The effect of Haversian remodeling on the tensile properties of human cortical bone

The purpose of this study was to determine the effect of Haversian remodeling on the tensile properties of human cortical bone by testing specimens containing, as far a possible, a single type of bone tissue. Fifty-one specimens were prepared from sixteen fresh tibias, removed at autopsy. Age range was 19-35. Regions were selected so that the specimens would consist almost exclusively of either primary bone or Haversian bone. The ultimate tensile strength, ultimate strain and Young's modulus of elasticity were determined at a loading rate of 0.05 mm s-1. The primary bone specimens were found to have a significantly higher ultimate tensile strength and modulus of elasticity than those formed of Haversian bone.     

The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone

The Young's modulus of elasticity, the calcium content and the volume fraction (1-porosity) of 23 tension specimens and 80 bending specimens, taken from compact bone of 18 species of mammal, bird and reptile, were determined. There was a strong positive relationship between Young's modulus and both calcium content and volume fraction. A power law model fits the data better than a linear model. Young's modulus has a roughly cubic relationship with both calcium content and volume fraction. Over 80% of the total variation in Young's modulus in this data set is explained by these two variables.     

The underestimation of Young's modulus in compressive testing of cancellous bone specimens

In order to determine the accuracy of measurements of Young's modulus of cancellous bone by conventional compression testing, two independent strain measurements were made simultaneously during non-destructive uniaxial compression to 0.8% strain of rectangular specimens (n = 18). Strain was measured by an extensometer attached to the compression anvils close to the specimen and by an optical system covering the central half of the specimens. Mean Young's modulus determined by the extensometer technique was 689 MPa, but was 871 MPa when determined by the optical technique (mean difference = 182 MPa, SED = 50 MPa, p less than 0.002). Uneven strain distribution due to lack of support of cut vertical trabeculae at the anvil-specimen interface is believed to be causing the underestimation of Young's modulus measured by the extensometer technique. The influence of friction at the specimen-anvil interface was studied by performing a finite element analysis. It is concluded that Young's modulus of specimens of the chosen geometry on average is underestimated by about 20% by conventional compressing testing. The underestimation seems not to be dependent upon specimen density.     

Evaluation of filler materials used for uniform load distribution at boundaries during structural biomechanical testing of whole vertebrae

This study was designed to compare the compressive mechanical properties of filler materials, Wood's metal, dental stone, and polymethylmethacrylate (PMMA), which are widely used for performing structural testing of whole vertebrae. The effect of strain rate and specimen size on the mechanical properties of the filler materials was examined using standardized specimens and mechanical testing. Because Wood's metal can be reused after remelting, the effect of remelting on the mechanical properties was tested by comparing them before and after remelting. Finite element (FE) models were built to simulate the effect of filler material size and properties on the stiffness of vertebral body construct in compression. Modulus, yield strain, and yield strength were not different between batches (melt-remelt) of Wood's metal. Strain rate had no effect on the modulus of Wood's metal, however, Young's modulus decreased with increasing strain rate in dental stone whereas increased in PMMA. Both Wood's metal and dental stone were significantly stiffer than PMMA (12.7 +/- 1.8 GPa, 10.4 +/- 3.4 GPa, and 2.9 +/- 0.4 GPa, respectively). PMMA had greater yield strength than Wood's metal (62.9 +/- 8.7 MPa and 26.2 +/- 2.6 MPa). All materials exhibited size-dependent modulus values. The FE results indicated that filler materials, if not accounted for, could cause more than 9% variation in vertebral body stiffness. We conclude that Wood's metal is a superior moldable bonding material for biomechanical testing of whole bones, especially whole vertebrae, compared to the other candidate materials.     

Mechanical behavior of intact and low-grade degenerated cartilage.

Young's modulus, elastic and plastic deformation, mechanical hardness and load at failure were determined for low-grade degenerated hyaline cartilage in a porcine model. Osteochondral plugs from the medial condyle of 30 female pigs were used. Cartilage defects were classified using the International Cartilage Repair Society (ICRS) protocol. Mechanical hardness was measured using a Shore A testing device. Total stiffness and plastic deformation was evaluated in the range 50-200 N using a 5-mm indenter. The load at failure was then determined. ICRS grade I specimens showed significantly lower stiffness than grade 0 specimens. ICRS grade 0 specimen showed no significant plastic deformation within the load range 25-100 N. In degenerated cartilage, plastic deformation started at a significantly lower load (50 N). The Young's modulus at 25 N in ICRS grade 0 specimens (18.8 MPa) was significantly higher than in grade I (11.1 MPa) or grade II (10.5 MPa) specimens. Intact cartilage showed significantly higher tension at failure and mechanical Shore A hardness. Young's modulus and tension at failure showed strong correlation. Cartilage degeneration is associated with a significant loss of elasticity and mechanical stress resistance. Shore hardness measurement is an adequate method for rapid biomechanical evaluation of cartilage specimens.     

Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique

The Hopkinson bar stress technique and a universal testing machine (Instron 1125) have been used to investigate the dynamic and static mechanical properties of cortical bone taken from a human femur respectively. We found that the average dynamic Young's modulus value (Ed = 19.9 GPa) to be 23% higher than the average static Young's modulus value (Ed = 16.2 GPa). Furthermore, the Poisson's ratio did not exhibit any significant variation for the two different types of loading. No difference was observed between the values of the dynamic Young's modulus in tension and those found in compression. A comparison was made of the results of this study with those found by other researchers using different techniques, such as ultrasonics, and it was found that they agree well with most of the results of previous studies. Finally, the viscosity for cortical bone found in this study correlates with viscosity reported by Tennyson et al. [Expl Mech. 12, 502-507 (1972)] for ten days post mortem age specimens.     

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.     

Tensile and compressive properties of cancellous bone

The relationship between the mechanical properties of trabecular bone in tension and compression was investigated by non-destructive testing of the same specimens in tension and compression, followed by random allocation to a destructive test in either tension or compression. There was no difference between Young's modulus in tension and compression, and there was a strong positive correlation between the values (R = 0.97). Strength, ultimate strain and work to failure was significantly higher in tensile testing than in compressive testing.     

Mechanical properties and chemical composition of avian long bones

We have studied the mechanical behaviour of avian long bones as whole structures, by calculating mechanical parameters such as maximum load, stiffness, bending strength and flexural Young's modulus; bones were always tested in three-point bending. Furthermore composition in several chemical elements and amino acids related to collagen content was also analysed. Correlations were established between body mass, mechanical parameters and chemical contents. Both bending strength and Young's modulus were negatively correlated to body mass. Significant correlations were found between nitrogen content and both strength and Young's modulus, with negative slopes in both cases. Magnesium and phosphorus appear to be the most important inorganic elements to the understanding of the mechanical behaviour of avian long bones.     

Mechano-acoustic determination of Young's modulus of articular cartilage

The compressive stiffness of an elastic material is traditionally characterized by its Young's modulus. Young's modulus of articular cartilage can be directly measured using unconfined compression geometry by assuming the cartilage to be homogeneous and isotropic. In isotropic materials, Young's modulus can also be determined acoustically by the measurement of sound speed and density of the material. In the present study, acoustic and mechanical techniques, feasible for in vivo measurements, were investigated to quantify the static and dynamic compressive stiffness of bovine articular cartilage in situ. Ultrasound reflection from the cartilage surface, as well as the dynamic modulus were determined with the recently developed ultrasound indentation instrument and compared with the reference mechanical and ultrasound speed measurements in unconfined compression (n=72). In addition, the applicability of manual creep measurements with the ultrasound indentation instrument was evaluated both experimentally and numerically. Our experimental results indicated that the sound speed could predict 47% and 53% of the variation in the Young's modulus and dynamic modulus of cartilage, respectively. The dynamic modulus, as determined manually with the ultrasound indentation instrument, showed significant linear correlations with the reference Young's modulus (r(2)=0.445, p<0.01, n=70) and dynamic modulus (r(2)=0.779, p<0.01, n=70) of the cartilage. Numerical analyses indicated that the creep measurements, conducted manually with the ultrasound indentation instrument, were sensitive to changes in Young's modulus and permeability of the tissue, and were significantly influenced by the tissue thickness. We conclude that acoustic parameters, i.e. ultrasound speed and reflection, are indicative to the intrinsic mechanical properties of the articular cartilage. Ultrasound indentation instrument, when further developed, provides an applicable tool for the in vivo detection of cartilage mechano-acoustic properties. These techniques could promote the diagnostics of osteoarthrosis.     

Incidence and mechanical significance of pneumatization in the long bones of birds

The incidence of pneumatization in avian long bones was studied, by direct observation, in a large sample of species. Only proximal bones (humerus and femur) presented pneumatization in the sample studied. The incidence obtained was related to the variation of the maximum cortical thickness and mechanical properties, such as bending strength and flexural Young's modulus. Cortical thickness, bending strength and flexural Young's modulus were significantly lower in pneumatized bones than in marrow-filled bones. Furthermore, some congruence was found between pneumatization and systematic groups when compared. In this sense, Charadriformes was the only order studied with total absence of long bone pneumatization. Results on cortical thickness appear to be in agreement with modelling predictions previously made and with results obtained on other groups of flying vertebrates. The possible selective advantage of reduction in cortical thickness in relation to flying is suggested.     

The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity

The objective of this study was to examine the dependence of the elastic properties of cortical bone as a transversely isotropic material on its porosity. The longitudinal Young's modulus, transverse Young's modulus, longitudinal shear modulus, transverse shear modulus, and longitudinal Poisson's ratio of cortical bone were determined from eighteen groups of longitudinal and transverse specimens using tensile and torsional tests on a servo-hydraulic material testing system. These cylindrical waisted specimens of cortical bone were harvested from the middle diaphysis of three pairs of human femora. The porosity of these specimens was assessed by means of histology. Our study demonstrated that the longitudinal Young's and shear moduli of human femoral cortical bone were significantly (p<0.01) negatively correlated with the porosity of cortical bone. Conversely, the elastic properties in the transverse direction did not have statistically significant correlations with the porosity of cortical bone. As a result, the transverse elastic properties of cortical bone were less sensitive to changes in porosity than those in the longitudinal direction. Additionally, the anisotropic ratios of cortical bone elasticity were found to be significantly (p<0.01) negatively correlated with its porosity, indicating that cortical bone tended to become more isotropic when its porosity increased. These results may help a number of researchers develop more accurate micromechanics models of cortical bone.     

Anatomical variation of orthotropic elastic moduli of the proximal human tibia

The anatomical variation of orthotropic elastic moduli of the cancellous bone from three human proximal tibiae was investigated using an ultrasonic technique. With this technique, it was possible to measure three orthogonal elastic moduli and three shear moduli from cubic specimens of cancellous bone as small as 8 mm per side. Correlation with mechanical tensile testing has shown this technique to offer a precise measure of cancellous modulus (Eten = 0.94Eult + 144.6 MPa, r2 = 0.96, n = 34). The cancellous bone of the proximal tibia was found to be very inhomogeneous, with the axial modulus ranging between 340 and 3350 MPa. A course map is presented, showing measured Young's moduli as a function of anatomical position. The anisotropy of the cancellous bone, determined by the relative differences between the three orthogonal moduli, was shown to be relatively constant over the entire range of cancellous densities tested. The relationship between the axial elastic modulus and the apparent density was found to be approximately linear, as reported by others for proximal tibial cancellous bone.     

Spatial orientation in bone samples and Young's modulus

Bone mass is the most important determinant of the mechanical strength of bones, and spatial structure is the second. In general, the spatial structure and mechanical properties of bones such as the breaking strength are direction dependent. The mean intercept length (MIL) and line frequency deviation (LFD) are two methods for quantifying directional aspects of the spatial structure of bone. Young's modulus is commonly used to describe the stiffness of bone, which is also a direction-dependent mechanical property. The aim of this article is to investigate the relation between MIL and LFD on one hand and Young's modulus on the other. From 11 human mandibular condyles, 44 samples were taken and scanned with high-resolution computer tomography equipment (micro-CT). For each sample the MIL and LFD were determined in 72602 directions distributed evenly in 3D space. In the same directions Young's modulus was determined by means of the stiffness tensor that had been determined for each sample by finite element analysis. To investigate the relation between the MIL and LFD on one hand and Young's modulus on the other, multiple regression was used. On average the MIL accounted for 69% of the variance in Young's modulus in the 44 samples and the LFD accounted for 72%. The average percentage of variance accounted for increased to 80% when the MIL was combined with the LFD to predict Young's modulus. Obviously MIL and LFD to some extent are complementary with respect to predicting Young's modulus. It is known that directional plots of the MIL tend to be ellipses or ellipsoids. It is speculated that ellipsoids are not always sufficient to describe Young's modulus of a bone sample and that the LFD partly compensates for this.     

Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content

Compact bone specimens from many species were examined to determine the relationships, in tension, between mineral content, Young's modulus, yield stress, yield strain, post-yield stress, post-yield strain, ultimate stress, ultimate strain and work under the stress-strain curve. Yield strain varied much less than the post-yield strain, and yield stress was strongly dependent on Young's modulus. Mineral content was a rather poor predictor of yield stress. However, post-yield events were predicted better by mineral (calcium) content than by Young's modulus. The greater the mineral content the less the post-yield work under the curve and the less the increase in post-yield stress and strain. The findings are compared with those of Les et al. who compressed specimens from equine metacarpals. Where they can be compared, the results are consistent with each other.     

The bulk elastic modulus and the reversible properties of cell walls in developing Quercus leaves

We examined the relationship between the bulk elastic modulus (epsilon) of an individual leaf obtained by the pressure-volume (P-V) technique and the mechanical properties of cell walls in the leaf. The plants used were Quercus glauca and Q. serrata, an evergreen and a deciduous broad-leaved tree species, respectively. We compared epsilon and Young's modulus of leaf specimens determined by the stretch technique at various stages of their leaf development. The results showed that epsilon increased from approximately 5 to 20 MPa during leaf development, although other potential determinants of epsilon such as the apoplastic water content in the leaf and the diameter of a palisade tissue cells remained almost constant. epsilon in these two species was similar at every developmental stages, although the apparent mechanical strength of the leaf lamina and thickness of mesophyll cell walls were greater in Q. glauca. There were significant linear relationships between Young's modulus and epsilon (P < 0.01; R (2) = 0.78 and 0.84 in Q. glauca and Q. serrata, respectively) with small y-intercepts. From these results, we conclude that epsilon is closely related to the reversible properties of the cell walls. From the estimation of epsilon based on a physical model, we suggest that the effective thickness of cell walls responsible for epsilon is smaller than the observed wall thickness.     

Glenoid cancellous bone strength and modulus.

The objectives of this study were to determine the strength and modulus of glenoid cancellous bone, including regional variations. The motivations were: to select a suitable bone substitute for standardized testing of glenoid prosthesis loosening, to assist in shoulder prosthesis design and to provide input data for finite element analyses. Ten glenoids from eight cadavers (mean age, 81) were tested by in situ indentation. Mean strength ranged from 6.7 to 17 MPa for the ten glenoids, the overall mean being 10.3 MPa. Mean E moduli ranged from 67 to 171 MPa for the individual glenoids, the overall mean being 99 MPa. These values are likely at the lower end of what would be expected for normal bone since strength and modulus decrease with age and the available specimens were older. These values may be appropriate for prosthesis design, however, since mechanical properties are reduced in rheumatoid arthritic bone. Regional trends were very similar for modulus and strength. The strongest region was postero-superior. The central column, correlating with the keel position in many glenoid components, was weaker than both the anterior and posterior regions but deeper. A large drop in strength and modulus below the subchondral layer emphasizes the importance of maintaining this layer during prosthetic replacement.     

New nanocomposite materials reinforced with flax cellulose nanocrystals in waterborne polyurethane

New nanocomposite films were prepared from a suspension of cellulose nanocrystals as the filler and a polycaprolactone-based waterborne polyurethane (WPU) as the matrix. The cellulose nanocrystals, prepared by acid hydrolysis of flax fiber, consisted of slender rods with an average length of 327 +/- 108 nm and diameter of 21 +/- 7 nm, respectively. After the two aqueous suspensions were mixed homogeneously, the nanocomposite films were obtained by casting and evaporating. The morphology, thermal behavior, and mechanical properties of the films were investigated by means of attenuated total reflection Fourier transform infrared spectroscopy, wide-angle X-ray diffraction, differential scanning calorimetry, scanning electron microscopy, and tensile testing. The results indicated that the cellulose nanocrystals could disperse in the WPU uniformly and resulted in an improvement of microphase separation between the soft and hard segments of the WPU matrix. The films showed a significant increase in Young's modulus and tensile strength from 0.51 to 344 MPa and 4.27 to 14.86 MPa, respectively, with increasing filler content from 0 to 30 wt %. Of note is that the Young's modulus increased exponentially with the filler up to a content of 10 wt %. The synergistic interaction between fillers and between the filler and WPU matrix played an important role in reinforcing the nanocomposites. The superior properties of the new nanocomposite materials could have great potential applications.     

Incompatible mechanical properties in compact bone

The covariation of a number of mechanical of properties, and some physical characteristics, of compact bones from a wide range of bones were examined. Young's modulus was well predicted by a combination of mineral content and porosity. Increasing Young's modulus was associated with: increasing stress at yield, increasing bending strength, and a somewhat higher resilience, tensile strength and fatigue strength. Contrarily, in the post-yield region a higher Young's modulus (and more clearly, a higher mineral content) was associated with: a reduced work to fracture in tension, a reduced impact strength and an increased notch sensitivity in impact. Increasing porosity is associated with deleterious effects in the pre-yield region, but has little effect in the post-yield region. Bone, like many other materials, is unable to have good qualities in both the pre- and post-yield regions. Since an increase in mineral or Young's modulus is more potent, that is deleterious, in the post-yield than it is advantageous in the pre-yield region, it is likely that mineral content will be selected to be slightly lower than would be the case if it were equally potent in both regions. As is usual in biology, different adaptive extremes are incompatible.     

Apparent Young's modulus of vertebral cortico-cancellous bone specimens

Up to now, due to cortical thickness and imaging resolution, it is not possible to derive subject-specific mechanical properties on the 'vertebral shell' from imaging modalities applicable in vivo. As a first step, the goal of this study was to assess the apparent Young's modulus of vertebral cortico-cancellous bone specimens using an inverse method. A total of 22 cortico-cancellous specimens were harvested from 22 vertebral bodies. All specimens were tested in compression until failure. To compute the apparent Young's modulus of the specimen from the inverse method, the boundary conditions of the biomechanical experiments were faithfully reproduced in a finite element model (FEM), and an optimisation routine was used. The results showed a mean of the apparent Young's modulus of 374?±?208?MPa, ranging from 87 to 791?MPa. By computing an apparent Young's modulus of a cortico-cancellous medium, this study gives mechanical data for an FEM of an entire vertebra including an external shell combining both bone tissues.