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Stress fractures are frequently observed in physically active populations, and they are believed to be associated with microcrack accumulation. There are not many tools for real-time monitoring of microdamage formation during fatigue of bone, in vivo or in vitro. Acoustic emission (AE) based detection of stress waves resulting from microdamage formation is a promising method to assess the rate and energetics of microdamage formation during fatigue. The current study aims to assess the time history of the occurrence of AE events during fatigue loading of human tibial cortical bone and to determine the associations between AE variables (energy content of waves, number of AE waveforms, etc.), fatigue life, and bone ash content. Fatigue test specimens were prepared from the distal diaphysis of human tibial cortical bone (N = 32, 22 to 52 years old, male and female). The initiation of acoustic emissions was concomitant with the nonlinear increase in sample compliance and the cumulative number of AE events increased asymptotically in the prefailure period. The results demonstrated that AE method was able to predict the onset of failure by 95% of the fatigue life for the majority of the samples. The variation in the number of emissions until failure ranged from 6 to 1861 implying a large variation in crack activity between different samples. The results also revealed that microdamage evolution was a function of the level of tissue mineralization such that more mineralized bone matrix failed with fewer crack events with higher energy whereas less mineralized tissue generated more emissions with lower energy. In conclusion, acoustic emission based surveillance during fatigue of cortical bone demonstrates a large scatter, where some bones fail with substantial crack activity and a minority of samples fail without significant amount of crack formation.

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.

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.

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.

Microdamage, in the form of small cracks, may accumulate in trabecular bone loaded in fatigue. Specimens of bovine trabecular bone were loaded in compressive fatigue at one of four normalized stresses and loading was stopped after the specimens reached one of six maximum strains. Microdamage was identified using a fluorochrome staining technique, and microdamage parameters, including the number of damaged trabeculae and the damaged area fraction, were measured. No microdamage was observed during loading to strains below the yield strain; at higher strains, all microdamage parameters increased with increasing maximum compressive strain. Few significant differences were observed in the type or amount of microdamage accumulation between specimens loaded to the same maximum strain at different normalized stresses; however, more trabecular fractures were observed at high numbers of cycles, which corresponded to low normalized stresses.

Fatigue loading of bone, from the activities of daily living in the elderly, or from prolonged exercise in the young, can lead to increased risk of fracture. Elderly patients with osteoporosis are particularly prone to fragility fractures of the vertebrae, where load is carried primarily by trabecular bone. In this study, specimens of bovine trabecular bone were loaded in compressive fatigue at four different normalized stresses to one of six maximum strains. The resulting change in modulus and residual strain accumulation were measured over the life of the fatigue test. The number of cycles to reach a given maximum compressive strain increased with decreasing normalized stress. Modulus reduction and specimen residual strain increased with increasing maximum compressive strain, but few differences were observed between specimens loaded to the same maximum strain at different normalized stresses.

The purpose of this study was to evaluate the effects of isolated alterations in mineral content on mouse bone torsional properties. The femora and tibiae from 25 eight-week-old male A/J strain mice were divided into five groups and selectively decalcified from 5% to 20%. The right femora were then tested to failure in torsion while the tibiae were ashed to determine final mineral content of the decalcified bones. Contralateral femora were serially cross-sectioned to determine geometric properties, and effective material properties were then calculated from the geometric and structural properties of each femoral pair. We found that the relationship between ash content and effective shear modulus or maximum effective shear stress could best be characterized through a power law, with an exponential factor of 6.79 (R2 = 0.85) and 4.04 (R2 = 0.67), respectively. This indicates that in a murine model, as with other species, small changes in ash content significantly influence effective material properties. Furthermore, it appears that (in adolescent A/J strain mice) effective shear modulus is more heavily affected by changes in mineralization than is maximum effective shear stress when these properties are derived from whole bone torsional tests to failure.

Both creep and crack growth contribute to the reduction in modulus associated with fatigue loading in bone. Here we simulate crack growth and subsequent strut failure in fatigue in an open-cell, three-dimensional Voronoi structure which is similar to that of low density, osteoporotic bone. The model indicates that sequential failure of struts leads to a precipitous drop in modulus: the failure of 1% of the struts leads to about a 10% decrease in modulus. A parametric study is performed to assess the influence of normalized stress range, relative density, initial crack size, crack shape and cell geometry on the fatigue life. The fatigue life is most sensitive to the relative density and the initial crack length. The results lead to a quantitative expression for the fatigue life associated with crack growth. Data for the fatigue life of trabecular bone are compared with the crack growth model described in this paper as well as with a previous model for creep of a three-dimensional Voronoi structure. In our models, creep dominates the fatigue behavior in low cycle fatigue while crack growth dominates in high cycle fatigue, consistent with previous observations on cortical bone. The large scatter in the trabecular bone fatigue data make it impossible to identify a transition between creep dominated fatigue and crack growth dominated fatigue. The parametric study of the crack growth model indicates that variations in relative density among specimens, initial crack size within trabeculae and crack shape could easily produce such variability in the test results.

In this work an extension of the adaptive-elasticity theory is proposed in order to include the contribution of bone microdamage as a stimulus. Some aspects of damaged-bone tissue adaptation, brought about by a change of the daily loading history, are investigated. In particular, under the assumption of a small strain approximation and isothermal conditions, the solution of the remodeling rate equation for steady homogeneous stress is discussed and the damage effect upon the remodeling time constant is shown. The result is both theoretical and numerical, based on a recent theory of internal damaged-bone remodeling (Ramtani, S., and Zidi, M., 1999, "Damaged-Bone Remodeling Theory: Thermodynamical Approach, " Mechanics Research Communications, Vol. 26, pp. 701-708. Ramtani, S., and Zidi, M., 2001, "A Theoretical Model of the Effect of Continum Damage on a Bone Adaption Model," Journal of Biomechanics, Vol. 34, pp. 471-479) and motivated by the works of Cowin, S. C., and Hegedus, D. M., 1976, "Bone Remodeling I: Theory and Adaptive Elasticity," Journal of Elasticity, Vol. 6, pp. 471-479 and Hegedus, D. H., and Cowin, S. C., 1976, "Bone Remodeling II: Small Strain Adaptive Elasticity," Journal of Elasticity, Vol. 6, pp. 337-352.

In this study we investigated how microdamage accumulated with increasing compressive strain in bovine trabecular bone. We found that little damage is created in the linear elastic region, up to -0.4 percent strain. At an average strain of -0.76 percent +/-0.25 percent, the stress-strain curve became nonlinear, and peaked at -1.91 percent +/-0.55 percent strain. Microdamage increases rapidly during the peak of the stress-strain curve, and a localized band of damage formed. At strains beyond the ultimate strain, the damaged band widened and the density of damage within the band increased. Microdamage occurred as groupings of cracks; the majority of damage occurred as regions of cross-hatching. All microdamage parameters increased with increasing maximum compressive strain. We also observed exponential relationships between crack numerical density and damage (1(o) - (o)Esec/E0) and between crack length density and damage.