Tensile damage and its effects on cortical bone

Bone collagen tensile properties of the aging human proximal femur

Despite the dominant role of bone mass in osteoporotic fractures, aging bone tissue properties must be thoroughly understood to improve osteoporosis management. In this context, collagen content and integrity are considered important factors, although limited research has been conducted on the tensile behavior of demineralized compact bone in relation to its porosity and elastic properties in the native mineralized state. Therefore, this study aims (i) at examining the age-dependency of mineralized bone and collagen micromechanical properties; (ii) to test whether, and if so to which extent, collagen properties contribute to mineralized bone mechanical properties. Two cylindrical cortical bone samples from fresh frozen human anatomic donor material were extracted from 80 proximal diaphyseal sections from a cohort of 24 female and 19 male donors (57 to 96 years at death). One sample per section was tested in uniaxial tension under hydrated conditions. First, the native sample was tested elastically (0.25 % strain), and after demineralization, up to failure. Morphology and composition of the second specimen was assessed using micro-computed tomography, Raman spectroscopy, and gravimetric methods. Simple and multiple linear regression were employed to relate morphological, compositional, and mechanical variables with age and sex. Macro-tensile properties revealed that only elastic modulus of native samples was age dependent whereas apparent elastic modulus was sex dependent (p < 0.01). Compositional and morphological analysis detected a weak but significant age and sex dependency of relative mineral weight (r = -0.24, p < 0.05) and collagen disorder ratio (I∼1670/I∼1640, r = 0.25, p < 0.05) and a strong sex dependency of bone volume fraction while generally showing consistent results in mineral content assessment. Young's modulus of demineralized bone was significantly related to tissue mineral density and Young's modulus of native bone. The results indicate that mechanical properties of the organic phase, that include collagen and non-collagenous proteins, are independent of donor age. The observed reduction in relative mineral weight and corresponding overall stiffer response of the collagen network may be caused by a reduced number of mineral-collagen connections and a lack of extrafibrillar and intrafibrillar mineralization that induces a loss of waviness and a collagen fiber pre-stretch.

Mesh-independent damage model for trabecular bone fracture simulation and experimental validation

We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton-Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

Bioinspired mineralized collagen scaffolds for bone tissue engineering

Successful regeneration of large segmental bone defects remains a major challenge in clinical orthopedics, thus it is of important significance to fabricate a suitable alternative material to stimulate bone regeneration. Due to their excellent biocompatibility, sufficient mechanical strength, and similar structure and composition of natural bone, the mineralized collagen scaffolds (MCSs) have been increasingly used as bone substitutes via tissue engineering approaches. Herein, we thoroughly summarize the state of the art of MCSs as tissue-engineered scaffolds for acceleration of bone repair, including their fabrication methods, critical factors for osteogenesis regulation, current opportunities and challenges in the future. First, the current fabrication methods for MCSs, mainly including direct mineral composite, in-situ mineralization and 3D printing techniques, have been proposed to improve their biomimetic physical structures in this review. Meanwhile, three aspects of physical (mechanics and morphology), biological (cells and growth factors) and chemical (composition and cross-linking) cues are described as the critical factors for regulating the osteogenic feature of MCSs. Finally, the opportunities and challenges associated with MCSs as bone tissue-engineered scaffolds are also discussed to point out the future directions for building the next generation of MCSs that should be endowed with satisfactorily mimetic structures and appropriately biological characters for bone regeneration.

Combining specimen-specific finite-element models and optimization in cortical-bone material characterization improves prediction accuracy in three-point bending tests

Although the beam theory is widely used for calculating material parameters in three-point bending test, it cannot accurately describe the biomechanical properties of specimens after the yield. Hence, we propose a finite element (FE) based optimization method to obtain accurate bone material parameters from three-point bending test. We tested 80 machined bovine cortical bone specimens at both longitudinal and transverse directions using three-point bending. We then adopted the beam theory and the FE-based optimization method combined with specimen-specific FE models to derive the material parameters of cortical bone. We compared data obtained using these two methods and further evaluated two groups of parameters with three-point bending simulations. Our data indicated that the FE models with material properties from the FE-based optimization method showed best agreements with experimental data for the entire force-displacement responses, including the post-yield region. Using the beam theory, the yield stresses derived from 0.0058% strain offset for the longitudinal specimen and 0.0052% strain offset for the transverse specimen are closer to those derived from the FE-based optimization method, compared to yield stresses calculated without strain offset. In brief, we conclude that the optimization FE method is more appropriate than the traditional beam theory in identifying the material parameters of cortical bone for improving prediction accuracy in three-point bending mode. Given that the beam theory remains as a popular method because of its efficiency, we further provided correction functions to adjust parameters calculated from the beam theory for accurate FE simulation.

SMALL PUNCH TESTING: AN ALTERNATIVE TESTING TECHNIQUE TO EVALUATE TENSILE BEHAVIOR OF CORTICAL BONE

The tensile properties of cortical bone are usually determined with the help of uniaxial tensile test which requires enough amount of bone material. Further, it is very complicated to examine the heterogeneity and anisotropy associated with the deformational properties of cortical bone with the help of uniaxial tensile test. Through this study, small punch testing has been proposed as an alternate technique to evaluate the deformational behavior of cortical bone utilizing optimum amount of bone material. The comparison between elastic modulus values obtained from tensile test and stiffness values obtained through small punch testing was done for validation. The values of these properties were found to be having a significant positive correlation with each other. The effects of bone density and compositional parameters on these properties were also found to be having a similar trend. It is observed through this study that stiffness values from small punch technique are having a similarity with elastic modulus values from uniaxial tensile testing. It is proposed that small punch testing technique can be used as an alternate to examine the deformational behavior of cortical bone.

Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly

The growing incidence of skeletal fractures poses a significant challenge to ageing societies. Since a major part of physiological loading in the lower limbs is carried by cortical bone, it would be desirable to better understand the structure-mechanical property relationships and scale effects in this tissue. This study aimed at assessing whether microindentation properties combined with chemical and morphological information are usable to predict macroscopic elastic and strength properties in a donor- and site-matched manner. Specimens for quasi-static macroscopic tests in tension, compression, and torsion and microindentation were prepared from a cohort of 19 male and 20 female donors (46 to 99 years). All tests were performed under fully hydrated conditions. The chemical composition of the extra-cellular matrix was investigated with Raman spectroscopy. The results of the micro-mechanical tests were combined with morphological and compositional properties using a power law relationship to predict the macro-mechanical results. Microindentation properties were not gender dependent, remarkably constant over age, and showed an overall small variation with standard deviations of approximately 10 %. Similar results were obtained for chemical tissue composition. Macro-mechanical stiffness and strength were significantly related to porosity for all load cases (p<0.05). In case of macroscopic yield strain and work-to-failure this was only true in torsion and compression, respectively. The correlations of macro-mechanical with micro-mechanical, morphological, and chemical properties showed no significance for cement line density, mineralisation, or variations in the microindentation results and were dominated by porosity with a moderate explanatory power of predominately less than 50 %. The results confirm that age, with minor exceptions gender, and small variations in average mineralisation have negligible effect on the tissue microindentation properties of human lamellar bone in the elderly. Furthermore, our findings suggest that microindentation experiments are suitable to predict macroscopic mechanical properties in the elderly only on average and not on a one to one basis. The presented data may help to form a better understanding of the mechanisms of ageing in bone tissue and of the length scale at which they are active. This may be used for future prediction of fracture risk in the elderly.

Primary cup stability in THA with augmentation of acetabular defect. A comparison of healthy and osteoporotic bone

BACKGROUND CONTEXT

Reconstruction of acetabular defect has been advocated as standard procedure in total hip arthroplasty. The presence of bony defects at the acetabulum is viewed as a cause of instability and acetabular wall augmentation is often used without proper consideration of surrounding bone density. The initial cup-bone stability is, however, a challenge and a number of studies supported by clinical follow-ups of patients suggested that if the structural graft needs supporting more than 50% of the acetabular component, a reconstruction cage device spanning ilium to ischium should be preferred to protect the graft and provide structural stability. This study aims to (1) investigate the relationship between cup motion and bone density and (2) quantify the re-distribution of stress at the defect site after augmentation.

HYPHOTESIS

Paprosky type I or II, acetabular defects, when reconstructed with bone screws supported by bioabsorbable calcified triglyceride bone cement are significantly less effective for osteoporotic bone than healthy bone.

MATERIALS AND METHODS

Acetabular wall defects were reconstructed on six cadaveric subjects with bioabsorbable calcified triglyceride bone cement using a re-bar technique. Data of the specimen with higher bone density was used to validate a Finite Element Model. Values of bone apparent density ranging from healthy to osteoporotic were simulated to evaluate (1) the cup motion, through both displacement and rotation, (2) and the von Mises stress distribution.

RESULTS

Defect reconstruction with bone screws and bioabsorbable calcified triglyceride bone cement results in a re-distribution of stress at the defect site. For a reduction of 65% in bone density, the cup displacement was similar to a healthy bone for loads not exceeding 300 N, as load progressed up to 1500 N, the reconstructed defect showed increase of 99 μm (128%) in displacement and of 0.08° in rotation angle.

CONCLUSIONS

Based on the results, we suggest that an alternative solution to wall defect augmentation with bone screws supported by bioabsorbable calcified triglyceride bone cement, be used for osteoporotic bone.

LEVEL OF EVIDENCE

Level IV, experimental and cadaveric study.

Insights into the effects of tensile and compressive loadings on human femur bone

Background:

Fragile fractures are most likely manifestations of fatigue damage that develop under repetitive loading conditions. Numerous microcracks disperse throughout the bone with the tensile and compressive loads. In this study, tensile and compressive load tests are performed on specimens of both the genders within 19 to 83 years of age and the failure strength is estimated.

Materials and Methods:

Fifty five human femur cortical samples are tested. They are divided into various age groups ranging from 19-83 years. Mechanical tests are performed on an Instron 3366 universal testing machine, according to American Society for Testing and Materials International (ASTM) standards.

Results:

The results show that stress induced in the bone tissue depends on age and gender. It is observed that both tensile and compression strengths reduces as age advances. Compressive strength is more than tensile strength in both the genders.

Conclusion:

The compression and tensile strength of human femur cortical bone is estimated for both male and female subjecting in the age group of 19-83 years. The fracture toughness increases till 35 years in male and 30 years in female and reduces there after. Mechanical properties of bone are age and gender dependent.

Micro-CT finite element model and experimental validation of trabecular bone damage and fracture

Most micro-CT finite element modeling of human trabecular bone has focused on linear and non-linear analysis to evaluate bone failure properties. However, prediction of the apparent failure properties of trabecular bone specimens under compressive load, including the damage initiation and its progressive propagation until complete bone failure into consideration, is still lacking. In the present work, an isotropic micro-CT FE model at bone tissue level coupled to a damage law was developed in order to simulate the failure of human trabecular bone specimens under quasi-static compressive load and predict the apparent stress and strain. The element deletion technique was applied in order to simulate the progressive fracturing process of bone tissue. To prevent mesh-dependence that generally affects the damage propagation rate, regularization technique was applied in the current work. The model was validated with experimental results performed on twenty-three human trabecular specimens. In addition, a sensitivity analysis was performed to investigate the impact of the model factors' sensitivities on the predicted ultimate stress and strain of the trabecular specimens. It was found that the predicted failure properties agreed very well with the experimental ones.

Finite element prediction with experimental validation of damage distribution in single trabeculae during three-point bending tests

There is growing evidence that information on trabecular microarchitecture can improve the assessment of fracture risk. One current strategy is to exploit finite element (FE) analysis applied to experimental data of mechanically loaded single trabecular bone tissue obtained from non-invasive imaging techniques for the investigation of the damage initiation and growth of bone tissue. FE analysis of this type of bone has mainly focused on linear and non-linear analysis to evaluate the bone's failure properties. However, there is a lack of experimentally validated FE damage models at trabecular bone tissue level allowing for the simulation of the progressive damage process (initiation and growth) till complete fracture. Such models are needed to perform enhanced prediction of the apparent failure mechanical properties needed to assess the fracture risk of bone organs. In the current study, we develop a FE model based on a continuum damage mechanics (CDM) approach to simulate the damage initiation and propagation of a single trabecula till complete facture in quasi-static regime. Three-point bending experiments were performed on single bovine trabeculae and compared to FE results. In order to validate the proposed FE mode, (i) the force displacement curve was compared to the experimental one and (ii) the damage distribution was correlated to the measured one obtained by digital image correlation based on stress whitening in bone, reported to be correlated to microdamage. A very good agreement was obtained between the FE and experimental results, indicating that the proposed damage investigation protocol based on FE analysis and testing is reliable to assess the damage behavior of bone tissue and that the current damage model is able to accurately simulate the damaging and fracturing process of single trabeculae under quasi static load.

ASSESSMENT OF THE BIOMECHANICAL COMPATIBILITY OF AN INTERSPINOUS IMPLANT FOR "DYNAMIC STABILIZATION" THROUGH THE FINITE ELEMENT METHOD

The paper addresses the biomechanical compatibility of an interspinous implant used for "dynamic stabilization" of a diseased intervertebral disc. A comparison between the behaviour of a titanium alloy ( Ti 6 Al 4 V ) implant and that of a superelastic alloy ( Ni - Ti ) implant has been carried out.

The assessment of the biomechanical compatibility was achieved by means of the finite element method, in which suitably implemented constitutive laws for the materials have been used. The L4–L5 lumbar system in healthy state has been assumed as target for a biomechanically compatible implant. The L4–L5 system with the interspinous implant subjected to compressive force and bending moments has been simulated. A strength analysis for the bearing bone tissue in the posterior processes was also carried out.

The results have shown that both implants were able to decrease the force on the apophyseal joints; however, the titanium-based implant exhibited a low biomechanical compatibility under extension-flexion in the sagittal plane; whereas the Ni - Ti exhibited a higher compatibility.

Compressive behaviour of child and adult cortical bone

In this study, cortical bone tissue from children was investigated. It is extremely difficult to obtain human child tissue. Therefore, the only possibility was to use bone tissue, free from any lesion, collected from young bone cancer patients. The compressive mechanical behaviour of child bone tissue was compared to the behaviour of adult tissue. Moreover, two hypotheses were tested: 1) that the mechanical behaviour of both groups is correlated to ash density; 2) that yield strain is an invariant. Small parts of the diaphysis of femora or tibiae from 12 children (4-15 years) and 12 adults (22-61 years) were collected. Cylindrical specimens were extracted from the cortical wall along the longitudinal axis of the diaphysis. A total of 107 specimens underwent compressive testing (strain rate: 0.1 s(-1)). Only the specimens showing a regular load-displacement curve (94) were considered valid and thereafter reduced to ash. It was found that the child bone tissue had significant lower compressive Young's modulus (-34%), yield stress (-38%), ultimate stress (-33%) and ash density (-17%) than the adult tissue. Conversely, higher compressive ultimate strain was found in the child group (+24%). Despite specimens extracted from both children and adults, ash density largely described the variation in tissue strength and stiffness (R(2)=in the range of 0.86-0.91). Furthermore, yield strain seemed to be roughly an invariant to subject age and tissue density. These results confirm that the mechanical properties of child cortical bone tissue are different from that of adult tissue. However, such differences are correlated to differences in tissue ash density. In fact, ash density was found to be a good predictor of strength and stiffness, also for cortical bone collected from children. Finally, the present findings support the hypothesis that compressive yield strain is an invariant.

Effects of osteoporosis and nutrition supplements on structures and nanomechanical properties of bone tissue

In this study, the bone structures, nanomechanical properties and fracture behaviors in different groups of female C57BL/6 mice (control, sham operated, ovariectomized, casein supplemented, and fermented milk supplemented) were examined by micro-computed tomography, scanning and transmission electron microscopy, and nanoindentation. The control and sham operated mice showed dense bone structures with high cortical bone mineral densities of 544 mg/cm(3) (average) and high hardness of 0.9-1.1 GPa; resistance to bone fracture was conferred by microcracking, crack deflections and ligament bridging attributed to aligned collagen fibers and densely packed hydroxyapatite crystals. Bone mineral density, hardness and fracture resistance in ovariectomized mice markedly dropped due to loose bone structure with randomly distributed collagens and hydroxyapatites. The acidic casein supplemented mice with blood acidosis exhibited poor mineral absorption and loose bone structure, whereas the neutralized casein or fermented milk supplemented mice were resistant to osteoporosis and had high bone mechanical properties.

Hierarchies of damage induced loss of mechanical properties in calcified bone after in vivo fatigue loading of rat ulnae

During fatigue loading of whole bone, damage to bone tissue accumulates, coalesces and leads to fractures. Whether damage affects tissue material properties similarly at the nanoscale (less than 1 μm), microscale (less than 1 mm), and whole bone scale has not been fully evaluated. Therefore, in this study, we examine scale-dependent loss of calcified tissue material properties in rat ulnae, after fatigue loading of rat forearms using the forearm compression model. In vivo fatigue loading was conducted on the right forearms until a displacement end-point was reached. The non-fatigued left forearms served as contralateral controls. Subsequently, three-point bending tests to failure on excised ulnae demonstrated a 41% and 49% reduction in the stiffness and ultimate strength as compared to contralateral control ulnae, respectively. Depth-sensing microindentation demonstrated an average decrease in material properties, such as elastic modulus and hardness, of 28% and 29% respectively. Nanoindentation measured elastic modulus and hardness were reduced by 26% and 29% in damaged bone relative to contralateral controls, respectively. The increased loss of whole bone material properties compared to tissue material properties measured using indentation is mainly attributed to the presence of a macrocrack located in the medial compressive region at the site of peak strains. The similar magnitude of changes in material properties by microindentation and nanoindentation is attributed to damage that may originate at an even smaller scale, as inferred from 10% differences in connectivity of osteocyte canaliculi in damaged bone.

Constitutive relationship of tissue behavior with damage accumulation of human cortical bone

Microdamage accumulation has been identified as a major conduit for bone tissues to absorb fracture energy. Due to the poor understanding of its underlying mechanism, however, an adequate constitutive relationship between damage accumulation and the mechanical behavior of bone has not yet been established. In this study, the constitutive relationship between the damage accumulation induced by overload and the evolution of mechanical properties of bone with incremental deformation was established based on the experimental results obtained from a novel progressive loading protocol developed in our laboratory. First, a decayed exponential model was proposed to capture the damage accumulation (modulus loss) with increase in applied strain. Next, a power law function was proposed to represent the progression of plastic deformation with damage accumulation. Finally, a linear combination of the Kohlrausch-Williams-Watts (KWW) and the Debye functions was used to depict the viscoelastic behavior of bone associated with damage accumulation. The results of this study may help in developing a constitutive model for predicting the mechanical behavior of cortical bone tissues.

Characterization of indentation response and stiffness reduction of bone using a continuum damage model

Indentation tests can be used to characterize the mechanical properties of bone at small load/length scales offering the possibility of utilizing very small test specimens, which can be excised using minimally-invasive procedures. In addition, the need for mechanical property data from bone may be a requirement for fundamental multi-scale experiments, changes in nano- and micro-mechanical properties (e.g., as affected by changes in bone mineral density) due to drug therapies, and/or the development of computational models. Load vs. indentation depth data, however, is more complex than those obtained from typical macro-scale experiments, primarily due to the mixed state of stress, and thus interpretation of the data and extraction of mechanical properties is more challenging. Previous studies have shown that cortical bone exhibits a visco-elastic response combined with permanent deformation during indentation tests, and that the load vs. indentation depth response can be simulated using a visco-elastic/plastic material model. The model successfully captures the loading and creep displacement behavior, however, it does not adequately reproduce the unloading response near the end of the unloading cycle, where a pronounced decrease in contact stiffness is observed. It is proposed that the stiffness reduction observed in bone results from an increase in damage; therefore, a plastic-damage model was investigated and shown capable of simulating a typical bone indentation response through an axisymmetric finite element simulation. The plastic-damage model was able to reproduce the full indentation response, especially the reduced stiffness behavior exhibited during the latter stages of unloading. The results suggest that the plastic-damage model is suitable for describing the complex indentation response of bone and may provide further insight into the relationship between model parameters and mechanical/physical properties.

Mechanical behavior of human cortical bone in cycles of advancing tensile strain for two age groups

The capacity of bone for post-yield energy dissipation decreases with age. To gain information on the causes of such a change, we examined age-related changes in the mechanical behavior of human cadaveric bone as a function of progressive deformation. In this study, tensile specimens from tibiae of nine middle aged and eight elderly donors were loaded till failure in an incremental and cyclic (load-dwell-unload-dwell-reload) scheme. The elastic modulus, maximum stress, permanent strain, stress relaxation, permanent strain energy, elastic release strain energy, and hysteresis energy were determined in each loading cycle at incremental strains. Similar with previous work, the results of the present study also indicated that elderly bone failed at much lower strains compared to middle aged bone. However, no significant differences in the mechanical behavior of bone were observed between the two age groups except for the premature failure of elderly bone. After yielding, the energy dissipation and permanent strain of bone appeared to linearly increase with increasing strain applied, while nonlinear changes occurred in the modulus loss and stress relaxation with increasing strain. Moreover, stress relaxation tended to peak at 1% strain beyond which few elderly bone specimens survived. This study suggests that damaging mechanisms in bone vary with deformation, and aging affects the post-yield mechanisms, thus giving rise to the age-related differences in the mechanical properties of bone, especially the capacity of the tissue for energy dissipation.

The effects of embalming using a 4% formalin solution on the compressive mechanical properties of human cortical bone

BACKGROUND

The use of formalin fixed bone tissue is often avoided because of its assumed influence on the mechanical properties of bone. Fixed bone tissue would minimise biological risks and eliminate preservation issues for long duration experimental tests. This study aimed to determine the short- and long-term effects of embalming, using a solution with 4% formalin concentration, on the mechanical properties of human cortical bone.

METHODS

Three-millimetre cylindrical specimens of human cortical bone were extracted from two femoral diaphyses and divided in four groups. The first group was used as control, the remaining three groups were left in the embalming solution for 48 h, 4 week, and 8 week, respectively. Compressive mechanical properties, hardness and ash density were assessed. The last was used to check the homogeneity among the four groups.

FINDINGS

No significant differences were found among the four groups in yield stress, ultimate stress and hardness. The specimens stored for 8 week in the embalming solution had significant lower Young's modulus (-24%), higher yield strain (+20%) and ultimate strain (+53%) compared to the other groups.

INTERPRETATION

On a short-term perspective, embalming did not affect the compressive mechanical properties, nor hardness of human cortical bone, whereas a long-term preservation (8 week) did significantly affect Young's modulus, yield strain and ultimate strain in compression. Preserving bone segments for up to 4 week in an embalming solution with low formalin concentration seems to be an interesting alternative when collecting and/or managing fresh or fresh-frozen bone segments for biomechanical experiments is not possible.

Indirect determination of trabecular bone effective tissue failure properties using micro-finite element simulations

Trabecular bone strength is marked not only by the onset of local yielding, but also by post-yield behavior. To study and predict trabecular bone elastic and yield properties, micro-finite element (micro-FE) models were successfully applied. However, trabecular bone strength predictions require micro-FE models incorporating post-yield behavior of trabecular bone tissue. Due to experimental difficulties, such data is currently not available. Here we used micro-FE modeling to determine failure behavior of trabecular bone tissue indirectly, by iteratively fitting FE simulation to experimental results. Failure parameters were fitted to an isotropic plasticity model based on Hill's yield function, using materially and geometrically nonlinear micro-FE models of seven bovine trabecular bone specimens. The predictive value of the averaged effective tissue properties was subsequently tested. The results showed that compression softening had to be included on the tissue level in order to accurately describe the apparent-level behavior of the bone specimens. A sensitivity study revealed that the simulated response was less sensitive to variations in the post-yield properties of the bone tissue than variations in the elastic and yield properties. Due to fitting of the tissue properties, apparent-level behavior could be accurately reproduced for each specimen separately. Predictions based on the averaged and fixed tissue properties were less accurate, due to inter-specimen variations in the tissue properties.

High frequency ultrasound prediction of mechanical properties of cortical bone with varying amount of mineral content

In this study, we evaluate if high frequency ultrasound impedance measurements can predict the mechanical properties of bones where the amount of bone mineral is varied. The motivation stems from the potential utility of ultrasound as a noninvasive technique to evaluate and monitor the mechanical properties of bone during treatment of diseased states where the ratio of mineral content to organic matrix content could change (e.g., metabolic bone diseases, osteoarthritis, osteogenesis imperfecta, fracture healing). Eleven cortical bovine femur samples, which were taken along the long axis of femur, were used in each group. Bone samples with reduced mineral content (estimated to be 21% and 35% less than the control) were obtained by immersing samples into fluoride ion solution for 3 and 12 d. Control and fluoride treated samples were first tested mechanically in tension. Acoustic impedances of the mechanically tested samples were obtained by using scanning acoustic microscopy (SAM). Results from mechanical tests indicate that the tensile elastic modulus of the samples was highly correlated to the yield strength (r(2) = 0.94, p < 0.01) and to the ultimate strength (r(2) = 0.75, p < 0.01). SAM results indicate that the acoustic impedances were significantly correlated to the elastic modulus (r(2) = 0.85, p < 0.01), yield strength (r(2) = 0.86, p < 0.01) and ultimate strength (r(2) = 0.70, p < 0.01). These results show that ultrasonic techniques could potentially be used to predict the in vivo ultimate strength of bone tissue caused by changes in mineral content.

The effect of recovery time and test conditions on viscoelastic measures of tensile damage in cortical bone

Stiffness degradation and strength degradation are often measured to monitor and characterize the effects of damage accumulation in bone. Based on evidence that these properties could be affected by not only damage magnitude but also test conditions, the present study investigated the effect of hold condition and recovery time on measures of tensile damage. Machined human femoral cortical bone specimens were subjected to tensile tests consisting of a pre-damage diagnostic loading cycle, a damage loading cycle and post-damage cycle. Controlled variables were recovery time (1, 10, and 100 min) and hold condition (zero load or zero strain) after the damage cycle. Damage measures were calculated as the ratio of each post-damage cycle to the pre-damage value for loading modulus, secant modulus, unloading modulus, stress relaxation and strain (stress) recovery at 1 min post-diagnostic time. The damage cycle caused reductions in all measures, and some measures varied with recovery time and hold condition. Apparent modulus degradation for both hold conditions decreased with recovery time. Stress relaxation was unaffected by recovery time for both hold conditions. Zero-strain hold conditions resulted in lower values for degradation of modulus and change of relaxation. Stress or strain recovery after the damage cycle was evident through 100 min, but 90% of the recovery occurred within 10 min. The results demonstrate that choice of test conditions can influence the apparent magnitude of damage effects. They also indicate that 10 min recovery time was sufficient to stabilize most measures of the damage state.

A novel approach to assess post-yield energy dissipation of bone in tension

In this study, we proposed a novel approach to assess the energy dissipation during the post-yield deformation of bone. Based on the stress-strain behavior in an incremental and cyclic loading-unloading-reloading scheme in uniaxial tension, we partitioned the post-yield energy dissipation of bone into three distinct pathways: released elastic strain energy (U(er)); irreversible energy (U(i)); and hysteresis energy (U(h)). Among them, U(er) depends on the stiffness loss, U(i) is the energy permanently consumed, and U(h) reflects changes in the viscoelastic behavior of bone in the process of post-yield deformation. As an example, bone specimens from human cadaveric femurs of middle-aged and elderly donors were tested using this approach. The results of this study indicate that there exist age-related differences in post-yield energy dissipation and modulus degradation. These results implicate that this novel approach could detect the age-related differences in energy dissipation of bone and may aid in understanding the underlying mechanisms of such changes.

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.

Do sacrificial bonds affect the viscoelastic and fracture properties of bone?

Sacrificial bonds have been suggested as a toughening mechanism for bone tissue. Ionic bridges formed by divalent calcium ions between collagen molecules have been proposed as candidates for sacrificial bonds. If this mechanism is active at the macroscopic level, we should observe changes in mechanical properties of bone when calcium ions are maintained or removed from the tissue. To test this hypothesis, we measured viscoelastic and monotonic mechanical properties of cortical bone subjected to differing ionic environments. Storage modulus of bone could be changed up to 3.8% by the presence or absence of Na+ or Ca++ in the environment in a reversible fashion when bones were monitored continuously during treatments. A long-term one-time treatment increased the viscoelastic properties of bone soaked in Na+ solutions whereas the viscoelastic properties of bones soaked in Ca++ solutions were maintained. However, the strength and toughness of bone specimens soaked and fractured in treatment solutions were not improved. The presence of Ca++ affected the mechanical behavior of mineralized bone tissue at the macro scale. These effects were reversible, consistent with the original proposal. However, these effects may not necessarily indicate an increase in strength or toughness of the tissue at the macro scale.

Effect of mineral content on the nanoindentation properties and nanoscale deformation mechanisms of bovine tibial cortical bone

In this paper, a multitechnique experimental and numerical modeling methodology was used to show that mineral content had a significant effect on both nanomechanical properties and ultrastructural deformation mechanisms of samples derived from adult bovine tibial bone. Partial and complete demineralization was carried out using phosphoric and ethylenediamine tetraacetic acid treatments to produce samples with mineral contents that varied between 37 and 0 weight percent (wt%). The undemineralized samples were found to have a mineral content of approximately 58 wt%. Nanoindentation experiments (maximum loads approximately 1000 microN and indentation depths approximately 500 nm) perpendicular to the osteonal axis for the approximately 58 wt% samples were found to have an estimated elastic modulus of approximately 7-12 GPa, which was 4-6x greater than that obtained for the approximately 0 wt% samples. The yield strength of the approximately 58 wt% samples was found to be approximately 0.24 GPa; 3.4x greater than that of the approximately 0 wt% sample. These results are discussed in the context of in situ and post-mortem atomic force microscopy imaging studies which show clear residual deformation after indentation for all samples studied. The partially demineralized samples underwent collagen fibril deformation and kinking without loss of the characteristic banding structure at low maximum loads (approximately 300 microN). At higher maximum loads (approximately 700 microN) mechanical denaturation of collagen fibrils was observed within the indent region, as well as disruption of interfibril interfaces and slicing through the thickness of individual fibrils leading to microcracks along the tip apex lines and outside the indent regions. A finite element elastic-plastic continuum mechanical model was able to predict the nanomechanical behavior of all samples on loading and unloading.

Effect of ultrastructural changes on the toughness of bone

The ultrastructure of bone can be considered as a conjunction between the biology and the biomechanics of the tissue. It is the result of cellular and molecular activities of bone formation, and its organization dominates the mechanical behavior of bone. Following this perspective, the objective of this review is to provide a current understanding of bone ultrastructure and its relationships with the toughness of the tissue. Therefore, we first provide a discussion on the organization of bone constituents, namely collagen, mineral, and water. Then, we present evidence on how the toughness of bone relates to its ultrastructure through the formation of micro damage. In addition, attention is given to how damage accumulation serves as a toughening mechanism. Finally, we describe how changes in the ultrastructure-caused by osteogenesis imperfecta, gamma irradiation, fluoride treatment, and aging affect the toughness and competence of bone.

Mechanical and functional properties of the equine superficial digital flexor tendon

The in vitro and in vivo mechanical properties of the superficial digital flexor tendon have been described. To date the focus has been on single load to failure testing, however refined in vivo methods may prove useful to evaluate the effects of treatment and exercise on tendons. During maximal exercise, the adult superficial digital flexor tendon operates close to its functional limits with a narrow biomechanical safety margin. This combined with exercise and age associated microdamage, and a limited adaptive ability may increase the risk of fatigue failure. Studies evaluating treatment regimens for tendonitis have focused on repair and regeneration and yielded varying results. It would appear that the superficial digital flexor tendon has a limited ability if any to adapt positively to exercise after maturity. In contrast, the foal's superficial digital flexor tendon may have a greater adaptive ability and may respond to an appropriate exercise regimen to produce a more functionally adapted tendon. Recent studies have shown that foals allowed free pasture exercise develop a larger, stronger, more elastic tendon compared to foals that were confined or subjected to a training program. Effects on the non-collagenous matrix appear to be responsible for these differences. In contrast, training or excess exercise may have permanent detrimental effects on the biomechanical and functional properties of the superficial digital flexor tendon in the foal. The implication is that the determination of optimum exercise intensity and timing, and the role of the non-collagenous matrix in tendon physiology in the young horse may hold the key to developing tendons more capable of resisting injury.