Human Cortical Bone Specimens Research Articles

Cortical Bone Water Concentration: Dependence of MR Imaging Measures on Age and Pore Volume Fraction

To quantify bulk bone water to test the hypothesis that bone water concentration (BWC) is negatively correlated with bone mineral density (BMD) and is positively correlated with age, and to propose the suppression ratio (SR) (the ratio of signal amplitude without to that with long-T2 suppression) as a potentially stronger surrogate measure of porosity, which is evaluated ex vivo and in vivo. Human subject studies were conducted in compliance with institutional review board and HIPAA regulations. Healthy men and women (n = 72; age range, 20-80 years) were examined with a hybrid radial ultrashort echo time magnetic resonance (MR) imaging sequence at 3.0 T, and BWC was determined in the tibial midshaft. In a subset of 40 female subjects, the SR was measured with a similar sequence. Cortical volumetric BMD (vBMD) was measured by means of peripheral quantitative computed tomography (CT). The method was validated against micro-CT-derived porosity in 13 donor human cortical bone specimens. Associations among parameters were evaluated by using standard statistical tools. BWC was positively correlated with age (r = 0.52; 95% confidence interval [CI]: 0.22, 0.73; P = .002) and negatively correlated with vBMD at the same location (r = -0.57; 95% CI: -0.76, -0.29; P < .001). Data were suggestive of stronger associations with SR (r = 0.64, 95% CI: 0.39, 0.81, P < .001 for age; r = -0.67, 95% CI: -0.82, -0.43, P < .001 for vBMD; P < .001 for both), indicating that SR may be a more direct measure of porosity. This interpretation was supported by ex vivo measurements showing SR to be strongly positively correlated with micro-CT porosity (r = 0.88; 95% CI: 0.64, 0.96; P < .001) and with age (r = 0.87; 95% CI: 0.62, 0.96; P < .001). The MR imaging-derived SR may serve as a biomarker for cortical bone porosity that is potentially superior to BWC, but corroboration in larger cohorts is indicated.

Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy

The objective of the study was to evaluate the ability of a nonlinear ultrasound technique, the so-called nonlinear resonant ultrasound spectroscopy (NRUS) technique, for detecting early microdamage accumulation in cortical bone induced by four-point bending fatigue. Small parallelepiped beam-shaped human cortical bone specimens were subjected to cyclic four-point bending fatigue in several steps. The specimens were prepared to control damage localization during four-point bending fatigue cycling and to unambiguously identify resonant modes for NRUS measurements. NRUS measurements were achieved to follow the evolution of the nonlinear hysteretic elastic behavior during fatigue-induced damage. After each fatigue step, a small number of specimens was removed from the protocol and set apart to quantitatively assess the microcrack number density and length using synchrotron radiation micro-computed tomography (SR-µCT). The results showed a significant effect of damage steps on the nonlinear hysteretic elastic behavior. No significant change in the overall length of microcracks was observed in damaged regions compared to the load-free control regions. Only an increased number of shortest microcracks, those in the lowest quartile, was noticed. This was suggestive of newly formed microcracks during the early phases of damage accumulation. The variation of nonlinear hysteretic elastic behavior was significantly correlated to the variation of the density of short microcracks. Our results suggest that the nonlinear hysteretic elastic behavior is sensitive to early bone microdamage. Therefore NRUS technique can be used to monitor fatigue microdamage progression in in vitro experiments.

In situ mechanical behavior of mineral crystals in human cortical bone under compressive load using synchrotron X-ray scattering techniques

It is of great interest to delineate the effect of orientation distribution of mineral crystals on the bulk mechanical behavior of bone. Using a unique synergistic approach combining a progressive loading scheme and synchrotron X-ray scattering techniques, human cortical bone specimens were tested in compression to examine the in situ mechanical behavior of mineral crystals aligned in different orientations. The orientation distribution was quantitatively estimated by measuring the X-ray diffraction intensity from the (002) plane in mineral crystals. In addition, the average longitudinal (c-axis), transverse (a-axis), and shear strains of the subset of mineral crystals aligned in each orientation were determined by measuring the lattice deformation normal to three distinct crystallographic planes (i.e. 002, 310, and 213) in the crystals. The experimental results indicated that the in situ strain and stress of mineral crystals varied with orientations. The normal strain and stress in the longitudinally aligned mineral crystals were markedly greater than those in the transversely oriented crystals, whereas the shear stress reached a maximum for the crystals aligned in ±30° with respect to the loading direction. The maximum principal strain and stress were observed in the mineral crystals oriented along the loading axis, with a similar trend observed in the maximum shear strain and stress. By examining the in situ behavior, the contribution of mineral crystals to load bearing and the bulk behavior of bone are discussed.

Nonlinear resonant ultrasound spectroscopy is sensitive to the level of cortical bone damage

The objective of the study was to evaluate the sensitivity of nonlinear resonant ultrasound spectroscopy (NRUS) measurements to the accumulation of damage in cortical bone by fatigue or by controlled crack propagation. Two groups of human cortical bone specimens were prepared from the femoral mid-diaphysis. The specimens from the first group were taken through a progressive fatigue protocol consisting of four steps of cyclic four-point bending. The specimens from the second group were taken through a toughness protocol consisting of initiation and controlled propagation of a stable crack induced by 4-point bending mechanical loading. Our results evidenced a progressive increase of the normalized nonlinear elastic parameter during fatigue testing or during toughness experiments. While in specimens subjected to mechanical fatigue cycling the relative variation of nonlinear elasticity was significantly related to the relative variation of the number density of small cracks assessed with micro-computed tomogr...

Visualization of 3D osteon morphology by synchrotron radiation micro‐CT

Cortical bone histology has been the subject of scientific inquiry since the advent of the earliest microscopes. Histology - literally the study of tissue - is a field nearly synonymous with 2D thin sections. That said, progressive developments in high-resolution X-ray imaging are enabling 3D visualization to reach ever smaller structures. Micro-computed tomography (micro-CT), employing conventional X-ray sources, has become the gold standard for 3D analysis of trabecular bone and is capable of detecting the structure of vascular (osteonal) porosity in cortical bone. To date, however, direct 3D visualization of secondary osteons has eluded micro-CT based upon absorption-derived contrast. Synchrotron radiation micro-CT, through greater image quality, resolution and alternative contrast mechanisms (e.g. phase contrast), holds great potential for non-destructive 3D visualization of secondary osteons. Our objective was to demonstrate this potential and to discuss areas of bone research that can be advanced through the application of this approach. We imaged human mid-femoral cortical bone specimens derived from a 20-year-old male (Melbourne Femur Collection) at the Advanced Photon Source synchrotron (Chicago, IL, USA) using the 2BM beam line. A 60-mm distance between the target and the detector was employed to enhance visualization of internal structures through propagation phase contrast. Scan times were 1 h and images were acquired with 1.4-μm nominal isotropic resolution. Computer-aided manual segmentation and volumetric 3D rendering were employed to visualize secondary osteons and porous structures, respectively. Osteonal borders were evident via two contrast mechanisms. First, relatively new (hypomineralized) osteons were evident due to differences in X-ray attenuation relative to the surrounding bone. Second, osteon boundaries (cement lines) were delineated by phase contrast. Phase contrast also enabled the detection of soft tissue remnants within the vascular pores. The ability to discern osteon boundaries in conjunction with vascular and cellular porosity revealed a number of secondary osteon morphologies and provided a unique 3D perspective of the superimposition of secondary osteons on existing structures. Improvements in resolution and optimization of the propagation phase contrast promise to provide further improvements in structural detail in the future.

In situ accumulation of advanced glycation endproducts (AGEs) in bone matrix and its correlation with osteoclastic bone resorption

Advanced glycation end products (AGEs) have been observed to accumulate in bone with increasing age and may impose effects on bone resorption activities. However, the underlying mechanism of AGEs accumulation in bone is still poorly understood. In this study, human cortical bone specimens from young (31±6years old), middle-aged (51±3years old) and elderly (76±4years old) groups were examined to determine the spatial-temporal distribution of AGEs in bone matrix and its effect on bone resorption activities by directly culturing osteoclastic cells on bone slices. The results of this study indicated that the fluorescence intensity (excitation wave length 360nm and emission wave length 470±40nm) could be used to estimate the relative distribution of AGEs in bone (pentosidine as its marker) under an epifluorescence microscope. Using the fluorescence intensity as the relative measure of AGEs concentration, it was found that the concentration of AGEs varied with biological tissue ages, showing the greatest amount in the interstitial tissue, followed by the old osteons, and the least amount in newly formed osteons. In addition, AGEs accumulation was found to be dependent on donor ages, suggesting that the younger the donor the less AGEs were accumulated in the tissue. Most interestingly, AGEs accumulation appeared to initiate from the region of cement lines, and spread diffusively to the other parts as the tissue aged. Finally, it was observed that the bone resorption activities of osteoclasts were positively correlated with the in situ concentration of AGEs and such an effect was enhanced with increasing donor age. These findings may help elucidate the mechanism of AGEs accumulation in bone and its association with bone remodeling process.

Contrast-enhanced micro-computed tomography of fatigue microdamage accumulation in human cortical bone

Conventional methods used to image and quantify microdamage accumulation in bone are limited to histological sections, which are inherently invasive, destructive, two-dimensional, and tedious. These limitations inhibit investigation of microdamage accumulation with respect to volumetric spatial variation in mechanical loading, bone mineral density, and microarchitecture. Therefore, the objective of this study was to investigate non-destructive, three-dimensional (3-D) detection of microdamage accumulation in human cortical bone using contrast-enhanced micro-computed tomography (micro-CT), and to validate micro-CT measurements against conventional histological methods. Unloaded controls and specimens loaded in cyclic uniaxial tension to a 5% and 10% reduction in secant modulus were labeled with a precipitated BaSO 4 stain for micro-CT and basic fuchsin for histomorphometry. Linear microcracks were similarly labeled by BaSO 4 and basic fuchsin as shown by backscattered electron microscopy and light microscopy, respectively. The higher X-ray attenuation of BaSO 4 relative to the bone extracellular matrix provided enhanced contrast for the detection of damage that was otherwise not able to be detected by micro-CT prior to staining. Therefore, contrast-enhanced micro-CT was able to nondestructively detect the presence, 3-D spatial location, and accumulation of fatigue microdamage in human cortical bone specimens in vitro. Microdamage accumulation was quantified on segmented micro-CT reconstructions as the ratio of BaSO 4 stain volume (SV) to total bone volume (BV). The amount of microdamage measured by both micro-CT (SV/BV) and histomorphometry (Cr.N, Cr.Dn, Cr.S.Dn) progressively increased from unloaded controls to specimens loaded to a 5% and 10% reduction in secant modulus ( p < 0.001). Group means for micro-CT measurements of damage accumulation were strongly correlated to those using histomorphometry ( p < 0.05), validating the new methods. Limitations of the new methods in the present study included that the precipitated BaSO 4 stain was non-specific and non-biocompatible, and that micro-CT measurements exhibited greater variability compared to conventional histology. Nonetheless, contrast-enhanced micro-CT enabled non-destructive imaging and 3-D spatial information, which are not possible using conventional histological methods.

Improved accuracy of cortical bone mineralization measured by polychromatic microcomputed tomography using a novel high mineral density composite calibration phantom

Microcomputed tomography (micro-CT) is increasingly used as a nondestructive alternative to ashing for measuring bone mineral content. Phantoms are utilized to calibrate the measured x-ray attenuation to discrete levels of mineral density, typically including levels up to 1000 mg HA/cm3, which encompasses levels of bone mineral density (BMD) observed in trabecular bone. However, levels of BMD observed in cortical bone and levels of tissue mineral density (TMD) in both cortical and trabecular bone typically exceed 1000 mg HA/cm3, requiring extrapolation of the calibration regression, which may result in error. Therefore, the objectives of this study were to investigate (1) the relationship between x-ray attenuation and an expanded range of hydroxyapatite (HA) density in a less attenuating polymer matrix and (2) the effects of the calibration on the accuracy of subsequent measurements of mineralization in human cortical bone specimens. A novel HA-polymer composite phantom was prepared comprising a less attenuating polymer phase (polyethylene) and an expanded range of HA density (0-1860 mg HA/cm3) inclusive of characteristic levels of BMD in cortical bone or TMD in cortical and trabecular bone. The BMD and TMD of cortical bone specimens measured using the new HA-polymer calibration phantom were compared to measurements using a conventional HA-polymer phantom comprising 0-800 mg HA/cm3 and the corresponding ash density measurements on the same specimens. The HA-polymer composite phantom exhibited a nonlinear relationship between x-ray attenuation and HA density, rather than the linear relationship typically employed a priori, and obviated the need for extrapolation, when calibrating the measured x-ray attenuation to high levels of mineral density. The BMD and TMD of cortical bone specimens measured using the conventional phantom was significantly lower than the measured ash density by 19% (p < 0.001, ANCOVA) and 33% (p < 0.05, Tukey's HSD), on average, respectively. The BMD and TMD of cortical bone specimens measured using the HA-polymer phantom with an expanded range of HA density was significantly lower than the measured ash density by 8% (p < 0.001, ANCOVA) and 10% (p < 0.05, Tukey's HSD), on average, respectively. The new HA-polymer calibration phantom with a less attenuating polymer and an expanded range of HA density resulted in a more accurate measurement of micro-CT equivalent BMD and TMD in human cortical bone specimens compared to a conventional phantom, as verified by ash density measurements on the same specimens.

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 ( ε ˙ ) ranging from low (0.08 s −1) to high (18 s −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 1 s −1, while strain at yield was invariant for most strain rates and only decreased at rates higher than 10 s −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.

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.

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 scratching approach for measuring age-related changes in the in situ toughness of bone

A scratch test using a nanoindentation system was proposed in this study to assess the age-related changes in the in situ toughness of bone matrix at ultrastructural levels. A tissue removal energy density ( u r ) was defined and estimated as the work done by the scratch ( U T ) divided by the total volume of the scratch groove ( u s ). The value of u s was used as a relative measure of the in situ toughness of the tissue. Human cortical bone specimens obtained from middle-aged (between 49 and 59 years old) and elderly groups (over 69 years old) were tested using this technique. A significant difference in the estimated removal energy density ( u s ) in the secondary osteons was found between the middle-aged and elderly groups (5.49±0.696 vs. 4.09±1.30 N/mm 2, respectively).

Susceptibility of aging human bone to mixed-mode fracture increases bone fragility

Since bone-mass-based measurements have demonstrated limited success in predicting age-related increase in fracture incidence, recent emphasis has been placed on quantification of bone quality. Specifically, material parameters such as strength, stiffness, and toughness have been quantified to characterize bone quality through mechanical testing. This study is the first one to report multiaxial failure characteristics of bone (quality) by conducting fatigue tests on human cortical bone specimens under physiologically relevant loading involving simultaneous application of axial and torsional loading to produce previously reported in vivo shear/normal stress ratios. Our results show that, compared to uniaxial tests, multiaxial fatigue tests show up to a 20-fold reduction in the fatigue life of human cortical bone. More significantly, the susceptibility of mixed-mode failure increases bone fragility in aging human bone. Furthermore, since the magnitude of mixed-mode loading varies with physiological activities, results of this study also suggest that a reduction in the activities involving significant mixed-mode loading may lower the overall fracture incidence among older individuals.

Assessment of cortical bone microstructure and material properties using high resolution scanning acoustic microscopy

Combined evaluation of bone microstructural and mechanical information remains a challenging task which is required for bone phenotyping or accurate finite element modeling. Our objective was to assess the value of quantitative scanning acoustic microscopy (SAM) for bone characterization in comparison to synchrotron radiation computed tomography (SR-CT). Ten specimens of human cortical bone (radius) were investigated using SR-CT and SAM (200 MHz) with spatial resolution of 10 and 8 μm, respectively. An image fusion and analysis software was developed to derive site-matched estimates of (1) microstructural parameters, e.g., haversian cavity density and mean diameter and porosity, and (2) tissue properties such as mineral density (MD, SR-CT) and acoustic impedance (Z, SAM) for distinct anatomical regions of interest (osteons, interstitial tissue). Local stiffness c33 was derived from the combination of MD and Z. An almost perfect correlation was found for all microstructural indices derived by both techniques. Impedance was correlated to the square of MD (R2=0.39, p&amp;lt;1e−4). The derived stiffness c33 (35.9±12.8) was highly correlated with Z (R2=0.99, p&amp;lt;1e−4). These findings suggest that SAM fulfills the requirement for a simultaneous evaluation of cortical bone microstructure and material properties at the tissue level.

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

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

An X-ray diffraction study of the effects of heat treatment on bone mineral microstructure

A series of human cortical bone specimens has been heated to temperatures up to 1200°C and the mineral content examined in detail by X-ray diffraction. Line profile analysis of the diffraction data has been undertaken to characterise the microstructural (crystallite size and microstrain) features of the mineral at each temperature. Individual profile fitting of several maxima from each diffractogram has also provided precise lattice parameters of the apatite at each temperature. The apatite did not show any significant decomposition over the temperature range although CaO was increasingly formed at temperatures above 600°C. Both finite crystallite size and microstrain contributed significantly to the diffraction peak broadening below 600°C. When heated to >800°C, the small, rod-like mineral crystallites changed from a highly anisotropically strained state to one with significantly larger equidimensional crystals possessing little microstrain. The findings are discussed in the context of graft bone substitutes and surgical heating of bone.

Diffuse damage accumulation in the fracture process zone of human cortical bone specimens and its influence on fracture toughness.

This study was concerned with the mechanics and micromechanisms of diffuse (ultrastructural) damage occurrence in human tibial cortical bone specimens subjected to tension-tension fatigue. A nondestructive technique was developed for damage assessment on the surfaces of intact compact tension specimens using laser scanning confocal microscopy. Results indicated that diffuse damage initiates as a result of fractures in the inter-canalicular regions. Subsequent growth of those microscopic flaws demonstrated multiple deflections from their paths due to 3D spatial distribution of microscopic porosities (lacunae-canalicular porosities) and the stress-concentrating effects of lacunae. Damage dominating effects in the early stages of fatigue had been verified by the observed variations of the fracture toughness due to artificially induced amounts of damage. Toughening behavior was observed as a function of diffuse damage.

A combined finite element method and continuum damage mechanics approach to simulate the in vitro fatigue behavior of human cortical bone.

The fatigue of bone, in particular the associated modulus degradation and accumulation of permanent strain, has been implicated as the cause of femoral neck fractures and the migration of total joint replacements. The objective of this study was to develop a technique to simulate the tensile fatigue behavior of human cortical bone. A combined continuum damage mechanics (CDM) and finite element analysis (FEA) approach was used to predict the number of cycles to failure, modulus degradation and accumulation of permanent strain of human cortical bone specimens. The simulation of fatigue testing of eight dumb-bell specimens of cortical bone were performed and the predictions compared with existing experimental data. The predictions from the finite element models were in close agreement with the experimental data. The models predicted similar development of modulus degradation and permanent strain as observed in the experimental tests. The technique is capable of predicting the accumulation of permanent strain without the need for simulating every single load step. These findings suggest that the complex fatigue behavior of human cortical bone can be simulated using the described approach and forms the first step for simulating the more complex mechanisms associated with femoral neck fractures and implant migration.

Cumulative damage and the response of human bone in two-step loading fatigue

It has already been shown that in fatigue tests in vitro human cortical bone accumulates damage in the form of microcracks and that the total number of microcracks generated prior to the creation of the fatal macrocrack, and their effect (softening) on the material properties, depends on the level of applied stress. At each stress level the amount of accumulated damage has also been shown to be a non-linear function of the cycle number ( Zioupos et al. 1996a, b; Pattin et al., 1996). The theoretical implications of the previous findings and two possible models for cumulative damage were put to the test here by performing tensile fatigue tests in two-step level ( high/ low or low/ high) loading on human cortical bone specimens. The results indicate that the accumulation of damage in-vitro is highly dependent on the level of stress and the stress history. Usual linear expressions for fatigue lifetime predictions, like the Palmgren–Miner rule, substantially over or underestimate the outcome depending on whether the stress was applied in a high/ low or a low/ high sequence, respectively. In view of these discrepancies we conclude that predicting the fatigue lifetime of any bone in vivo under variable loading and complex history regimes is an extremely difficult task to which the study of accumulation of damage can offer a significant but, perhaps, still limited contribution.

Comparison of damage accumulation measures in human cortical bone

Elastic modulus degradation, strength reduction, and energy dissipation have traditionally been the properties of choice to monitor the damage process in cortical bone. However, these properties only provide limited insight into the damage process given the complex mechanical nature of bone. In the current study, alternative measures of the damage process were investigated for machined human cortical bone specimens loaded under torsion. Seventy-two bone specimens from 6 human femurs were subjected to a series of torsional relaxation cycles in which damage was induced during a single relaxation cycle and the effects of damage on the elastic, yield, viscous, and failure properties were determined from pre- and post-damage relaxation cycles. The results revealed that degradation of all torsion properties exhibited a significant twist magnitude effect. However, the yield stress and strain, the relaxation rate, and the total relaxation exhibited 5–10 fold greater degradation than both strength and modulus, when residual strength tests were conducted at high shear strain rates. For the loading conditions examined in this study, the results indicated that the relaxation and yield properties of cortical bone are more sensitive to shear damage accumulation and better measures of the damage process than either strength or modulus. Further, the results reveal an important interaction between damage and the viscous behavior of bone which provides new insight into the effects of damage on bone mechanical properties.