Trabecular bone microdamage and microstructural stresses under uniaxial compression

The balance between local remodeling and accumulation of trabecular bone microdamage is believed to play an important role in the maintenance of skeletal integrity. However, the local mechanical parameters associated with microdamage initiation are not well understood. Using histological damage labeling, micro-CT imaging, and image-based finite element analysis, regions of trabecular bone microdamage were detected and registered to estimated microstructural von Mises effective stresses and strains, maximum principal stresses and strains, and strain energy density (SED). Bovine tibial trabecular bone cores underwent a stepwise uniaxial compression routine in which specimens were micro-CT imaged following each compression step. The results indicate that the mode of trabecular failure observed by micro-CT imaging agreed well with the polarity and distribution of stresses within an individual trabecula. Analysis of on-axis subsections within specimens provided significant positive relationships between microdamage and each estimated tissue stress, strain and SED parameter. In a more localized analysis, individual microdamaged and undamaged trabeculae were extracted from specimens loaded within the elastic region and to the apparent yield point. As expected, damaged trabeculae in both groups possessed significantly higher local stresses and strains than undamaged trabeculae. The results also indicated that microdamage initiation occurred prior to apparent yield at local principal stresses in the range of 88-121 MPa for compression and 35-43 MPa for tension and local principal strains of 0.46-0.63% in compression and 0.18-0.24% in tension. These data provide an important step towards understanding factors contributing to microdamage initiation and establishing local failure criteria for normal and diseased trabecular bone.     

Resting Sarcomere Length-Tension Relation in Living Frog Heart

The sarcomere pattern and tension of isolated resting frog atrial trabeculae were continuously monitored. In the absence of any resting tension the sarcomere lengths varied with the diameter of the trabeculae. In over 75 % of the trabeculae the value exceeded 2.05 µm, the estimated in vivo length of the thin filaments, and it was never less than 1.89 µm. When the trabeculae were stretched the increase in length of the central undamaged portion could be completely accounted for by an increase in sarcomere length. The width of the A band was constant only at sarcomere lengths between 2.3 and 2.6 µm it decreased at smaller and increased at larger sarcomere lengths. A group of spontaneously active cells stretched the sarcomeres in cells in series to longer lengths than could be produced by passive tension applied to the ends of the trabeculae, but they did not influence the sarcomeres of adjacent cells. It is proposed that the connective tissue is a major factor in determining sarcomere length and that there are interactions between thick and thin filaments in resting muscles.     

Trabecular bone scales allometrically in mammals and birds

Many bones are supported internally by a latticework of trabeculae. Scaling of whole bone length and diameter has been extensively investigated, but scaling of the trabecular network is not well characterized. We analysed trabecular geometry in the femora of 90 terrestrial mammalian and avian species with body masses ranging from 3 g to 3400 kg. We found that bone volume fraction does not scale substantially with animal size, while trabeculae in larger animals' femora are thicker, further apart and fewer per unit volume than in smaller animals. Finite element modelling indicates that trabecular scaling does not alter the bulk stiffness of trabecular bone, but does alter strain within trabeculae under equal applied loads. Allometry of bone's trabecular tissue may contribute to the skeleton's ability to withstand load, without incurring the physiological or mechanical costs of increasing bone mass.     

The fabric dependence of the orthotropic elastic constants of cancellous bone

It has been proposed that the orthotropic elastic constants of cancellous bone depend upon a tensorial measure of anisotropy called fabric as well as the tissue's structural density. Cowin (1985, Mechanics Mater, 4, 137-147; 1986, J. biomech. Engng 108, 83-88) developed explicit relationships for the elastic constant, structural density and fabric relationship. In this study the orthotropic elastic moduli, structural density, and fabric components were measured for 11 cancellous bone specimens from five bovine femora and for 75 specimens from three human proximal tibiae and fitted to these relationships using a least squares analysis. The relationships explained between 72 and 94% of the variance in the elastic constants. The relationships between the elastic constants and squared or cubed power functions of structural density had better predictive value over the entire distribution of the data than did expressions with linear functions of structural density.     

A cellular solid criterion for predicting the axial-shear failure properties of bovine trabecular bone.

In a long-term effort to develop a complete multi-axial failure criterion for human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai-Wu, Principal Strain, and von Mises phenomenological criteria--all normalized to minimize effects of interspecimen heterogeneity of strength--to predict the on-axis axial-shear failure properties of bovine trabecular bone. The Cellular Solid criterion that was developed here assumed that vertical trabeculae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, respectively. Twenty-seven bovine tibial trabecular bone specimens were destructively tested on-axis without end artifacts, loaded either in combined tension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6). For compression-shear, the mean (+/- S.D.) percentage errors between measured values and criterion predictions were 7.7 +/- 12.6 percent, 19.7 +/- 23.2 percent, 22.8 +/- 18.9 percent, and 82.4 +/- 64.5 percent for the Cellular Solid, Tsai-Wu, Principal Strain, and von Mises criteria, respectively; corresponding mean errors for tension-shear were -5.2 +/- 11.8 percent, 14.3 +/- 12.5 percent, 6.9 +/- 7.6 percent, and 57.7 +/- 46.3 percent. Statistical analysis indicated that the Cellular Solid criterion was the best performer for compression-shear, and performed as well as the Principal Strain criterion for tension-shear. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More importantly, the results firmly establish the importance of cellular solid analysis for understanding and predicting the multiaxial failure behavior of trabecular bone.     

Tensile and compressive behaviour of the bovine periodontal ligament

The mechanical response of the bovine periodontal ligament (PDL) subjected to uniaxial tension and compression is reported. Several sections normal to the longitudinal axis of bovine incisors and molars were extracted from different depths. Specimens with dimensions 10 x 5 x 2 mm including dentine, PDL and alveolar bone were obtained from these sections. Scanning electron microscopy suggested a strong similarity between the bovine PDL and the human PDL microstructure described in the literature. The prepared specimens were tested in a custom made uniaxial testing machine. They were clamped on their bone and dentine extremities and immersed in a saline solution at 37 degrees C. Stress-strain curves indicated that the PDL is characterized by a non-linear and time-dependent mechanical behaviour with the typical features of collagenous soft tissues. The curves exhibited hysteresis and preconditioning effects. The mechanical parameters evaluated in tension were maximum tangent modulus, strength, maximizer strain and strain energy density. For the molars, all these parameters increased with depth except for the apical region. For the incisors, all parameters increased with depth except ultimate strain which decreased. It was assumed that collagen fibre density and orientation were responsible for these findings.     

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.     

Mechanical properties of single bovine trabeculae are unaffected by strain rate

For a better understanding of traumatic bone fractures, knowledge of the mechanical behavior of bone at high strain rates is required. Importantly, it needs to be clarified how quasistatic mechanical testing experiments relate to real bone fracture. This merits investigating the mechanical behavior of bone with an increase in strain rate. Various studies examined how cortical and trabecular bone behave at varying strain rates, but no one has yet looked at this question using individual trabeculae. In this study, three-point bending tests were carried out on bovine single trabeculae excised from a proximal femur to test the trabecular material's strain rate sensitivity. An experimental setup was designed, capable of measuring local strains at the surface of such small specimens, using digital image correlation. Microdamage was detected using the bone whitening effect. Samples were tested through two orders of magnitude, at strain rates varying between 0.01 and 3.39 s(-1). No linear relationship was observed between the strain rate and the Young's modulus (1.13-16.46 GPa), the amount of microdamage, the maximum tensile strain at failure (14.22-61.65%) and at microdamage initiation (1.95-12.29%). The results obtained in this study conflict with previous studies reporting various trends for macroscopic cortical and trabecular bone samples with an increase in strain rate. This discrepancy might be explained by the bone type, the small sample geometry, the limited range of strain rates tested here, the type of loading and the method of microdamage detection. Based on the results of this study, the strain rate can be ignored when modeling trabecular bone.     

Fracture prediction for the proximal femur using finite element models: Part I--Linear analysis.

Over 90 percent of the more than 250,000 hip fractures that occur annually in the United States are the result of falls from standing height. Despite this, the stresses associated with femoral fracture from a fall have not been investigated previously. Our objectives were to use three-dimensional finite element models of the proximal femur (with geometries and material properties based directly on quantitative computed tomography) to compare predicted stress distributions for one-legged stance and for a fall to the lateral greater trochanter. We also wished to test the correspondence between model predictions and in vitro strain gage data and failure loads for cadaveric femora subjected to these loading conditions. An additional goal was to use the model predictions to compare the sensitivity of several imaging sites in the proximal femur which are used for the in vivo prediction of hip fracture risk. In this first of two parts, linear finite element models of two unpaired human cadaveric femora were generated. In Part II, the models were extended to include nonlinear material properties for the cortical and trabecular bone. While there was poor correspondence between strain gage data and model predictions, there was excellent agreement between the in vitro failure data and the linear model, especially using a von Mises effective strain failure criterion. Both the onset of structural yielding (within 22 and 4 percent) and the load at fracture (within 8 and 5 percent) were predicted accurately for the two femora tested. For the simulation of one-legged stance, the peak stresses occurred in the primary compressive trabeculae of the subcapital region.(ABSTRACT TRUNCATED AT 250 WORDS)     

The elastic and ultimate properties of compact bone tissue

The use of a tranversely isotropic model is tested for the elastic behavior of bovine and human bone and the five independent constants of this model are determined. The accuracy of the model is tested for eight cases by comparing the off-axis modulus predicted by a rotation of stiffness matrix with an experimentally determined off-axis modulus.

Ultimate properties are presented for bovine and human bone for tension, compression, and torsional loads. A Hankinson type failure criterion is proposed for off-axis ultimate stress and this predicted value compared with experimental values for nine cases.     

Fracture properties of bovine tibial bone

Linear elastic fracture mechanics predicts that the fracture stress of precracked materials is dependent on the length of the initial crack tip radius of curvature, as supported by the Griffith and Inglis equations. In order to determine the applicability of these equations and the effects of other variables, tensile specimens of bovine tibia were produced with edge cracks of known dimensions and tested to fracture. Longitudinal sheet tensile specimens were taken from the midposterior diaphysis of bovine tibiae that had been kept frozen in saline soaked towels. Each specimen had a milled gauge length of 25 mm, 16 mm width and 2 mm thickness. All specimen preparation was performed under a saline drip. An edge crack, centered along the gauge length, was milled in the specimen perpendicular to its long axis. The crack lengths used were 4, 6, 8, 10 and 12 mm. The crack tip was formed with drill bits having nominal diameters of 1/32, 1/16, and 3/32 in. All the combinations of crack length and crack tip radius were repeated five times for a total of 75 specimens. The testing order was randomly selected. Each specimen was tested in tension to fracture at a constant deformation rate of 7.5 X 10(-3) mm s-1, on an Instron mechanical testing device, and the fracture stress was measured. A linear load-deflection curve to fracture was exhibited by all of the specimens. The weight percent calcium of each specimen was determined by atomic absorption spectrophotometry. Microradiographs were used to determine the fractional void area and to histologically evaluate each bone sample.(ABSTRACT TRUNCATED AT 250 WORDS)     

Lengthening-contractions in isolated myocardium impact force development and worsen cardiac contractile function in the mdx mouse model of muscular dystrophy

Lengthening-contractions exert eccentric stress on myofibers in normal myocardium. In congestive heart failure caused by a variety of diseases, the impact of lengthening-contractions of myocardium likely becomes more prevalent and severe. The present study introduces a method to investigate the role of stretching imposed by repetitive lengthening-contractions in myocardium under near-physiological conditions. By exerting various stretch-release ramps while the muscle is contracting, consecutive lengthening-contractions and their potential detrimental effect on cardiac function can be studied. We tested our model and hypothesis in age-matched (young and adult) mdx and wild-type mouse right ventricular trabeculae. These linear and ultrathin muscles possess all major cardiac cell types, and their contractile behavior very closely mimics that of the whole myocardium. In the first group of experiments, 10 lengthening-contractions at various magnitudes of stretch were performed in trabeculae from 10-wk-old mdx and wild-type mice. In the second group, 100 lengthening-contractions at various magnitudes were conducted in trabeculae from 10- and 20-wk-old mice. The peak isometric active developed tension (F(dev), in mN/mm(2)) and kinetic parameters time to peak tension (TTP, in ms) and time from peak tension to half-relaxation (RT50, in ms) were measured. Our results indicate lengthening-contractions significantly impact contractile behavior, and that dystrophin-deficient myocardium in mdx mice is significantly more susceptible to these damaging lengthening-contractions. The results indicate that lengthening-contractions in intact myocardium can be used in vitro to study this emerging contributor to cardiomyopathy.     

Elastic modulus of trabecular bone material

An ultrasonic technique was used to measure both the elastic modulus (Young's modulus) of trabecular bone material and the elastic modulus of the cancellous structure. The average trabecular modulus, measured on specimens obtained from three human and one bovine distal femora, was 13.0 GPa (S.D. 1.47) and 10.9 GPa (S.D. 1.57), respectively. On human specimens the structural elastic modulus was found to be related to the structural (apparent) density raised to the 1.88 power. The elastic modulus from the bovine specimens showed a more linear relationship with the density of the cancellous structure (density raised to the 1.57 power).     

Yield behavior of bovine cancellous bone

The compressive yield strain was measured for 61 specimens of bovine cancellous bone from three distal femora. There was no significant relationship (p = 0.08, R2 = 0.051) between yield strain and the degree of trabecular orientation. There was a significant positive correlation (p less than 0.00001, R2 = 0.319) between yield strain and structural (apparent) density and significant negative correlation (p less than 0.0025, R2 = 0.145) between yield strain and bone density. Yield strain correlated best with bone solid volume fraction Vv (epsilon y = 0.592 +2- 1.446vv, R2 = 0.337). The quantity, yield strain, is highly dependent on specific definitions of the yield point and the point of zero strain. For this study the yield point was defined by a 0.0003 offset criterion, and the point of zero strain was defined as the point where the tangent at 15 percent of yield crosses zero. The results using these definitions were compared with results using yield strain values determined by other definitions of the yield point and zero strain. The correlations between yield strain and trabecular orientation, structural density and bone density changed very little for differing definitions of yield. The results suggest that yield strain in cancellous bone is isotropic or independent of textural anisotropy, so the yield behaviour may be characterized by a maximum strain yield criterion. The results also suggest that the primary mode of yield in cancellous bone is buckling of the trabeculae.     

Tensile strength of bovine trabecular bone

Data on the tensile and compressive properties of trabecular bone are needed to define input parameters and failure criteria for modeling total joint replacements. To help resolve differences in reports comparing tensile and compressive properties of trabecular bone, we have developed new methods, based on porous foam technology, for tensile testing of fresh/frozen trabecular bone specimens. Using bovine trabecular bone from an isotropic region from the proximal humerus as a model material, we measured ultimate strengths in tension and compression for two groups of 24 specimens each. The average ultimate strength in tension was 7.6 +/- 2.2 (95% C.I.) MPa and in compression was 12.4 +/- 3.2 MPa. This difference was statistically significant (p = 0.013) and was not related to density differences between the test groups (p = 0.28). Strength was related by a power-law function of the local apparent density, but, even accounting for density influences, isotropic bovine trabecular bone exhibits significantly lower strengths in tension than in compression.     

Nonlinear behavior of trabecular bone at small strains

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress-strain nonlinearity, that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean +/- SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07+/- 3.24 percent in compression and 13.8 +/- 4.79 percent in tension. At 0.40 percent strain, these values were 23.5 +/- 5.71 and 35.7+/- 7.10 percent, respectively. The magnitude of the nonlineari't depended on both anatomic site (p < 0.001) and loading mode (p < 0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p < 0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress-strain behavior more thoroughly.     

A femoral neck fracture model in rabbits

A technique was developed to create a reproducible femoral neck fracture in vitro using 5-month-old JW/CSK series male rabbits. Force attenuation of a newly developed damping material was also evaluated using this model. Ten pairs of the femora with smaller deviations in length and weight were harvested and cleaned of soft tissue. Either a right or left of each pair of the specimens was randomly selected and put into either the control or the experimental group, both of which contained equal numbers of the right and left femora. The specimens were attached to an L-shaped plate and embedded in a resin from the proximal diaphysis to the distal end so as to maintain a consistent position of the femora. They were mounted and fixed on a pedestal slanted in the coronal plane at 20 degrees. The impact load testing was conducted using an impact mallet dropped from a height of 3 cm. The impact load was applied onto the femoral head. To the specimens in the experimental group, attenuated impact forces were loaded through the damping material, but those in the control group were subjected to forces directly transmitted without the material. All the impact testing was performed in a temperature and humidity controlled chamber. All of the femoral specimens exposed to the direct impact forces (controlled group) sustained fracture at the neck. The fracture line passed from the base of the femoral head laterally and to the calcar area just proximal to the minor trochanter medially. The location of each fracture line was almost identical among the specimens. None of the specimens that were exposed to the impact force through the damping material (experimental group) sustained fracture macroscopically and roentgenographically.     

Heterogeneous glycation of cancellous bone and its association with bone quality and fragility

Non-enzymatic glycation (NEG) and enzymatic biochemical processes create crosslinks that modify the extracellular matrix (ECM) and affect the turnover of bone tissue. Because NEG affects turnover and turnover at the local level affects microarchitecture and formation and removal of microdamage, we hypothesized that NEG in cancellous bone is heterogeneous and accounts partly for the contribution of microarchitecture and microdamage on bone fragility. Human trabecular bone cores from 23 donors were subjected to compression tests. Mechanically tested cores as well as an additional 19 cores were stained with lead-uranyl acetate and imaged to determine microarchitecture and measure microdamage. Post-yield mechanical properties were measured and damaged trabeculae were extracted from a subset of specimens and characterized for the morphology of induced microdamage. Tested specimens and extracted trabeculae were quantified for enzymatic and non-enzymatic crosslink content using a colorimetric assay and Ultra-high Performance Liquid Chromatography (UPLC). Results show that an increase in enzymatic crosslinks was beneficial for bone where they were associated with increased toughness and decreased microdamage. Conversely, bone with increased NEG required less strain to reach failure and were less tough. NEG heterogeneously modified trabecular microarchitecture where high amounts of NEG crosslinks were found in trabecular rods and with the mechanically deleterious form of microdamage (linear microcracks). The extent of NEG in tibial cancellous bone was the dominant predictor of bone fragility and was associated with changes in microarchitecture and microdamage.     

Microstructure-based Finite Element Modelling and Characterisation of Bovine Trabecular Bone

1 Introduction The mechanical behaviour of trabecular bone is dependent on both the properties of individual trabeculae as well as the three-dimensional architecture into which they are arranged. Hence, a comprehensive study of trabecular bone requires the consideration of microscopic as well as macroscopic length scales. Nanoindentation is a technique particularly suited to the mechanical characterisation of single trabecula[1?3] owing to the impracticalities of isolating individual tra- becu…     

Contribution, development and morphology of microcracking in cortical bone during crack propagation

A fracture mechanics study of cortical bone is presented to investigate the contribution, development morphology of microcracking in cortical bone during crack propagation. Post-hoc analyses of microcrack orientation, crack propagation velocity and fracture surface roughness were conducted on previously tested human and bovine bone compact tension specimens. It was found that, consistent with its higher toughness, bovine bone formed significantly more longitudinal, transverse and inclined microcracks than human bone. However, in human bone more of the microcracks that formed were longitudinal than transverse or inclined, a feature that would optimise bone's toughness. Crack propagation velocity in human and bovine bone displayed the same characteristic pattern with crack extension, where an increase in velocity is followed by a consequent decrease and vice versa. On the basis of this pattern, a model or crack propagation has been proposed. It provides a detailed account of mocrocrack formation and contribution towards the propagation of a fracture crack. Analyses of fracture surfaces indicated that, consistent with its higher toughness, bovine bone displays a rougher surface than human bone but they both have the same basic fractured element, i.e. a mineralised collagen fibril.