Damage rate is a predictor of fatigue life and creep strain rate in tensile fatigue of human cortical bone samples

We present results on the growth of damage in 29 fatigue tests of human femoral cortical bone from four individuals, aged 53-79. In these tests we examine the interdependency of stress, cycles to failure, rate of creep strain, and rate of modulus loss. The behavior of creep rates has been reported recently for the same donors as an effect of stress and cycles. In the present paper we first examine how the evolution of damage (drop in modulus per cycle) is associated with the stress level or the "normalized stress" level (stress divided by specimen modulus), and results show the rate of modulus loss fits better as a function of normalized stress. However, we find here that even better correlations can be established between either the cycles to failure or creep rates versus rates of damage than any of these three measures versus normalized stress. The data indicate that damage rates can be excellent predictors of fatigue life and creep strain rates in tensile fatigue of human cortical bone for use in practical problems and computer simulations.     

Creep does not contribute to fatigue in bovine trabecular bone

In both cortical and trabecular bone loaded in fatigue, the stress-strain loops translate along the strain axis. Previous studies have suggested that this translation is the result of creep associated with the mean stress applied in the fatigue test. In this study, we measured the residual strrain (corresponding to the translation of the stress-strain loops) in fatigue tests on bovine trabecular bone and compared it to an upper bound estimate of the creep strain in each test. Our results indicate that the contribution of creep to the translation of the stress-strain loops is negligible in bovine trabecular bone. These results, combined with models for fatigue in lower density bone, suggest that that creep does not contribute to the fatigue of normal human bone. Creep may make a significant contribution to fatigue in low-density osteoporotic bone in which trabeculae have resorbed, reducing the connectivity of the trabecular structure.     

Simulation of creep in non-homogenous samples of human cortical bone

Characterising the mechanisms causing viscoelastic mechanical properties of human cortical bone, as well as understanding sources of variation, is important in predicting response of the bone to creep and fatigue loads. Any better understanding, when incorporated into simulations including finite element analysis, would assist bioengineers, clinicians and biomedical scientists. In this study, we used an empirically verified model of creep strain accumulation, in a simulation of 10 non-homogeneous samples, which were created from micro-CT scans of human cortical bone of the femur midshaft obtained from a 74-year-old female cadaver. These non-homogeneous samples incorporate the presence of Haversian canals and resorption cavities. The influence of inhomogeneity on the response and variation in the samples in both creep and stress relaxation tests are examined. The relationship between steady-state creep rate, applied loads (stress relaxation and creep tests) and microstructure, that is bone apparent porosity, is obtained. These relations may provide insight into damage accumulation of whole human bones and be relevant to studies on osteoporosis.     

Simulation of creep in non-homogenous samples of human cortical bone

Characterising the mechanisms causing viscoelastic mechanical properties of human cortical bone, as well as understanding sources of variation, is important in predicting response of the bone to creep and fatigue loads. Any better understanding, when incorporated into simulations including finite element analysis, would assist bioengineers, clinicians and biomedical scientists. In this study, we used an empirically verified model of creep strain accumulation, in a simulation of 10 non-homogeneous samples, which were created from micro-CT scans of human cortical bone of the femur midshaft obtained from a 74-year-old female cadaver. These non-homogeneous samples incorporate the presence of Haversian canals and resorption cavities. The influence of inhomogeneity on the response and variation in the samples in both creep and stress relaxation tests are examined. The relationship between steady-state creep rate, applied loads (stress relaxation and creep tests) and microstructure, that is bone apparent porosity, is obtained. These relations may provide insight into damage accumulation of whole human bones and be relevant to studies on osteoporosis.     

Time-dependent circumferential deformation of cortical bone upon internal radial loading

Short and long duration tests were conducted on hollow femoral bone cylinders to study the circumferential (hoop) creep response of cortical bone subjected to an intramedullary radial load. It was hypothesized that there is a stress threshold above which nonlinear creep effects dominate the mechanical response and below which the response is primarily determined by linear viscoelastic material properties. The results indicate that a hoop stress threshold exists for cortical bone, where creep strain, creep strain rate and residual strain exhibited linear behavior at low hoop stress and nonlinear behavior above the hoop stress threshold. A power-law relationship was used to describe creep strain as a function of hoop stress and time and damage morphology was assessed.     

Fatigue of immature baboon cortical bone

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

Fracture toughness and fatigue crack propagation rate of short fiber reinforced epoxy composites for analogue cortical bone

Third-generation mechanical analogue bone models and synthetic analogue cortical bone materials manufactured by Pacific Research Laboratories, Inc. (PRL) are popular tools for use in mechanical testing of various orthopedic implants and biomaterials. A major issue with these models is that the current third-generation epoxy-short fiberglass based composite used as the cortical bone substitute is prone to crack formation and failure in fatigue or repeated quasistatic loading of the model. The purpose of the present study was to compare the tensile and fracture mechanics properties of the current baseline (established PRL "third-generation" E-glass-fiber-epoxy) composite analogue for cortical bone to a new composite material formulation proposed for use as an enhanced fourth-generation cortical bone analogue material. Standard tensile, plane strain fracture toughness, and fatigue crack propagation rate tests were performed on both the third- and fourth-generation composite material formulations using standard ASTM test techniques. Injection molding techniques were used to create random fiber orientation in all test specimens. Standard dog-bone style tensile specimens were tested to obtain ultimate tensile strength and stiffness. Compact tension fracture toughness specimens were utilized to determine plane strain fracture toughness values. Reduced thickness compact tension specimens were also used to determine fatigue crack propagation rate behavior for the two material groups. Literature values for the same parameters for human cortical bone were compared to results from the third- and fourth-generation cortical analogue bone materials. Tensile properties of the fourth-generation material were closer to that of average human cortical bone than the third-generation material. Fracture toughness was significantly increased by 48% in the fourth-generation composite as compared to the third-generation analogue bone. The threshold stress intensity to propagate the crack was much higher for the fourth-generation material than for the third-generation composite. Even at the higher stress intensity threshold, the fatigue crack propagation rate was significantly decreased in the fourth-generation composite compared to the third-generation composite. These results indicate that the bone analogue models made from the fourth-generation analogue cortical bone material may exhibit better performance in fracture and longer fatigue lives than similar models made of third-generation analogue cortical bone material. Further fatigue testing of the new composite material in clinically relevant use of bone models is still required for verification of these results. Biomechanical test models using the superior fourth-generation cortical analogue material are currently in development.     

Creep contributes to the fatigue behavior of bovine trabecular bone.

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53 degrees C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.     

Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone

Cortical and trabecular bone have similar creep behaviors that have been described by power-law relationships, with increases in temperature resulting in faster creep damage accumulation according to the usual Arrhenius (damage rate approximately exp (-Temp.-1)) relationship. In an attempt to determine the phase (collagen or hydroxyapatite) responsible for these similar creep behaviors, we investigated the creep behavior of demineralized cortical bone, recognizing that the organic (i.e., demineralized) matrix of both cortical and trabecular bone is composed primarily of type I collagen. We prepared waisted specimens of bovine cortical bone and demineralized them according to an established protocol. Creep tests were conducted on 18 specimens at various normalized stresses sigma/E0 and temperatures using a noninvasive optical technique to measure strain. Denaturation tests were also conducted to investigate the effect of temperature on the structure of demineralized bone. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates at all applied normalized stresses and temperatures. Strong (r2 > 0.79) and significant (p < 0.01) power-law relationships were found between the damage accumulation parameters (steady-state creep rate d epsilon/dt and time-to-failure tf) and the applied normalized stress sigma/E0. The creep behavior was also a function of temperature, following an Arrhenius creep relationship with an activation energy Q = 113 kJ/mole, within the range of activation energies for cortical (44 kJ/mole) and trabecular (136 kJ/mole) bone. The denaturation behavior was characterized by axial shrinkage at temperatures greater than approximately 56 degrees C. Lastly an analysis of covariance (ANCOVA) of our demineralized cortical bone regressions with those found in the literature for cortical and trabecular bone indicates than all three tissues creep with the same power-law exponents. These similar creep activation energies and exponents suggest that collagen is the phase responsible for creep in bone.     

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.     

Some viscoplastic characteristics of bovine and human cortical bone

Multiple cycle tensile creep tests were performed on human and bovine cortical bone specimens. The tests enabled total strain to be decomposed into elastic, linear viscoelastic, creep and permanent plastic components. The results indicate that a stress threshold exists; above which time dependent effects dominate material response and below which the behavior is primarily linear viscoelastic, with time effects playing only a secondary role. A constant stress above the threshold produces a constant steady state creep rate, with the magnitude of the creep rate being an exponential function of the stress magnitude. Additionally, it was found that a major portion of the inelastic strain is always recovered on unloading and that the accumulation of creep strain increases the material compliance on subsequent loadings below the threshold. These two factors suggest that a damage mechanism is responsible for the nonlinear behavior.     

Near-terminal creep damage does not substantially influence fatigue life under physiological loading

Cortical bone specimens were damaged using repeated blocks of tensile creep loading until a near-terminal amount of creep damage was generated (corresponding to a reduction in elastic modulus of 15%). One group of cortical bone specimens was submitted to the near-terminal damage protocol and subsequently underwent fatigue loading in tension with a maximum strain of 2000 με (Damage Fatigue, n=5). A second group was submitted to cyclic fatigue loading but was not pre-damaged (Control Fatigue, n=5). All but one specimen (a damaged specimen) reached run-out (10 million cycles, 7.7 days). No significant differences in microscopic cracks or other tissue damage were observed between the two groups or between either group and additional, completely unloaded specimens. Our results suggest that damage in cortical bone allograft that is not obvious or associated with a stress riser may not substantially affect its fatigue life under physiologic loading.     

A fatigue damage model for the cement-bone interface

Loss of fixation at the cement-bone interface can contribute to clinical loosening of cemented total hip replacements. In this study, the fatigue damage response was determined for cement-bone constructs subjected to shear fatigue loading. A typical three-phase fatigue response was observed with substantial early damage, followed by a long constant damage rate region and a final abrupt increase in damage to fracture. All of the damage resulted from creep (permanent) deformation during fatigue loading and there was no loss in cyclic stiffness. Using a Von Mises equivalent stress/strain concept, a general damage model was developed to describe the fatigue creep response of the cement-bone interface under either shear or tensile fatigue loading. Time to failure was highly correlated (r2=0.971) with equivalent creep strain rate and moderately related (r2=0.428) with equivalent initial strain for the two loading regimes. The equivalent creep strain at failure (0.052+/-0.018) was found to be independent of the applied equivalent stress. A combination of the creep damage model (to describe the damage process) with a constant final equivalent strain (as a failure criteria) could be used to assess the cement-bone failure response of cemented implant systems.     

Impacted morselized cancellous bone: mechanical effects of defatting and augmentation with fine hydroxyapatite particles

Geotechnical engineering testing techniques were used to study the mechanical properties of morselized cancellous bone (MCB) and the effects of defatting and augmentation with fine hydroxyapatite (HA) particles. Bovine and human cancellous bone was morselized, rinsed, and manually squeezed to remove excess fluid, producing a standard surgical MCB sample that was also used as a control. Some of the MCB was defatted with heat and detergent and mixed with HA particles in ratios ranging from 0% to 100% HA. Compaction tests were used to determine the effects of moisture content and the amount of MCB that can be packed into a confined space. One-dimensional consolidation tests were used to determine the uniaxial strain behavior, confined modulus, and steady-state creep rate. The compaction tests demonstrated that defatting and adding HA particles significantly increased density. The one-dimensional consolidation tests showed that strain was decreased, modulus was increased and the creep rate was decreased by defatting and adding HA.     

Nonlinear viscoelastic characterization of bovine trabecular bone

The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness–density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep–recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples (\(n = 19\)). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery’s nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep–recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening–softening behaviour with increasing stress.     

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

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

A phenomenological model for predicting fatigue life in bovine trabecular bone

Cyclic loading of bone during daily activities can lead to fatigue degradation and increased risk of fracture in both the young and elderly population. Damage processes under cyclic loading in trabecular bone result in the reduction of the elastic modulus and accumulation of residual strain. These effects increase with increasing stress levels, leading to a progressive reduction in fatigue life. The present work analyzes the effect of stress and strain variation on the above damage processes in bovine trabecular bone, and develops a phenomenological model relating fatigue life to the imposed stress level. The elastic modulus reduction of the bone specimens was observed to depend on the maximum compressive strain, while the rate of residual strain accumulation was a function of the stress level. A model was developed for the upper and lower bounds of bone elastic modulus reduction with increasing number of cycles, at each stress range. The experimental observations were described well by the model. The model predicted the bounds of the fatigue life with change in fatigue stress. The decrease in the fatigue life with increasing stress was related to corresponding increases in the residual strain accumulation rates at the elevated stress levels. The model shows the validity of fatigue predictions from relatively few cyclic experiments, by combining trends observed in the monotonic and the cyclic tests. The model also presents a relatively simple procedure for predicting the endurance limit for bovine trabecular bone specimens.     

Cortical bone tissue resists fatigue fracture by deceleration and arrest of microcrack growth

Knowledge of kinetics of fatigue crack growth of microcracks is important so as to understand the dynamics of bone adaptation, remodeling, and the etiology of fatigue-based failures of cortical bone tissue. In this respect, theoretical models (Taylor, J. Biomech., 31 (1998) 587-592; Taylor and Prendergast, Proc. Instn. Mech. Engrs. Part H 211 (1997) 369-375) of microcrack growth in cortical bone have predicted a decreasing microcrack growth rate with increasing microcrack length. However, these predictions have not been observed directly. This study investigated microcrack growth and arrest through observations of surface microcracks during cyclic loading (R=0.1, 50-80MPa) of human femoral cortical bone (male, n=4, age range: 37-40yr) utilizing a video microscopy system. The change in crack length and orientation of eight surface microcracks were measured with the number of fatigue cycles from four specimens. At the applied cyclic stresses, the microcracks propagated and arrested in generally less than 10,000 cycles. The fatigue crack growth rate of all microcracks decreased with increasing crack length following initial identification, consistent with theoretical predictions. The growth rate of the microcracks was observed to be in the range of 5x10(-5) to 5x10(-7)mmcycle(-1). In addition, many of the microcracks were observed not to grow beyond 150 microm and a cyclic stress intensity factor of 0.5MNm(-3/2). The results of this study suggest that cortical bone tissue may resist fracture at the microscale by deceleration of fatigue crack growth and arrest of microcracks.     

Creep fracture in bones with different stiffnesses.

Creep fracture experiments were used to examine the differences in time to fracture of bones with very different Young's moduli (bovine bone and red deer antler) and the implications of these differences for the 'cumulative-damage' model of Caler and Carter [J. Biomechanics 22, 625-635 (1989)] for bone fracture. Using normalised stress as the explanatory variable, the slopes of the distributions agreed quite well with that of Caler and Carter for human bone. However, antler took far longer to fracture at any given normalised stress than did bovine bone. Using stress alone as the explanatory variable, the relationships within each bone type almost disappeared. Within any bone type strain is the important determinant of time to fracture, but less mineralised bone takes much longer to fracture at any given strain, or normalised stress, which seems not to be in accord with the cumulative-damage model. The rate of damage accumulation in lightly mineralised bone at high strains (greater than 1%) is much less than that occurring in more heavily mineralised bone.     

Structural role of osteocalcin and osteopontin in energy dissipation in bone

Non-collagenous proteins are a vital component of bone matrix. Amongst them, osteocalcin (OC) and osteopontin (OPN) hold special significance due to their intimate interaction with the mineral and collagenous matrix in bone. Both proteins have been associated with microdamage and fracture, but their structural role in energy dissipation is unclear. This study used bone tissue from genetic deficient mice lacking OC and/or OPN and subjected them to a series of creep-fatigue-creep tests. To this end, whole tibiae were loaded in four-point bending to 70% stiffness loss which captured the three characteristic phases of fatigue associated with initiation, propagation, and coalescence of microdamage. Fatigue loading preceded and followed creep tests to determine creep and dampening parameters. Microdamage in the form of linear microcracks and diffuse damage were analyzed by histology. It was shown that OC and OPN were ‘activated’ following stiffness loss associated with fatigue damage where they facilitated creep and dampening parameters (i.e. increased energy dissipation). More specifically, post-fatigue creep rate and dampening were significantly greater in wild-types (WTs) than genetic deficient mice (p < 0.05). These results were supported by microdamage analysis which showed significant increase in creep-associated diffuse damage formation in WTs compared to genetic deficient groups (p < 0.05). Based on these findings, we propose that during local yield events, OC and OPN rely on ionic interactions of their charged side chains and on hydrogen bonding to dissipate energy in bone.