Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue

The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.     

A comparison of the fatigue behavior of human trabecular and cortical bone tissue

The fatigue properties of trabecular bone tissue (single trabeculae) and similarly sized cortical bone specimens from human tibia were experimentally determined on a microstructural level using four-point bending cyclic tests, and they were compared based on modulus, mineral density, and microstructural characteristics. The results showed that trabecular specimens had significantly lower moduli and lower fatigue strength than cortical specimens, despite their higher mineral density values. Fracture surface and microdamage analyses illustrated different fracture and damage patterns between trabecular and cortical bone tissue, depending upon their microstructural characteristics. Based on the results from mechanical tests and qualitative observations, a possible mechanical role of the cement lines in trabecular tissue microfracture was suggested.     

The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

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.     

Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.     

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).     

An application of nanoindentation technique to measure bone tissue Lamellae properties

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells thait coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of 17.7 +/- 4.0 GPa for osteons and 19.3 +/- 4.7 GPa for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average 0.52 +/- 0.15 GPa for osteons and 0.59 +/- 0.20 GPa for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a 5-nm/s loading rate were significantly lower than the values at the 10- and 20-nm/s loading rates while the 10- and 20-nm/s rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.     

Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur.

The mechanical properties of bone tissue are determined by composition as well as structural, microstructural and nanostructural organization. The aim of this study was to quantify the elastic properties of bone at the lamellar level and compare these properties among osteonal, interstitial and trabecular microstructures from the diaphysis and the neck of the human femur. A nanoindentation technique with a custom irrigation system was used for simultaneously measuring force and displacement of a diamond tip pressed 500 nm into the moist bone tissue. An isotropic elastic modulus was calculated from the unloading curve with an assumed Poisson ratio of 0.3, while hardness was defined as the maximal force divided by the corresponding contact area. The elastic moduli ranged from 6.9 +/- 4.3 GPa in trabecular tissue from the femoral neck of a 74 yr old female up to 25.0 +/- 4.3 GPa in interstitial tissue from the diaphyseal cortex of a 69 yr old female. The mean elastic modulus was found to be significantly influenced by the type of lamella (p < 10(-6)) and by donor (p < 10(-6)). The interaction between the type of lamella and the donor was also highly significant (p < 10(-6)). Hardness followed a similar distribution as elastic modulus among types of lamellae and donor, but with lower statistical contrast. It is concluded that the nanostructure of bone tissue must differ substantially among lamellar types, anatomical sites and individuals and suggests that tissue heterogeneity is of potential importance in bone fragility and adaptation.     

A micro-computed tomography study of the trabecular bone structure in the femoral head

The goal of this study was to characterize the trabecular microarchitecture of the femoral head using micro-computed tomography (ICT). Femoral head specimens were obtained from subjects following total hip replacement. Cylindrical cores from the specimens were scanned to obtain 3-D images with an isotropic resolution of 26 Im. Bone structural parameters were evaluated on a per millimeter basis: relative bone volume (BV/TV), trabecular number (Tb.N), thickness (Tb.Th) and separation (Tb.Sp), structure model index (SMI), and connectivity (Conn.D). The ICT data show that the first two millimeters, starting at the joint surface, are characterized by more plate-like trabeculae, and are significantly denser than the underlying trabecular bone. Regional differences in the trabecular architecture reveal that the superior pole has significantly higher BV/TV, Tb.N and Tb.Th values, with lower Tb.Sp compared to the inferior and side poles. Because subchondral bone is essential in the load attenuation of joints, the difference in bone structure between the subchondral and trabecular bone might arise from the different functions each have within joint-forming bones. The denser trabecular structure of the superior pole as compared to the inferior pole can be interpreted as a functional adaptation to higher loading in this area.     

Fatigue of immature baboon cortical bone

Strain-controlled uniaxial fatigue and monotonic tensile tests were conducted on turned femoral cortical bone specimens obtained from baboons at various ages of maturity. Fatigue loading produced a progressive loss in stiffness and an increase in hysteresis prior to failure, indicating that immature primate cortical bone responds to repeated loading in a fashion similar to that previously observed for adult human cortical bone. Bone fatigue resistance under this strain controlled testing decreased during maturation. Maturation was also associated with an increase in bone dry density, ash fraction and elastic modulus. The higher elastic modulus of more mature bone meant that these specimens were subjected to higher stress levels during testing than more immature bone specimens. Anatomical regions along the femoral shaft exhibited differences in strength and fatigue resistance.     

Some mechanical properties of goose femoral cortical bone

The ultimate compressive strength and modulus of elasticity of femoral cortical bone from adult geese (Anser anser), were determined by sex and by quadrant by compressing small right circular cylinders which were 2.4 mm in height and 0.8 mm in diameter. The average ultimate compressive strength was 183 +/- 29 MPa. The average modulus of elasticity was 13.2 +/- 3.4 GPa. The bending strength and bending modulus of elasticity were determined by a three point bend test on rectangular prisms which had the approximate dimensions 0.75 mm X 0.75 mm X 25 mm. The average bending strength was 263 +/- 44 MPa while the average bending modulus was 19.6 +/- 3.1 GPa. The calcium content was determined by atomic absorption spectrophotometry and no correlation was found with the mechanical properties. The histology of the cortical bone was examined both quantitatively and qualitatively. A unique type of Haversian bone is described. Goose bone was found to be morphologically similar to adolescent human bone and to have mechanical properties similar to those of adult human bone.     

A comparative analysis of the microarchitecture of cortical membranous and cortical endochondral onlay bone grafts in the craniofacial skeleton

Previous work in this laboratory established that an onlay bone graft's survival is determined primarily by its relative cortical and cancellous composition rather than its embryologic origin. A volumetric analysis of external bone graft resorption, however, does not explain the internal microarchitectural changes that may be occurring as these grafts become incorporated. To expand the knowledge of bone graft dynamics beyond volumetric parameters, a better understanding of the internal processes of bone graft remodeling is needed. In this comparative study of cortical onlay bone graft microarchitecture, the authors propose to show that cortical onlay bone grafts undergo measurable internal microarchitectural changes as they become incorporated into the surrounding craniofacial skeleton. In addition, the authors propose to further demonstrate similarities between the internal microarchitecture of cortical onlay bone grafts of different embryologic origin over time. Twenty-five adult New Zealand White rabbits were used for this study. They were divided into two groups of eight animals and one group of nine. The groups were killed at 3, 8, and 16 weeks. Cortical membranous and endochondral bone grafts were placed subperiosteally onto each rabbit's cranium. In addition, five ungrafted cortical endochondral and membranous bone specimens were used as controls. Microcomputed tomography (MCT) scanning and histomorphometric analysis were performed on all of the specimens to obtain detailed information regarding the microarchitecture of the cortical bone grafts. The parameters of bone volume fraction, bone surface area to volume, mean trabecular number, and anisotropy were used to give quantitative information about a bone's micro-organization. The results showed that there is no statistically significant difference between the cortical endochondral and the cortical membranous bone grafts for bone volume fraction, bone surface to volume, mean trabecular number, and anisotropy measurements for all time points. There were, however, statistically significant differences when comparing the control and 3-week groups to the 16-week group for all parameters. The advanced MCT technology and histomorphometric techniques proved to be effective in providing a qualitative and quantitative ultrastructural comparison of cortical endochondral and membranous onlay bone grafts over time. In this study, a statistically significant change in the internal microarchitecture of cortical onlay bone grafts of different embryologic origins was seen as they were remodeled and resorbed at all time points. Specifically, the onlay cortical bone grafts developed a less dense, more trabecular, and less organized internal ultrastructure. In addition, no difference in the three-dimensional ultrastructure of cortical endochondral and membranous bone was found. These results challenge some of the currently accepted theories of bone-graft dynamics and may eventually lead to a change in the way clinicians approach bone-graft selection for craniofacial surgery.     

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure–function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean±S.D.) 18.7±3.4 GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.     

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.     

Elastic constants of composites formed from PMMA bone cement and anisotropic bovine tibial cancellous bone

An ultrasonic pulse-transit time technique is used to determine the nine orthotropic engineering constants of 32 cement-cancellous bone composites as a function of volume fractions of bone ranging from 0.0 to 0.4. The composites are manufactured using well-aligned bovine cancellous bone from the proximal end of the tibia and low viscosity bone cement. Selected composites are also subjected to mechanical compression tests to compare with the ultrasonic results. There is excellent correlation between the dynamic or ultrasonically determined moduli and the static or mechanically determined moduli; the dynamic moduli are approximately twice the static moduli and this difference is thought to be due to the effect of strain rate. An orthotropic model is assumed requiring nine independent elastic constants to be determined. The dynamic Young's modulus in the direction of major trabecular alignment, E1, increases linearly from 4.9 to 10.4 GPa as bone volume fraction increases from 0 to 0.4; dynamic E2 and E3 values increase from 4.9 to 7 GPa as bone volume fractions increase from 0 to 0.4, with E2 being slightly higher than E3. The dynamic shear modulus, G12, increases from 1.8 to 3.0 GPa, and G31 and G23 increase slightly from 1.8 to 2.2 GPa as bone volume fractions increase from 0 to 0.4. The Poisson's ratios are more sensitive than the Young's moduli and shear moduli to experimental error in the velocity measurements. The mechanically tested modulus (static modulus) in the direction of major trabecular alignment, E1, increases with volume fraction of bone from 2.4 to 4.4 GPa as the bone volume fraction increases from 0 to 0.25; static E2 and E3 values are either equal to or lower than that of pure PMMA.     

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.     

Separate modeling of cortical and trabecular bone offers little improvement in FE predictions of local structural stiffness at the proximal tibia

Abstract

Quantitative computed tomography-based finite element (QCT-FE) modeling has potential to clarify the role of altered subchondral bone stiffness in osteoarthritis. The objective of this research was to evaluate different QCT-FE modeling and thresholding approaches to identify the method which best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error. Our results showed that separate modeling of proximal tibial cortical and trabecular bone offered little improvement in QCT-FE-predicted stiffness (0% to +3% improvement in explained variance) when compared to modeling the proximal tibia as a single structure. Based on the results of this study, we do not recommend separate modeling of cortical bone and trabecular bone when developing QCT-FE models of the proximal tibia for predicting subchondral bone stiffness.     

Trabecular bone strain changes associated with subchondral stiffening of the proximal tibia

Subchondral stiffening is a hallmark pathologic feature of osteoarthritis but its mechanical and temporal relationship to the initiation or the progression of osteoarthritis is not established. The mechanical effect of subchondral stiffening on the surrounding trabecular bone is poorly understood. This study employs a relatively new application of digital image correlation to measure strain in the trabecular region of the proximal medial tibia in normal specimens and in specimens with simulated subchondral bone stiffening. Coronal sections from eight normal human cadaveric proximal tibiae were loaded in static compression and high resolution contact radiographs were made. Repeat contact radiographs were collected after the subchondral bone near the jointline was stiffened using polymethylmethacrylate. Digital images, made from loaded and unloaded contact radiographs, were compared using in-house software to measure trabecular displacement and calculate trabecular bone strain. Overall strain was higher in the stiffened specimens suggesting experimental artifiact significantly affected our results. Consistent increases in median maximum shear strain, median maximum principal strain, median minimum principal strain, and peak shear strain were measured near the inner and outer edges of the stiffened segment. Our experiment provides direct experimental measurement of increases in trabecular bone strain caused by subchondral stiffening, however, the clinical and biologic importance of strain increases is unknown.     

The differential response of cortical and trabecular bone to aluminum administration in the rat

Osteomalacia has been noted following in vivo aluminum (Al) loading in the rat by some investigators but not by others. To determine whether the response of bone to Al differs as a function of the skeletal site examined, quantitative histology of cortical and trabecular bone was done in the tibiae from control (C, n = 10), Al-treated (AL, n = 9), nephrectomized control (NX-C, n = 7), and nephrectomized Al-treated (NX-AL, n = 8) rats given 2 mg/day of Al for 4 weeks. Bone Al content was determined by histochemical methods. In cortical bone, osteoid seam width, osteoid volume, and percent osteoid area were similar for all groups. In contrast, for trabecular bone, both forming surface (means +/- SD) (5.2 +/- 3.4 vs 1.8 +/- 1.1%, P less than 0.05) and osteoid volume (1.7 +/- 0.7 vs 1.0 +/- 0.4%, P less than 0.05) increased from control values in AL, although osteoid seam width did not differ. In NX-AL, trabecular forming surface (20.2 +/- 6.7 vs 6.2 +/- 2.4%, P less than 0.01), osteoid area (13.2 +/- 5.7 vs 3.5 +/- 0.8%, P less than 0.01), and osteoid width (18.7 +/- 5.7 vs 9.7 +/- 2.3 micron, P less than 0.01) all were greater than in NX-C. Deposits of Al were undetectable in C and NX-C, were minimal in cortical bone in AL and NX-AL, but were present at 40.5 +/- 11.5 and 71.1 +/ 6.5% of trabecular surfaces in AL and NX-AL, respectively. Osteoid area and osteoid surface each correlated with trabecular bone Al. Thus, (a) osteoid accumulates in trabecular, but not in cortical, bone after 4 weeks of Al loading; (b) the extent of osteoid accumulation correlates with the bone Al content; and (c) the histologic response to Al in cortical and trabecular bone is related to local differences in the uptake of Al into bone.     

Trabecular eccentricity and bone adaptation

It is well established that bones functionally adapt by mechanisms that control tissue density, whole bone geometry, and trabecular orientation. In this study, we propose the existence of another such powerful mechanism, namely, trabecular eccentricity, i.e. non-central placement of trabecular bone within a cortical envelope. In the human femoral neck, trabecular eccentricity results in a thicker cortical shell on the inferior than superior aspect. In an overall context of expanding understanding of bone adaptation, the goal of this study was to demonstrate the biomechanical significance of, and provide a mechanistic explanation for, the relationship between trabecular eccentricity and stresses in the human femoral neck. Using composite beam theory, we showed that the biomechanical effects of eccentricity during a habitual loading situation were to increase the stress at the superior aspect of the neck and decrease the stress at the inferior aspect, resulting in an overall protective effect. Further, increasing eccentricity had a stress-reducing effect equivalent to that of increasing cortical thickness or increasing trabecular modulus. We conclude that an asymmetric placement of trabecular bone within a cortical bone envelope represents yet another mechanism by which whole bones can adapt to mechanical demands.