone strength in healthy male and female adults

Objective:The purpose of this study was to examine whether a non-invasive, muscular fitness field test was a better predictor of bone strength compared to body mass in healthy adults.Methods:Hierarchical multiple regression analyses were used to determine the amount of variance that peak power explained for tibial bone strength compared to body mass. Peak power was estimated from maximal vertical jump height using the Sayer’s equation. Peripheral quantitative computed tomography scans were used to assess bone strength measures.Results:Peak power (β=0.541, p<0.001) contributed more to the unique variance in bone strength index for compression (trabecular bone) compared to body mass (β=-0.102, p=0.332). For polar strength strain index (cortical bone), the beta coefficient for body mass remained significant (β=0.257, p<0.006), however peak power’s contribution was similar (β=0.213, p=0.051).Conclusion:Compared to body mass, peak power was a better predictor for trabecular bone strength but similar to body mass for cortical bone strength. These data provide additional support for the development of a vertical jump test as an objective, valid and reliable measure to monitor bone strength among youth and adult populations.     

The effect of charge density on the velocity and attenuation of ultrasound waves in human cancellous bone

Cancellous bone is a highly porous material, and two types of waves, fast and slow, are observed when ultrasound is used for detecting bone diseases. There are several possible stimuli for bone remodelling processes, including bone fluid flow, streaming potential, and piezoelectricity. Poroelasticity has been widely used for elucidating the bone fluid flow phenomenon, but the combination of poroelasticity with charge density has not been introduced. Theoretically, general poroelasticity with a varying charge density is employed for determining the relationship between wave velocity and attenuation with charge density. Fast wave velocity and attenuation are affected by porosity as well as charge density; however, for a slow wave, both slow wave velocity and attenuation are not as sensitive to the effect of charge density as they are for a fast wave. Thus, employing human femoral data, we conclude that charged ions gather on trabecular struts, and the fast wave, which moves along the trabecular struts, is significantly affected by charge density.     

Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage ?1.16 %, tension damage 0.69 %, compression fracture ?2.91 % and tension fracture 1.98 %. Ultimate strength and post–ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile–brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post–ultimate strength softening.     

A comparative study of the trabecular bony architecture of the talus in humans, non-human primates, and Australopithecus

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.     

Multiaxial strength characteristics of trabecular bone

Bovine trabecular bone specimens were tested in multiaxial stress, including pure shear, in a special test device. Shear strength was proportional to apparent density to the exponent 1.65, in approximate agreement with theoretical and experimental studies on the shear strengths of porous foams. The mean shear strength was 6.60 +/- 1.66 MPa, after normalizing for apparent density. This compares well with normalized shear strengths from Saha and Gorman's (1981) study on human femora. A scanning electron microscope study indicated random trabecular architecture and a complex fracture mechanism at the level of the individual trabecular struts. Hoffmann's (1967) 3-D isotropic failure criterion was applied to the multiaxial test data, along with data from uniaxial compression tests, indicating a compressive strength approximately three times the tensile strength.     

Up,up, and away: relative importance of horizontal and vertical escape from predators for survival and senescence

Animals fleeing a potential predator can escape horizontally or vertically, although vertical flight is more expensive than horizontal flight. The ability to escape in three dimensions by flying animals has been hypothesized to result in greater survival and eventually slower senescence than in animals only fleeing in two dimensions. In a comparative study of flight initiation distance in 69 species of birds when approached by a human, I found that the amount of variance explained by flight initiation distance was more than four times as large for the horizontal than the vertical component of perch height when taking flight. The slope of the relationship between horizontal distance and flight initiation distance (horizontal slope) increased with increasing body mass across species, whereas the slope of the relationship between vertical distance and flight initiation distance (vertical slope) decreased with increasing body mass. Therefore, there was a negative relationship between horizontal and vertical slope, although this negative relationship was significantly less steep than expected for a perfect trade‐off. The horizontal slope decreased with increasing density of the habitat from grassland over shrub to forest, whereas that was not the case for the vertical slope. Adult survival rate increased and rate of senescence (longevity adjusted for survival rate, body mass and sampling effort) decreased with increasing vertical, but not with horizontal slope, consistent with the prediction that vertical escape indeed provides a means of reducing the impact of predation.     

Palaeohistology of the bones of pterosaurs (Reptilia: Archosauria): anatomy, ontogeny, and biomechanical implications

Thin sections from long bones of specimens representing pterosaurs ranging from the Early Jurassic to the latest Cretaceous provide a profile of bone histology across a range of sizes, skeletal elements, growth stages, and phylogenetic positions. Most pterosaur bone is fibro-lamellar, organized in an unusual way that suggests high growth rates through ontogeny. Fibro-lamellar deposits are finished by a relatively abrupt deceleration or cessation of growth represented by lamellar, poorly vascularized subperiosteal bone in what appear to be adults. Pterosaurs had the thinnest bone walls of any tetrapods; they complemented high rates of periosteal deposition with almost equally high rates of endosteal erosion. Pterosaurs show a great variety of histologic features that include articular calcified cartilage, sub-chondral bone plates, trabecular bone struts and related internal supports, and secondary deposition and remodeling of bone. They remodeled their bones internally by (1) depositing endosteal bone coatings on the inner cortex and over struts of pre-existing internal bone, (2) secondarily filling bone spaces, and (3) Haversian reworking. The construction of these struts reflects both developmental patterns of bone construction and biomechanical function. Alternating plywood-like layers of bone, heretofore undescribed in tetrapods, provided strength, as did the obliquely oriented system of reticular blood vessels in the bones. The distribution and ontogenetic features of pterosaur bone tissues, when combined with other evidence, suggest generally high growth rates, high metabolic levels, altricial birth, and extended parental care.     

Three-dimensional analysis of nonhuman primate trabecular architecture using micro-computed tomography

Until recently, detailed analyses of the architecture of nonhuman primate cancellous bone have not been possible due to a combination of methodological constraints, including poor resolution imaging or destructive protocols. The development of micro-computed tomography (microCT) and morphometric methods associated with this imaging modality offers anthropologists a new means to study the comparative architecture of cancellous bone. Specifically, microCT will allow anthropologists to investigate the relationship between locomotor behavior and trabecular structure. We conducted a preliminary study on the trabecular patterns in the proximal humerus and femur of Hylobates lar, Ateles paniscus, Macaca mulatta, and Papio anubis to investigate the quantitative differences in their trabecular architecture and evaluate the potential of microCT in anthropological inquiry. MicroCT allows the researcher to evaluate variables beyond simple two-dimensional orientations and radiographic densities. For example, this methodology facilitates the study of trabecular thickness and bone volume fraction using three-dimensional data. Results suggest that density-related parameters do not reliably differentiate suspensory-climbing species from quadrupedal species. However, preliminary results indicate that measurements of the degree of anisotropy, a measure of trabecular orientation uniformity, do distinguish suspensory-climbing taxa from more quadrupedal species. The microCT method is an advance over conventional radiography and medical CT because it can accurately resolve micron-sized struts that make up cancellous bone, and from these images a wide array of parameters that have been demonstrated to be related to cancellous bone mechanical properties can be measured. Methodological problems pertinent to any comparative microCT study of primate trabecular architecture are discussed.     

Compressive fatigue behavior of human vertebral trabecular bone

Damage accumulation under compressive fatigue loading is believed to contribute significantly to non-traumatic, age-related vertebral fractures in the human spine. Only few studies have explored trabecular bone fatigue behavior under compressive loading and none examined the influence of trabecular architecture on fatigue life. In this study, trabecular bone samples of human lumbar and thoracic vertebrae (4 donors from age 29 to 86, n=29) were scanned with a microCT system prior to compressive fatigue testing to determine morphology-mechanical relationships for this relevant loading mode. Inspired from previous fabric-based relationships for elastic properties and quasi-static strength of trabecular bone, a simple power relationship between volume fraction, fabric eigenvalue, applied stress and the number of cycles to failure is proposed. The experimental results demonstrate a high correlation for this relationship (R2=0.95) and detect a significant contribution of the degree of anisotropy towards prediction of fatigue life. Step-wise regression for total and residual strains at failure suggested a weak, but significant correlation with volume fraction. From the obtained results, we conclude that the applied stress normalized by volume fraction and axial fabric eigenvalue can estimate fatigue life of human vertebral trabecular bone in axial compressive loading.     

Trabecular Evidence for a Human-Like Gait in Australopithecus africanus

Although the earliest known hominins were apparently upright bipeds, there has been mixed evidence whether particular species of hominins including those in the genus Australopithecus walked with relatively extended hips, knees and ankles like modern humans, or with more flexed lower limb joints like apes when bipedal. Here we demonstrate in chimpanzees and humans a highly predictable and sensitive relationship between the orientation of the ankle joint during loading and the principal orientation of trabecular bone struts in the distal tibia that function to withstand compressive forces within the joint. Analyses of the orientation of these struts using microCT scans in a sample of fossil tibiae from the site of Sterkfontein, of which two are assigned to Australopithecus africanus, indicate that these hominins primarily loaded their ankles in a relatively extended posture like modern humans and unlike chimpanzees. In other respects, however, trabecular properties in Au africanus are distinctive, with values that mostly fall between those of chimpanzees and humans. These results indicate that Au. africanus, like Homo, walked with an efficient, extended lower limb.     

Trabecular shear stress in human vertebral cancellous bone: intra- and inter-individual variations

Correlation of the mean and standard deviation of trabecular stresses has been proposed as a mechanism by which a strong relationship between the apparent strength and stiffness of cancellous bone can be achieved. The current study examined whether the relationship between the mean and standard deviation of trabecular von Mises stresses can be generalized for any group of cancellous bone. Cylindrical human vertebral cancellous bone specimens were cut in the infero-superior direction from T12 of 23 individuals (inter-individual group). Thirty nine additional specimens were prepared similarly from the T4-T12 and L2-L5 vertebrae of a 63 year old male (intra-individual group). The specimens were scanned by micro-computed tomography (microCT) and trabecular von Mises stresses were calculated using finite element modeling. The expected value, standard deviation and coefficient of variation of the von Mises stress were calculated form a three-parameter Weibull function fitted to von Mises stress data from each specimen. It was found that the average and standard deviation of trabecular von Mises shear stress were: (i) correlated with each other, supporting the idea that high correlation between the apparent strength and stiffness of cancellous bone can be achieved through controlling the trabecular level shear stress variations, (ii) dependent on anatomical site and sample group, suggesting that the variation of stresses are correlated to the mean stress to different degrees between vertebrae and individuals, and (iii) dependent on bone volume fraction, consistent with the idea that shear stress is less well controlled in bones with low BV/TV. The conversion of infero-superior loading into trabecular von Mises stresses was maximum for the tissue at the junction of the thoracic and lumbar spine (T12-L1) consistent with this junction being a common site of vertebral fracture.     

On shear properties of trabecular bone under torsional loading: effects of bone marrow and strain rate

To further improve our understanding of trabecular bone mechanical behavior in torsion, our objective was to determine the effects of strain rate, apparent density, and presence of bone marrow on trabecular bone shear material properties. Torsion tests of cylindrical trabecular bone specimens from sheep lumbar vertebrae with and without bone marrow were conducted. The bones with marrow were divided into two groups and tested at shear strain rates of 0.002 and 0.05s(-1) measured at the specimen perimeter. The bones without marrow were divided into three groups and tested at shear strain rates of 0.002, 0.015, and 0.05s(-1). Comparing the results of bones with and without marrow tested at low (0.002s(-1)) and high (0.05s(-1)) strain rates, presence of bone marrow did not have any significant effect on trabecular bone shear modulus and strength. In specimens without marrow, power relationships were used to define shear strength and modulus as dependent variables in terms of strain rate and apparent density as independent variables. The shear strength was proportional to the apparent density raised to the 1.02 power and to the strain rate raised to the 0.13 power. The shear modulus was proportional to the apparent density raised to the 1.08 power and to the strain rate raised to the 0.07 power. This study provides further insight into the mechanism of bone failure in trauma as well as failure at the interface between bone and implants as it relates to prediction of trabecular bone shear properties.     

Relationship between reactive strength variables in horizontal and vertical drop jumps

The aim of this study was to investigate the relationship between reactive strength in a vertical and a horizontal drop jump (DJ). Subjects (n = 28) with previous jump training experience, performed 6 vertical DJs and 6 horizontal DJs from a 0.4-m box. Contact time, height jumped, distance jumped, and reactive strength index (RSI) were calculated and analyzed. Typical error measurements (TEMCV%) and intraclass correlations (ICCs) were used to assess the intrasubject reliability. Relationships between jumps and within jumps of the aforementioned variables were assessed using ICCs. The ICC (r > 0.789) and the TEMCV% (<10%) indicated good reliability for both vertical and horizontal DJs across each variable. Contact time showed no relationship between jumps (r = 0.222) and had no effect on the vertical DJ height (r = 0.152) or horizontal DJ distance (r = 0.261). The RSI correlation (r = 0.533) indicated a large relationship between reactive ability in the horizontal DJ and the vertical DJ. Contact times were significantly lower in vertical DJs compared with horizontal DJs (p < 0.0001). This study indicated that horizontal DJs are reliable and may be better used to train reactive movements that do not require brief contact times.     

A global relationship between trabecular bone morphology and homogenized elastic properties.

An alternative concept of the relationship between morphological and elastic properties of trabecular bone is presented and applied to human tissue from several anatomical locations using a digital approach. The three-dimensional morphology of trabecular bone was assessed with a microcomputed tomography system and the method of directed secants as well as the star volume procedure were used to compute mean intercept length (MIL) and average bone length (ABL) of 4 mm cubic specimens. Assuming isotropic elastic properties for the trabecular tissue, the general elastic tensors of the bone specimens were determined using the homogenization method and the closest orthotropic tensors were calculated with an optimization algorithm. The assumption of orthotropy for trabecular bone was found to improve with specimen size and hold within 6.1 percent for a 4 mm cube size. A strong global relationship (r2 = 0.95) was obtained between fabric and the orthotropic elastic tensor with a minimal set of five constants. Mean intercept length and average bone length provided an equivalent power of prediction. These results support the hypothesis that the elastic properties of human trabecular bone from an arbitrary anatomical location can be estimated from an approximation of the anisotropic morphology and a prior knowledge of tissue properties.     

Similarity in the fatigue behavior of trabecular bone across site and species

Within the context of improving knowledge of the structure-function relations for trabecular bone for cyclic loading, we hypothesized that the S-N curve for cyclic compressive loading of trabecular bone, after accounting for differences in monotonic strength behavior, does not depend on either site or species. Thirty-five cores of fresh-frozen elderly human vertebral trabecular bone, harvested from nine donors (mean+/-S.D., age=74+/-17 years), were biomechanically tested in compression at sigma/E(0) values (ratio of applied stress to pre-fatigue elastic modulus) ranging from 0.0026 to 0.0070, and compared against literature data (J. Biomech. Eng. 120 (1998) 647-654) for young bovine tibial trabecular bone (n=37). As reported for the bovine bone, the number of cycles to failure for the human vertebral bone was related to sigma/E(0) by a power-law relation (r(2)=0.54, n=35). Quantitative comparison of these data against those reported for the bovine bone supported our hypothesis. Namely, when the differences in mean monotonic yield strain between the two types of bone were accounted for, a single S-N curve worked well for the pooled data (r(2)=0.75, n=72). Since elderly human vertebral and young bovine tibial trabecular bone represent two very different types of trabecular bone in terms of volume fraction and architecture, these findings suggest that the dominant failure mechanisms in trabecular bone for cyclic loading occur at the ultrastructural level.     

Simulation of bone strain by orthodontic implants using the finite element method]

Load direction of applied forces, implant geometry and other biomechanical parameters lead to varying reactions in the surrounding bone structure. Three types of endosseous implant measuring 9 mm in length and 3.3 mm in diameter with and without superperiosteal step, and a threaded surface were investigated with the aid of a finite element method using the COSMOS/M 2.5 program. The load on the implant was investigated under vertical, horizontal, and diagonal forces of between 0.01 N and 100 N. Vertical loading of simple implants caused bone deformation of more than 600 mu eps. The application of the superperiosteal step clearly reduced the deformation. The largest deformations under vertical loading were observed in the trabecular bone with all 3 implant geometries. On horizontal loading the deformation shifted from the trabecular to the cortical bone and was particularly marked at the transition between the two. The smallest deformations, less than 300 mu eps, were measured at implants with a superperiosteal step under diagonal loading. The thread did not improve loading capacity. Implants with a superperiosteal step are recommended since they contribute to more rapid healing and strengthening of the bone.