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.     

A damage model for nonlinear tensile behavior of cortical bone.

To describe the time-dependent nonlinear tensile behavior observed in experimental studies of cortical bone, a damage model was developed using two internal state variables (ISV's). One ISV is a damage parameter that represents the loss of stiffness. A rule for the evolution of this ISV was defined based on previously observed creep behavior. The second ISV represents the inelastic strain due to viscosity and internal friction. The model was tested by simulating experiments in tensile and bending loading. Using average values from previous creep studies for parameters in the damage evolution rule, the model tended to underestimate the maximum nonlinear strains and to overestimate the nonlinear strain accumulated after load reversal in the tensile test simulations. Varying the parameters for the individual tests produced excellent fits to the experimental data. Similarly, the model simulations of the bending tests could produce excellent fits to the experimental data. The results demonstrate that the 2-ISV model combining damage (stiffness loss) with slip and viscous behavior could capture the nonlinear tensile behavior of cortical bone in axial and bending loading.     

The effect of damage on the viscoelastic behavior of human vertebral trabecular bone

The present study examines the viscoelastic behavior of cancellous bone at low strains and the effects of damage on this viscoelastic behavior. It provides experimental evidence of interaction between stress relaxation behavior and the effect of accumulated damage. The results suggest that damage is at least orthotropic in trabecular bone specimens under uniaxial loading. Simple linear models of viscoelasticity described the time-dependent stress-strain behavior at low strains before and after specimen damage, although better fits of these models were obtained prior to damage. Modeling the observed changes in relaxation times with damage accumulation appears necessary to successfully predict the post-damage viscoelastic response.     

The multiscale meso-mechanics model of viscoelastic cortical bone

Biomechanics and Modeling in Mechanobiology - Cortical bone is a complex hierarchical structure consisting of biological fiber composites with transversely isotropic constituents, whose...     

Anisotropic viscoelastic properties of cortical bone

Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted): E(t)=E0 (A1 exp[-(t/tau1)beta]+(1-A1) exp[-(t/tau2)gamma]), [0 < A1, beta, gamma < 1], where E0 is the initial modulus value E0. Tau1 and tau2(>tau1) are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and beta and gamma are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.     

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.     

Systematic error in mechanical measures of damage during four-point bending fatigue of cortical bone

Accumulation of fatigue microdamage in cortical bone specimens is commonly measured by a modulus or stiffness degradation after normalizing tissue heterogeneity by the initial modulus or stiffness of each specimen measured during a preloading step. In the first experiment, the initial specimen modulus defined using linear elastic beam theory (LEBT) was shown to be nonlinearly dependent on the preload level, which subsequently caused systematic error in the amount and rate of damage accumulation measured by the LEBT modulus degradation. Therefore, the secant modulus is recommended for measurements of the initial specimen modulus during preloading. In the second experiment, different measures of mechanical degradation were directly compared and shown to result in widely varying estimates of damage accumulation during fatigue. After loading to 400,000 cycles, the normalized LEBT modulus decreased by 26% and the creep strain ratio decreased by 58%, but the normalized secant modulus experienced no degradation and histology revealed no significant differences in microcrack density. The LEBT modulus was shown to include the combined effect of both elastic (recovered) and creep (accumulated) strain. Therefore, at minimum, both the secant modulus and creep should be measured throughout a test to most accurately indicate damage accumulation and account for different damage mechanisms. Histology revealed indentation of tissue adjacent to roller supports, with significant sub-surface damage beneath large indentations, accounting for 22% of the creep strain on average. The indentation of roller supports resulted in inflated measures of the LEBT modulus degradation and creep. The results of this study suggest that investigations of fatigue microdamage in cortical bone should avoid the use of four-point bending unless no other option is possible.     

Tensile damage and its effects on cortical bone

Plexiform bovine bone samples are repeatedly loaded in tension along their longitudinal axis. In order to induce damage in the bone tissue, bone samples are loaded past their yield point. Half of the bone samples from the damaged group were stored in saline to allow for viscoelastic recovery while the others were decalcified. Tensile tests were conducted on these samples to characterize the effects of damage on the mechanical behavior of the organic matrix (decalcified samples) as well as on bone tissue (stored in saline). The ultimate strain of the damaged decalcified bone is 29% higher compared to that of non-damaged decalcified (control) bone. The ultimate stresses as well as the elastic moduli are similar in both decalcified groups. This phenomenon is also observed in other collagenous tissue (tendon and ligament). This may suggest that damage in bone is caused by shear failure of the organic matrix; transverse separation of the collagen molecules or microfibrils from each other. In contrast, there is a trend towards lowered ultimate strains in damaged bone, which is soaked in saline, with respect to control bone samples (not damaged). The damaged bone tissue exhibits a bi-linear behavior in contrast to the mechanical behavior of non-damaged bone. The initial elastic modulus (below 55 MPa) and ultimate strength of damaged bone are similar to that in non-damaged bone.     

Effect of mineral dissolution from bone specimens on the viscoelastic properties of cortical bone

Although physiological saline (0.15 M NaCl aqueous solution) has been used as a storage solution to prevent bone specimens from drying, there have been reports that Ca²⁺ ions dissolve from bone specimens during the storage in saline. In order to determine whether such storage has a marked effect on mechanical properties, the relaxation modulus of bovine cortical bone stored in physiological saline was compared with that stored in a buffer solution containing a sufficient amount of Ca²⁺ ions. After storage in saline, the modulus value of specimens was significantly reduced from that before storage. On the other hand, the modulus value of specimens soaked in the solution containing sufficient Ca²⁺ ions did not change after storage. The relaxation rate of a bone specimen stored in physiological saline was larger than that of a specimen stored in Ca²⁺-buffered saline solution and that of the control specimens. The results suggest that by the dissolution of Ca²⁺ ions from a bone specimen during storage in physiological saline, percolated paths of mineral phase and of reinforced matrix phase are disjoined, resulting in reduction in the elastic modulus and change in the viscoelastic properties of bone.     

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.     

Analysis of creep strain during tensile fatigue of cortical bone

During fatigue tests of cortical bone specimens, at the unload portion of the cycle (zero stress) non-zero strains occur and progressively accumulate as the test progresses. This non-zero strain is hypothesised to be mostly, if not entirely, describable as creep. This work examines the rate of accumulation of this strain and quantifies its stress dependency. A published relationship determined from creep tests of cortical bone (Journal of Biomechanics 21 (1988) 623) is combined with knowledge of the stress history during fatigue testing to derive an expression for the amount of creep strain in fatigue tests. Fatigue tests on 31 bone samples from four individuals showed strong correlations between creep strain rate and both stress and "normalised stress" (sigma/E) during tensile fatigue testing (0-T). Combined results were good (r(2)=0.78) and differences between the various individuals, in particular, vanished when effects were examined against normalised stress values. Constants of the regression showed equivalence to constants derived in creep tests. The universality of the results, with respect to four different individuals of both sexes, shows great promise for use in computational models of fatigue in bone structures.     

Inelastic strain accumulation in cortical bone during rapid transient tensile loading

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of +/- 420 MPa/s. Loads were reversed at pre selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.     

Mechanisms for recovery of motor function following cortical damage

Recent studies of focal injury to the cerebral cortex have demonstrated that the remaining, intact tissue undergoes structural and functional changes that could play a substantial role in neurological recovery. New information regarding the molecular and cellular environment in the adjacent, intact tissue has suggested that waves of growth promotion and inhibition modulate the self-repair processes of the brain. Furthermore, recent studies have documented widespread neurophysiological and neuroanatomical changes in regions remote from a focal cortical injury, suggesting that entire cortical networks participate in the recovery process.     

The effects of refreezing on the viscoelastic and tensile properties of ligaments

Biomechanical testing protocols for ligaments can be extensive and span two or more days. During this time, a specimen may have to undergo more than one cycle of freezing and thawing. Thus, the objective of this study was to evaluate the effects of refreezing on the viscoelastic and tensile properties of ligaments. The femur-medial collateral ligament-tibia complexes (FMTC) from six pairs of rabbit knees were used for this study. Following sacrifice, one leg in each pair was assigned to the fresh group and the FMTC was immediately dissected and prepared for testing. The contralateral knees were fresh-frozen at -20 degrees C for 3 weeks, thawed, dissected and then refrozen for one additional week before being tested as the refrozen group. The cross-sectional area and shape of the medial collateral ligament (MCL) was measured using a laser micrometer system. Stress relaxation and cyclic stress-relaxation tests in uniaxial tension were performed followed by a load to failure test. When the viscoelastic behavior of the MCL was described by the quasi-linear viscoelastic (QLV) theory, no statistically significant differences could be detected for the five constants (A, B, C, tau1, and tau2) between the fresh and refrozen groups (p > or = 0.07) based on our sample size. In addition, the structural properties of the FMTCs and the mechanical properties of the MCLs were also found to be similar between the two groups (p > or = 0.68). These results suggest that careful refreezing of the specimens had little or no effect on the biomechanical properties measured.     

The effect of pH on potentially lethal damage recovery in A549 cells

The radiation sensitivity and potentially lethal damage recovery (PLDR) capacity of A549 human lung carcinoma cells have been studied. For unfed monolayer cultures, radiation sensitivity was greater in plateau phase than in log phase of growth. PLDR was observed when plateau-phase cells were held in their own spent medium postirradiation, such that the dose-response curve with 24 h holding was similar to that for log-phase cells plated immediately after irradiation. The high PLDR capacity of A549 plateau-phase cells (recovery factor between 40 and 70 for 24 h holding after 10 Gy) was reduced 10-fold or more by alkalinizing the pH of the spent medium immediately after irradiation from a value of 6.5 +/- 0.1 to a value of 7.6. Medium alkalinization resulted in an increase in the rate of glycolysis, with subsequent reacidification to a pH of 7.3 within 2 h of the pH adjustment. No change in cell cycle distribution was observed in the plateau-phase cultures up to 32 h after change of medium pH, and no increase in cell density was found after 48 h. A slight increase in the rate of incorporation of radiolabeled thymidine into acid-precipitable material was observed at 4 and 24 h after alkalinization of the medium. While it is not possible at present to define a mechanism for this pH effect, our results demonstrate that, at least for this cell line, variables such as medium pH and glucose concentration can profoundly influence the observation of PLDR.     

The viscoelastic basis for the tensile strength of elastin

Purified aortic elastin displays failure behaviour characteristic of an amorphous, noncrystalizing elastomer with failure properties showing a strong dependence on viscoelastic behaviour. Tensile breaking stresses and breaking strains measured over a range of temperatures, hydration levels, and strain rates are reducible to single curves by the application of shift factors obtained from dynamic mechanical tests. The breaking stress of rubbery elastin is similar to that found in other elastomers, but glassy elastin is about an order of magnitude less strong than expected. We suggest elastin's ability to be strengthened through viscous dissipation of strain energy and crack tip blunting is limited by its fibrillar structure.     

Relationship between bone tissue strain and lattice strain of HAp crystals in bovine cortical bone under tensile loading

Cortical bone is a composite material composed of hydroxyapatite (HAp) and collagen. As HAp is a crystalline structure, an X-ray diffraction method is available to measure the strain of HAp crystals. However, HAp crystals in bone tissue have been known to have the low degree of crystallization. Authors have proposed an X-ray diffraction method to measure the lattice strain of HAp crystals from the diffusive intensity profile due to low crystallinity. The precision of strain measurement was greatly improved by this method. In order to confirm the possibility of estimating the bone tissue strain with measurements of the strain of HAp crystals, this work investigates the relationship between bone tissue strain on a macroscopic scale and the lattice strain of HAp crystals on a microscopic scale. The X-ray diffraction experiments were performed under tensile loading. Strip bone specimens of 40x6x0.8mm in size were cut from the cortical region of a shaft of bovine femur. A stepwise tensile load was applied in the longitudinal direction of the specimen. By detecting the diffracted X-ray beam transmitted through the specimen, the lattice strain was directly measured in the loading direction. As a result, the lattice strain of HAp crystals showed lower value than the bone tissue strain measured by a strain gage. The bone tissue strain was described with the mean lattice strain of the HAp crystals and the elastic modulus.