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.     

A cellular solid model for modulus reduction due to resorption of trabeculae in bone

In osteoporotic trabecular bone, bone loss occurs by thinning and subsequent resorption of the trabeculae. In this study, we compare the effects of density reductions from uniform thinning of struts or from removal of struts in a random, open-cell, three-dimensional Voronoi structure. The results of this study, combined with those previous studies on other regular and random structures, suggest that the modulus and strength of trabecular bone are reduced more dramatically by density losses from resorption of trabeculae than by those from uniform thinning of trabeculae.     

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.     

Numerical Simulation of Bone Plate with Fatigue Crack and Investigation of Attraction Hole for Retarding Crack Growth

Premature fracture of the bone plate caused by fatigue crack is the main failure mode in treating femoral shaft fracture. In order to improve the durability of the plate, this study proposed a crack attraction hole (CAH) to retard the crack propagation based on the fracture mechanics. In this paper, a numerical model of the femoral fracture internal fixation system was constructed, in which the femur was developed using a validated simplified model. First, the fatigue crack initiation location was defined at the stress concentration through static analysis. Next, with the joint simulation method of Franc3D and ABAQUS, the fatigue crack path in the bone plate was predicted. Meanwhile, the Paris parameters of Ti-6Al-4V obtained through experiments were encoded into Franc3D to calculate the crack propagation life. Finally, we considered the influence of CAH designs with different relative vertical distances (2.0, 3.0, and 4.0 mm) and diameters (1.5, 2.0, and 2.5 mm) on the crack propagation path and life of the bone plate. Additionally, the effects of all CAH configurations on the biomechanical performance of the bone plate fixation system were evaluated. The results indicated that the fatigue crack growth path in the bone plate is comparable to a straight line, and the crack growth rate significantly increases when the crack tip reaches the outer boundary of the plate. The findings suggest that the addition of CAH in the bone plate will lead to the deflection of the crack path and increase the fatigue life. Equally important, the improvement of the fatigue life was positively correlated with the diameter of CAH and negatively correlated with the relative vertical distance. In addition, the biomechanical properties of the bone plate system were slightly affected by CAH, substantiating the feasibility of this method. Finally, the comparative analysis verified that a CAH with a relative vertical distance of 3 mm and a diameter of 2 mm exhibited superior improvement in the comprehensive performance on the bone plate.     

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.     

Do microcracks decrease or increase fatigue resistance in cortical bone?

Fatigue of cortical bone produces microcracks; it has been hypothesized that these cracks are analogous to those occurring in engineered composite materials and constitute a similar mechanism for fatigue resistance. However, the numbers of these linear microcracks increase substantially with age, suggesting that they contribute to increased fracture incidence among the elderly. To test these opposing hypotheses, we fatigued 20 beams of femoral cortical bone from elderly men and women in load-controlled four point bending having initial strain ranges of 3000 or 5000 microstrain. Loading was stopped at fracture or 10(6) cycles, whichever occurred first, and microcrack density and length were measured in the loaded region and in a control region that was not loaded. We studied the dependence of fatigue life and induced microdamage on initial microdamage, cortical region, subject gender and age, and several other variables. When the effect of modulus variability was controlled, longer fatigue life was associated with higher rather than lower initial crack density, particularly in the medial cortex. The increase in crack density following fatigue loading was greater in specimens from older individuals and those initially having longer microcracks. Crack density increased as much in specimens fatigued short of the failure point as in those that fractured, and microcracks were, on average, shorter in specimens with greater numbers of resorption spaces, a measure of remodeling rate.     

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.     

Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue

Relatively small amounts of microdamage have been suggested to have a major effect on the mechanical properties of bone. A significant reduction in mechanical properties (e.g. modulus) can occur even before the appearance of microcracks. This study uses a novel non-linear microdamaging finite-element (FE) algorithm to simulate the low-cycle fatigue behavior of high-density trabecular bone. We aimed to investigate if diffuse microdamage accumulation and concomitant modulus reduction, without the need for complete trabecular strut fracture, may be an underlining mechanism for low-cycle fatigue failure (defined as a 30% reduction in apparent modulus). A microCT constructed FE model was subjected to a single cycle monotonic compression test, and constant and variable amplitude loading scenarios to study the initiation and accumulation of low-cycle fatigue microdamage. Microcrack initiation was simulated using four damage criteria: 30%, 40%, 50% and 60% reduction in bone element modulus (el-MR). Evaluation of structural (apparent) damage using the four different tissue level damage criteria resulted in specimen fatigue failure at 72, 316, 969 and 1518 cycles for the 30%, 40%, 50% and 60% el-MR models, respectively. Simulations based on the 50% el-MR model were consistent with previously published experimental findings. A strong, significant non-linear, power law relationship was found between cycles to failure (N) and effective strain (Deltasigma/E(0)): N=1.394x10(-25)(Deltasigma/E(0))(-12.17), r(2)=0.97, p<0.0001. The results suggest that microdamage and microcrack propagation, without the need for complete trabecular strut fracture, are mechanisms for high-density trabecular bone failure. Furthermore, the model is consistent with previous numerical fatigue simulations indicating that microdamage to a small number of trabeculae results in relatively large specimen modulus reductions and rapid failure.     

The effect of cement creep and cement fatigue damage on the micromechanics of the cement–bone interface

The cement–bone interface provides fixation for the cement mantle within the bone. The cement–bone interface is affected by fatigue loading in terms of fatigue damage or microcracks and creep, both mostly in the cement. This study investigates how fatigue damage and cement creep separately affect the mechanical response of the cement–bone interface at various load levels in terms of plastic displacement and crack formation. Two FEA models were created, which were based on micro-computed tomography data of two physical cement–bone interface specimens. These models were subjected to tensile fatigue loads with four different magnitudes. Three deformation modes of the cement were considered: ‘only creep’, ‘only damage’ or ‘creep and damage’. The interfacial plastic deformation, the crack reduction as a result of creep and the interfacial stresses in the bone were monitored. The results demonstrate that, although some models failed early, the majority of plastic displacement was caused by fatigue damage, rather than cement creep. However, cement creep does decrease the crack formation in the cement up to 20%. Finally, while cement creep hardly influences the stress levels in the bone, fatigue damage of the cement considerably increases the stress levels in the bone. We conclude that at low load levels the plastic displacement is mainly caused by creep. At moderate to high load levels, however, the plastic displacement is dominated by fatigue damage and is hardly affected by creep, although creep reduced the number of cracks in moderate to high load region.     

Can deterministic mechanical size effects contribute to fracture and microdamage accumulation in trabecular bone?

Failure of bone under monotonic and cyclic loading is related to the bone mineral density, the quality of the bone matrix, and the evolution of microcracks. The theory of linear elastic fracture mechanics has commonly been applied to describe fracture in bone. Evidence is presented that bone failure can be described through a non-linear theory of fracture. Thereby, deterministic size effects are introduced. Concepts of a non-linear theory are applied to discern how the interaction among bone matrix constituents (collagen and mineral), microcrack characteristics, and trabecular architecture can create distinctively differences in the fracture resistance at the bone tissue level. The non-linear model is applied to interpret pre-clinical data concerning the effects of anti-osteoporotic agents on bone properties. The results show that bisphosphonate (BP) treatments that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is reduced. Selective estrogen receptor modulators (SERMs) that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is increased. The consequences of these changes are reflected in bone mechanical response and predictions are consistent with experimental observations in the animal model which show that BP treatment is associated with more brittle fracture and microcracks without altering the average length of the cracks, whereas SERM treatments lead to a more ductile fracture and mainly increase crack length with a smaller increase in microcrack density. The model suggests that BPs may be more effective in cases in which bone mass is very low, whereas SERMS may be more effective when milder osteoporotic symptoms are present.     

Fatigue creep damage at the cement–bone interface: An experimental and a micro-mechanical finite element study

The goal of this study was to quantify the micromechanics of the cement–bone interface under tensile fatigue loading using finite element analysis (FEA) and to understand the underlying mechanisms that play a role in the fatigue behavior of this interface. Laboratory cement–bone specimens were subjected to a tensile fatigue load, while local displacements and crack growth on the specimen's surface were monitored. FEA models were created from these specimens based upon micro-computed tomography data. To accurately model interfacial gaps at the interface between the bone and cement, a custom-written erosion algorithm was applied to the bone model. A fatigue load was simulated in the FEA models while monitoring the local displacements and crack propagation. The results showed the FEA models were able to capture the general experimental creep damage behavior and creep stages of the interface. Consistent with the experiments, the majority of the deformation took place at the contact interface. Additionally, the FEA models predicted fatigue crack patterns similar to experimental findings. Experimental surface cracks correlated moderately with FEA surface cracks (r²=0.43), but did not correlate with the simulated crack volume fraction (r²=0.06). Although there was no relationship between experimental surface cracks and experimental creep damage displacement (r²=0.07), there was a strong relationship between the FEA crack volume fraction and the FEA creep damage displacement (r²=0.76). This study shows the additional value of FEA of the cement–bone interface relative to experimental studies and can therefore be used to optimize its mechanical properties.     

A morphological model of vertebral trabecular bone

In their micro-structures, typical natural cellular materials such as vertebral trabecular bone have a network of doubly tapered struts, thickening near the strut joints. However, past analytical models for vertebral trabecular bone do not take account of the effect of strut taper on the mechanical properties.This paper presents an analytical cell model comprised of doubly tapered struts to predict the global mechanical properties of vertebral trabecular bone. The predicted results for male, female, and both sexes fit the experimental data well. By considering several strut taper geometries, it is shown that the horizontal Young's modulus and the horizontal uniaxial collapse stress are, in some cases, approximately 1.8- and 2.2-fold higher, respectively, than those of the uniform strut model. This finding illustrates the importance of increased trabecular thickening near the strut joints (i) for improving the accuracy of calculating the mechanical properties and (ii) for the effective treatment of aged bone using drug therapy. It also highlights the need to combine trabecular architecture measurements with information about the morphology near the strut joints.     

A comparison of the fatigue behavior of human trabecular and cortical bone tissue

The fatigue properties of trabecular bone tissue (single trabeculae) and similarly sized cortical bone specimens from human tibia were experimentally determined on a microstructural level using four-point bending cyclic tests, and they were compared based on modulus, mineral density, and microstructural characteristics. The results showed that trabecular specimens had significantly lower moduli and lower fatigue strength than cortical specimens, despite their higher mineral density values. Fracture surface and microdamage analyses illustrated different fracture and damage patterns between trabecular and cortical bone tissue, depending upon their microstructural characteristics. Based on the results from mechanical tests and qualitative observations, a possible mechanical role of the cement lines in trabecular tissue microfracture was suggested.     

The limitations of canine trabecular bone as a model for human: a biomechanical study

Distal canine femurs were sectioned into 8 mm cubic specimens. Orthogonal compression tests were performed to preyield in two or three directions and to failure in a third. Apparent density and ash weight density were measured for a subset of specimens. The results were compared to the human distal femur results of Ciarelli et al. (Transactions of the 32nd Annual Meeting of the Orthopaedic Research Society, Vol. 11, p. 42, 1986). Quantitative similarities existed in the fraction of components comprising the trabecular tissue of the two species. Qualitative similarities were seen in the positional and anisotropic variation of the mechanical properties, and also in the form and strength of the relationships between the mean modulus and bone density, ultimate stress and density, and ultimate stress and modulus. However, significantly different regression equations resulted for the mean modulus-density, and ultimate stress modulus relationships, indicating that for the same density, canine trabecular bone displays a lower modulus than human, and may achieve greater compressive strains before failure.     

Compressive fatigue behavior of human vertebral trabecular bone

Damage accumulation under compressive fatigue loading is believed to contribute significantly to non-traumatic, age-related vertebral fractures in the human spine. Only few studies have explored trabecular bone fatigue behavior under compressive loading and none examined the influence of trabecular architecture on fatigue life. In this study, trabecular bone samples of human lumbar and thoracic vertebrae (4 donors from age 29 to 86, n=29) were scanned with a microCT system prior to compressive fatigue testing to determine morphology-mechanical relationships for this relevant loading mode. Inspired from previous fabric-based relationships for elastic properties and quasi-static strength of trabecular bone, a simple power relationship between volume fraction, fabric eigenvalue, applied stress and the number of cycles to failure is proposed. The experimental results demonstrate a high correlation for this relationship (R2=0.95) and detect a significant contribution of the degree of anisotropy towards prediction of fatigue life. Step-wise regression for total and residual strains at failure suggested a weak, but significant correlation with volume fraction. From the obtained results, we conclude that the applied stress normalized by volume fraction and axial fabric eigenvalue can estimate fatigue life of human vertebral trabecular bone in axial compressive loading.     

Age-related differences in the morphology of microdamage propagation in trabecular bone

Microdamage density has been shown to increase with age in trabecular bone and is associated with decreased fracture toughness. Numerous studies of crack propagation in cortical bone have been conducted, but data in trabecular bone is lacking. In this study, propagation of severe, linear, and diffuse damage was examined in trabecular bone cores from the femoral head of younger (61.3±3.1 years) and older (75.0±3.9 years) men and women. Using a two-step mechanical testing protocol, damage was first initiated with static uniaxial compression to 0.8% strain then propagated at a normalized stress level of 0.005 to a strain endpoint of 0.8%. Coupling mechanical testing with a dual-fluorescent staining technique, the number and length/area of propagating cracks were quantified. It was found that the number of cycles to the test endpoint was substantially decreased in older compared to younger samples (younger: 77,372±15,984 cycles; older: 34,944±11,964 cycles, p=0.06). This corresponded with a greater number of severely damaged trabeculae expanding in area during the fatigue test in the older group. In the younger group, diffusely damaged trabeculae had a greater damage area, which illustrates an efficient energy dissipation mechanism. These results suggest that age-related differences in fatigue life of human trabecular bone may be due to differences in propagated microdamage morphology.     

Comparison of trabecular bone behavior in core and whole bone samples using high-resolution modeling of a vertebral body

Computational analysis of trabecular bone normally involves the modeling of (experimental tests of) cored samples. However, the lack of constraint on the sides of the extracted trabecular bone samples limits the information that can be inferred regarding true in situ behavior. Here, the element-by-element voxel-based finite element method was applied via, a custom-written software suite (FEEBE), to a 72 μm resolution model of an ovine vertebra. The difference between the apparent modulus of eight concentric core cylinders when modeled as part of the whole bone (containing 84 × 10⁶ degrees of freedom) and independent of the whole bone was investigated. The results showed that cored trabecular bone apparent modulus depended significantly on the core diameter when modeled as an extracted core (r ² = 0.975) and as part of a whole bone (r ² = 0.986). The cause of this result was separated into the side-artifact effect and bone volume fraction (BV/TV) effect. For the independently modeled cores, the apparent modulus of an inner core region of interest varied with increasing thickness of the outer annulus. This was attributed to the side-artifact effect, given that the BV/TV of the core region was constant. Within the whole trabecular structure, the side artifact was eliminated as the entire bone structure was modeled. However, a BV/TV effect influenced the apparent modulus depending on the size of the core selected for determining apparent modulus. Changing the size of the core varied the overall BV/TV of the core, and this significantly (r ² = 0.999) influences the apparent modulus. Therefore, determining a ‘true’ apparent modulus for trabecular bone was not achievable. The independently modeled cores consistently under-predict the in vivo apparent modulus. It is recommended that if a ‘true’ apparent modulus is required, the BV/TV at which it is required needs to be first determined. Apparent modeling of entire bones at microscale resolution allowed regions of low and high tissue strains to be identified, consistent with patterns of trabecular bone remodeling and resorption reported in literature. The basivertebral vein cavity underwent the highest strains within the entire vertebral body, suggesting that failure might initiate here, despite containing visibly thicker struts and plate trabeculae. Although computationally expensive, analysis of the entire vertebral body provided a full picture of in situ trabecular bone deformation.     

Shear strength and toughness of trabecular bone are more sensitive to density than damage

Microdamage occurs in trabecular bone under normal loading, which impairs the mechanical properties. Architectural degradation associated with osteoporosis increases damage susceptibility, resulting in a cumulative negative effect on the mechanical properties. Treatments for osteoporosis could be targeted toward increased bone mineral density, improved architecture, or repair and prevention of microdamage. Delineating the relative roles of damage and architectural degradation on trabecular bone strength will provide insight into the most beneficial targets. In this study, damage was induced in bovine trabecular bone samples by axial compression, and the effects on the mechanical properties in shear were assessed. The damaged shear modulus, shear yield stress, ultimate shear stress, and energy to failure all depended on induced damage and decreased as the architecture became more rod-like. The changes in ultimate shear strength and toughness were proportional to the decrease in shear modulus, consistent with an effective decrease in the cross-section of trabeculae based on cellular solid analysis. For typical ranges of bone volume fraction in human bone, the strength and toughness were much more sensitive to decreased volume fraction than to induced mechanical damage. While ultimately repairing or avoiding damage to the bone structure and increasing bone density both improve mechanical properties, increasing bone density is the more important contributor to bone strength.     

Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage ?1.16 %, tension damage 0.69 %, compression fracture ?2.91 % and tension fracture 1.98 %. Ultimate strength and post–ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile–brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post–ultimate strength softening.