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.     

Elastic moduli, yield stress, and ultimate stress of cancellous bone in the canine proximal femur

Elastic moduli, yield stress and ultimate compressive stress were determined for cancellous bone from the femoral head and neck regions of the canine femur. Unconfined compression tests were performed on 5 mm cubic samples which were cut from two femurs. Elastic moduli were measured in three orthogonal directions, and the yield stress and ultimate stress were measured along the proximal-distal axis. The results from this investigation support previous assumptions that the mechanical behavior of canine cancellous bone is qualitatively similar to human cancellous bone. The canine cancellous bone was observed to be anisotropic in elastic modulus. For two thirds of the cubic specimens tested, the elastic modulus was largest in the load-bearing, proximal-distal direction. A linear relationship between yield stress and elastic modulus was observed for canine bone, as is typical of human bone. A similar linear relationship between ultimate stress and elastic modulus was observed. Thus, for canine bone as well as for human bone, failure appears to be governed by a strain level which is position independent. The yield strain of 0.0259 and ultimate strain of 0.0288 for canine bone were both less than the yield strain of 0.0395 reported for human bone.     

Changing the structurally effective mineral content of bone with in vitro fluoride treatment

Bovine femur cortical bone specimens were tested in tension after being treated in vitro for 3 days with sodium fluoride solutions of different molarity (0.145, 0.5, and 2.0M). The treatments alter the mechanical properties of the bone samples with different degrees as compared to control samples (untreated). The mechanical properties of the treated samples have lower elastic modulus, yield and ultimate stress, acoustic impedance and hardness, and higher ultimate strain and toughness as compared to control samples. The observed effects were intensified with the increasing molarity of the treatment solutions. This study shows that the fluoride treatment can be used to investigate the composite behavior of bone tissue by altering the structurally important bone mineral content in a controlled manner.     

Compressive properties of trabecular bone in the distal femur

Early loosening and implant migration are two problems that lead to failures in cementless (press-fit) femoral knee components of total knee replacements. To begin to address these early failures, this study determined the anterior-posterior mechanical properties from four locations in the human distal femur. Thirty-three cylindrical specimens were removed perpendicular to the press-fit surface after the surgical cuts on 10 human cadaveric femurs (age 71.5+/-14.2 years) had been made. Compression testing was performed that utilized methods to reduce the effects of end-artifacts. The bone mineral apparent density (BMAD), apparent modulus of elasticity, yield and ultimate stress, and yield and ultimate strain were measured for 28 cylindrical specimens. The apparent modulus, yield and ultimate stress, and yield and ultimate strain each significantly differed (p<0.05) in the superior and inferior locations. Linear and power law relationships between superior and inferior mechanical properties and BMAD were determined. The inferior apparent modulus and stresses were higher than those in the superior locations. These results show that the press-fit fixation characteristics of the femoral knee component differ on the anterior shield and posterior condyles. This information will be useful in the assignment of mechanical properties in finite element models for further investigations of femoral knee components. The property-density relations also have applications for implant design and preoperative assessment of bone strength using clinically available tools.     

Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory

The effect of mineral volume fraction on the tensile mechanical properties of cortical bone tissue is investigated by theoretical and experimental means. The mineral content of plexiform, bovine bone was lowered by 18% and 29% by immersion in fluoride solutions for 3 days and 12 days, respectively. The elastic modulus, yield strength and ultimate strength of bone tissue decreased, while the ultimate strain increased with a decrease in mineral content. The mechanical behavior of bone tissue was modeled by using a micromechanical shear lag theory consisting of overlapped mineral platelets reinforcing the organic matrix. The decrease in yield stress, by the 0.002 offset method, of the fluoride treated bones were matched in the theoretical curves by lowering the shear yield stress of the organic matrix. The failure criterion used was based on failure stresses determined from a failure envelope (Mohr's circle), which was constructed using experimental data. It was found that the model predictions of elastic modulus got worse with a decrease in mineral content (being 7.9%, 17.2% and 33.0% higher for the control, 3-day and 12-day fluoride-treated bones). As a result, the developed theory could not fully predict the yield strain of bones with lowered mineral content, being 12.9% and 21.7% lower than the experimental values. The predicted ultimate stresses of the bone tissues with lower mineral contents were within +/- 10% of the experimental values while the ultimate strains were 12.7% and 26.3% lower than the experimental values. Although the model developed in this study did not take into account the presence of hierarchical structures, voids, orientation of collagen molecules and micro cracks, it still indicated that the mechanical properties of the organic matrix depend on bone mineral content.     

Strain rate dependence of the mechanical properties of reindeer antler and the cumulative damage model of bone fracture

Carter and Caler have produced a 'cumulative damage' model for the fracture of bone, based on creep experiments on human bone, which has been corroborated by monotonic tensile tests on bone, loaded at various strain rates. Monotonic tensile tests on reindeer's antler, which has a lower modulus of elasticity than human bone, produce very similar results. Unlike human bone, reindeer antler always shows a large post-yield strain, and it is possible to distinguish pre-yield and post-yield behaviour. The 'final stiffness' (ultimate stress/ultimate strain) is invariant with strain rate. This is confirmation that bone fractures when a certain amount of damage has accumulated. However, reindeer antler shows a considerable post-yield increase in stress. This is difficult to accommodate in a cumulative damage model.     

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.     

Modeling the tensile mechanical behavior of bone along the longitudinal direction

The tensile stress-strain behavior of bone along its longitudinal axis is modeled by using a simple shear-lag theory, wherein, stresses and strains in a unit cell consisting of an organic matrix reinforced by overlapped mineral platelets are computed. It is assumed that loads are transferred between overlapped mineral-platelets by shear in the organic matrix. The mechanical behavior of bone in which the matrix partially or completely debonds from the sides of the overlapped mineral platelets (after an ultimate interfacial shear stress value is exceeded) is modeled. It is shown that the tensile mechanical behavior of bone can be modeled only by assuming little or no debonding of the organic from the mineral. A physical phenomenon that explains the tensile behavior of bone is, after the interfacial shear stress has reached a constant value over the length of the mineral platelets, the collagen molecules/microfibrils (with the associated mineral platelets) move relative to one another. The tensile stress-strain curve of bovine bone is modeled using this model. The theory predicts the mechanical behavior of the tissue in the elastic, yield and post-yield region. The ultimate strain and strengths are not predicted in the present model.     

Physical characteristics affecting the tensile failure properties of compact bone

Compact bone specimens from a wide variety of reptiles, birds, and mammals were tested in tension, and their failure properties related to mineral volume fraction, porosity and histological orientation. The principal findings were that the ultimate strain and the work under the stress-strain curve declined sharply with mineralisation, as did the stress and strain appearing after the specimen had yielded. Ultimate tensile strength was not simply related to any combination of the possible explanatory variables, but some relatively poorly mineralised bones, notably antlers, had high stresses at failure. These high strengths were allowed by a great increase in stress after the bones had yielded at quite low stresses.     

Synthesis, characterization, and in vitro degradation of a biodegradable photo-cross-linked film from liquid poly(epsilon-caprolactone-co-lactide-co-glycolide) diacrylate

There has been little study on the effect of composition or molecular weight on the biodegradation rate of photo-cross-linked biodegradable aliphatic polyesters though such information is important for tissue engineering scaffolds. We have synthesized a new series of photopolymerizable linear poly(epsilon-caprolactone-co-lactide-co-glycolide) diacrylates with different molecular weights (Mn = 1800, 4800, and 9300 Da) and compositions (20%, 40%, and 60% epsilon-CL) and studied their biodegradation rates. The resultant oligomers were amorphous and appeared as viscous liquids at room temperature. Liquid-to-solid polymerization was carried out by UV irradiation in the presence of a photoinitiator. The photocuring yield was high (greater than 95%), and the photo-cross-linked polymers were amorphous and rubbery. Mechanical measurements showed that the polymers can be stretchable or rigid; the high molecular weight/low epsilon-CL network has a strain of 176% and a modulus of 1.66 MPa while the low molecular weight/high epsilon-CL network has a strain of 21% and a modulus of 12.3 MPa. In a 10 week in vitro biodegradation study, the polymers exhibited a two-stage degradation behavior. In the first stage, the polymer weight and strain remained almost constant, but a linear decrease in the Young's modulus (E) and ultimate stress (sigma) were observed. Lower oligomer molecular weight or epsilon-CL content correlated with a faster decrease in Young's modulus. In the second stage, which began when the Young's modulus dropped below 1 MPa, there was rapid weight loss and strain increase. The lower the epsilon-CL content, the earlier the second stage happened. Low molecular weight and high epsilon-CL content correlated with a longer modulus half-life (time for the modulus to degrade to 50% of its initial value). The degradation results suggest principles that may be helpful in predicting the biodegradation behavior of similar polymeric cross-linked networks. Films formed from these new polymers have excellent biocompatibility with smooth muscle cells.     

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.     

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.     

Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure

It is difficult to define the 'physiological' mechanical properties of bone. Traumatic failures in-vivo are more likely to be orders of magnitude faster than the quasistatic tests usually employed in-vitro. We have reported recently [Hansen, U., Zioupos, P., Simpson, R., Currey, J.D., Hynd, D., 2008. The effect of strain rate on the mechanical properties of human cortical bone. Journal of Biomechanical Engineering/Transactions of the ASME 130, 011011-1-8] results from tests on specimens of human femoral cortical bone loaded in tension at strain rates (epsilon ) ranging from low (0.08s(-1)) to high (18s(-1)). Across this strain rate range the modulus of elasticity generally increased, stress at yield and failure and strain at failure decreased for rates higher than 1s(-1), while strain at yield was invariant for most strain rates and only decreased at rates higher than 10s(-1). The results showed that strain rate has a stronger effect on post-yield deformation than on initiation of macroscopic yielding. In general, specimens loaded at high strain rates were brittle, while those loaded at low strain rates were much tougher. Here, a post-test examination of the microcracking damage reveals that microcracking was inversely related to the strain rate. Specimens loaded at low strain rates showed considerable post-yield strain and also much more microcracking. Partial correlation and regression analysis suggested that the development of post-yield strain was a function of the amount of microcracking incurred (the cause), rather than being a direct result of the strain rate (the excitation). Presumably low strain rates allow time for microcracking to develop, which increases the compliance of the specimen, making them tougher. This behaviour confirms a more general rule that the degree to which bone is brittle or tough depends on the amount of microcracking damage it is able to sustain. More importantly, the key to bone toughness is its ability to avoid a ductile-to-brittle transition for as long as possible during the deformation. The key to bone's brittleness, on the other hand, is the strain and damage localisation early on in the process, which leads to low post-yield strains and low-energy absorption to failure.     

Tensile behavior of cortical bone: dependence of organic matrix material properties on bone mineral content

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic-perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress-strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress-strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.     

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 effect of specimen geometry on the mechanical behaviour of trabecular bone specimens.

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens was studied by non-destructive uniaxial compression to 0.4% strain using cylindrical specimens with different sizes and length-to-diameter ratios, and by comparing cubic and cylindrical specimens with the same cross-sectional area. Both the length and the cross-sectional area of the specimen had a highly significant influence on the mechanical behaviour (p less than 0.0001). Within the actual range of length (2.75-11.0 mm) the normalized stiffness (Young's modulus) was related nearly linearly to the specimen length. This dependency on specimen length is suggested to be caused mainly by structural disintegrity of the trabecular specimens near the surface. The normalized stiffness (Young's modulus) was also positively correlated to the cross-sectional area. This dependency on cross-sectional area is probably due to friction-induced stress inhomogeneity at the platen-specimen interface. A cube with side length 6.5 mm or a cylindrical specimen with 7.5 mm diameter and 6.5 mm length are suggested as standard specimens for comparative studies on trabecular bone mechanics.     

Zonal and directional variations in tensile properties of bovine articular cartilage with special reference to strain rate variation

THE AIMS of this study were: (i) to investigate the variation in the tensile properties of articular cartilage with depth through cartilage thickness and fibre orientation; (ii) to determine the effect of strain rate on tensile properties of articular cartilage. MATERIALS AND METHOD: All experimental work was performed on cartilage specimens taken from two bovine knee joints. Osteochondral plugs 12 mm in diameter were harvested with a special reamer from the femur and the tibial plateaux of each knee. Slices (0.2 mm thick), of articular cartilage were cut from the plug with a microtome. The predominant orientation of the collagen fibres on the cartilage surface was determined using the pinpricking technique. Each specimen used for the tensile test was cut, so as to produce a dumbbell shape, with a gauge length of 6 mm. Uniaxial tensile tests were performed on each specimen in order to determine the tensile Young's modulus, and ultimate tensile strength (UTS). In this investigation, these tensile tests were carried out at different strain rate: 1, 20, 50 and 70%/sec. RESULTS: As regards the zonal properties, it was found that tensile stiffness was greater in the superficial layer than in deep layer. However, a few specimens from the deep layer displayed similar or greater stiffness compared to the superficial layer. With respect to the directional properties, the specimens oriented parallel to the predominant alignment of collagen, were stiffer than those, which were perpendicular to it in each layer. However, only the results regarding the deep layer can be considered statistically significant. In regard to the variation of modulus with the strain-rate, the results showed that there is no significant increase of the modulus with increasing strain rate from 20 to 50% per second. However, at 70% per second, articular cartilage stiffness considerably increased by up to one order of magnitude greater than that determined at lower strain rates in both the superficial and deep layer. Moreover, the UTS of cartilage specimens tested at 70% per second showed a significant rise, reaching values of four to five times that of those measured at 1, 20 or 50% per second. CONCLUSION: The steep increases in both the stiffness and ultimate tensile strength of cartilage at high strain rates point to the existence in cartilage of a mechanism for its protection from damage by stresses arising in trauma, which are usually applied at high rates. This mechanism needs to be elucidated. The reduced anisotropy found in the present study pointed out that collagen is likely to be less organized in bovine cartilage than in the human and therefore, a study of its ultra-structure would be appropriate.     

A quantitative model of cellular elasticity based on tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.     

Stabilization of scleral collagen by glycerol aldehyde cross-linking

The paper aims at the evaluation of prospects for using glyceraldehyde as a cross-linking agent for the scleral tissue. Stability parameters (denaturation temperature, Young's modulus, ultimate tensile stress, proteolytic resistance) and analytical parameter (fluorescence intensity) were determined during the glycation process of isolated rabbit sclera. The analysis of fluorescence spectral characteristic provided information about some glycation products. The glyceraldehyde treatment was resulted in a significant increase in thermal stability, proteolytic resistance and improvement of biomechanical characteristics (Young's modulus, ultimate tensile stress). Unique properties of the reaction between scleral collagen and glyceraldehyde are observed at short cross-linking times. The appearance of intermediate collagen fraction with lowest thermal and proteolytic stability was detected.     

IL-1beta decreases the elastic modulus of human tenocytes.

Cellular responses to mechanical stimuli are regulated by interactions with the extracellular matrix, which, in turn, are strongly influenced by the degree of cell stiffness (Young's modulus). It was hypothesized that a more elastic cell could better withstand the rigors of remodeling and mechanical loading. It was further hypothesized that interleukin-1beta (IL-1beta) would modulate intracellular cytoskeleton polymerization and regulate cell stiffness. The purpose of this study was to investigate the utility of IL-1beta to alter the Young's modulus of human tenocytes. Young's modulus is the ratio of the stress to the strain, E = stress/strain = (F/A)/(deltaL/L0), where L0 is the equilibrium length, deltaL is the length change under the applied stress, F is the force applied, and A is the area over which the force is applied. Human tenocytes were incubated with 100 pM recombinant human IL-1beta for 5 days. The Young's modulus was reduced by 27-63%. Actin filaments were disrupted in >75% of IL-1beta-treated cells, resulting in a stellate shape. In contrast, immunostaining of alpha-tubulin showed increased intensity in IL-1beta-treated tenocytes. Human tenocytes in IL-1beta-treated bioartificial tendons were more tolerant to mechanical loading than were untreated counterparts. These results indicate that IL-1beta reduced the Young's modulus of human tenocytes by disrupting the cytoskeleton and/or downregulating the expression of actin and upregulating the expression of tubulins. The reduction in cell modulus may help cells to survive excessive mechanical loading that may occur in damaged or healing tendons.